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An exploration of the effect of the development of spatial awareness as a prerequisite science, technology, engineering, and math (STEM) skill on the STEM gender achievement gap: an innovation study

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An exploration of the effect of the development of spatial awareness as a prerequisite science, technology, engineering, and math (STEM) skill on the STEM gender achievement gap: an innovation study

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Content Running head: SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 1

An Exploration of the Effect of the Development of Spatial Awareness as a Prerequisite Science,
Technology, Engineering, and Math (STEM) Skill on the STEM Gender Achievement Gap:
An Innovation Study

by
Elizabeth Ackerman-Hicks

_____________________________________________________________________

A Dissertation Presented to the
FACULTY OF THE USC ROSSIER SCHOOL OF EDUCATION
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF EDUCATION

May 2018

©Copyright, Elizabeth Ackerman-Hicks 2018
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 2

DEDICATION
This work is dedicated my two daughters, Katarina Samora Hicks and Natasha Hisa
Hicks. Watching you grow up to become strong, intelligent women with a sense of curiosity and
love of learning, as well as a commitment to making things better for women of color in your
fields is a continual source of inspiration to me. This work would not have been possible without
your constant encouragement, support and belief in me. Thank you for being such caring
daughters. I love you!

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 3

ACKNOWLEDGEMENTS
Thank you so much to my dissertation chair, Dr. Corinne Hyde who through floods, the
flu and moving her entire household still managed to be there for me through every step of this
journey with expert guidance, support and a wonderful sense of humor. I appreciate all you did
for me, especially your pep talks at those rare moments when I was overwhelmed by the work.
Thank you to my dissertation committee members Dr. Maria Ott and Dr. Jennifer
Crawford. I am so grateful that you agreed to be on my committee. Your interest in my subject
matter and involved participation made the work that much stronger. I greatly admire your
commitment to making the public education system better and to the advancement of women’s
leadership and I appreciate your personal support during this process.
I want to extend my appreciation to Superintendent Dr. Michelle King who many years
ago encouraged me to go into administration, and more recently encouraged me to become a
fellow Trojan in this program. Your constant professional support and friendship means a great
deal.
And finally, thank you to the amazing teachers I have the privilege to work with every
day. Your commitment to the education of the young women at our school inspires me to do my
best, and makes our school community that much richer. I appreciate your hard work and
dedication to the vision we have created.

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 4
TABLE OF CONTENTS
Page
Dedication ....................................................................................................................................... 2
Acknowledgements ......................................................................................................................... 3
List of Tables .................................................................................................................................. 7
List of Figures ................................................................................................................................. 8
Abstract ........................................................................................................................................... 9
Chapter One: Introduction ............................................................................................................ 11
The Problem of Practice.................................................................................................... 11
Organizational Context and Mission ................................................................................ 13
Organizational Performance Status/Need ......................................................................... 15
Related Literature.............................................................................................................. 18
Importance of the Organizational Innovation ................................................................... 20
Organizational Performance Goal ..................................................................................... 21
Description of Stakeholder Groups ................................................................................... 23
Stakeholder Group for the Study ...................................................................................... 26
Purpose of the Project and Questions ............................................................................... 28
Methodological Framework .............................................................................................. 30
Key Definitions ................................................................................................................. 31
Organization of the Study ................................................................................................. 32
Chapter Two: Review of Literature .............................................................................................. 34
The STEM Gender Achievement Gap .............................................................................. 35
Advanced Placement ............................................................................................. 37
Teacher Bias.......................................................................................................... 39
Prerequisite Skill: Spatial Awareness ................................................................... 40
Teaching Spatial Awareness Skills ....................................................................... 43
Mediating the Effects of Gender Role Expectations............................................. 44
Study Focus ....................................................................................................................... 46
Clark and Estes’ (2008) Organizational Problem Solving Framework ............................ 47
Stakeholder Knowledge, Motivation, and Organizational Factors ................................... 48
Knowledge and Skills ........................................................................................... 49
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 5
Motivation ......................................................................................................................... 56
Goal Orientation.................................................................................................... 57
Interest................................................................................................................... 60
Self-Efficacy ......................................................................................................... 62
Organization ...................................................................................................................... 64
Cultural Models and Cultural Settings .................................................................. 64
Conceptual Framework: The Interaction of Stakeholders’ Knowledge and Motivation and
the Organizational Context ............................................................................................... 69
Chapter Three: Methodology ........................................................................................................ 76
Purpose of the Project and Questions ............................................................................... 76
Conceptual and Methodological Framework .................................................................... 77
Assessment of Performance Influences ............................................................................ 79
Participating Stakeholders and Purposeful Selection ....................................................... 82
Purposeful Selection ............................................................................................. 82
Recruitment ........................................................................................................... 83
Open-Ended Survey .............................................................................................. 86
Observation ........................................................................................................... 86
Interview ............................................................................................................... 87
Document Analysis ............................................................................................... 88
Data Collection ................................................................................................................. 88
Open-Ended Surveys ............................................................................................ 89
Observations ......................................................................................................... 89
Interview ............................................................................................................... 90
Document Analysis ............................................................................................... 90
Data Analysis .................................................................................................................... 90
Credibility and Trustworthiness ........................................................................................ 91
Chapter Four: Results and Findings .............................................................................................. 92
Participating Stakeholders ................................................................................................ 94
Results ............................................................................................................................... 96
Knowledge Results ............................................................................................... 97
Motivation Results .............................................................................................. 103
Organizational Results ........................................................................................ 108
Findings........................................................................................................................... 111
Research Questions ......................................................................................................... 116
Degree of Incorporation Into School Curriculum ............................................... 117
Teachers Develop and Implement Spatial Awareness Curriculum .................... 117
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 6
Organizational Support ....................................................................................... 118
Synthesis ......................................................................................................................... 119
Chapter Five: Implementation and Evaluation Plans .................................................................. 121
Recommendations for Practice to Address Knowledge, Motivational, and Organizational
Influences ........................................................................................................................ 123
Knowledge Recommendations ........................................................................... 123
Motivation Recommendations ............................................................................ 129
Organizational Recommendations .................................................................................. 133
Collaboration....................................................................................................... 135
Innovation ........................................................................................................... 136
Teacher Leadership ............................................................................................. 137
Integrated Implementation and Evaluation Plan ............................................................. 138
Implementation and Evaluation Framework ....................................................... 138
Organizational Purpose, Need, and Expectations ............................................... 139
Kirkpatrick Level 3: Behavior ............................................................................ 141
Kirkpatrick Level 2: Learning ............................................................................ 145
Kirkpatrick Level 1: Reaction ............................................................................. 147
Data Analysis and Reporting .............................................................................. 149
Summary ............................................................................................................. 150
Strengths and Weaknesses of the Approach ................................................................... 151
Limitations and Delimitations ......................................................................................... 152
Future Research .............................................................................................................. 154
Conclusion ...................................................................................................................... 155
References ................................................................................................................................... 157
Appendix A: Spatial Reasoning Instrument ............................................................................... 186
Appendix B: Survey Instrument ................................................................................................. 190
Appendix C: Observation Protocol ............................................................................................. 191
Appendix D: Interview Protocol ................................................................................................. 192

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 7

LIST OF TABLES
Page
Table 1. The Academy’s Mission, Organizational Performance Goal, and Stakeholder
Performance Goals ........................................................................................................ 28
Table 2. Knowledge Influence....................................................................................................... 56
Table 3. Motivational Influence .................................................................................................... 64
Table 4. Influence of the Organization on Teacher Motivation.................................................... 67
Table 5. Knowledge, Motivation, and Organizational Influences ................................................ 81
Table 6. Summary of Knowledge Influences and Recommendations ......................................... 124
Table 7. Summary of Motivation Influences and Recommendations .......................................... 129
Table 8. Summary of Organizational Influences and Recommendations ................................... 134
Table 9. Outcomes, Metrics, and Methods for External and Internal Outcomes ....................... 140
Table 10. Critical Behaviors, Metrics, Methods, and Timing for Teachers ............................... 141
Table 11. Required Drivers to Support Teachers’ Critical Behaviors ....................................... 142
Table 12. Components of Learning for the Program .................................................................. 147
Table 13. Components to Measure Reactions to the Program ................................................... 148

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 8

LIST OF FIGURES
Page
Figure 1. Sample Vandenburg and Kuse (1978) task. .................................................................. 41
Figure 2. Relationship between The Academy and its teachers’ knowledge and skills. .............. 72
Figure 3. Research steps. .............................................................................................................. 84
Figure 4. Final research steps. ...................................................................................................... 95
Figure 5. Participant summary. .................................................................................................... 96
Figure 6. SRI teacher scores. ........................................................................................................ 98
Figure 7. Teacher knowledge about spatial awareness skills. ...................................................... 99
Figure 8. Importance of teaching spatial awareness. .................................................................. 100
Figure 9. Cycle of evaluation. .................................................................................................... 146
Figure 10. Sample data chart. ..................................................................................................... 150

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 9
ABSTRACT
There is a gender gap in the college and career pipeline for science, technology, engineering and
math (STEM) in the United States today. Through literature review, this study identified leaks
along the educational pipeline and found that one particular skill, the prerequisite STEM skill of
spatial awareness, could hold a key to preparing young women for high-level STEM courses.
Nationally, the gap in spatial awareness skills between males and females is one of the mitigating
factors in STEM course completion for females. Although spatial awareness can be learned
within a fairly short period of time, this important skill for STEM success is not often
intentionally taught in schools. The purpose of this study was to explore the intentional teaching
of spatial awareness by examining lesson design at The Academy, a unique all-girls school, that
is geographically, racially, and economically diverse and is located in a large urban setting.
Using Clark and Estes’s (2008) gap analysis as a general frame, this study explored the
knowledge and motivation of the key stakeholder group, teachers at The Academy, to
collaboratively plan and deliver spatial awareness lessons, which were initially implemented
with sixth grade girls. The study reviewed the literature in several areas: leadership within an
innovative educational environment, elements of teacher leadership, collaboration, and the
development of a culture of innovation within a public educational setting. Using qualitative
research methods including document analysis, survey, observation, and interviews, the study
found that teachers collaboratively developed and implemented lessons that were research based,
hands-on, and collaborative. After being exposed to these lessons, students showed a great deal
of growth in spatial skills within a short period of time. Although this was a small study
conducted in a unique organization, it shows promise as an initial design for developing spatial
awareness lessons to build this prerequisite skill for later STEM course success. Further
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 10
longitudinal research is needed to analyze how teaching this skill affects skill development over
time and girls’ future STEM course success.
Keywords: STEM gender gap, spatial awareness, secondary instruction.

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 11
CHAPTER ONE
INTRODUCTION
The Problem of Practice
The United States has a need for professionals in the science technology engineering and
math (STEM) fields. In fact, if the current rate of educational preparation in STEM fields
remains constant, there will be a shortfall of one million engineers and scientists in the United
States in the next decade (President’s Council of Advisors on Science and Technology, 2012).
But there is a gender gap in STEM achievement, STEM degrees and STEM career choices. The
workforce in the science and engineering fields is predominantly male. Only 22% of the STEM
workforce is female, and only 4 % are women of color (National Science Foundation, 2015).
Women, particularly women of color, thus represent an underutilized workforce that could fill
the STEM employment gap. The minimum requirement for most STEM employment is an
undergraduate degree in a STEM field (National Association of Colleges and Employers, 2012).
Unfortunately, although many women (15%) begin college STEM majors, only half of those
women complete STEM degrees (Hill, Corbett, & St. Rose, 2010).
Dubbed the “leaky pipeline” (Berryman, 1983), the gender achievement gap in STEM
fields persists from high school, through college, and career, remaining a persistent issue
(National Women’s Law Center, 2014). But the leaky pipeline starts before secondary school.
In preschool and elementary school, teachers do not expose girls to the prerequisite skills, such
as spatial awareness, that enable success in high school STEM courses (Lord, 1985; Metoyer,
Bednarz, & Bednarz, 2015; Newcombe, 2010; Oostermeijer, Boonen, & Jolles, 2014).
According to teachers of mathematics and science, spatial awareness is a prerequisite skill for
mathematical reasoning, geometric understanding, measurement, and graphing (Hegarty, 2014:
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 12
Kersh, Casey, & Young, 2008; National Council, 2000). When girls fall behind in these
prerequisite skills, they struggle to keep up in STEM subjects, producing the first leak of female
students from the STEM pipeline.
For women, the educational equity promised by the Title IX Amendment of 1972 of the
Elementary and Secondary Education Act of 1965 remains unfulfilled in STEM fields (Title IX
of the Educational Amendments, 1972). Title IX states that no person in the United States shall
on the basis of sex be excluded from participation in, be denied the benefits of or be subjected to
discrimination under an education program or activity receiving federal funds. Yet each year in
public schools in the United States, girls not taught the prerequisite skills to be successful in
STEM courses or are discouraged from taking higher-level STEM courses (Hill, C., et al., 2010;
Kersh et al., 2008). In fact, female high school students nationally comprise only 21% of
enrollment in physics, computer/information science, engineering, and science courses, and are
far less likely to enroll in STEM Advanced Placement (AP) courses (U.S. Department of
Education, 2014). Females take 10,000 fewer AP tests in mathematics than do males in the
United States (U.S. Department of Education, 2014). In order to reach educational parity,
schools must develop programs that not only encourage girls to take STEM courses but provide
academic support for STEM success, including teaching the prerequisite skills.
The lack of women in STEM is not only a problem in terms of educational equity; it is
also a problem in terms of career and salary equity, because STEM fields are the most lucrative
occupations for holders of college degrees (National Association of Colleges and Employers,
2012). STEM jobs are high-quality, knowledge-intensive jobs that lead to innovation, discovery,
and new technology; STEM jobs produce up to 85% of all growth in the U.S. economy (National
Academies, 2011). A robust and diverse STEM workforce provides a variety of perspectives and
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 13
approaches and produces more innovation in the field (Hira, 2010). Without the voices and
innovations of all women, our STEM-based economy will miss valuable contributions that may
be critical to maintaining the current global leadership of the United States and to the developing
a strong, resilient economy (The White House, 2013).
Organizational Context and Mission
The Academy (a pseudonym) is a public all-girls school serving grades six through 12 in
Ocean City School District (OCSD, a pseudonym), a large urban school district in California.
The Academy was started by a small group of educators that was led by the researcher, who is
the founder and the current leader of the school. This group began with the question “Why?”
Can the public school system offer a single-gender school—a model that has been a successful
one for girls, particularly girls of color—in a large urban setting? Can OCSD use the school
choice model to offer an affordable single-gender public school for families who lack the
financial resources for private school? Can OCSD offer a STEM model school that uses best
teaching practices to address the gender and racial achievement gap in STEM education? These
questions led a team of educators, community members, and parents to gather data within
OCSD. They found that girls’ math and science scores drop when they matriculate from
elementary school to middle school, and drop further in high school; they found only a small
percentage of girls taking high-level AP math, science, and computer science courses. This
committee conceptualized one solution for the STEM gap in OCSD: a single-gender school
providing a clear pathway to STEM careers for girls, particularly girls of color. Single-gender
schools have been shown to graduate students at a higher rate than co-ed schools, and they
graduate girls interested in STEM majors at a six times higher rate than co-ed schools do (Sax,
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 14
Arms, Woodruff, Riggers, & Eagan, 2009). Single-gender schools are particularly advantageous
to students of color in urban settings (Riordan, 1994).
The Academy, which shares a campus with a large historic high school in the mid-city
area, is an open enrollment school that serves girls from all over the city; current enrollment
represents 79 zip codes in Ocean City. The Academy is secondary school that spans sixth
through 12th grade. The Academy is a predominantly Hispanic, Asian, Black, and other
(PHABO) school with 74% of its enrollment made up of girls of color (its racial demographic
breakdown for 2017–2018 includes 22% African American, 1% American Indian, 9% Asian,
27% White, 2% Hawaiian/Pacific Islander, 34% Latino, 5% more than one). It is also a full
federal Title One school, with 58% of students meeting the federal guidelines for free and
reduced price lunch qualification. The curricular focus is on science, technology, engineering,
and math, with a special emphasis on engineering and computer science pathways. Students
follow a rigorous college preparatory curriculum, completing a sequence of courses that exceed
OCSD and California graduation requirements and the University of California A–G
requirements (the minimum subject requirements for university entrance). Teachers follow the
California and district curriculum standards, including Common Core Mathematics (CC
Mathematics), Common Core English Language Arts (CC ELA), and Next Generation Science
Standards (NGSS). As a new school, The Academy has instituted several innovative practices,
including standards-based grading and mastery learning; students earn grades based on mastering
specific state standards. Standards-based grading and mastery learning are relatively new
practices in OCSD, which began training teachers in these practices in 2015; currently, only 5%
of OCSD schools have their entire faculties using these practices. In the OCSD system, this
means that teachers identify clear learning goals based on the standards, develop lessons that use
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 15
various modes of learning to meet those goals, and allow enough time and support for children to
reach mastery of the standards. At The Academy, teachers and administration espouse the
growth mindset philosophy, which is the basis of mastery learning. Growth mindset, based on
concepts originated by Benjamin Bloom, is the philosophy that all children can learn if provided
with the conditions that support their learning (Bloom, 1974). One goal of The Academy is to
provide the necessary conditions for girls to succeed in STEM courses. This fits in with The
Academy’s larger mission: to provide girls with a highly rigorous college preparatory STEM-
focused education in an all-girls environment fostering academic excellence, ethical leadership,
and intellectual curiosity. The OCSD school board approved The Academy school plan with the
express intention of reducing the STEM gender achievement gap and providing inner-city girls,
particularly girls of color, with a pathway to college and then to lucrative and engaging STEM
careers.
Organizational Performance Status/Need
In order to fulfill its mission of providing girls with a highly rigorous college-preparatory
STEM-focused education, it is imperative that The Academy teachers and administration
monitor and improve student performance on CC Mathematics standards and NGSS. By 2018,
The Academy aims to have 85% of its students meeting the standards laid out in CC
Mathematics and NGSS, as measured by standards-based grading in math and science courses.
Students at The Academy have self-selected to enroll in a STEM focused school, which
may skew the data toward success in math and science. Of the incoming sixth grade class (class
of 2024) entering The Academy, 23% come from charter or independent schools that do not
participate in standards-based testing, so there is no data for this group. The remaining 77% of
girls entering the sixth grade class in 2017 tested on the Smarter Balanced Assessment
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 16
Consortium (SBAC), the California state tests of standards in math. Of these girls, 38%
exceeded standards, 14% met standards, 20% nearly met standards, and 5% did not meet
standards. The Ocean City District average is 14% exceeded standards, 16% met standards, 27%
nearly met standards and 45% did not meet standards. The Academy scores indicate a student
population with a higher propensity toward success on the math standards than the district
average. SBAC is a relatively new test for the State of California, and the 2016-2017 school
year is the first year for which data has been recorded. Although the students’ entering SBAC
scores are impressive, The Academy will need to maintain and build upon those scores as
students move through the seven years from sixth grade through graduation to ensure that the
students are ready for the rigors of a STEM college major and entrance into the STEM fields.
One important indicator for success in STEM and prerequisite skill for higher-level math
and science courses is spatial awareness. Spatial awareness consists of three areas of cognitive
skill: spatial perception, spatial visualization and spatial orientation (National Research Council,
2006). Spatial awareness skills are the foundation of using space to model the world, structure
problems, find answers and communicate solutions, all skills vital to STEM success (National
Research Council, 2006). Spatial awareness can be measured (Lee & Bednarz 2012; National
Research Council, 2006; Vandenberg & Kuse, 1978). The most common test of spatial
awareness is the Vandenberg and Kuse (1978) motor rotation and spatial awareness task. The
Vandenberg and Kuse task has been modified to make it a more comprehensive and accessible
test of spatial awareness for middle school students. The modified version uses the validated
Spatial Reasoning Instrument (SRI), which tests students’ ability in mental rotation, spatial
orientation and spatial visualization (Ramful, Lowrie & Logan, 2017). To measure baseline data
for the entering sixth grade students’ spatial ability skills, The Academy teachers administered
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 17
the SRI to girls before teaching the spatial awareness lessons to ascertain the students’ original
level of spatial awareness skills (SRI sample used is in Appendix A). The SRI scores, combined
with the SBAC scores, gave teachers a starting point for developing and refining spatial
awareness lessons and teaching methods. Posttests, administered after the spatial awareness
lessons were taught, enabled teachers to measure each student’s growth in spatial awareness
skills. The baseline SRI information helped teachers ascertain whether their methods were
helping the students develop spatial awareness skills so that they could modify their instructional
practices as needed. This assessment and adjustment of teaching methods is based in design
thinking, a model that Academy teachers regularly employ in their curriculum design and
evaluation. Design thinking in curriculum development allows teachers to use data to develop a
prototype, test the prototype in practice, and then continually refine the prototype using data and
feedback to continually inform the design process (Koh, Chai, Wong & Hong, 2015). Data from
the SBAC and SRI are only the start of the curricular design process, but this data helps to
inform the design and refinement process at each stage.
National testing using the Vandenberg and Kuse task shows a gender achievement gap in
the skill of spatial awareness, a gap that the girls at The Academy were deemed likely to share,
despite the fact that they had self-selected to be part of a STEM school. This is because there is
no direct instruction on spatial awareness in OCSD curricular guides for elementary school, and
OCSD students thus have little opportunity to learn this prerequisite STEM skill. It is therefore
especially important that the students at The Academy have direct instruction in spatial
awareness skills early in their STEM education to improve their performance in standards-based
math and science courses and to help them succeed in higher-level math and science courses.
This aligns with The Academy mission to provide a clear pathway to STEM college majors and
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 18
STEM careers for girls. It also supports The Academy’s specific outcome of 100% four-year
cohort graduation and 100% college matriculation.
Related Literature
As early as 1974, psychologists explored gender difference in spatial ability, and mental
rotation of objects (Maccoby & Jacklin, 1974). Spatial ability involves the ability to think and
reason through the transformation of mental pictures (Casey, Nuttall, & Pezaris, 2001). Tests of
mechanical reasoning and spatial awareness show a difference between males and females, with
males consistently showing higher levels of spatial awareness than females (Voyer, et al., 1995).
Psychological researchers disagree over when spatial ability develops. Determining the
age of development has implications for psychologists in terms of biological determination as
compared to environmental exposure. Maccoby and Jacklin (1974) assumed that spatial
awareness developed during a particular developmental stage, adolescence. However, Linn and
Petersen (1985), who performed a meta-analysis of 172 studies with participants between 10 and
60 years old, established that spatial awareness begins before adolescence. Some studies say that
spatial ability is determined by genetics (Levine, Huttenlocher, Taylor & Langrock, 1999) and
others that it develops through environmental exposure in early childhood (Quinn & Liben,
2008). But at every age, according to Linn and Peterson’s (1985) review, males outperform
females in spatial awareness, and additional studies confirm this difference (Hedges & Nowell,
1995; Moè, 2009; Voyer et al., 1995).
Spatial awareness is a prerequisite skill for the development of mathematical reasoning,
geometric understanding, measurement, and graphing (Kersh et al., 2008). Spatial awareness is
also connected to scientific reasoning, and to the visuospatial processes in physics, chemistry,
and geography (Hegarty, 2014). Spatial visualization and awareness are correlated with
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 19
construction play-play with items such as blocks, Lego and construction toys (Kersh et al, 2008).
This correlation between construction play, spatial ability, and mathematical reasoning was
shown in a study of 128 Dutch students conducted by Oostermeijer et al. (2014). Students were
given mathematical reasoning, and picture rotation tests, and parents answered questions about
their child’s play activities. The students with better spatial skills showed higher performance in
solving math problems. The children (mostly male) who frequently engaged in construction play
with blocks and Legos, tested higher in spatial ability, and showed higher performance on math
word problems (Oostermeijer et al., 2014). Another study found that girls are less likely than
boys to play with construction toys in preschool and elementary school (Etaugh & Liss, 1992).
These studies of spatial awareness skill development imply that girls need exposure to activities
that build spatial awareness in order to develop the prerequisite skills for mathematics and
science.
In fact, in 2000, results of studies on spatial awareness studies like these prompted the
National Council of Teachers of Mathematics to add an entire section on developing
visualization, spatial reasoning and geometric modeling to the to the Table of Standards and
Expectations for kindergarten through 2
nd
grade (National Council of Teachers of Mathematics,
2000). And Matthewson (1999) found when teachers are trained to do so, they are able to
incorporate the teaching of visuospatial awareness in science through age-appropriate visual,
activities, active learning activities, and computer graphics imaging activities (Mathewson,
1999). Although is a gap between males and females in the development of spatial ability, when
schools consciously develop girls’ spatial ability through mathematics, science, computer coding
and hands-on skills, the male advantage in spatial awareness can be neutralized (Brosnan, 1998;
Jones, 2010; Moè,, 2016). Unfortunately, very few schools specifically teach spatial awareness
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 20
skills (Lord, 1985; Metoyer et al., 2015; Newcombe, 2010). It is therefore important to study
how teachers consciously develop of lessons to improve spatial awareness skills within a school
setting.
Importance of the Organizational Innovation
As previously mentioned, it is especially important for teachers in The Academy to
implement specific teaching practices designed to develop spatial awareness in girls. This is
because spatial awareness is a prerequisite skill for success in mathematics and science courses
(Hegarty, 2014: Kersh et al., 2008) and the mission of The Academy is to provide girls with a
highly rigorous college preparatory STEM- focused education in an all-girls environment. By
consciously developing the prerequisite spatial awareness skills, The Academy provides girls
with one of the foundations of success in STEM courses. This curricular design, and the
methods and strategies that grew out of it, can also be duplicated in co-ed schools across OCSD,
inviting more success for girls in STEM courses.
National testing of spatial awareness consistently reveals a gender gap in this skill
(Hedges & Nowell, 1995; Moè,, 2009; Voyer et al., 1995) and The Academy must implement
specific teaching practices designed to develop spatial awareness in girls in order to increase
students’ chances of success in STEM courses. Curricular guides for teaching spatial awareness
do not currently exist in OCSD, and OCSD offers no professional development (PD) sessions on
this topic. Most students entering The Academy have therefore had little or no direct instruction
on spatial awareness. Yet, this is a skill that can be learned (Mathewson, 1999; Moè,, 2016;
National Council of Teachers of Mathematics, 2000). To neutralize the spatial awareness skill
gap, teachers in The Academy must provide direct instruction in spatial awareness to entering
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 21
students. Inaction would perpetuate the underlying gap in achievement for girls in STEM
courses, contradicting the mission of The Academy.
Organizational Performance Goal
The mission of The Academy is to provide girls with a highly rigorous college
preparatory STEM- focused education in an all-girls environment. The Academy’s overall
organizational performance goal for 2018 is to have 100% of the students on target to graduate
with the STEM skills necessary for A-G eligibility. A-G requirements are the University of
California’s minimum subject requirements, and they must be completed for students to be
eligible to apply for university entrance (UCOP Office of the President, 2017). The progress
toward this overall goal is measured by students’ enrollment in A-G STEM courses and their
completion of those courses with a standards-based grade of “C” or better. For the school to
reach this goal, the students need to improve their performance in CC Mathematics and NGSS.
Therefore, the schools’ intermediate goal, and the focus of this research study, is to improve
entering students’ spatial awareness, the necessary prerequisite skill for STEM course success.
Teachers in The Academy have previously participated in PD on design thinking and
most of the school’s curriculum was designed collaboratively. Design thinking, sometimes
called user-centered design, began in the business world and its key insight is that the user is
central to the design process (Norman, 2013). Design thinking is just beginning to be applied to
curricular design (Koh et al., 2015). Design thinking consists of three stages; innovation, in
which the designer identifies the opportunity; ideation, in which the designer conceives a general
solution; and implementation in which the design is implemented (Brown, 2009). Ideation, one
of the most important phases of design includes developing an initial prototype and testing it in
real situations. The responses to the prototype guides changes to the design before
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 22
implementation (Brown, 2009). A combination of design thinking and the practitioner research
model of teaching, in which teachers are involved in planning, implementing and critiquing their
own practice, frame this study’s research design.
To start the curricular design process, the teachers in The Academy participated in a
collaboratively created PD on spatial awareness as a prerequisite skill for STEM success. This
PD aimed to build all Academy teachers’ knowledge of how spatial awareness is connected to
STEM success, and to convey the urgency of teaching this skill to girls in The Academy. The
teachers were then invited to participate in planning and implementing explicit lessons on spatial
awareness. To help teachers assess students’ entrance-level spatial awareness, portions of the
SRI were given as a baseline measurement to all girls entering the sixth grade in The Academy.
Teachers followed the school’s data-informed instruction and design thinking norms, using this
measurement to target specific spatial skills to be learned or reinforced. As is the practice at the
school, teachers collaborated to develop specific instructional techniques and exercises to build
spatial awareness. Teachers then implemented these lessons. Teachers were invited to peer
review each others planned lessons and to follow up by sharing lesson outcomes. Because
research indicates that the spatial awareness skill can be taught in a short period of time (Feng,
Spence & Pratt, 2007; Moè, 2016; Uttal, Meadow et al., 2013), teachers retested students using
the SRI to assess progress and to refine the prototype lessons for further use. The teachers also
participated in interviews to reflect on their practice. As part of their ongoing lesson design and
evaluation process, the teachers used the posttest results to determine whether the students’ level
of spatial awareness increased significantly enough to improve student performance in CC Math
and NGSS as measured by standards-based grades.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 23
The teachers and principal of The Academy collaborated to established the performance
goal through research on best practices for teaching spatial awareness, experience provided by
the National Coalition of Girls School (NCGS), sample lessons and advice from the Columbus
School for Girls faculty and librarian, and advice from computer science researchers at Stanford
University.
Description of Stakeholder Groups
Three primary stakeholder groups from The Academy are involved in this study, the
teachers, the administration and the students. The Academy is a new school within OCSD that
opened in 2016 with 160 students in grades six and nine; it opened with seven teachers, one
principal and a half-time counselor. In 2017-2018, The Academy has 340 students in grades six,
seven, nine and ten, and a staff of 14 teachers, one principal, one full-time counselor and one
out-of-classroom coordinator. In 2018-19 the school will grow to include grades eight and
eleven, and finally in the 2019-2020 school year The Academy will be a full span school with
grades six through 12 and a maximum enrollment of 100 girls per grade level (700 students
total).
The stakeholder group primarily responsible for implementing the performance goal is
the teachers at The Academy, who are responsible for developing and implementing the lesson
plans to teach spatial awareness skills to the students. Fourteen teachers currently teach at The
Academy including two multiple-subject elementary-credentialed teachers teaching English and
History in sixth grade, three secondary math teachers, three secondary science teachers, one
secondary history teacher, two secondary English language arts teachers, one secondary
computer science teacher, one secondary Language Other Than English (LOTE) teacher, and one
secondary physical education teacher. Teachers are fully credentialed in their subject area and
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 24
70% of the teachers hold master’s degrees in education. All teachers are new to teaching in a
single-gender school, and they range in experience from first-year teachers to teachers with eight
years of teaching experience. All teachers teach five classes in their subject area and one
elective class, for which they are credentialed. All teachers also have an advisory class in which
core social emotional skills are taught, including growth mindset. The growth mindset
philosophy is a key component in the school’s pedagogical orientation as it can mitigate some
aspects of the STEM gender achievement gap particularly for females (Dar-Nimrod & Heine,
2006; Leslie, Cimpian, Meyer & Freeland, 2015; Schmidt, Shumow & Kackar-Cam, 2015). All
teachers at the school were invited to be part of the research study.
The second stakeholder group implementing the performance goal is the school’s
leadership team comprising the school principal, and two out-of-classroom personal, the Title 1
coordinator/instructional coach and the academic/college counselor. The principal, who is the
only on-site administrator, is the founder of The Academy and the researcher for this study. All
leadership team members hold teaching credentials, administrative credentials and master’s
degrees. The counselor also has a Pupil Personnel Services Credential and holds a Marriage and
Family Therapists license. Although this team is called the school leadership team, The
Academy is a collaboratively run school. In fact this distributed leadership structure is written
into the schools plan, which was approved by OCSD; all teachers have a voice in all decisions
related to curriculum, including developing the course of study, planning the master schedule of
courses, interviewing teacher candidates, and creating standards and rubrics for standards and
mastery grading. The principal and the leadership team ensure that all decisions are made with
the vision and mission of the school in mind, work collaboratively with teachers in decision-
making processes, and put systems in place to support teachers. This stakeholder group provided
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 25
the initial PD event on spatial awareness skills, working with the science department chair. This
event made up part of the school’s practice of regular PD: all staff engage in weekly PD sessions
that are collaboratively developed and delivered. The administration also supported the teachers
with time and materials to develop and implement the spatial awareness lessons and provided the
SRI pre- and posttests. As part of the collaborative team practice that the school has used since
its inception, the principal and instructional coach met with the teacher stakeholder group as
contributing practitioners.
The final stakeholder group is the students of The Academy. Although they did not
directly participate in the study, the students received the innovative teaching practices in spatial
awareness designed by the teachers. For reasons of practicality (an immediate effect on skills
and least disruption of coursework), only the 108 incoming sixth-grade girls received the spatial
awareness lessons.
As previously detailed, the incoming students in the sixth-grade, the entry point for
admission to The Academy, represent the geographic, economic and racial diversity of OCSD.
The students in the class of 2024 (the sixth graders who are incoming in the 2017-2018 school
year) also represent a wide range of academic preparation. Students come from 69 different
schools, some within OCSD, and some from outside the system, such as charter and independent
(private) schools. These non-OCSD schools may use different teaching practices and standards,
particularly in STEM courses. Some students enter the school with no academic preparation in
STEM, while others come from STEM-focused magnets. Included in the sixth grade population
are five English learners (EL), 25 students who were recently redesignated as English-proficient
students (RFEP), and six students following Individual Education Plans (IEP) that require
additional support services or scaffolding for academic access and success. Because of the
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 26
school’s commitment to standards-based grading, mastery learning and growth mindset, students
are in heterogeneous groups and teachers differentiate for learning within the classroom. Class
size is relatively small, with 25 or fewer students in sixth grade core courses.
Numerous studies show that teachers are the most important factor determining student
success (Darling-Hammond, 2000; Sanders, Wright & Horn, 1997; Wayne & Youngs, 2003).
Teachers are particularly important to student success in math and science courses (Hill, Rowan
& Ball, 2005; Sadler, Sonnert, Coyle, Cook-Smith & Miller, 2013). This study therefore
examined whether the planning and delivering of explicit lessons about spatial awareness
positively affected the spatial awareness skills of the entering class of 2024. Although this
research is particular to a unique student population and school setting, some elements of the
design process, and the lessons that were taught may be useful for other grade levels at the
school and for other schools in OCSD. Table 1 shows the performance goals for each
stakeholder group at The Academy.
Stakeholder Group for the Study
The stakeholder group primarily responsible for implementing the performance goal
comprises the 14 teachers currently employed at The Academy. In the first year of The
Academy, the principal hired seven teachers. In the second (current) year an additional seven
teachers were hired through a collaborative process with teachers and principal serving on the
hiring committee. The requirements for teaching at The Academy (several of which exceeded
OCSD-required qualifications) included being able to teach multiple courses, having experience
with mastery learning and standards-based grading practices, having strong classroom
management skills based on restorative practices, working in collaborative grade-level and
departmental-level teams, and developing innovative teaching practices within a single-gender
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 27
environment. At The Academy, teachers are in leadership positions as part of the school’s
distributed leadership model, which is grounded in the concept of the professional learning
community (PLC). All teachers are involved in lesson study particularly around growing best
practices in STEM across the curriculum. Although the idea of spatial awareness as an indicator
of STEM success was new to most of the teachers, when it was introduced through PD, the
teachers incorporated the skill-building lessons into their ongoing practice. The teachers were
active participants in the study, in the tradition of participant action research (PAR) and design
thinking principles. PAR is defined by two guiding principles; that people working within a
given research setting can be actively involved in the research process, and that the research is
oriented toward making improvements in practices by the participants themselves (Kemmis,
McTaggart & Nixon, 2014). The principal, as the researcher, is also involved in PAR as an
administrator-practitioner and as a facilitator of PLC. Administrator-practitioner research is a
fairly new form of research that comes out of the tradition of teacher-practitioner research and is
firmly rooted in the feminist social action tradition (Anderson & Jones, 2000). The teachers in
this study were already involved in educational innovation for they deeply examine issues of
equity in a unique public all-girls educational setting. The practices of the school include
teachers being involved in a continuous cycle of design thinking-inflected curricular
development, so developing innovative curriculum and practices are part of the cultural norm at
The Academy. This shaped the research design. As part of the established practice of the
school, all teachers participated in PD about spatial awareness and the importance of developing
this prerequisite STEM skill for females. This PD was collaboratively led by the school
principal, who is also the researcher, and the science department chair who has knowledge of
spatial awareness as a necessary prerequisite STEM skill. All teachers were invited to be
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 28
participant researchers in the study, which aimed to plan and implement lessons to help develop
students’ spatial awareness.
Table 1

The Academy’s Mission, Organizational Performance Goal, and Stakeholder Performance
Goals

The Academy Mission
The mission of The Academy is to provide girls with a highly rigorous college preparatory
STEM-focused education in an all-girls environment fostering academic excellence, ethical
leadership, and intellectual curiosity.
Organizational Performance Goal
The Academy incoming sixth-grade students will increase by 50% their scores on the SRI, which
measures the prerequisite STEM success skill of spatial awareness, between November 2017 and
the first semester of the 2017–2018 school year.
Stakeholder Performance Goals
The Academy Teachers The Academy Administration The Academy Students
By August 2017, teachers
will participate in PD on
spatial awareness as a
prerequisite skill for STEM
success.
By September 2017,
teachers will
collaboratively develop
spatial awareness lessons
and a plan for
implementation of those
lessons.
By October 2017, teachers
will deliver the spatial
awareness lessons and
reflect on their practice.
By August 2017, the principal
and science department chair will
collaborate to design a PD for
teachers in spatial awareness as a
prerequisite STEM skill. They
will jointly deliver the PD to
teachers.
By October 2017, the sixth-
grade students will participate
in the spatial awareness
lessons and take SRI pre- and
posttests to measure change in
spatial awareness skills.

Purpose of the Project and Questions
The purpose of this study is to explore the innovative practice of deliberately teaching the
prerequisite STEM success skill of spatial awareness to girls in a unique educational setting, that
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 29
of a single-gender public school in a large urban school district. Nationally, the gap in spatial
awareness skills between males and females is one of the factors in females’ lower rates of
STEM course success for females (Hegarty, 2014; Kersh et al., 2008). Yet spatial awareness can
be learned within a fairly short period of time (Feng et al., 2007; Moè, 2016; Uttal, Meadow et
al., 2013). This innovative study used practitioner action and design thinking, practices, which
are already in use at the school, to collaboratively, design the innovation.
Using Clark and Estes’s (2008) gap analysis as a frame, this study explored the
knowledge and motivation of the key stakeholder group, The Academy teachers, to
collaboratively plan and deliver spatial awareness lessons which were initially implemented with
the entering class of sixth-grade girls. This study also examined the role of The Academy’s
organizational culture in supporting collaboration and innovation. If The Academy culture
supports teachers in developing and teaching innovative lesson plans in spatial awareness to
entering sixth-grade students of The Academy, then according to existing literature, those
students should perform better in CC Math and NGSS. This, in turn, should result in students’
completion of higher level STEM courses-one step in diminishing the achievement, college and
career gender gap in STEM.
Because spatial awareness is a prerequisite skill for success in mathematics and science
courses, it is important to study the intentional teaching of this skill (Hegarty, 2014; Kersh et al.,
2008). By consciously developing students’ spatial awareness, The Academy will provide girls
with a foundation for success in math and science courses. Successful completion of math and
science courses is the basis of The Academy’s mission to provide girls with a highly rigorous
college preparatory STEM- focused education in an all-girls environment fostering academic
excellence, ethical leadership, and intellectual curiosity.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 30
The following questions guide the study:
1. To what extent are the prerequisite spatial awareness skills incorporated into The
Academy curriculum and teaching practices?
2. To what extent do the teachers in The Academy have the knowledge, skills and
motivation to develop and implement the prerequisite spatial awareness curriculum?
3. How are the teacher’s knowledge and motivation to develop and implement the
spatial awareness lessons impacted by The Academy’s organizational culture?
Methodological Framework
This study conducts a needs analysis based on Clark and Estes’ (2008) gap analysis, a
systematic, analytical method for clarifying organizational goals and identifying the gap between
goals and actual performance levels. Gap analysis originated as an effort to improve
performance in business settings by diagnosing the causes for performance gaps and selecting
appropriate solutions based on knowledge, motivation and organizational (KMO) dimensions
(Clark & Estes, 2008). Although this method was originally designed for use in the business
community, it can also be effectively used to analyze performance gaps in the educational setting
(Rueda, 2011). To conduct a gap analysis, first the organization’s goals are identified; then the
gaps in knowledge, motivation and organizational support needed to reach those goals are
analyzed; finally, targeted solutions to close those gaps and meet the goals are developed (Clark
& Estes, 2008; Rueda, 2011). For this research study on the STEM gender achievement gap, the
organization’s goal was already clearly established in the mission and vision statement for the
school; The Academy aims to improve its students’ performance in A-G STEM courses. The
identified gap-the need to develop students’ spatial awareness skills, which are a prerequisite for
STEM success-was established by the literature review, and by the pretest of student skill level.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 31
The gap in the knowledge, motivation and organizational areas was examined both by analyzing
relevant literature and through qualitative research, with methods including document review, an
open-ended survey of all teachers, observation of PD on spatial awareness as a prerequisite
STEM skill, observation of the collaborative lesson design process, observation of the
implementation of the lesson plans, and reflective interviews with teachers on their innovative
practice. Through collaboration, design thinking and gap analysis, The Academy developed and
refined lessons to best meet the needs of their students; these lessons provide a model for future
use.
Key Definitions
A-G requirements: A series of courses required by the University of California as its
minimum entrance requirements. The intent of the requirements is to ensure that students have
attained a body of general knowledge that will provide breadth and perspective to new, more
advanced study (UCOP Office of the President, 2017).
Advanced Placement: Advanced Placement (AP) classes are college-level curriculum
taught on a high school campus by validated teachers; the curriculum is validated by national AP
examinations issued by the College Board (College Board, 2015).
College Board: A mission-driven non-profit organization formed in 1900 to expand
access to higher education. The College Board provides SAT and AP programs and testing
(College Board, 2015).
Common Core Mathematics Standards: A set of high-quality math standards adopted by
42 states that lay out learning goals for what students should know and do by the end of each
grade level. The standards were created to ensure that all students graduate from high school
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 32
with the skills necessary to succeed in college or career, regardless of where they live (Common
Core State Standards Initiative, 2016).
Next Generation Science Standards: A set of high-quality science standards adopted by
42 states that lay out learning goals for what students should know and do by the end of each
grade level. The standards were created to ensure that all students graduate from high school
with the skills necessary to succeed in college or career, regardless of where they live (Next
Generation Science Standards, 2016).
Spatial Awareness: spatial awareness consists of three areas of cognitive skills; spatial
perception, spatial visualization and spatial orientation (National Research Council, 2006).
STEM: An acronym for the academic fields of science, technology, engineering and
math, which are grouped together by the National Science Foundation because practitioners use
their knowledge of all four fields to figure out how the world works (National Science
Foundation, 2015).
Organization of the Study
There are five chapters in this research study. Chapter 1 has provided the reader with the
key concepts and terminology for discussion of the STEM gender achievement gap, and has laid
out the importance of developing the prerequisite STEM skill of spatial awareness, a skill that is
needed to access and succeed in a rigorous STEM curriculum. This chapter has also described
the organization of the study and the stakeholders for the study: given an overview of the main
research site, The Academy, and its mission and goals; and laid out the initial framework, the
gap analysis framework (Clark & Estes, 2008). Chapter 2 provides a review of current literature
relevant to the study, covering topics including how to stem the leak in the STEM pipeline, the
development of spatial awareness skills and the Common Core Mathematics and next generation
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 33
Science Standards. Chapter 3 details the knowledge and motivation needed by the teachers at
The Academy to develop and implement the innovative of spatial awareness lessons, and it
examines how The Academy’s organizational culture impacts this process. It also describes the
preliminary research design and the methods of participant selection, data collection, and
analysis that were used. Chapter 4 examines the qualitative data gathered to triangulate the
findings in this study, including data gathered by document analysis, open-ended survey,
observations and reflective interviews. Chapter 5 details the analysis of the data collected, offers
suggestions for further research, and details an implementation and evaluation plan based on the
New World Kirkpatrick Model (Kirkpatrick & Kirkpatrick, 2016).
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 34
CHAPTER TWO
REVIEW OF LITERATURE
This chapter reviews the literature that examines the leaks along the education-to-career-
pipeline that contribute to the STEM gender achievement gap, and frames the paucity of women
in STEM in terms of educational experience. It begins by looking at girls’ lack of experience
with manipulatives in preschool (which leads to underdeveloped spatial awareness skills). Next,
it examines teacher bias and gender expectations in elementary school. It then turns to girls’
limited access to AP STEM courses in high school. Finally, it examines the lack of women in
STEM college majors. All of these factors ultimately contribute to a paucity of women in STEM
careers.
Many of the leaks along this STEM education-to-career-pipeline can be plugged, often in
a short period of time. Educators may address girls’ lack of experience with manipulatives at
any time in the educational process by deliberately teaching spatial awareness skills. The teacher
bias and gender expectations can be addressed using PD and awareness techniques, and, in this
case, by providing a single-gender environment. Encouraging girls to stay in STEM fields and
providing female role models for girls in STEM can also increase the number of women in
STEM careers. The focus of this study, which is based in a secondary school, will be the
deliberate teaching of spatial awareness, which is the prerequisite skill for STEM course success.
Gap analysis, a research-based diagnostic of performance gaps, was used to diagnose knowledge,
motivation, and organizational problems. The gap analysis focused on examining the teachers’
knowledge about and motivation for teaching the prerequisite skill of spatial awareness, as well
as the ways in which the school’s organizational culture affected teachers’ knowledge and
motivation to develop the innovative lesson design.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 35
The STEM Gender Achievement Gap
Since the passage of the 1972 Title IX Amendment to the Elementary and Secondary
Education Act of 1965, which prohibited sex discrimination in educational programs and
activities receiving federal funds, women have made great gains in educational attainment (Title
IX of the Educational Amendments, 1972). Forty years ago, more males than females attended
college, but today women comprise 56% of the total undergraduate enrollment in college in the
United States (National Center for Educational Statistics, 2016). However, these gains are not
apparent in the STEM fields. Only 15% of undergraduate women start out in STEM majors, and
almost half of these women drop out of STEM majors by graduation; only 20% of those women
actually earn undergraduate degrees in STEM (Hill, Corbett, et al., 2010). Although relatively
few women graduate in STEM fields, about half of the undergraduate women who declare
majors in the biological sciences complete their degrees. But in chemistry, physics, and
computer science, very few bachelor’s degrees are awarded to women, and even fewer doctoral
degrees (Hill et al., 2010; Turk-Bicakci, Berger, & Haxton, 2014). For women of color, the
statistics are even more dire. Only 600 African American women received undergraduate
physical science degrees across the nation in 2007; only 0.97% of African American women
received engineering undergraduate degrees in 2014 (National Science Foundation, 2009;
National Science Foundation, 2017).
Even if women complete undergraduate degrees in STEM, completing a graduate degree
in these fields is still a struggle. As early as 1983, researchers coined the phrase “leak in the
educational pipeline” to describe the lack of female doctoral candidates in science (Berryman,
1983). In the foundational study Project Access, Sonnert and Holton (1995) found that even the
talented women scientists who received National Science Foundation grants for their doctoral
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 36
research left the science fields in droves. Reasons for leaving ranged from overt discriminatory
practices to more covert prejudicial attitudes (Sonnart & Holton, 1995). Female PhD holders are
more likely to leave the STEM field than men, and women of color, particularly African
American women, are the most likely to leave (Turk-Bicakci et al., 2014; Williams, Phillips, &
Hall, 2014). Similarly, once they take jobs in STEM fields, more women than men leave the
profession (Turk-Bicakci et al., 2014; Williams et al., 2014). The reasons for leaving are varied,
but the most often cited reason is discrimination (overt or subtle), including hiring males over
females due to the perception that males will be better at science and math (Foschi, 2000; Moss-
Racusin, Dovidio, Brescoll, Graham, & Handelsman, 2012; Reuben, Sapienza, & Zingales,
2014). Another reason cited for leaving is what is called the marriage penalty, or the difficulty in
balancing the demands of family and children with the demands of research—demands that
include the rigid schedules required by most science laboratories (Correll, Benard, & Paik, 2007;
Cuddy, Fiske, & Glick, 2004). For women of color, gender discrimination intersects with racial
discrimination, producing a kind of double jeopardy in hiring and retention within STEM fields
(Turk-Bicakci et al., 2014; Williams et al., 2014).
The paucity of women in STEM fields is a concern for the United States, as the STEM
workforce must grow by as much as one million to meet the increasing demands of STEM
occupations (President’s Council of Advisors on Science and Technology, 2012). STEM
occupations are some of the highest paid occupations in the United States (National Academies,
2011). For women, gaining and maintaining access to the very lucrative STEM workforce will
become even more important in terms of economic equity in the next decade (National
Academies, 2011). Furthermore, the creative design process in STEM needs the diversity of
thought and experience that women, particularly women of color, can provide (Turk-Bicakci et
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 37
al., 2014). The diversity of thought provided by women is all but missing from STEM fields,
and in turn, women are unable to take advantage of the lucrative incomes in STEM (National
Association of Colleges and Employers, 2012). The leaks in the educational pipeline must be
plugged to increase access to and equity for women in STEM fields.
The leaky pipeline to STEM career paths can be traced back to much earlier leaks in
educational opportunity, beginning as early as preschool and continuing through elementary and
secondary education (National Women’s Law Center, 2014). Lack of access to and attainment in
AP curriculum in high school; lack of access to elementary and middle school teachers with
adequate training in STEM curriculum and awareness of their own possible gender bias; and
even lack of access to manipulative toys in preschool contribute to the paucity of women in
STEM fields.
Advanced Placement
The College Board Advanced Placement program offers thirty courses in a range of
subjects for high school students. Successful completion of AP courses gives high school
students the opportunity to earn college credit while still in high school or to gain higher
placement in college courses when accepted to college (College Board, 2015). Taking and
succeeding in high school AP courses is one way for students to stand out in the college
admissions process as being ready to succeed in an undergraduate environment (College Board,
2015). The College Board national data between 1997 and 2007 shows an increase in girls
taking all AP subject exams, except the AP Chemistry, AP Physics, AP Calculus, and AP
Computer Science exams, the gateway courses for STEM college success (College Board, 2014;
Morris, 2013; Quick, 2013).
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 38
For girls of color, the lack of access to AP courses is even greater; nationally, only 5% of
girls of color are enrolled in AP-level math and science courses (Smith-Evans, George, Graves,
Kaufmann, & Frohlich, 2014). Taking AP courses, achieving in those courses, and receiving a
high qualifying grade (4 or 5) in AP course exams is one predictor of academic success after
high school (Ackerman, Kanfer, & Calderwood, 2013). For STEM fields, the most important
predictor for completing a STEM major in college is completing AP Calculus in high school
(Ackerman et al., 2013; Sadler, Sonnert, Hazari, & Thi, 2014). The lack of access to AP STEM
courses in high school is one of the major leaks in the STEM education-to-career pipeline for
girls, particularly girls of color.
The College Board recommends growing the AP program in several ways: by preparing
students with high-level teaching in lower grade levels; by identifying underrepresented students
through AP potential data reports, which are based on the Preliminary Scholastic Aptitude Test
(PSAT) and show students’ potential to do well in AP courses; and by eliminating barriers to AP
course enrollment, such as prerequisite honors courses (College Board, 2014). Unfortunately,
despite these recommendations, AP enrollment often requires teacher recommendations for
placement, making teacher perception a key barrier to enrollment (Ackerman et al., 2013;
Gewertz, 2008). Teachers are less likely to recognize potential for success in AP STEM courses
in girls, and they are least likely to recognize that potential in girls of color (Campbell, 2012;
Morris, 2013; Quick, 2013). Teacher perception, which acts as a barrier to AP course
enrollment, thus creates a leak in the educational pipeline for women. But this teacher-
perception leak begins far earlier, with how teachers perceive girls’ academic ability in math and
science courses in middle school and elementary school.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 39
Teacher Bias
The groundbreaking book Failing at Fairness (Sadker & Sadker, 1994) opened a
discussion of educational practices around elementary school teachers’ perceptions of fairness
and gender neutrality. In the elementary classroom setting, the resource of time and attention
from the teacher is one of the most important variables for educational success (Sadker &
Sadker, 1994). After decades of observation, the Sadkers found that even the least biased teacher
devotes more of their valuable time and attention to boys (Sadker & Sadker, 1994). In 2009,
David Sadker released a second book, Still Failing at Fairness, which showed that even after a
decade of awareness and anti-bias training exercises, there were still substantial differences
between the way males and females were treated within the classroom setting, with teachers
continuing to devote more time and attention to males in their classes. These foundational
studies revealed that in elementary school, teachers call more often on male students, spend more
time asking probing high-level questions with male students, and provide less active instruction
to female students. These instructional practices have a profound effect on girls, particularly in
the area of STEM, where the development of critical thinking skills through exposure to probing
questioning is vital (Common Core, 2016; Next Generation Science Standards, 2016; Sadker &
Zittleman, 2009).
From kindergarten to 5th grade, girls lose ground in math; their self-perception of math
skills drops due to both stereotype threat and in-group associations (Galdi, Cadinu, & Tomasetto,
2014). Stereotype threat refers to a decrease in performance when individuals feel that their
performance will support a negative stereotype about their identity group’s ability (Steele, 1997).
Stereotype threat has a particularly negative effect on females’ performance in math
(Franceschini, Galli, Chiesi, & Primi, 2014; Spencer, Steele, & Quinn, 1999). Girls are also
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 40
heavily influenced by teachers’ perception of their math skills (Good, Aronson, & Harder, 2008;
Tiedemann, 2002). Teachers consistently perceive girls’ math skills as being lower than boys’
skills (Fryer & Levitt, 2010; Robinson, Lubienski, & Copur, 2011). Additionally, teachers
attribute boys’ skills to natural ability, but they attribute girls’ skills to educationally compliant
behavior, and they often underevaluate girls’ mathematics abilities (Robinson et al., 2011). This
is equally true for girls in science, particularly in the physical sciences, where girls are seen as
less proficient than boys (Kahle, Parker, Rennie, & Riley, 1993; Şahin, 2014). The combination
of negative self-perception, stereotype threat, and elementary school teacher perception of their
math and science skills has a detrimental influence on girls’ success in science and math courses
as early as elementary school.
As girls progress through the educational pipeline, teacher perception of their ability in
math and science continues to influence their pursuit of math and science career paths (Li, 1999;
Lindberg, Hyde, Petersen, & Linn, 2010). For girls of color, there is a multiplying factor:
teachers not only perceive girls of color as having low math skills but also doubt that girls of
color are serious about or committed to studying science and math (Pringle, Brkich, Adams,
West ‐Olatunii, & Archer ‐Banks, 2012). In fact, girls rate teacher perception as one of the largest
barriers to their success in STEM courses (Fouad et al., 2010). The effect of teacher bias in
STEM courses on girls’ confidence and motivation to stay in the STEM fields contributes further
to leaks in the STEM educational pipeline.
Prerequisite Skill: Spatial Awareness
At the very start of the STEM pipeline is a small but important component for girls’
success in STEM, the development of the skill of spatial awareness. Spatial awareness consists
of three areas of cognitive skills: spatial perception, visualization, and orientation (National
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 41
Research Council, 2006). Spatial awareness skills are the foundation of several skills vital to
STEM success: using space to model the world which enables students to structure problems,
find answers, and communicate those answers (National Research Council, 2006). The
development of spatial awareness begins as early as preschool. Play with blocks and
construction toys, such as Lego and wooden building blocks, assist with the development of
spatial awareness and visualization (Kersh et al., 2008; Oostermeijer et al., 2014). However,
girls in preschool are less likely to play with construction or building toys, and they develop an
experience gap with the items of play that teach this vital STEM skill (Etaugh & Liss, 1992;
Todd, Barry, & Thommessen, 2016).
Spatial awareness involves the ability to reason through the transformation of mental
pictures (Casey et al., 2001). The skill of spatial awareness is one of the most important
prerequisite skills to STEM course success (Hegarty, 2014; Kersh et al., 2008; National Council,
2000). One of the most common tests of spatial awareness, the Vandenberg and Kuse (1978)
measurement, requires the mental rotation of three-dimensional (3D) objects. Test participants
must identify matching shapes presented in different configurations, testing their ability to
mentally picture the item in different spatial orientations (see Figure 1).

Figure 1. Sample Vandenburg and Kuse (1978) task.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 42
There is a notable difference between men and women in spatial awareness skills, as
measured by the Vandenberg and Kuse measurement (Geiser, Lehmann, & Eid, 2008; Maccoby
& Jacklin, 1974; Voyer et al., 1995). This may be in part because the ability to mentally rotate
items is enhanced by experience with real-life 3D items, such as building blocks, Lego,
construction, or video games requiring rotation of objects (Feng et al., 2007; Kersh et al., 2008;
Oostermeijer et al., 2014). Many girls have less access to these real-life experiences, and this
leads to another leak in the STEM educational pipeline, because many studies show a
particularly high correlation between the mental rotation ability and ability in mathematical
reasoning, geometric understanding, measurement, and graphing (Kersh et al, 2008; Wei, Yuan,
Chen, & Zhou, 2012).
As early as 1974, psychologists observed a difference between males and females in the
skill of spatial awareness (Maccoby & Jacklin, 1974), and men consistently outperform women
in the Vandenberg and Kuse test of spatial awareness (Voyer et al., 1995; Geiser et al., 2008).
Some research points to structural differences between men and women, specifically hormonal
differences, as causing the skill gap (Hausmann, Slabbekoorn, Van Goozen, Cohen-Kettenis, &
Güntürkün, 2000). Other studies point to non-biological factors in the mental rotation skill gap,
such as testing situations (Peters, 2005; Voyer & Saunders, 2004), experience that develops
spatial awareness skills (Ginn & Pickens, 2005; Ginn & Stiehl, 1999), and gender role mediation
(Nash, 1979; Reilly & Neumann, 2013; Casey et al., 2001; Sherman, 1967). Whatever the cause
of the gap, the skill of spatial awareness is a crucial prerequisite skill for girls to successfully
develop as math and science students, and this skill gap may be the very first leak in the STEM
education pipeline (Hegarty, 2014; Kersh et al., 2008).
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 43
Luckily, recent research shows us that this particular leak in the STEM educational
pipeline can be shored up, and in a fairly short period of time (Feng et al., 2007; Hawes, Moss,
Caswell, Naqvi, & MacKinnon, 2017; Moè, 2016; Moè, 2018; Uttal, Meadow et al., 2013). For
instance, in the Feng, Spence, and Pratt (2007) study of undergraduate college students, females
were able to increase their spatial awareness and mental rotation skills by 20% simply by playing
an action video game for 10 hours or more in one week. Similarly, in the study by Hawes et al.
(2017), K–2 students were able to increase their ability in spatial awareness through a targeted
32-hour geometry program. Therefore, the deliberate development and implementation of
spatial awareness lessons for girls could provide the prerequisite skill needed for STEM course
success and serve as one effective measure for decreasing the STEM gender achievement gap.
Teaching Spatial Awareness Skills
Spatial awareness can be learned, often in a relatively short period of time (Feng et al.,
2007; Hawes et al., 2017; Moè, 2016; Moè, 2018; Uttal, Meadow et al., 2013). Several studies
demonstrate that spatial awareness skills can be enhanced by providing students with experience
in manipulating physical 3D objects, sketching 3D objects, or manipulating 3D objects in space
via a digital platform (Sorby, 2009; Uttal, Meadow et al., 2013). Providing students with these
types of experience with prerequisite skills does not require a fundamental change in the
curriculum; the NGSS require that most lessons have a project-based element (Next Generation
Science Standards, 2016). However, the curriculum to teach this prerequisite skill must be
carefully developed and planned by the teachers who will carry out the lessons.
Curriculum planning was once thought to be a task only for the experts. However, the
role of the teacher as a professional educator with a distinct knowledge base and professional
expertise was codified in two reports on teaching in 1986: the Holmes report and the Carnegie
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 44
report (Carnegie Forum, 1986; Holmes Group, 1986). The Holmes report called for
professionalizing teaching, including establishing professional standards; it argued that teachers
should specialize in their subject matter and should have expertise in both pedagogy and
knowledge of human development (Holmes Group, 1986). At the same time, the Carnegie
Forum called for teacher practice to be viewed as a professional area worthy of study and
refinement by the practitioners themselves (Carnegie Forum, 1986). Today, this view of the
teacher as curriculum developer and refiner of practice is encoded in both national and state
standards for the teaching profession (National Board, 2016). In fact, the simple act of planning,
implementing, and revising curriculum engages teachers more deeply with their teaching
practices (Spillane, 1999; Spillane & Jennings, 1997; Voogt et al., 2011). Voogt et al. (2011)
studied nine teacher design teams in six countries to examine the effect of collaborative
curriculum design on teaching. All design teams used the design thinking cycle of problem
analysis, design of curriculum, implementation, and reflection/redesign. Based on analysis of the
collaboratively designed classroom practices, this study identified professional growth in
teachers in two areas: first, in developing positive relationships with other teachers and higher
job satisfaction; second, in changes in classroom practices and beliefs about what good teaching
is (Voogt et al., 2011). Shared curricular design is especially important for teachers of science
and mathematics, because teachers’ ability to translate mathematical and scientific curricular
standards into effective practice is crucial to student progress (Krajcik, McNeill, & Reiser, 2008;
Spillane & Zeuli, 1999).
Mediating the Effects of Gender Role Expectations
Even the earliest research on spatial skills established that gender-role identity could
inhibit the development of cognitive ability in highly gender-typed domains such as spatial
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 45
ability (Nash, 1979; Sherman, 1967; Signorella, Jamison & Krupa, 1989). Nash (1979)
identified three areas that influence the development of spatial ability, including gender typing of
subject areas, gender role conformity, and self-efficacy beliefs. Both Sherman (1967) and Nash
(1979) recognized gender typing of subject areas as a deterrent to the development of the skill.
The belief that science and math subjects are appropriate for males, and that reading and
language subjects are appropriate for females negatively impacts girls’ achievement in math and
science, particularly on the test of spatial ability (Nash, 1979; Reilly & Neumann, 2013;
Sherman, 1967). Such gender typing of subject area persists today, reinforced by gender role
expectations that men are naturally better at math and science, and that these occupations are
naturally a masculine domain (Halpern, Straight & Stephenson, 2011; Reilly, Neumann &
Andrews, 2016; Rosenthal, London, Levy & Lobel, 2011). When 309 university students were
given cognitive verbal and spatial tests combined with gender identity tests, a strong correlation
was found between masculine identity and spatial confidence and between feminine identity and
verbal confidence, indicating that gender identity is related to perception of ability in various
educational fields (Reilly, Neumann, & Andrews, 2016). Another study found that even in a
Women in Science and Engineering (WISE) program dedicated to keeping women in college
science and engineering majors, participants felt that as women in the field, they did not belong,
and this had an effect on their persistence in the field (Rosenthal, London, Levy, & Lobel, 2011).
Girls often undervalue their skills in math and science and indicate a disinterest in these subject
areas in an effort to conform to societal gender norms (Halpern et al., 2011; Rosenthal et al.,
2011). This disinterest in STEM fields and occupations is reflected in the lack of female
enrollment in college STEM courses, and majors (Wang & Eccles, 2013). The combination of
negative belief about their academic ability in math and science and lowered self-evaluation can
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 46
negatively impact girls’ performance on cognitive tasks related to STEM such as the Vandenberg
and Kuse measurement (Syzmanowicz & Furnham, 2011).
These gender expectations are often reinforced by authority figures. For example, when
family members believe that girls are not as good at science or math as boys, that belief
reinforces these gender role expectations (Furnham, Reeves, & Budhani, 2002; Halpern, Straight,
& Stephenson, 2011). Similarly, teachers’ lowered expectations for girls’ success in math and
science can profoundly affect girls’ efficacy in these subjects (Fryer & Levitt, 2010; Robinson et
al., 2011). Fortunately, if teachers recognize and address their own gender bias, and if female
teachers understand their role as a STEM role model, female students’ beliefs may be tempered
and their success in STEM courses can improve (Beilock, Gunderson, Ramirez, & Levine, 2010;
Li, 1999). Teachers, particularly female math and science teachers, play a large role in
mitigating the effects of gender role expectations on girls, and unbiased teaching can thus reduce
the loss of women in STEM through the leaky education-to-career pipeline.
Study Focus
This literature review has surveyed several leaks in the STEM education-to-career
pipeline leading to a paucity of women in the STEM fields. One of the first leaks in a girl’s
educational pipeline is the development in preschool and elementary school of the skill of spatial
awareness, which is a prerequisite skill for STEM course success in high school. The literature
reveals that this skill can be learned at any time during the educational journey, and within a
fairly short period of time. The gap in spatial awareness skills between males and females is one
of the factors that reduce females’ STEM course success. This study seeks to explore the
innovative practice of deliberately teaching spatial awareness skills to girls.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 47
Using Clark and Estes’s (2008) gap analysis as a framework, this study explored the
knowledge and motivation of the key stakeholder group in the study, the teachers at The
Academy, to collaboratively plan and deliver spatial awareness lessons to sixth-grade girls. The
Academy is a single-gender girls school, which somewhat mitigated the role played by teacher
gender bias toward boys in math and science subjects, as there are no male students in the
school. The study also examined the impact of The Academy organizational culture on the
teachers’ development of the spatial awareness lessons.
Clark and Estes’ (2008) Organizational Problem Solving Framework
The conceptual frame for this analysis of the STEM gender achievement gap is gap
analysis. Gap analysis is a systematic problem-solving approach aimed at improving
performance and achieving organizational goals (Clark & Estes, 2008). Although this
framework was originally designed for business, it is equally relevant to the educational setting,
as it provides a problem-solving orientation (Rueda, 2011).
In order to begin gap analysis, the goals of the organization must be clearly defined. The
task is then to identify and measure the gap between the intended goal and the progress toward
attaining the goal (Clark & Estes, 2008). During the analysis process, three factors are
considered: people’s knowledge and skills, their motivation, and any organizational barriers to
completing the work (Clark & Estes, 2008). Assessing knowledge includes examining whether
employees have the information and skills needed to achieve their performance goals; assessing
motivation includes examining the internal psychological process that helps employees continue
to pursue the performance goals; and assessing organizational barriers includes identifying the
lack of resources or systems needed to reach the performance goal, or the existence of systemic
barriers to reaching that goal (Clark & Estes, 2008).
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 48
Gap analysis is solution oriented, for once the gaps are identified and analyzed, solutions
and strategies can be devised to narrow the gap to reach the performance goal (Clark & Estes,
2008). In an educational setting, these solutions can increase student success in meaningful ways
(Rueda, 2011). It is important to continually evaluate the solutions being implemented to make
sure that they are effective (Clark & Estes, 2008). In an educational setting, the Clark and Estes
model can be implemented to increase opportunities for students to learn and to create a more
motivating educational environment, in which teachers and administrators collaborate to meet
the needs of their students (Rueda, 2011). In this analysis of the STEM gender achievement gap,
the researcher examines the knowledge, skill, and motivation of the teachers in The Academy to
develop lessons and teach spatial awareness skills, and examines how the organizational
structures in place in The Academy support teachers’ knowledge of and motivation to implement
this innovative curricular model.
Stakeholder Knowledge, Motivation, and Organizational Factors
This section offers an overview of the literature relevant to the three factors upon which
the theoretical frame depends: knowledge, motivation, and organization. First, it describes the
general theory regarding knowledge and skills, and then it describes the specific knowledge and
skills needed by the teachers in this study. Some areas of teacher knowledge identified by the
researcher include knowledge of CC Mathematics and NGSS, knowledge of spatial awareness
skills, and knowledge of spatial awareness lesson plan development. In terms of motivation,
teachers need self-knowledge of their own possible gender bias; knowledge that, as female
teachers, they provide role models for girls in STEM courses; and self- and collective efficacy.
The section includes descriptions of two theories of motivation relevant to the teachers in the
study: goal orientation theory and interest theory. Finally, this section demonstrates the need for
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 49
the organizational structure to be supportive, innovative and collaborative; this need is explored
through the lens of the school’s innovative growth mindset culture.
Knowledge and Skills
According to Anderson, Krathwohl, and Bloom (2001), there are four types of
knowledge: factual, conceptual, procedural, and metacognitive. All four types of knowledge are
needed in the teaching profession, according to the National Board for Professional Teaching
Standards (National Board), the organization established by teachers to define and recognize
accomplished teaching. National Board standards focus less on content knowledge and more on
pedagogy, specifically content pedagogy (National Board, 1987). To meet The Academy’s goal
of improving girls’ STEM outcomes through instruction in spatial awareness, the teachers in the
study will need to utilize all these types of knowledge: factual knowledge of the subject matter
and of spatial awareness skills; conceptual knowledge and procedural knowledge, mostly related
to pedagogy and content pedagogy; and metacognitive knowledge, which is particularly
important in examining unconscious gender bias.
Teachers’ factual knowledge includes the knowledge that is basic to their specific
discipline (Anderson et al., 2001). One of the main tenets of the National Board is that teachers
must have a firm command of their subject area, including both factual information and the
major themes and concepts of their discipline (National Board, 1987). Science and math
teachers must be well versed in the CC Mathematics and NGSS, which are the national standards
for these subject areas (Common Core, 2016). One of the CC Mathematics and NGSS skills that
teachers in math and science must have knowledge of is the spatial awareness skill, the
prerequisite skill for math and science success (National Council Mathematics, 2000).
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 50
Conceptual knowledge comprises the facts, concepts, processes, and principles we are
aware of learning (Clark & Estes, 2008); conceptual knowledge is also a way of categorizing or
organizing knowledge (Anderson et al., 2001). Mathematics and science teachers are tasked
with organizing the CC Mathematics and NGSS standards in a way that is meaningful (Common
Core, 2016; National Research Council, 2015). This can include identifying power standards
and sequencing the standards in a way that makes sense and is most applicable to the student
population (Common Core, 2016;National Research Council, 2015).
Procedural knowledge is the subject-specific method of performing a task, including
criteria for appropriate use of the method (Anderson et al., 2001). For educators, procedural
knowledge includes the techniques of teaching, or pedagogy. As early as 1904, John Dewey
recognized that teachers should be trained not only in the subject matter but also in pedagogy
(Dewey, 1904). The synthesis of content knowledge and pedagogy forms a second kind of
procedural knowledge, that of content pedagogy, or the application of pedagogy to the specific
subject field by the teacher (Shulman, 1986). Effective teachers must have knowledge of their
subject area and its required methods and skills; pedagogical skills; and a deep commitment to
helping students learn (Darling-Hammond & Bransford, 2007).
For teachers of mathematics, procedural knowledge requires combining knowledge of
mathematics with learning theory specific to issues in mathematics (Ball & Bass, 2000). This is
specifically spelled out in the CC Mathematics teaching standards, which require teachers to
focus their mathematics pedagogy toward teaching performance tasks and toward open-ended
inquiry (Common Core, 2016; National Research Council, 2015). Teachers’ pedagogical
awareness can help them anticipate areas of difficulty for the learner (Ball & Bass, 2000). For
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 51
the teachers in this study, an important component of their content pedagogy—their procedural
knowledge—is the application of learning theory to the development of spatial awareness skills.
Metacognitive knowledge is the awareness of one’s own cognition and cognitive
processes (Anderson et al., 2001). Metacognitive knowledge allows one to know when and why
to do something, and it is a key aspect in problem solving (Anderson et al., 2001). For teachers,
metacognition is a vital skill, for it is central to the transfer of knowledge to the student (Pintrich,
2002). Teachers must also explicitly teach their students metacognition, because metacognitive
strategies are a tool that allows students to analyze their own learning processes and identify
their strengths and weaknesses, enabling them to adjust their learning strategies (Pintrich, 2002).
As students develop as learners, teachers can deepen their practice, providing support for
inquiry-based processes, which are particularly important to science education and make up the
basis for NGSS (National Research Council, 2015; Schraw, Crippen, & Hartley, 2006).
The following review of literature applies the general theory of knowledge to the specific
knowledge needs of teachers in this study. The review begins by exploring the literature relevant
to teachers’ knowledge: their factual knowledge of spatial awareness and of CC Math and
NGSS; their conceptual knowledge, or their ability to apply the CC Math and NGSS standards to
teach spatial awareness skills to their specific student population; their procedural knowledge
about developing content pedagogy, designing lessons, and teaching the prerequisite spatial
awareness skills; and their metacognitive knowledge, both as the subject of explicit teaching and
for teachers’ own self-knowledge of possible gender bias and their positions as role models for
female success in science and math courses.
Knowledge and application of new state standards. The CC Mathematics and NGSS
are relatively new standards, having been adopted by many states as recently as 2012 (Common
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 52
Core, 2016). The Academy teachers were previously trained in earlier iterations of state
mathematics and science standards; during the period of this study, they shifted to CC
Mathematics and NGSS, which require a more cognitively complex design and application of
content knowledge (Conley, 2011). The Academy teachers’ prior knowledge of content
standards connects with their new knowledge of CC Mathematics and NGSS, helping them
construct meaning (Maccoby & Jacklin, 1974). Both CC Mathematics and NGSS have
components of practical application as well as integration between math, science, engineering,
and English language arts, particularly in using evidence to support findings (Common Core,
2016; National Research Council, 2015; Pruitt, 2014). These new performance expectations
required teachers to carefully redesign and plan curricular modules (Common Core, 2016; Pruitt,
2014). Both CC Mathematics and NGSS place the teacher in the role of curriculum designer;
they offer suggested classroom practice but do not provide a rigid pedagogical map (Common
Core, 2016; National Research Council, 2015; Pruitt, 2014). The Academy teachers were
already steeped in the practices of standards-based grading, mastery learning, and growth
mindset, and the adoption of the CC Mathematics and NGSS standards carried these existing
practices further, allowing the teachers to design the hands-on and collaborative lessons so
necessary to STEM instruction that is responsive to students’ needs.
Knowledge and application of spatial awareness skills. Because The Academy is an
all-girls school, teachers needed to be aware of the gender gap in spatial awareness, which can
affect the attainment of CC Mathematics and NGSS Standards (Moè, 2016; Schraw &
McCrudden, 2006; Voyer et al., 1995). Spatial awareness is a prerequisite skill for the
development of mathematical reasoning, geometric understanding, measurement, and graphing
(Kersh et al., 2008). Spatial awareness is also connected to scientific reasoning and to the
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 53
visuospatial processes in physics, chemistry, and geography (Hegarty, 2014). Studies show that
students exposed to spatial thinking through intentional teacher practices in motor rotation skills
show a rapid increase in spatial awareness (Mathewson, 1999; Moè, 2016: National Council of
Teachers of Mathematics, 2000). Teachers can thus teach spatial attention and awareness skills
in a relatively short period of time (Feng et al., 2007; Moè, 2016; Uttal, Meadow et al., 2013).
Several studies demonstrate that spatial awareness skills can be enhanced by providing students
with experience in manipulating physical 3D objects, sketching 3D objects, manipulating 3D
objects in space via a digital platform, and translating 3D objects into 2D drawings (Uttal, Miller,
& Newcombe, 2013; Sorby, 2009). Intentionally teaching the prerequisite skill of spatial
awareness, combined with the practical application of project-based learning, may increase
grades in science and math classes (Moè, 2016). At The Academy, the intentional teaching of
spatial awareness was integrated in order to help students meet the school’s goal of 100%
successful attainment of the standards laid out in CC Mathematics and NGSS.
Knowledge of application of state standards in a hands-on project-based
curriculum. There is a gender gap in knowledge acquisition for secondary students in science
and math (National Center, 2012; National Science Foundation, 2015). To address this gender
gap, The Academy teachers must develop appropriate instructional strategies to help its all-girl
student body meet the standards laid out in CC Mathematics and NGSS. One important strategy
recognized by NGSS is hands-on, project-based learning.
Both CC Mathematics and NGSS require that teachers develop real-life, problem-based
instruction to challenge students to think more deeply within the subject area (Conley, 2011). In
fact, each NGSS standard specifically details scientific investigation and scientific modeling
components for experiential learning (Workosky & Willard, 2015). The role of experience in the
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 54
learning process is laid out in information processing systems theory, which asserts that
providing experiences that help people make sense of the material will help the learner construct
meaning from the instruction (Schraw & McCrudden, 2006). One method for practical
application of learned material is project-based learning, which must be designed carefully to
make sure that the projects correlate to authentic inquiry (Clough, 2002). The development of
project-based curriculum, where the students make meaning of their knowledge, forms the basis
of instructional design for The Academy teachers, and project-based instructional design furthers
the development of spatial awareness skills by providing hands-on experience with 3D objects
(Smith, Burton, Kokkas, Priestnall, & Polmear, 2008). Activities that offer this experience with
3D objects include manipulating 3D objects, sketching 3D objects, and translating 3D to 2D
sketches, and all of these help students improve their spatial awareness skills, particularly mental
rotation (Sorby, 2009).
Collaborative, hands-on, project-based learning is particularly relevant in an all-girls
school. Multiple studies indicate that hands-on learning is of particular benefit to girls in science
education (Burkam, Lee, & Smerdon, 1997; Cavallo & Laubach, 2001; Freedman, 2002;
Goldschmidt & Bogner, 2016). A foundational study of a nationally representative sample of
12,120 high school sophomores by Burkam, Lee, and Smerdon (1997) found that hands-on
experiments in high school science classes produced learning for all students but was particularly
advantageous for female students; it also found that whole group instruction was particularly
disadvantageous to female students. Furthermore, the study found that instructional design
affected students’ performance in science, and that girls particularly benefited from cooperative
groups, hands-on learning, and experiment-based learning. Because all students at The Academy
are girls, the study aimed to mitigate the gender gap in spatial awareness by offering the types of
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 55
lessons that research has shown works well for improving girls’ spatial skills: collaborative,
hands-on experiences with 3D objects in hands-on, project-based lessons. This curriculum
design is an important step toward meeting The Academy’s goal of improving student
performance in CC Mathematics and NGSS standards.
Knowledge of teacher bias and role model effect. Teachers at The Academy regularly
review and reflect upon their instructional practice, and they focus specifically on classroom
climate, teacher attitude, and instructional practice in these reflections. This is because
classroom climate and teacher modeling are two of the most important predictors for female
students’ success in science and math classes (Beilock et al., 2010; Fouad et al., 2010). In math
classes where teachers have high levels of content knowledge and demonstrate low levels of
math anxiety, female students have higher test results (Beilock et.al. 2010). Similarly, female
students are more efficacious in math and science courses when they have female teachers or
other female math and science role models (Burkam et.al., 1997). Heaverlo (2011) found that
certain specific teacher behaviors are associated with improving success in science and math for
girls, including willingness to provide encouragement, willingness to answer questions, and high
expectations for students.
The teachers in The Academy needed to be self-reflective as they designed their
instruction for this study’s intervention. They especially needed to reflect on their instructional
practices, classroom climate, and modeling behaviors, because these practices can positively or
negatively influence girls’ science and math course success. Table 2 outlines the conceptual,
procedural, and metacognitive knowledge that the teachers in the study needed for this
intervention, as well as how these areas of knowledge were assessed.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 56
Table 2

Knowledge Influence

Assumed knowledge influence How will it be assessed?
Teachers know what spatial awareness is and
that teaching spatial awareness is a prerequisite
skill for success for girls in STEM
Teachers use the CC and NGSS as a basis for
instruction
Teachers know the elements of design for spatial
awareness and hands-on, project-based
curriculum
Pretest of teacher spatial awareness skill
Open-ended survey
Document analysis/observation
Observation

Motivation
Motivation is the key to successful teaching at The Academy. Motivation, an internal
state that initiates and maintains goal-directed behavior, can be based on interest, beliefs,
attribution, goals, and partnership (Mayer, 2011). The three types of motivational processes are
active choice, persistence, and mental effort (Clark & Estes, 2008). Teachers in The Academy
made the active choice to teach in a single-gender environment with a focus on STEM. When
they made this choice, they knew that they were joining an organization built on design
practices, creativity, and innovation, and that one of the job requirements was to participate in
collective and innovative teaching practices. In an organization, creativity differs from
innovation: creativity centers on idea generation, and innovation centers on idea implementation
(Anderson, Potočnik, & Zhou, 2014). In this study on developing and implementing innovative
lessons on spatial awareness, Academy teachers needed to actively choose creativity and
innovation in their lesson plan design and implementation. These creative and innovative
practices were designed with a focus on helping girls, particularly girls of color, to attain success
in STEM courses, college, and career. Given the research on spatial awareness as an entry-level
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 57
skill for science and math course success, teachers’ practice included making the active choice to
develop and implement lesson plans to improve spatial awareness skills in their students.
Additionally, teachers in The Academy were persistent as they collaborated with the
other teachers to develop interdisciplinary, hands-on, project-based lessons focused on teaching
spatial awareness skills to their students. Collaboration in lesson plan and design has been
shown to increase teacher satisfaction, which may increase teachers’ persistence in and interest
in continuing the design process (Voogt et al., 2011).
Finally, teachers needed to have high levels of self-efficacy to creatively and
collaboratively design lesson plans for STEM success. Self-efficacy is a person's belief about
their abilities and their ability to exercise control over their own level of functioning and over
events that affect their lives (Bandura, 1993). For teachers, self-efficacy beliefs include the
extent to which the teacher believes they may affect student performance (Tschannen-Moran,
Hoy, & Hoy, 1998). The following literature review examines the three key theories of
motivation (goal orientation, interest, and self-efficacy) that influence The Academy teachers’
ability to recognize and evaluate student skills in spatial awareness, creatively and
collaboratively develop spatial awareness lessons, and implement those innovative lesson plans
in the classroom.
Goal Orientation
Goal orientation theory is a social cognitive theory of achievement motivation (Yough &
Anderman, 2006). The theory classifies goals into two major types, mastery goals and
performance goals. Mastery goals are those goals where the focus is on self-improvement, or
truly mastering a learning goal. A mastery goal orientation leads one to approach a task simply
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 58
in order to learn it (Yough & Anderman, 2006). In contrast, performance goals are those goals
where the focus is on comparison or competition with others (Yough & Anderman, 2006).
A mastery goal orientation can enable learners to view feedback - positive or negative—
as information relevant to modifying skills and capabilities (Dweck, 1986; Dweck & Leggett,
1988). There is a positive relationship between mastery goal orientation and the likelihood of
seeking feedback, and between mastery goal orientation and viewing difficulties as positive
challenges (Dweck, 1986; Dweck & Leggett, 1988). Learners’ mastery goal orientation enables
them to increase effort and persistence to overcome the challenge (Dweck & Leggett, 1988;
Tuckey, Brewer & Williamson, 2002).
In education, two interrelated concepts, growth mindset and mastery learning, join
together to support the mastery goal orientation framework. Mastery learning, first described by
Benjamin Bloom (1974), is the idea that all children can learn when provided with conditions
that are appropriate to their learning. When applied to the educational process, mastery learning
requires teaching a concept, assessing student learning, then, based on the results, re-teaching the
concept in a different way (Guskey, 1980). Mastery learning requires appropriate time to plan,
teach, and reteach the concept—to provide appropriate feedback and corrective instruction to the
student (Guskey, 1980; Guskey, 2007). If approached with fidelity mastery learning can be
instrumental in closing achievement gaps (Guskey, 1980; Guskey, 2007).
Growth mindset is the concept that intellectual ability is not fixed but can be cultivated
and developed through application and instruction (Dweck, 2000). Recent studies show that
growth mindset can mitigate some of the effects of the gender achievement gap in math and
science (Dar-Nimrod & Heine, 2006; Leslie et al., 2015; Schmidt et al., 2015). Placing these two
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 59
philosophies, mastery learning and growth mindset, as core values in a single-gender setting
may help math and science teachers mitigate the effect of gender bias on their students.
Teacher goal orientation. Goal orientation theory focuses on the learner’s purpose in
engaging in achievement behaviors: for performance or for mastery (Pintrich, 2003). Goal
orientation also affects teachers’ attitudes toward their students; teaching aimed at meeting
performance goals looks very different than teaching aimed at meeting mastery goals. At The
Academy, mastery learning and growth mindset frame both teaching and curriculum. Teachers
in The Academy employ growth mindset techniques by actively teaching the concept of growth
mindset to students and by practicing praise for process, both techniques that increase student
achievement, particularly in math and science (Blackwell, Trzesniewski, & Dweck, 2007;
Schmidt et al., 2015).
One of the principles of mastery goal–oriented teaching is to provide learning tasks that
are novel, interesting, and challenging (Yough & Anderman, 2006). For teachers in The
Academy, the novel task will be to develop innovative project-based instruction that helps
students access and succeed in CC Mathematics and NGSS standards. The best practice for
developing project-based instruction is to design projects collaboratively (Clough, 2002; Fallik,
Eylon & Rosenfeld, 2008). Collaborative design not only develops sound instructional models
for the students but also develops teachers as educators. Through collaboration and self-
reflection, teachers develop their professional practice and feel more efficacious in their teaching
(Turner, Warzon, & Christensen, 2011). Teachers in The Academy also face the challenging
task of meeting The Academy’s goal of graduating 100% of girls in their four-year cohort and
preparing them for the rigors of college. Developing a growth mindset and a continuous cycle of
improvement may help the teachers develop resiliency to meet their goal.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 60
Interest
Interest has a strong influence on individuals’ cognitive and affective functioning
(Ainley, 2006; Schiefele & Krapp, 1996). There are two types of interest: situational and
personal (Schraw & Lehman, 2009). Situational interest may be activated by a novel situation,
and is spontaneous, while personal interest is more sustained and activated by personal value
(Schraw & Lehman, 2009). Both situational and personal interest results in higher levels of
engagement, learning, and achievement (Pintrich, 2003). Interest is also one of the central
components of intrinsic motivation, where activity is taken on for self-satisfaction, not for an
external reward (Pintrich, 2003).
Interest is a primary predictor for success in the STEM fields, but girls’ interest in STEM
steadily declines over the course of their educational career (Hill et al., 2010; Sadler, Sonnert,
Hazari, & Tai, 2012). Developing the sustained interest in STEM for girls in The Academy will
be a key task for teachers. Teachers must be motivated by their own interest in the subject
matter, and they must understand that they serve as models for their students both for interest in
STEM courses and for resilience in STEM careers.
Teacher interest. Interest theory is based on the idea that students work harder to learn
material if it has some personal interest or value (Mayer, 2011). Activating and building upon
personal interest can increase learning and motivation (Schraw & Lehman, 2009). For teachers
in The Academy, the interest domain includes their personal interest in the subject matter, their
interest in helping girls learn, and their responsibility to grow students’ interest in the subject
matter by serving as a role model of interest in math and science.
Teachers’ interest in both their subject and in professional innovation shaped The
Academy’s rigorous recruiting and hiring process. In the first year, the founding teachers were
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 61
interviewed by the principal and observed at their current school during and after teaching. The
observations were meant to establish the teachers’ expertise in teaching practices and their
relationships with students. Teachers’ positive relationships with students have been shown to
increase student engagement and performance (Klem & Connell, 2004; Skinner, & Belmont,
1993). In the second year, the founding teachers hired teachers collaboratively and the principal,
who asked during interviews about the specific skills needed to teach in an innovative single-
gender school. All of the teachers hired were chosen based on three key criteria: their expertise
in their subject, their interest in STEM and their commitment to innovation in teaching practices.
The teachers demonstrated active choice, one of the key components of motivation, in choosing
to teach in the innovative environment of The Academy. They also showed persistence and
mental effort as they developed both a new curricular design, and innovative teaching and
grading practices. The collaborative design process gave them the freedom to try new ideas, and
take on new responsibilities – key motivators for teachers (Sylvia, & Hutchinson, 1985). These
teachers’ interest in their subject matter is demonstrated by their initiation of PD and their
development of project-based learning activities, and the school gives the freedom and resources
to make their innovations come to life. At The Academy, the established correlation between
hope, a sense of calling to teach, and ongoing commitment to the teaching field is evident
(Bullough & Hall-Kenyan, 2012).
At The Academy, all teachers, including non-STEM teachers, must display interest in
STEM subjects to positively motivate both teachers and students to succeed. Skinner and
Belmont (1993), who analyzed 144 third-grade students across the school year, found that
teacher emotional engagement and involvement were crucial to student engagement, and that
student engagement had a reciprocal effect on the teacher’s engagement. The enthusiasm for
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 62
STEM displayed by the teachers in The Academy is an important ingredient in their own and
students’ positive motivation. The Academy teachers must have a genuine desire to help girls
learn and succeed in STEM, for one of the most important factors affecting girls’ interest in
science and math is teachers’ attitude toward their subject matter (Heaverlo, Cooper, & Lannan,
2013). Teacher attitudes that positively influence girls’ interest in STEM include willingness to
provide encouragement, willingness to answer questions, and high expectations (Heaverlo et al.,
2013). Teachers in The Academy are truly excited about math and science and demonstrate this
interest daily to students.
Finally, The Academy teachers, the majority of whom are female, must be aware of their
effect on female students as role models for STEM success. Exposure to female faculty in high
school has a larger effect on college attendance and persistence in college for female students
than any other factor except family background (Nixon & Robinson, 1999). These teachers’
knowledge that they are role models who can have a profound effect on a young woman’s life
provides a strong motivating factor.
Self-Efficacy
Self-efficacy refers to the beliefs people hold about their abilities and about their control,
both over their own functioning and over events that affect their lives (Bandura, 1993). Self-
efficacy includes beliefs about performance, and these beliefs influence how much effort is put
forth, how long one will persist in the face of obstacles, and how resilient one is the face of
failure (Bandura, 1997).
For teachers, self-efficacy includes the teacher’s belief that they have the capacity to
affect student performance and can influence how well students learn (Bergman, McLaughlin,
Bass, Pauly, & Zellman, 1977; Guskey & Passaro, 1994). As early as 1976, the foundational
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 63
RAND study of a federal reading program within Los Angeles Unified School District
elementary schools found a strong correlation between teachers’ sense of self-efficacy and
reading achievement of minority students (Armor, 1976). Teacher self-efficacy has been found
to strongly influence student achievement, student motivation, and student self-efficacy
(Midgley, Feldlaufer, & Eccles, 1989; Moore & Esselman, 1992;Vieluf, Kunter, & van de
Vijver, 2013). Several studies of math and science teachers have shown that teacher self-
efficacy has a particularly strong correlation to student achievement and self-efficacy in math
and science courses (Andersen, Dragsted, Evans, & Sørensen, 2004; Khourey-Bowers &
Simonis, 2004; Midgley et al., 1989). This is particularly true for female students in STEM
courses (Beilock et al., 2010; Burkam et.al., 1997; Swars, Daane, & Giesen, 2006). To increase
student self-efficacy and performance, teachers at The Academy must have a strong sense of
self-efficacy in their teaching.
In addition to individual self-efficacy, in the school environment there is also a need for
collective self-efficacy. Bandura (2006) defines collective self-efficacy as the shared belief in
collective power that a group needs to collectively work toward its goals (Bandura, 2006). In the
school environment, this translates to the teachers sharing the feeling that the school can affect
student achievement (Goddard, Hoy, & Hoy, 2000). Teachers’ collective sense of their own and
their profession’s efficacy is one of the most powerful predictors of teacher pedagogical
decisions and effectiveness (Hoy, Davis & Pape, 2006). In this study, teachers needed to make
collective pedagogical decisions as they creatively designed lessons to teach spatial awareness.
As indicated in Table 3, the primary motivation factors for teachers in The Academy are goal
orientation, interest, and self-efficacy.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 64
Table 3

Motivational Influence

Assumed motivational influence How will it be assessed?
Female teachers are role models for young
women
Teachers demonstrate interest in their subject
matter
Teachers demonstrate personal and collective
self-efficacy
Observation, survey

Observation, survey

Observation, survey

Organization
For an organization to achieve its goals, it must have efficient and effective
organizational processes and material resources (Clark & Estes, 2008). In the case of
educational organizations, material resources are sometimes unavailable or misused, especially
within an urban setting (Clark & Estes, 2008). And there is a lack of attention to the social and
cultural context of the educational organizations, which makes it difficult to effect change
(Rueda, 2011). But in any organization, change can occur when new social and cultural climates
are created and maintained (Schneider, Brief, & Guzzo, 1996). True advancement in education
thus requires bold leadership, collaboration, and innovation. For The Academy to accomplish its
mission (to provide girls with a highly rigorous college preparatory STEM-focused education in
an all-girls environment that fosters academic excellence, ethical leadership, and intellectual
curiosity), its organizational structure must encourage a culture of collaboration, innovation, and
leadership.
Cultural Models and Cultural Settings
To encourage a culture of innovation, an organization must develop a new social culture
and new leadership within the organization (Belsky, 2016). For The Academy to develop as an
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 65
organization of advancement, it must develop a culture of innovation and collaborative
leadership. Innovative organizational cultures exist in organizations whose precepts encourage
innovation, engage a broader community, and develop leadership capacity (Schneider et.al.,
1996).
Cultural model: Innovation. To foster innovation in an organization, its leaders must
instill in others a genuine desire to take ownership in their work and to act together, motivated by
a shared purpose (Belsky, 2016). The teachers in The Academy were selected based on their
skill, their positive relationships with students, and their enthusiasm for being part of an
innovative, new model of single-gender education within a traditional public school setting. By
selecting teachers who share and take ownership of the design of the school, The Academy has
set the stage for creativity and innovation. The philosophy of growth mindset, which serves as
the baseline for all work in The Academy, establishes change as part of the school’s social and
cultural norms. A growth mindset is one that is not fixed or predetermined but allows for growth
through hard work and resiliency (Dweck, 2006). Experimentation, mistakes, and evaluation are
seen as an integral part of the learning process (Dweck, 2006). By instituting the growth mindset
as an essential component of The Academy, leadership fosters the organization’s ability to
change and innovate.
Fruitful innovation requires a unique capacity to capitalize on fears and doubts—to
reframe them as new opportunities for innovation (Belsky, 2016). Within The Academy,
teachers have a practice of bringing forth new ideas and exploring these ideas with other teachers
in vertical (across grade level) and horizontal (across subject area) teams. The teams meet
regularly and are provided with the materials and time needed to practice the mainstays of
disruptive innovation: associating, questioning, observing, networking, and experimentation
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 66
(Dyer, Gregersen, & Christensen, 2013). The teams also share their knowledge with other
teachers through peer-led PD, which is one of the most effective models of learning in an
educational environment (Hord, 2009). Peer-led PD also encourages the development of a
culture of collaboration in The Academy.
Cultural model: Collaboration. Collaboration within The Academy is exemplified by
its organizational structure, which is based on team leadership. In team leadership, members
share common goals, are interdependent, and must work collectively to achieve their goals
(Northouse, 2015). Team leadership results in greater productivity, better use of resources,
better decisions, better problem-solving, and greater innovation (Northouse, 2015). For this
model to succeed, teams must be supported and encouraged by material and organizational
support (Northouse, 2015). This is the model at The Academy, where the principal makes
budgetary decisions that provide teachers with paid time for teacher PD and curricular design in
vertical and horizontal teams. Teachers meet at least weekly to develop integrated curriculum
and discuss student progress, a process that develops a culture of support and collaboration.
Collaborative culture in an organization fosters the development of collective self-efficacy, or
shared beliefs that collective power can produce desired effects (Bandura, 2000). Collective
self-efficacy allows an organization to build motivation, stay strong in times of adversity, and
achieve great things (Bandura, 2000). The building of collaborative school culture is important
for teacher motivation and school-wide innovation; it is equally important to student
achievement. For example, collaborative teaching leads to improved student achievement,
particularly in math and English (Ronfeldt, Farmer, McQueen, & Grissom, 2015), an important
outcome for The Academy, whose mission is to provide girls with the skills necessary to
graduate high school and pursue the STEM field through college matriculation. Providing
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 67
teachers with time and materials for collaboratively planning innovative lesson designs helps
support teachers’ development of a sense of collective self-efficacy—a confidence that the
group’s actions have an important effect on student outcomes. Table 4 shows The Academy’s
organizational factors that influence the culture of collaboration and innovation, leading to
improved student outcomes.
Table 4

Influence of the Organization on Teacher Motivation

Assumed organizational influence How will it be assessed?
Teachers are encouraged by the organizational
culture of collaboration to design STEM-related
curriculum, particularly related to spatial awareness
The organizational structure provides teachers with
authentic leadership opportunities
The organizational structure provides PD, materials,
and time for teachers to develop, implement, and
reflect on their spatial awareness lesson design
Document analysis, observation, open-
ended survey

Survey, interview

Document analysis, survey, interview

Clark and Estes (2008) developed a systematic approach to identifying and closing gaps
between organizations’ goals and their performance. In this study, the STEM gender
achievement gap was identified as the performance gap, and the deliberate teaching of spatial
awareness through innovative project design from motivated teachers was the solution. It is
clear from the review of the literature that the deliberate teaching of the prerequisite STEM skill
of spatial awareness is crucial for girls’ success in math and science (Hegarty, 2014; Kersh et al.,
2008; Linn & Petersen, 1985; Oostermeijer et al., 2014). The literature also supports teaching
this and other skills through a model of innovatively designed teaching practices, in which
teachers develop and teach projects that are informed by standards-based curriculum in science
and math courses (Burkam et al., 1997; Clough, 2002; Conley, 2011). Several studies
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 68
demonstrate that spatial awareness skills can be enhanced by providing students with experiences
that train these skills: manipulating physical 3D objects, sketching 3D objects, manipulating 3D
objects in space via a digital platform, and translating 3D objects into 2D drawings (Uttal, Miller
et al., 2013; Sorby, 2009). Teachers involved in the study used elements of practitioner action
research; they had autonomy in both their lesson design and the immediate practical application
of the lesson design (Anderson & Jones, 2000; Kemmis et al., 2014). Additionally, because the
literature shows that teachers involved in innovative practice must continually review their
practice and motivation for innovative project design (Clough, 2002; Fallik et al., 2008; Turner
et al., 2011), the teachers in this study engaged in regular reflection and assessment. The
literature also showed that teachers must be aware that their self-efficacy and modeling of
science and math builds girls’ self-efficacy in these subjects (Beilock et al., 2010; Fouad et al.,
2010; Heaverlo, 2011).
A qualitative approach to research was used to investigate this innovative design study.
Qualitative methods focused on establishing The Academy’s teachers’ knowledge and
motivation to collaboratively develop hands-on lessons to teach spatial awareness skills to sixth-
grade girls. Additionally, the study explored the impact of The Academy’s organizational
culture on the development of that curriculum. Qualitative methods used included an open-
ended survey, document analysis, teacher interviews, and classroom observations. Although a
pre- and posttest of spatial awareness skills was used to measure teacher knowledge during the
initial PD session and to measure students’ gains in spatial awareness, the test results were not
used as a quantitative measure in the study; they were used only to assess growth in the learning
process.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 69
Conceptual Framework: The Interaction of Stakeholders’ Knowledge
and Motivation and the Organizational Context
A conceptual frame is a system of concepts, assumptions, expectations, beliefs, and
theories that supports and informs a research project (Maxwell, 2012). It is essentially a
statement of the researcher’s beliefs—the logic behind the research design (Maxwell, 2012).
Every researcher has a point of view, or philosophical worldview, and it is important to
understand and to acknowledge that point of view in the preliminary design of the research
(Creswell, 2013). The worldview for this study is feminist research. Feminist research positions
gender at the center of the inquiry (Hesse-Biber, 2013). A feminist research framework allows
researchers to acknowledge the interplay of power in research methods and their own emotional
connections to the research study—an important acknowledgment, since the appearance of
objectivity in most studies is false (Hesse-Biber, 2013). Feminist research comes out of a rich
tradition of research for social change that seeks to examine and address inequity, with special
emphasis on women’s lives and the differences in women’s experience produced by race,
economic position, and global context (Hesse-Biber, 2013). Two of the sub-frameworks for this
study, administrator-practitioner research and teacher-practitioner research, are both firmly
rooted in feminist social action tradition (Anderson & Jones, 2000).
In this case, the study positions gender at the center of the inquiry by seeking to examine
gender inequity in STEM education, which causes the STEM gender achievement gap. The
motivation for the study is to investigate how educators might affect the STEM gender
achievement gap by teaching the prerequisite skill of spatial awareness to girls in a very
particular environment, an all-girls public school with racial, economic, and geographical
diversity. The female researcher is also the school leader, an additional impetus for the feminist
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 70
theoretical orientation and the practitioner action research framework. The study evaluated an
innovative project design model, conceived and carried out in a very particular environment.
Teachers at this school are immersed in the philosophy of growth mindset, collaborative culture,
and innovation, which the organizational structure supports. The organization is a single-gender
girls school, and this may serve to reduce the impact of gender bias in teachers, which has been
shown in previous research. This is an ideal situation in which to study the development of
spatial awareness skills, which have been identified as prerequisite skills for STEM course
success, and in which female students often lag behind. The study aimed to explore the
deliberate teaching of spatial awareness skills to female students through innovative project
design from motivated teachers within an educational organization that supports innovation; it
also aimed to generate ideas for effective teaching practices to reduce the spatial awareness gap
between males and females, which may be one step toward reducing the gender achievement gap
in STEM course success.
As the literature has shown, the deliberate teaching of the prerequisite STEM skill of
spatial awareness is crucial for the success of girls in math and science (Hegarty, 2014; Kersh et
al., 2008; Linn & Petersen, 1985; Oostermeijer et al., 2014). The literature also supports an
innovative model of teaching practice design: teachers develop and teach hands-on, project-
based curriculum, grounded in standards, to enhance students’ skill in spatial awareness, which is
a prerequisite skill in science and math courses (Burkam et al., 1997; Clough, 2002; Conley,
2011). The act of planning, implementing, and revising curriculum engages teachers more
deeply with their teaching practices (Spillane, 1999; Spillane & Jennings, 1997; Voogt et al.,
2011). Additionally, as the literature reiterates, teachers involved in innovative practice must
continually review their practice and their motivation for innovative project design (Clough,
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 71
2002; Fallik et al., 2008: Turner et al., 2011). And teachers must also be aware that they are role
models for female science and math success and persistence, building girls’ self-efficacy in these
subjects (Beilock et al., 2010; Fouad et al., 2010; Heaverlo, 2011). The literature indicates that
for teachers to participate in innovative practices and maintain the motivation for change, they
must be situated in an organization with a culture of innovation and an organizational structure in
which members share common goals, are interdependent, and must work collectively to achieve
their goals (Belsky, 2016; Northouse, 2015; Schneider et al, 1996). There must be a sense of
collective efficacy; teachers and leadership team together must believe that their collective action
can positively affect student achievement (Bandura, 2000; Goddard, Hoy, & Hoy, 2000).
Figure 2 depicts the relationship between the two key stakeholders in this study: The
Academy’s teachers and its leadership team. The Academy itself started because OCSD data
showed a lack of achievement for female students, particularly female students of color, in
STEM courses. When the data was reviewed looking at it from the point of view that gender is
central, or using a gender lens, one solution to the STEM gender achievement gap in OCSD was
to open an all-girls school focused on STEM. Once the structure of The Academy was in place,
the leadership team of The Academy embraced the gender lens and expanded the frame by
including the philosophy of growth mindset, collaboration and innovation. Thus, the frame that
structures both the school’s development and this research is gender.

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 72

Figure 2. Relationship between The Academy and its teachers’ knowledge and skills.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 73
The literature review has established many issues for females along the STEM education-
to-career pipeline and has revealed that spatial awareness is a prerequisite skill for STEM course
success for females. The gap analysis method pioneered by Clark and Estes (2008) was used to
analyze the gaps in the knowledge and motivation of the key stakeholders as well as identify any
gaps in organizational support needed to meet the organizational goal. For this study, the key
stakeholders are the teachers, who use their knowledge and skills in curricular design to develop
students’ spatial awareness skills, and who are motivated by growth mindset, self-efficacy, and
awareness of their unique position as role models of STEM success for the female students. For
the intervention to succeed, the organization must support teacher leadership, collaboration,
innovation and growth mindset. Finally, leadership team members and teachers must use
elements of practitioner action research to design the innovation in order to keep the importance
of the lesson design in mind.
The Academy’s leadership team hired teachers who subscribed to these philosophies and
who would work well within The Academy’s organizational model, which is based on
collaboration and innovation. This model enables the teachers, the key stakeholders in the study,
to build collective self-efficacy and maintain motivation for curricular development and
innovation. For this study, the teachers were tasked in a PD with growing their knowledge of
spatial awareness skills and of these skills’ importance as prerequisite STEM skills. Continuing
PD sessions allowed teachers to explore research on spatial awareness skill lessons and sample
lessons from other educational institutions. From this knowledge and motivation base, teachers
collaboratively developed lessons to increase their students’ spatial awareness skills—lessons
that were tailored to the current student population. The teachers collaboratively decided on the
implementation procedures and followed up on the lessons. The leadership of The Academy
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 74
provided the initial PD on spatial awareness, as well as the material and organizational supports
for developing the spatial awareness lessons. The collaboration between the teachers and the
organizational structure supported the development of these lessons, which addressed the
organizational goal of improving students’ performance in CC Mathematics and NGSS by
deliberately teaching spatial awareness skills.
The Academy grew out of an innovative idea that was collaboratively developed by a
group of educators, parents and community members into a school design, which was approved
by OCSD after several years. This process shaped the school’s organizational culture into one of
collaboration and innovation.
Innovation in an organization’s culture comes from three components: the people, the
processes, and the philosophy of innovation (Dyer et al., 2013). For innovation to thrive, the
people on the team must have a balance of discovery- and delivery-driven skills (Dyer et al.,
2013). Discovery-driven skills are those that develop the innovation by questioning current
practices, observing and networking innovative designs, and producing experimental designs that
are then prototyped (Dyer et al., 2013). Delivery-driven skills are the planning and
implementing skills, which allow a prototype to be made and then analyzed (Dyer et al., 2013).
Organizations must sustain both of these skills to have an innovative culture (Dyer et al., 2013).
In the case of The Academy, teachers’ internal process of discovery, use of design, and
prototyping are supported by the organization. Teachers are given autonomy to develop their
innovations as they participate in elements of practitioner action research, making individual and
collective discoveries while teaching the spatial awareness lessons. The Academy provides the
material needs for the design process and the support of an organizational culture in which
change is not only expected, but is inevitable (Dyer et al., 2013). The Academy leadership’s
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 75
investment in the development of the spatial awareness lessons supports the teachers’ innovative
design, for innovative design requires leaders who both supportive and have a deep personal
interest in the innovation (Dyer et al., 2013).
Innovation in an organization also requires active participation by all members of the
organization (Dyer et al., 2013). If active participation of all stakeholders is not embedded in the
organizational structure, innovation will ultimately stagnate (Dyer, et al, 2013). Innovative
organizations have processes in place that encourage employees to network and experiment
(Dyer, et al, 2013). The Academy, as an educational environment that promotes innovation,
supports teacher networking and experimentation by providing the teachers with the time,
materials, and encouragement to work together in grade-and school-level teams.
In educational environments, the basis of learning culture must be the assumption that
humans are proactive problem solvers and learners and that learning cannot be imposed on
participants, who must be included in changes (Schein, 2010). In this case, the learning culture
needs to provide the necessary backdrop for the key stakeholders, the teachers, to work in a
culture of collaboration.
The Academy, as an educational organization seeking innovation and change, follows a
growth mindset philosophy. Growth mindset espouses the view that all people can learn if given
the support and materials needed (Dweck, 2006). Innovation involves a continuous cycle of
design by innovating, prototyping the innovation, seeing the innovation in practice, then
reassessing and refining the innovation (Dyer et al., 2013). The cycle of design can be seen as an
application of growth mindset, helping educational institutions to design more effective
processes. This study examined teachers’ development of innovative curriculum that aimed to
increase spatial awareness skills within the context of an innovative organizational structure.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 76
CHAPTER THREE
METHODOLOGY
Purpose of the Project and Questions
The purpose of this study was to explore the development and implementation of
collective teaching practice in the context of teachers developing spatial awareness lessons
within a unique secondary school setting. The literature review detailed the leaks in the STEM
education-to-career pipeline for women. Although there are several reasons for this gap, the skill
gap between males and females in spatial awareness is one that can be addressed in an
educational setting within a short period of time. This study explores the deliberate teaching of
spatial awareness skills to girls within an all-girls public school. The unique setting will
hopefully mitigate the teacher attention gap between males and females described in the
literature review. Using Clark and Estes’s (2008) gap analysis, this study explores the
knowledge and motivation of the teachers and the impact of the organizational structure on the
creation of the spatial awareness curriculum. By providing sixth-grade students with lessons in
the spatial awareness, their ability with this prerequisite STEM skill should increase. By
increasing the students’ spatial awareness skills and reducing the gendered skill gap, students
will be more likely to successfully complete higher-level STEM courses, taking one step toward
decreasing the number of women who drop out of the STEM pipeline.
Spatial awareness is a prerequisite skill for success in mathematics (Kersh et al., 2008)
and science (Hegarty, 2014) courses. By consciously developing girls’ spatial awareness skills,
The Academy teachers can provide girls with a foundation for success in math and science
courses, which forms the basis for The Academy mission: to provide girls with a highly rigorous
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 77
college preparatory STEM-focused education in an all-girls environment fostering academic
excellence, ethical leadership, and intellectual curiosity.
The questions that guide the study are the following:
1. To what extent are the prerequisite spatial awareness skills incorporated into The
Academy curriculum and teaching practices?
2. To what extent do the teachers in The Academy have the knowledge, skills, and
motivation to develop and implement the prerequisite spatial awareness curriculum?
3. How are the teachers’ knowledge and motivation to develop and implement the
spatial awareness lessons impacted by The Academy organizational culture?
Conceptual and Methodological Framework
The conceptual framework for this analysis of the STEM gender achievement gap is
Clark and Estes’ (2008) gap analysis. A gap analysis framework enables analysis of current
performance gaps and implementation of appropriate performance solutions (Clark & Estes,
2008). It provides a way to clarify both short- and long-term organizational and individual goals,
assess them, and describe the gaps between the current performance and the goals (Clark &
Estes, 2008). For educational systems, gap analysis provides a framework with which to look at
both organizational factors and learning and motivational theory (Rueda, 2011).
Gap analysis begins by identifying and clearly defining the organization’s goals, then
measuring the gap between the goals and the current performance (Clark & Estes, 2008). In an
educational organization, a mission or vision statement often outlines global goals, which are
then further defined by intermediate and short-term goals with benchmarks of progress (Rueda,
2011).
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 78
In this case the organization, The Academy, an all-girls public school that serves sixth
through 12th grade, has an overall organizational goal of providing girls with a highly rigorous
college preparatory STEM-focused education in an all-girls environment fostering academic
excellence, ethical leadership, and intellectual curiosity. The overall organizational performance
goal for The Academy is that by 2018, 100% of the students will be on target to graduate with
the STEM skills necessary for A–G eligibility. This will be measured by enrollment in and
completion of A–G STEM courses with a “C” or better standards-based grade. In order to reach
this goal, the students will need to improve their performance in CC Mathematics and NGSS.
The intermediate goal, and the focus of this research study, is to help students develop their
spatial awareness as they enter The Academy, thus providing them with the necessary
prerequisite skill for STEM success. The key stakeholders in the study, The Academy teachers,
were charged with developing the spatial awareness lesson plans.
During the gap analysis process, researchers examine three key factors: people’s
knowledge and skills, their motivation, and any organizational barriers to completing the work
(Clark & Estes, 2008). For the first factor, knowledge, the analysis examines whether employees
know how to use their knowledge and skills to achieve their performance goals; for the second
factor, motivation, the analysis examines the internal psychological process that helps employees
continue to pursue the performance goals; and for the third factor, organizational barriers, the
analysis examines the lack of needed resources or systems or the presence of systemic barriers
blocking the performance goals (Clark & Estes, 2008). By examining these three factors,
researchers can evaluate the best solutions for closing the gap (Clark & Estes, 2008). In
educational organizations, it is vital to analyze and address gaps in performance in order to
improve student outcomes (Rueda, 2011). For this study, the researcher examined the teachers’
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 79
knowledge and motivation to design and implement spatial awareness lessons, as well as the role
of the organizational culture in the development of these lessons.
Assessment of Performance Influences
Three performance factors were examined in this study: the knowledge of spatial
awareness as a prerequisite STEM skill by the key stakeholder group, the teachers in The
Academy; the teachers’ motivation to create innovative spatial awareness lesson plans: and the
impact of The Academy’s organizational culture on the first two factors. As the literature review
clearly showed, the deliberate teaching of spatial awareness is crucial to girls’ success in math
and science (Hegarty, 2014; Kersh et al., 2008; Linn, & Petersen, 1985; Oostermeijer et al.,
2014), and teachers should address spatial awareness by collaboratively developing hands-on and
project-based curriculum (Burkam et al., 1997; Conley, 2011; Clough, 2002). Thus the assumed
knowledge influences for teachers include the following things: CC Math and NGSS Standards,
of spatial awareness skills, of the importance of teaching prerequisite spatial skills for girls’
STEM success, and of the elements of design for hands-on and project-based learning.
As the literature review established, teachers’ attitudes toward and interest in math and
science is one of the most important factors in girls’ STEM success (Heaverlo et al., 2013; Nixon
& Robinson, 1999), and a female role model, particularly a female math or science teacher, is an
important factor for girls’ STEM success (Beilock et al., 2010; Li, 1999). Teacher self-efficacy
has a particularly strong correlation to student achievement and student self-efficacy in STEM
courses (Andersen et al., 2004; Khourey-Bowers & Simonis, 2004; Midgley et al., 1989),
especially for female students in STEM courses (Beilock et.al., 2010, Burkam et.al., 1997; Swars
et al., 2006). Thus, the assumed motivational influences in this study are teacher’s self-efficacy,
and their ability to demonstrate to students their interest and success in STEM.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 80
Finally, the literature revealed that innovative change requires innovative, collaborative
organizations with leadership opportunities at all levels (Belsky, 2016; Dyer et al., 2013). In
order for teachers to participate in innovative practice, and maintain the motivation for change,
they must be part of an organization with a culture of collaboration and innovation (Belsky,
2016; Northouse, 2015; Schneider et al, 1996) that provides material and other support (Rueda,
2011). In this study, the organization was assumed to influence the teachers’ lesson design in the
following ways: through material support and through its culture of collaboration, innovation,
and leadership. The knowledge, motivation, and organizational influences for this study are
depicted in Table 5.
This study is a qualitative study. Qualitative researchers are interested in understanding
the meanings people construct, or how they make sense of the world (Merriam & Tisdell, 2015).
Qualitative research analyzes a particular context to provide a deep understanding of the
worldviews held in that context (Merriam & Tisdell, 2015); it generates results that are credible
to the participants and to others researchers, and it may improve existing practices or programs,
as it is often action oriented (Maxwell, 2012).
In this study, qualitative methods were used to develop a meaningful description of the
process of designing the spatial awareness intervention. This description aims to be useful to the
participants as well as to other practitioners and scholars in the field. This research is not,
however, designed to be replicable nor numerically validated, as is the case in quantitative
research (Creswell, 2013). This study’s qualitative methods fit with its conceptual frame,
feminist research, which historically has a transformative worldview. A transformative
worldview (which requires qualitative inquiry strategies) contains an action agenda for change
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 81
(Creswell, 2013). Feminist research seeks to examine and address inequity, with special
emphasis on women’s lives and the differences in women’s experience (Hesse-Biber, 2013).
Table 5

Knowledge, Motivation, and Organizational Influences

Assumed influence Assessment
Knowledge
Teachers know what spatial awareness is and that
teaching spatial awareness is a prerequisite skill
for success for girls in STEM
Teachers use the CC and NGSS as a basis for
instruction
Teachers know the elements of design for spatial
awareness and hands-on, project-based
curriculum

Pretest of teacher spatial awareness skill
Observation notes from initial PD session
Open-ended survey
Post-lesson implementation interview
Document analysis lesson plans
Lesson observation
Observation of lesson plan design session
Observation of lesson implementation
Motivation
Female teachers as role models for young
women.
Teachers demonstrate interest in their subject
matter
Teachers demonstrate personal and collective
self-efficacy

Open-ended survey
Lesson implementation observation
Post-lesson implementation interviews
Observation of PD
Observation of lesson plan design session
Organization
Teachers are encouraged by the organizational
culture of collaboration to design STEM-related
curriculum, particularly related to spatial
awareness
The organizational structure provides teachers
with authentic leadership opportunities
The organizational structure provides PD,
materials, and time for teachers to develop,
implement, and reflect on their spatial awareness
lesson design

Open-ended survey of teachers
Observation of lesson plan design session
Observation of PD and lesson design
meetings
Post-lesson implementation interviews
Document analysis, PD session materials,
observation of PD sessions
Post-lesson implementation interviews

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 82
This study took place in The Academy, an all-girls secondary school that was designed to
address the needs of girls, particularly girls of color, in an urban setting. This particular research
environment is ideal for the theoretical framework of transformative feminist research, which
calls for a qualitative approach. Similarly, the subject of the research, teachers’ innovative
design of curriculum to address the gender gap in spatial awareness, calls for the types of
descriptive or narrative research that are associated with qualitative research design (Creswell,
2013).
This study used qualitative methods at several stages: in examining teachers’ knowledge
and motivation to develop and teach the innovation; in describing the initial implementation of
the innovation; and in identifying to what degree the school organization supported teachers’
innovation. The qualitative methods used include open-ended survey, observation, interview,
and document analysis. Although the study included a pre- and posttest of teacher and student
knowledge of spatial awareness, this quantitative test was used only for informational purposes,
as part of a continuous cycle of design improvement.
Participating Stakeholders and Purposeful Selection
Purposeful Selection
The stakeholder group primarily responsible for implementing the performance goal is
the teachers at The Academy. There are 14 teachers currently teaching in The Academy, and all
teachers were invited to participate in the study. This study of an innovative practice within a
specific school setting situates itself in the tradition of feminist and practitioner action research,
and its aims and methods are similar to those of case studies. Case study design often uses
purposeful selection of study participants (Maxwell, 2012). In purposeful selection, sample
participants are selected based on how much can be learned from them (Merriam & Tisdell,
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 83
2015). In this study, all teachers initially participated in a PD on spatial awareness (PD is a
common practice of the school); all teachers were invited to participate in the PAR project of
collaboratively developing and implementing lesson plans teaching spatial awareness skills to
students. The teachers who agreed to be part of the study made up the purposeful sample group.
The following criteria were used for participant selection:
Criterion 1. Participants must be teachers in The Academy.
Criterion 2. Participants must be teachers with subject area credentials.
Criterion 3. Participants must be teachers who agree to be part of the research.
Recruitment
This study, which was designed to delve deeply into one innovative practice within a
unique organization, resembles a case study. In case studies, a researcher explores in depth a
program, event, or activity of one or more individuals (Creswell, 2013). This study was not
intended to be generalizable to teachers in other organizations; it was intended to deeply
understand the perspective of the teachers in this particular organization. In the initial stages of
the study, the researcher reviewed documents related to PD and school structure in order to get a
picture of the organizational culture. Next, an open-ended survey was distributed to all teachers
in The Academy in order to get a sense of how the teachers perceived the organizational culture,
to gauge the teachers’ knowledge of spatial awareness, and to survey teachers’ attitudes about
being a STEM role model and about the school’s growth mindset philosophy. The open-ended
survey produced data relevant to all three research questions.
The next step in the research process was to provide PD on spatial awareness for all the
teachers. As is the practice at the school, the science department chair and the school principal
(the researcher) collaborated to provide a PD session to all teachers on spatial awareness and the
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 84
STEM gender achievement gap. The researcher was a participant observer during this session
and gathered data for questions one and two. During this PD session, teachers were invited to
take part in the study as participant researchers by collaboratively developing the lesson plan.
The teachers who agreed to do so participated in subsequent collaborative lesson design
meetings, prepare lessons to be delivered primarily to the sixth-grade girls. The researcher was a
participant observer during the lesson design meetings and observed the lessons when they were
taught. These observations gathered data for questions 1 and 2. Finally, the teachers were
invited to participate in follow-up interviews about their experience with the lesson plan
implementation. These interviews provided data for the entire study and continued the teachers’
reflective practice, which is part of the school culture. By using a combination of several
qualitative methods, the researcher was able to triangulate results, gain a full picture of the
school culture, and provide a rich description of the innovation process. The steps to the
qualitative research are summarized in Figure 3.

Figure 3. Research steps.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 85
In educational settings, it is standard practice for teachers to engage in observation and to
reflect on their educational practices (Danielson, 2011; Danielson & McGreal, 2000). Teachers
in this study were already involved in collaborative lesson design and collaborative
administrative and peer observations to increase the effectiveness of their STEM teaching
practices. The teachers designed a series of PD opportunities for 2017–2018 that included
lessons in STEM-teaching efficacy. The study observations were thus part of the normal process
at The Academy, and they do not require any special permission, although teachers’ participation
in the research study was voluntary. The idea of spatial awareness as a prerequisite STEM skill
was introduced early in the 2017–2018 school year by the principal in collaboration with the
science department chair, who was already interested in exploring this concept. Teachers were
not offered any additional compensation for designing the lessons, as The Academy already
provides paid planning hours before and after the school day. After the final observation and
interview, the researcher provided $50 gift certificates to the teachers who participated in the
study as a gesture of appreciation for their time.
Feminist research frameworks allow researchers to acknowledge the interplay of power
in research methods and their own emotional connections to the research study (Hesse-Biber,
2013). In this study, the researcher was the leader of the school and had an ongoing relationship
with The Academy teachers, which could have created an inequitable power relationship
between researcher and participants. However, for purposes of this study, the researcher
relinquished any power associated with the role of principal, and explicitly stated that
relinquishment in all recruitment processes. Additionally, the study was designed to include
components of practitioner action research, and both teachers and researcher shared the goal of
providing a practical solution to the issue in order to benefit the students. The researcher
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 86
acknowledged her own emotional connection to the research and the fact that the gender lens
influenced her desire for this case study to be successful. Acknowledging these relational and
emotional biases allowed the researcher to consistently monitor her actions as a researcher to
ensure that the study included fair and accurate descriptions. Additionally, the established
relationship between the researcher and the teachers created a rapport that enabled participants’
honest disclosure.
Open-Ended Survey
Open-ended surveys elicit both information and opinion (Merriam & Tisdell, 2015). An
open-ended survey was chosen as the first activity in the study in order to gather data on two
elements: teacher knowledge of spatial awareness and teacher knowledge of the role played by
spatial awareness in the STEM gender achievement gap. The survey was also designed to enable
participants to give their opinions about the structures and culture of The Academy, and it was
therefore conducted anonymously through an online platform. Anonymity was chosen to ensure
that teachers offer honest personal and organizational evaluations.
Observation
Observation, a practice that helps us make sense of the world, gives us first-hand
knowledge of the research phenomenon and guides further action (Merriam & Tisdell, 2015),
was used in this study to gather information on teachers’ knowledge and motivation as they
planned and implemented the spatial awareness lessons. There were three observations in this
study. During the first observation, which took place in the initial PD on spatial awareness, the
researcher was a participant observer. In the second observation, the lesson plan design sessions,
the researcher was again a participant observer. In the third observation, the researcher observed
the implementation of the lesson designs in the classroom. These observations gathered data
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 87
relevant to all three questions in the study. The Academy has a common practice of non-
evaluative review of teaching practices, both from peers and from administrators, and the
observers regularly use an internal non-evaluative observation sheet based on elements of
Danielson’s Framework for Teaching (Danielson, 2011); the observation sheet prompts later
reflective discussion of professional teaching practices. Because the researcher has a prior
relationship with The Academy teachers, she had previously participated in peer reflection and
lesson study with the teachers.
Interview
Interviews involve first deciding whom to interview, based on what the researcher wants
to know and the potential of each interviewee to add insight to the study (Merriam & Tisdell,
2015). In this study, the researcher determined that interviews of the teachers who implemented
the spatial awareness lesson plans would be the most useful. The purpose of an interview is to
allow us to understand another person’s perspective and how they are interpreting the world
around them (Merriam & Tisdell, 2015). In this study, it was important to understand the
perspective of the teachers as they developed and implemented the strategies for spatial
awareness. This gave insight into these processes that could not be ascertained in any other way;
it could also be helpful for teachers who wish to replicate the curriculum design in another
setting.
This study used semi-structured informal interviews. Semi-structured interviews begin
with structured questions that elicit require specific data from all respondents, then give the
interviewer the flexibility to move into exploratory questions (Merriam & Tisdell, 2015). Each
teacher had particular insights into the curriculum design and implementation, and these
differing views could support the expansion of the practice. These interviews were conducted in
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 88
order to help the researcher understand more fully how the curricular plan was developed and
refined as it went from design to implementation, information that may be helpful for any
teachers or schools interested in mirroring the process of curricular design used here.
Document Analysis
Documents and artifacts are a natural part of the research setting, and have the advantage
of not intruding upon the setting (Merriam & Tisdell, 2015). Schools, in general, are often rich
sources of documents and artifacts; The Academy is a new school (opened in 2016) and
therefore has few documents, but the documents available offer data relevant to question 3, about
the school’s organizational culture. The main documents analyzed included the original school
design plan that was adopted by OCSD and the PD agendas, sign-in sheets, and minutes for
2016–2017 and 2017–2018. This data offered information about The Academy’s organizational
structure and design. Other documents analyzed included the collaboratively developed teacher
lesson plans and rubrics associated with standards-based grading and mastery learning. These
documents offered an understanding of both The Academy structures and of teacher knowledge
of and skills with CC Mathematics and NGSS standards.
Data Collection
Each data collection instrument used had a different purpose. Open-ended surveys and
document analysis were primarily used to answer the question about the organizational culture of
The Academy. The observations and interviews were primarily used to understand the
knowledge and motivation of the teachers in the study and to offer data bearing on the questions
about current practice and about and implementation of the spatial awareness lessons. These
multiple data points were triangulated in order to offer a clearer, richer picture of the innovation;
triangulation examines different data sources for themes, and these themes (once identified) can
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 89
help add validity to the study if they appear in more than one data source (Creswell, 2013).
Member checking was also used to add validity; as participant researchers, teachers had access to
the research, and they could practice member checking, which is the process of allowing
participants to judge the accuracy of the findings (Creswell, 2013). Data collection was
approved by both the University of Southern California Review Board and the OCSD Review
Board.
Open-Ended Surveys
This study’s open-ended survey was modified from a survey conducted by UCLA
Teacher Center X in a study on teacher effectiveness (MacCalla, 2014). The survey was sent out
electronically to all teachers through Survey Monkey, which does not track IP addresses,
ensuring that the results are anonymous. No demographic information questions were asked.
Two reminders were sent out via email, a week apart. A copy of the survey instrument is in
Appendix B.
Observations
The observation protocol for this study is modified from Danielson’s Framework for
Teaching (Danielson, 2011) that includes professional teaching practices such as self-reflection
and professional conversations about teaching and learning. The modified observation tool is
already in use at the Academy and is a standard practice at the school for peer and self-
evaluation. A copy of the observation protocol is in Appendix C. With the permission of the
teachers being observed, the observation was video recorded for accuracy. The observations
were transcribed verbatim.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 90
Interview
The interview protocol used for this study was also modified from Danielson’s
Framework for Teaching (Danielson, 2011), specifically from the sections covering teacher self-
reflection and reflection on lesson plan design. The protocol left room for unstructured questions
to deepen the review of the lesson. A copy of the interview protocol is in Appendix D.
Document Analysis
Two documents were examined to understand the organizational context and culture.
The first document was The Academy school plan, a 30-page document detailing the intentions
behind the school design. This document is in the public records of the Ocean City school board
sessions, and it was obtained from school board minutes. The second set of documents analyzed
included the PD agendas and minutes from The Academy’s PD sessions. These documents were
publicly available at the school, where they were accessed by the researcher. The documents
were analyzed to collect data for a rich description of The Academy’s organizational culture.
Data Analysis
Case studies such as this one require a description of the setting and an analysis of the
themes or issues (Creswell, 2013). For this study, the researcher used multiple data sources to
describe and analyze the process of developing and implementing the spatial awareness
curriculum. The document analysis, survey results, and interviews contributed to a rich
description of The Academy. The observations and individual interviews were coded for
emerging information related to the curricular design and implementation process. Coding is the
process of organizing data in chunks that are then organized in categories and labeled with a
relevant term, or “code” (Creswell, 2013). Initial codes for this study were based on categories
expected from the research, such as teachers’ knowledge of spatial awareness, teachers’
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 91
knowledge of lesson design, teachers’ motivation as role models of interest in STEM, and
organizational structures that supported the lesson design. However, other codes were developed
through the analysis, as the researcher is not always able to anticipate the results in a study
(Creswell, 2013). These emergent codes included lesson design elements such as using hands-on
materials and collaboration for student learning.
Credibility and Trustworthiness
This study used several research methods, including open-ended survey, observation,
interview, and document analysis, in order to enable triangulation of the findings to increase
credibility. The study also provided credibility through member checking, which is the process
of taking the qualitative findings back to the participants to determine whether the participants
feel that they are accurate. In this study, the researcher reviewed findings for accuracy with the
teachers involved. Because the researcher had a prior relationship with the teachers in The
Academy, it was important to guard against bias in favor of a positive outcome from the lessons.
Building in member checking of the findings helped to mitigate this bias. The prior relationship
was also an asset: the researcher had access to all documents and the school site, and she had a
preexisting trusting relationship with the teachers, increasing participants’ comfort level in
interviews and observation. Because observation and self-reflection are standard practice in the
school, many study processes felt like normal parts of school functioning.
This research study was not intended to be generalizable to teachers in other
organizations; it was intended to deeply understand the perspective of the teachers in this
particular organization. The innovative practice of designing specific lessons on spatial
awareness is detailed in Chapter 4 and can be duplicated by following the specifics in the study,
but it may have different outcomes in different contexts.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 92
CHAPTER FOUR
RESULTS AND FINDINGS
In STEM fields, there is a gender achievement, college, and career gap; the number of
women in STEM fields steadily declines from high school through college and career (Hill et al.,
2010; National Women’s Law Center, 2014). Preschools and elementary schools do not expose
girls to the prerequisite skills (such as spatial awareness) that enable success in high school
STEM courses (Oostermeijer et al., 2014). Teachers of mathematics and science view spatial
awareness as a prerequisite skill for mathematical reasoning, geometric understanding,
measurement, and graphing (Hegarty, 2014; Kersh et al., 2008; National Council of Teachers of
Mathematics, 2000). When girls fall behind in these prerequisite skills, they struggle to keep up
in STEM subjects, creating the first leak of female students from the STEM education-to-career
pipeline (Hedges & Nowell, 1995; Moè, 2009; Voyer et.al., 1995).
According to the literature, deliberate teaching of this prerequisite skill is most successful
when teachers develop and teach relevant hands-on, project-based curriculum based in science
and math standards (Burkam et al., 1997; Clough, 2002; Conley, 2011). The act of planning,
implementing, and revising curriculum engages teachers more deeply with their teaching
practices (Spillane, 1999; Spillane & Jennings, 1997; Voogt et al., 2011). Teachers involved in
innovative practice must continually review their practice and motivation for innovative project
design (Clough, 2002; Fallik et al., 2008: Turner et al., 2011). Teachers must also be aware that
their modeling of science and math builds girls’ self-efficacy in these subjects (Beilock et al.,
2010; Fouad et al., 2010; Heaverlo, 2011). In order for teachers to participate in innovative
practice and maintain the motivation for change, they must work in an organization with a
culture that supports innovation and with a structure in which members share common goals, are
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 93
interdependent, and must work collectively to achieve their goals (Belsky, 2016; Northouse,
2015; Schneider et al., 1996).
The purpose of this study was to explore the innovative practice of deliberately teaching
the prerequisite STEM success skill of spatial awareness to girls. Nationally, the gap in spatial
awareness skills between males and females is one of the contributing factors to girls’ lower
STEM course success (Hegarty, 2014; Kersh et al., 2008). Yet spatial awareness can be learned
within a fairly short period of time (Feng, Spence, & Pratt, 2007; Moè, 2016; Uttal, Meadow et
al., 2013). Spatial awareness skills can be enhanced by providing students experience with
manipulating physical 3D objects, sketching 3D objects, manipulating 3D objects in space via a
digital platform, and translating 3D objects into 2D drawings (Uttal, Miller et al., 2013; Sorby,
2009).
Using Clark and Estes’s (2008) gap analysis as a frame, this study explored the
knowledge and motivation of the key stakeholder group, The Academy teachers, to
collaboratively plan and deliver spatial awareness lessons that were initially implemented with
the entering class of sixth-grade girls. The study also examined the role played by The
Academy’s organizational culture in supporting collaboration and innovation. The study posited
that if the teachers instructed students in the necessary prerequisite skill of spatial awareness
during their sixth-grade entry year to The Academy, students would improve their performance
in CC Mathematics and NGSS. This outcome supports The Academy’s mission: to provide girls
with a highly rigorous college preparatory STEM-focused education in an all-girls environment
fostering academic excellence, ethical leadership, and intellectual curiosity. It might also be one
small step toward diminishing the achievement and college/career gender gap in STEM.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 94
The questions that guided the study were the following:
1. To what extent are the prerequisite spatial awareness skills incorporated into The
Academy curriculum and teaching practices?
2. To what extent do the teachers in The Academy have the knowledge, skills, and
motivation to develop and implement the prerequisite spatial awareness curriculum?
3. How are teachers’ knowledge and motivation to develop and implement the spatial
awareness lessons impacted by The Academy organizational culture?
The subject of the research, an innovative design of curriculum to address the gender gap
in spatial awareness, called for descriptive or narrative research, both of which are associated
with qualitative design (Creswell, 2013). Qualitative methods in this research study focused on
discovering the knowledge and motivation of the teachers to provide and develop the innovation,
on describing the innovation in the initial implementation, and on examining the degree to which
the school culture supports the innovation. Qualitative methods used included open-ended
survey, observation, interview, and document analysis. The research consisted of multiple steps
and methodology to assist in triangulation of the findings. Member checking of the research was
also employed. The research steps are delineated in Figure 4.
Participating Stakeholders
The stakeholder group primarily responsible for implementation of the performance goal
is the teachers at The Academy. All 14 teachers currently teaching in The Academy were invited
to participate in the study, and all 14 participated in the PD on spatial awareness led by the
principal and science department chair. Two teachers went on medical leave during the course
of the study and were unable to participate in the remainder of the study activities. Of the
remaining 12 teachers, who were invited to participate in the open-ended survey, nine teachers
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 95
completed the survey. All 12 teachers participated in the lesson design meetings. The lesson
design meetings were framed with elements of PAR; this allowed the teachers to decide how
they would design and implement the spatial awareness lessons.

Figure 4. Final research steps.
At the lesson design meeting, the teachers spent a great deal of time discussing spatial
awareness as a skill, and the best way to teach the skill, and together they researched specific
lessons they would be willing to implement. They also decided that instead of implementing the
lessons instead of through their regular curriculum and courses, they would present them as a full
day of workshops during a day when the high school students at the school would be involved in
taking the PSAT. This would allow those teachers who taught both middle school and high
school to focus on teaching the spatial awareness skill to the middle school students. The
workshop schedule would also allow the teachers to deliver different lessons focusing on spatial
awareness through a rotating workshop during the day. However, the high school testing
required proctors, which eliminated most of the high school faculty from participating in the
delivery of the spatial awareness lessons. The six teachers who actually taught the lessons
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 96
included five middle school teachers and one high school teacher, all of these teachers
participated in both the lesson delivery (observation) and in reflection on their instruction
(interview). Two of the six teachers were science teachers (one high school science), two were
English language arts teachers, one was a math teacher, and one was a computer science teacher;
five were female and one was male. All 108 girls in the sixth-grade class participated in the
spatial awareness workshops. Figure 5 shows a summary of the participation for each part of the
research.

Figure 5. Participant summary.
Results
The sample size from the research was quite small, ranging from 12 to six teachers during
the course of the study. Although a sample size this small is not statistically relevant, it did
allow the researcher to develop a rich description of the stakeholder opinions through survey,
interview, and observations.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 97
Knowledge Results
The literature review for this study established that spatial awareness is one of the
mitigating factors in STEM course success for females (Hegarty, 2014; Kersh et al., 2008); that it
can be learned and within a fairly short period of time (Feng, Spence, & Pratt, 2007; Moè, 2016;
Uttal, Meadow et al., 2013); and that teachers should address spatial awareness by
collaboratively developing hands-on and project-based curriculum (Burkam et al., 1997; Conley,
2011; Clough, 2002). Based on this literature review, the assumed knowledge influences for this
study included teachers’ knowledge of spatial awareness; teachers’ knowledge that spatial
awareness is a prerequisite skill for success for girls in STEM; teachers’ knowledge that CC
Mathematics and NGSS should be used as a basis for instruction; and teachers’ knowledge of
how to design hands-on, project-based curriculum to teach spatial awareness.
Teachers’ knowledge of spatial awareness. As a start-up activity during the spatial
awareness PD session, teachers took the SRI (the same measure that was later given to students
as pre- and posttests) to assess their pre-instruction knowledge of spatial awareness. Teachers
had 8 minutes to complete four measures, two that tested mental rotation of objects and two that
tested spatial visualization. Of the 12 teachers taking the pretest, only four responded correctly
to all four items, a success rate of only 33%. As depicted in Figure 6, the rest of the scores
showed that teachers had some knowledge of the skill; only one teacher could not correctly
answer any of the questions.
This 33% success rate on the SRI was surprising, and many teachers felt that they were
better at the skill then the data indicated. Discussion during this part of the PD session revealed
that teachers were quite surprised at the difficulty of the task. In fact, one of the math teachers
repeatedly asked to look at the answers because she couldn’t believe she answered items
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 98
incorrectly. Another math teacher went through the work with her to explain the answers and
assisted other teachers with corrections to the items. Once the errors were pointed out, most
teachers could see where they made mistakes. The result of the pretest showed that even those
teachers who thought they were adept at spatial awareness realized they needed to work on the
skill. Using the SRI to begin the PD made the session more action oriented; all of the teachers
were anxious to build spatial awareness, both their own and the students’.

Figure 6. SRI teacher scores.
The PD continued with information on the importance of the prerequisite spatial
awareness skill, particularly for girls, and the teachers became even more invested in teaching
the skill. One English teacher stated, “I never knew how important this skill is for female
students, and I really want to help build this skill across all the curriculum. I’m happy to be part
of the lesson design session.” Several of the math and science teachers were vocal about their
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 99
sense of urgency about beginning to plan the lessons. In fact, the teachers decided that teaching
the skill was so important that they scheduled the lesson design session to begin within a week of
the initial PD. The PD was thus very successful in helping teachers to understand their own level
of spatial awareness skills and in helping them understand the need to teach the skill to the
students. The teachers’ sense of urgency, created by their realization that their skills were low,
was an unexpected result.
A second assessment of teachers’ knowledge was embedded in the open-ended survey
question “What do you know about spatial awareness?” As Figure 7 shows, one respondent said
that she had no idea about spatial awareness; the answers of the other eight respondents all
expressed that spatial awareness was a way of visualizing space around you in different
dimensions. Three of the respondents indicated that boys were better than girls at this skill, as
they typically are more exposed to the skill through experience with blocks and video games.

Figure 7. Teacher knowledge about spatial awareness skills.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 100
Teaching spatial awareness to girls. As stated above, in their answers to the open-
ended survey, three respondents were aware that there is a disparity in spatial awareness skills
between boys and girls. The survey asked, “Do you believe spatial awareness is an important
skill to teach girls interested in STEM?” The answers were based on a Likert scale; seven
respondents answered strongly agree, two answered agree, and zero respondents answered
disagree, strongly disagree, or no opinion. The results are displayed in Figure 8.

Figure 8. Importance of teaching spatial awareness.
In the follow-up interviews with teachers, conducted after the spatial awareness lessons
were taught, several respondents said that until the PD they had not been aware that spatial
awareness was something that needed to be specifically taught as a skill. In fact, one of the
science teachers proclaimed,
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 101
I was definitely not comfortable or aware that this was something that I needed to do in
the classroom. This is something I learned naturally from my parents, from my own
education, but I wasn’t aware it was being taught to me . . . I wasn’t aware that I needed
to do this.
Later in the interview she stated,
I saw big improvement over the course of the day with the girls as they got to do different
aspects of spatial awareness. So I think if we can continue to implement this on a more
day-to-day basis in the classroom, it would be beneficial . . . so more PD on it, more
collaboration, especially within our department, especially in science.
The experience of teaching the spatial awareness workshops over the course of a day appeared to
inspire the teachers to continue to develop spatial awareness lessons.
CC Mathematics and NGSS Standards as a basis for instruction. Document analysis
of The Academy school plan that was adopted by the OCSD showed that the math and science
texts and the training materials used are aligned to CC Mathematics and NGSS standards.
Document analysis of yearly PD sessions and departmental meetings revealed extensive planning
for Interim Assessments in ELA, math, and science as well as planning of standards aligned
curriculum through standards-based grading and mastery learning. Agendas from all established
departments (ELA/social studies, math, science, electives) revealed that teachers were in the
process of identifying scaffolded learning targets by grade level, common rubrics, and common
math and science practices in order to create standards-based grading that was consistent across
all departments. Agendas from PD sessions also showed that teachers were in the process of
developing CC ELA practices and common rubrics for writing across the curriculum to be used
across all departments. Observation of the lesson plan design meeting revealed rich discussions
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 102
of the use of CC math, CC ELA, and NGSS in lesson development. For example, the ELA
teachers worked with the science and math teachers to develop a list of spatial awareness
vocabulary that all teachers might use as a word wall during the spatial awareness sessions and
beyond. During the lesson plan session, the teachers worked together to research literature and
innovative lesson plans through CC Mathematics and NGSS websites, and they shared these
resources as they discussed their plans.
Teachers know the elements of design for hands-on, project-based curriculum.
Document review of PD sessions revealed sessions on design thinking, growth mindset, Kagan
strategies, cooperative learning groups, and integrated standard-based project design.
Observations of the lesson plan design session showed collaborative work and a commitment to
hands-on projects. All of the lesson plans developed were hands-on: designs included
(a) complex 2D to 3D origami and vocabulary for geometric shapes; (b) building shapes with
tangrams, using imagination to sketch shapes, and using spatial vocabulary to describe; (c) using
Scratch coding to produce name plates; (d) using 3D pens to make cubes and writing an
instruction manual using spatial vocabulary; (e) drawing plans for a Rube Goldberg machine to
do a simple task, then building the machine from common backpack items; and (f) using a flight
simulator to develop a flight pattern. During the interview process, all teachers explained that
they had purposely built an element of struggle into the design of their lessons. They did not
want to explain everything; instead they wanted to have the students struggle through finding an
answer. For instance the English teacher did not explain how to build the cubes with the 3D
pens, instead letting the girls work out how to make the cube, and the math teacher gave written
instructions for the origami but did not demonstrate how to make the folds. All workshop
lessons were designed to include collaborative group learning, partially as a necessity (not
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 103
enough 3D pens or flight simulator software for individual use) and partially because it is a best
teaching practice, one that is commonly used in the classrooms at The Academy. In the follow-
up interviews, common statements included, “I didn’t want to tell them how to use the pens for
this element. I wanted it to be part of the process,” and “I wanted the students to really engage
with the equipment on their own, and go through the discovery process.”
Motivation Results
The literature review includes three key theories of what drives motivation: mastery goal
orientation, interest, and self-efficacy. All of these types of motivation influence The Academy
teachers’ ability to recognize and evaluate student skills in spatial awareness, to creatively and
collaboratively develop spatial awareness lessons, and to implement these innovative lesson
plans in the classroom. Mastery goal orientation allows teachers to provide learning tasks for
students that are novel, interesting and challenging (Yough & Anderman, 2006). Teachers
activate and build upon personal interest by providing novel and challenging tasks, which can
increase both teacher and student learning and motivation (Pintrich, 2003; Schraw & Lehman,
2009; Sylvia & Hutchison, 1985); in fact, teachers’ interest in STEM is one of the most
important factors in fostering girls’ interest in science and math (Heaverlo et al., 2013; Nixon &
Robinson, 1999). Math and science teachers with strong STEM self-efficacy are particularly
strongly correlated to female student achievement and student self-efficacy in STEM courses
(Beilock et.al., 2010; Burkam et.al., 1997; Swars et al., 2006). Teachers’ collective self-efficacy,
or their shared feeling that the collective group can affect student achievement, motivates
teachers, but is particular to the school setting (Bandura, 2006; Goddard et al., 2000). Based on
the literature review, the motivational influences are teachers as role models, teachers
demonstrating interest in their subject matter, and individual and collective teacher self-efficacy.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 104
The study’s results, which indicate that each of these influences is at work in teachers at The
Academy, are described in the following sections.
Teachers are role models. In the initial survey, teachers were asked, “As a teacher, do
you feel that you are a role model for STEM?” All nine respondents answered positively to this
question. Answers from STEM teachers included the following statements: “I am a female
teaching advanced STEM courses, so that is proof to the girls that they can master STEM
content”; “It wasn’t until I had personally had female science teachers that I felt capable of
pursuing STEM. I like being able to provide that example to girls”; and “Having a teacher that
can inspire you in the STEM field can make you interested in the STEM field.” One non-STEM
teacher answered,
Even though I may not be skilled or proficient in all areas of STEM, I model a growth
mindset and love of learning as I build expertise and content knowledge. I feel that I am
a strong female role model for the girls.
During the observations of the spatial awareness lessons being taught, teachers made
comments to students indicating that they expected the girls to pursue STEM careers; comments
also often conveyed teachers’ sense of themselves as STEM role models. For instance, in the
computer design session, the teacher stated, “When I was working in animation, we used
elements of Scratch to design, so designers, let’s get ready to use our creativity and imaginations
today!” During the flight simulator session, another teacher stated,
I’ve never flown a plane, but I have learned by experimentation how to use the flight
simulators. I know I still have a great deal to learn, and I know you are going to help me
today by going even farther than I have on the sims. Maybe you will fly a plane that I’m
a passenger on in the future.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 105
Teachers demonstrate interest in their subject matter. In the initial survey, two
teachers, responded to the question “As a teacher, do you feel that you are a role model for
STEM?” by connecting their status as a role model to their interest in their subject matter. One
said, “I have a passion for STEM, and the girls all know how excited I am about STEM-related
topics and activities. I believe that modeling enthusiasm, as much as content, is an important
part of being a role model.” The other said, “I love teaching and love modeling a growth mindset
and love of learning as I build expertise and content knowledge.”
Teachers’ interest was also apparent in the lesson design session, which included all 12
teachers. Field notes from the session show that teachers displayed enthusiasm for their own
subject matter, for STEM, and for collaboration. Some of the pertinent dialogue from this
session is reproduced here:
Teacher 1: I can totally see how doing origami can help with understanding in geometry.
That’s a great idea. I’m just wondering as an English teacher, how do I connect? How
can I teach spatial awareness? What do I do?
Teacher 2: I could see maybe building some vocabulary? That fits with the ELA
standards, maybe?
Teacher 1: Oh: that’s great! I love that. Let’s all throw out some terms and I can build a
word wall, then we can all use the words. I can have them illustrate the words too, or
maybe we all can and that might be like the 2D to 3D we were talking about.
Teacher 3: I just did a lesson with tangrams at a workshop I went to last month. I had to
describe the tangram sequence to my partner to help her make the design. Maybe you
could have the girls make a shape with the tangrams and describe it.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 106
Teacher 1: Or I can have them build the tangrams, then try to write a description of how
they built them, as like an instruction manual kind of activity. Then I can have them
actually use the spatial awareness vocabulary. This is great! Can I get some tangrams to
experiment with later?
Teacher 3: Sure, I’ll bring you some after the meeting. We can also spend some more
time on the vocabulary. I’m looking some up right now. [Both teachers look at
computer.]
Another dialogue included the following exchange:
Teacher 3: I’m really excited to try the Rube Goldberg lesson with them. I can’t wait to
see what machines they will build!
Teacher 2: If you want to give them building sticks, I have some from the engineering
project we did.
Teacher 3: That sounds good, but I’m thinking maybe it should be a bit less structured. I
think I will ask them to only use what is in their backpack. That way they will have more
of a challenge. I want them to plan it out, so I’ll give them a plan sheet. Then they have
to translate from the 2D plan to the 3D building. It’s a little sophisticated, but I think
they can manage it!
When the lesson plans were taught, observations showed all six of the six teachers
displaying enthusiasm, even as they repeated the same workshops several times throughout the
day. Teachers were all observed circulating to assist groups throughout each workshop. One
teacher said,
Today we are focusing on spatial awareness. This is something you use a lot in the
courses you get to take later on, like geometry, but I wanted to give you a little
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 107
introduction now. We are going to use origami to discover shapes and angles, and I can’t
wait to work on this with you. But fair warning, I’m not going to show you how to do
this. I want you guys and your great brains to wrestle with the instructions.
Another teacher stated,
Today we are going to learn to describe objects. We are going to use the descriptive
vocabulary we have been learning to help us describe and communicate and draw a
picture in our mind’s eye of the object. This is a really important and fun skill, especially
for scientific writers, like you all, so I can’t wait to begin and see where we go.
Self and collective efficacy. Teachers showed self-efficacy, or the belief that the teacher
(or teachers, in collective self-efficacy) can affect student performance. In answering the survey
question “What do you like the most about your school?” all teachers showed both personal and
collective self-efficacy. Examples of comments include, “I like working with a lot of excellent
teachers who believe strongly that they are making a difference in the lives of our students”; “I
like knowing that my colleagues are also working their hardest to make the vision a reality for
our students”; and “I love how The Academy is committed to bringing a high-quality education
to students of all backgrounds and how we create a supportive, nurturing environment for the
students to develop socially, emotionally, and of course academically.”
During the lesson design sessions, the 12 participating teachers displayed self-efficacy as
they designed the lessons, as demonstrated in the above dialogue. Additionally, during the
follow-up interviews, each of the six teachers displayed self-efficacy in their answers to the
question “Did you feel prepared to teach the lesson?” One teacher stated, “Yes, even though I
had never tried this particular lesson before, I felt excited to try it. The girls reacted really well,
and I saw over the course of the day that they got better and better.” Another stated, “I didn’t
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 108
entirely feel prepared, because in the beginning I didn’t have the correct tangrams. I had to keep
modifying the lesson . . . But by the end I thought it was great.”
Organizational Results
Innovative organizational culture emerges when the precepts of the organization
encourage innovation, engage a broader community, and develop leadership capacity (Schneider
et.al., 1996). Leading for innovation in an organization depends on instilling in employees’
hearts and minds a genuine desire to take ownership in their work and to act together, motivated
by a shared purpose (Belsky, 2016). Fruitful innovation requires a unique capacity to capitalize
on fears and doubts, a capacity to reframe doubts as new opportunities for innovation (Belsky,
2016). The philosophy of growth mindset, which is the baseline for all work in The Academy,
establishes innovative change as part of the organization’s social and cultural norms. A growth
mindset is one that sees success not as predetermined but as a function of growth, which is
achieved through hard work and resiliency; experimentation, mistakes, and evaluation are seen
as an integral part of the learning process (Dweck, 2006). By making the growth mindset an
essential component of The Academy, leadership fosters innovation as a foundational
component. Another organizational influence is the school’s culture of collaboration. The
organizational structure provides teachers with authentic leadership opportunities; it also
provides them with PD, materials, and paid time to develop, implement, and reflect on their
spatial awareness lessons.
All teachers seemed to see the school’s policies and organization as fostering their
motivation and innovation. In answer to the survey question “How do you feel about the growth
mindset frame of your school?” all nine respondents responded favorably. Teachers wrote,
“Growth mindset is an excellent frame for The Academy and I happily embrace it”; “I have
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 109
always wanted to teach somewhere that lifts EVERY student up, and I believe that having
growth mindset as a frame at The Academy actually does that”; “I think it provides a basis for
personal motivation to be successful. Students understand that they too can gain understanding
in subject matter they may not have previously felt successful in”; and “It is important for
students to maintain a growth mindset in every subject, but also for teachers to demonstrate the
relevance of a growth mindset as role models to the students.”
Teachers are encouraged to develop the spatial awareness lessons. At the initial PD
on spatial awareness, the teachers’ results on the SRI pretest increased their urgency to develop
the skill in themselves and their students. This sense of urgency was demonstrated by the
teachers’ decision to schedule the lesson planning session within a week of the PD. At that
lesson design meeting, the teachers came up with the idea to do a day of focused spatial
awareness workshops during the PSAT testing day. The principal attended the lesson plan
session as a participant observer and helped the teachers design the logistics for the day, but she
did not work on any of the lesson plans, allowing teacher–leaders to emerge during the design
process. The principal also provided material support for the lessons; she requested lists of the
supplies needed for each lesson and ordered or pulled in-stock supplies to meet those needs,
delivering the supplies to the teachers’ classrooms before the lessons were taught.
The teachers’ leadership and collaboration, which were fostered by the organization,
emerged in the follow-up reflective interviews. When teachers were asked how they decided on
the elements of the spatial awareness lessons, five of the six responded that they researched
lesson plans with other teachers during the lesson planning session. They also reported
collaborating on the decision about which element of spatial awareness (mental rotation, spatial
visualization, translation of 2D to 3D) each teacher would focus on to develop a well-rounded
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 110
workshop day for the students. One teacher responded that she had taught the lesson before, but
all the rest stated that these were new lessons. Although the encouragement to teach the lesson
came initially from the principal and the science department chair, the teachers quickly began to
encourage one another. It is important to note that although only six of the teachers were going
to actually teach the lessons (because of the need for PSAT proctors), all 12 of the teachers
participated in the planning of the lessons, indicating a collective sense of purpose.
Teachers are provided with leadership opportunities. The organization fosters
teacher leadership in its design and in its practices. As document review showed, distributed
leadership was designed into the school from the initial planning stages. According to document
analysis, teachers have volunteered to take on responsibilities typically done by an assistant
principal, such as testing coordination, English Learner support, gifted and talented support, and
intervention support, among other duties. Analysis of PD documents revealed that although PD
agendas typically include a start by the principal, the bulk of the sessions are taught by teacher–
leaders. PD occurs each Monday morning, when students have a late start day. Professional
development runs on a monthly cycle: week one has grade-level meetings for intervention and
integrated curriculum planning, week two has departmental meetings for vertical alignment,
week three has focus groups on topics agreed upon by faculty, and week four has a topic
determined by the central office or a school need, such as differentiated instruction.
Although the initial spatial awareness PD was led by the principal and the science
department chair, who worked in collaboration to develop the sequencing and research that
would be presented, and although the lesson planning session was initially led by the science
department chair and the math department chair, both of these meetings quickly became
collaborations by the 12 teachers.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 111
Teachers are provided with material and PD to support lesson development. The
data indicates that teachers feel that the organization materially supports their innovations. For
example, the follow-up reflective interview included the question “Do you feel you had the
necessary support, time and supplies from the school to teach the spatial awareness lessons?”
All six teachers answered affirmatively. One teacher responded that she had some technical
difficulties with a website during the lesson, but that this was not the school’s fault; she felt that
it was due to her own poor planning in not testing the technology prior to the lesson. Her
solution was to go next door to ask assistance from another teacher, and together they were able
to get the website to work.
A second interview question asked, “What further support might you need from the
school for these kinds of lessons?” All respondents mentioned more time to continue to refine
the lessons and incorporate them more into ongoing teaching practices. Collaboration within and
between the departments was also a high priority. Specifically, the ELA teachers wanted more
time with the science and math department to scaffold and develop particular vocabulary for
science and scientific writing. One math teacher mentioned that she wanted to design a planning
or reflection sheet to expand future spatial awareness lessons.
Findings
The literature review showed that spatial awareness is an important skill for STEM
success for females (Hegarty, 2014; Kersh et al., 2008) that can be taught within a fairly short
period of time (Feng, Spence & Pratt, 2007; Moè, 2016; Uttal, Meadow et al., 2013). Students at
The Academy have Smarter Balanced Scale Score Ranges (SBAC scores) that are higher than
the OCSD average in math, and they have self-selected for an interest in STEM by applying for
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 112
the school. Yet pretesting of these sixth-grade girls using the SRI instrument showed that only
11% of students successfully answered motor rotation and spatial awareness questions.
Once the PD helped establish the importance of the spatial awareness skill for girls’
STEM success, the teachers developed a sense of urgency and wanted teach the skill as soon as
possible to the middle school students in The Academy. The teachers decided to meet one week
after the initial PD session to research best practices and plan the spatial awareness lessons. In
that lesson planning session, the teachers decided to teach the lessons as a one-day workshop
with rotations through multiple hour long sessions. Based on observations of the lesson planning
sessions, both STEM and non-STEM teachers showed a high degree of interest as they worked
together, first to research other practices, then to refine those practices for the specific school site
and age group. When the teachers did not find many lesson plan examples through their
research, they began to discuss lessons they had previously taught or observed that would teach
the spatial awareness spectrum of skills. There was collaboration across departments; the ELA
teachers asked for assistance from the STEM teachers, and they jointly developed a word wall
for vocabulary and a set of descriptive skills relevant to both ELA and STEM. All 12 teachers
participated in the lesson planning, even though only six would teach the actual workshops. The
ideas were generated together, and then teams of teachers or individual teachers worked on the
details. The principal and leadership team organized logistical details for the workshop day,
including changing bell schedules, organizing the groups of students, providing materials, and
monitoring student transitions.
Observations of the day of spatial awareness workshops showed high levels of interest
from both teachers and students. The lessons were planned to be high interest, with hands-on
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 113
activities, collaborative groups, and student inquiry built in. The workshop lessons included the
following:
1. Origami: In this lesson, taught by a math teacher, students made a highly complex
origami star with multiple layers. Students were given written instructions. They had
to read the 2D directions and move to 3D hands-on building of the origami shapes.
The teacher purposely did not assist during the first part of the lesson, allowing the
students to collaborate for solutions and struggle with the move from 2D directions to
3D building. This workshop focused on motor rotation by moving from 2D
description to 3D object.
2. Tangrams, sketching, and spatial vocabulary: In this lesson, taught by an ELA
teacher, the teacher projected a tangram image on the board with students in pairs,
one facing the board and one facing away from the board. The student facing the
board had to describe the tangram to the student facing away well enough so that the
student facing away could draw the object. From this activity, the teacher debriefed
vocabulary that could be used when describing a geometric object, and the students
built a word wall with the vocabulary. After building the word wall, the student pairs
were given a set of eight colored tangrams. They could build any shape they wanted,
but then they had to draw a map of the tangram shape and write a description that
would enable another pair to duplicate the shape. When all pairs had completed the
maps and descriptions, they shared with another group and tried to build the shape
based on the description. This workshop focused on spatial visualization by asking
students to imagine and draw 3D objects and then convert them to a 2D description.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 114
3. Using Scratch design to build nameplates: In this lesson, the computer teacher used
basic elements of Scratch programming to help students build a nameplate. Students
were seated in pairs, but each used an individual Chromebook for this workshop. The
teacher projected a demonstration of how to use elements of Scratch design. Students
were given time after each demonstration to practice the design element. Then
students were given the task of creating a nameplate using two colors, movement of
at least one letter with one delay, and a background sound. Students were encouraged
to work in pairs, and to walk around the room to get help from other students when
they were stuck. The teacher also circulated. At the end of the design session, each
student showed their design and explained how they developed the elements. This
workshop focused on moving objects in space, an element of motor rotation.
4. Using 3D pens to make a cube and write an instruction manual: In this lesson, an
ELA teacher demonstrated the use of a 3D pen. She had a word wall of spatial
awareness vocabulary that she reviewed with the students. The students, in groups of
three, were given the task of building a cube using the 3D pens. While they built the
cube, they used the vocabulary to write an instruction manual to enable someone else
to follow their procedures in building the cube. Students then compared instruction
manuals as a whole class, sharing the best way to use the spatial awareness
vocabulary and the descriptive elements of instructions. This workshop focused on
spatial visualization by moving from 3D design to 2D instructions.
5. Building and describing Rube Goldberg machines: This workshop, taught by a
science teacher, started with a description and demonstration of a Rube Goldberg
machine (a complicated machine to do a simple task). Students, in groups of four,
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 115
were given the task of building a Rube Goldberg machine using only the contents of
their backpacks. They first decided what the machine was going to do. Then they
filled out a form that showed the plan for the steps of the machine, with a minimum
of four steps. Then they built and tried out their machine. They could continually
adjust the machine and their plan to make sure the machine worked. At the end of the
period, each group showed their machine and described the adjustments they made
from their original plan to make the machine functional. This workshop focused on
motor rotation.
6. Use of flight simulators to develop motor skills and basic calculations: A science
teacher worked with groups of students using two flight simulators. She offered
minimal instructions, because she wanted them to experiment with the various
controls, which included foot controls, steering wheel, and steering column levers.
Each group followed a flight pattern for landing as they tried to successfully land the
airplane. Each student had a turn at the simulator. At the end of the workshop,
students described what did and didn’t work for them in successfully landing the
plane. This workshop focused on motor rotation and spatial visualization.
At the end of the day of workshops, the students were given a posttest of the spatial
awareness test; 57% were able to answer the questions correctly. In the course of one day, he
number of students who could correctly answer all motor rotation and spatial visualization
questions on the SRI went from 11% to 57%. Anecdotal accounts from the teachers revealed
that students got much better at the tasks as they moved through the day. Both the difference in
SRI scores and the anecdotal evidence indicate great growth in spatial awareness skills in a very
short period of time. Additionally, in the follow-up interviews all teachers mentioned wanting to
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 116
continue to develop these skills by incorporating other lessons into their curriculum. What began
as a daylong series of workshops blossomed into long-term plans to continue developing
students’ spatial awareness skills.
The Academy teachers, after receiving PD on spatial awareness as a prerequisite STEM
skill for girls, initiated lesson planning and implementation for a day of spatial awareness lessons
emphasizing mental rotation of objects and spatial visualization. Anecdotal evidence from
teachers, gathered through reflective interviews, show that all teachers perceived that the
students gained in skill throughout the four rotations, with each successive rotation better than
the last. Student pre- and posttest scores showed improved; of the 108 students who took the
SRI, only 12 students got all items correct on the pretest, but by the end of the day, 62 students
got all items correct. This testing was meant only as a benchmark of progress for teachers, who
could modify the curriculum if needed, but the dramatic change does seem to indicate growth in
student skills.
Research Questions
This study used a framework of gap analysis, which includes analysis of the knowledge,
skills, and motivation of members in an organization and the role of an organization in assisting
with the development of these skills to meet an organizational goal (Clark & Estes, 2008). Gap
analysis is solution oriented, as once the gaps are identified and analyzed, solutions and
strategies can be devised to narrow the gap to reach the performance goal (Clark & Estes, 2008).
In an educational setting, these solutions can provide meaningful changes to student success
(Rueda, 2011). In an educational setting, the Clark and Estes model can help increase
opportunities for students to learn and create a more motivating educational environment in
which teachers and administrators can collaborate to meet the needs of their students (Rueda,
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 117
2011). This analysis of the STEM gender achievement gap examined the knowledge, skill, and
motivation of the teachers in The Academy to develop and teach lessons in spatial awareness
skills; it also examined the organizational structures in place in The Academy that supported the
teachers’ knowledge and motivation to create an innovative curricular model with which to teach
the prerequisite spatial awareness skills to girls in The Academy. Each of the questions that
guided the study is examined in this section.
Degree of Incorporation Into School Curriculum
To what extent are the prerequisite spatial awareness skills incorporated into The
Academy curriculum and teaching practices?
Document analysis, observations, and interview showed that the science and math
teachers at The Academy incorporated the prerequisite spatial awareness skill into the curriculum
through hands-on activities involving manipulation of 2D and 3D objects. However, in the six
reflective interviews, math and science teachers reported that they would like to further develop
these lessons by planning additional lessons sequentially by grade level and department. One of
the math teachers suggested developing a tool to help teachers become more deliberate about
spatial awareness lessons by identifying where spatial awareness could be integrated into the
curriculum. English teachers expressed an interest in continuing to develop the spatial awareness
vocabulary; they were also interested in collaborating with math and science departments to
develop students’ observational and writing skills to support STEM skills around spatial
awareness, including scientific writing and other STEM writing skills.
Teachers Develop and Implement Spatial Awareness Curriculum
To what extent do the teachers in The Academy have the knowledge, skills, and
motivation to develop and implement the prerequisite spatial awareness curriculum?
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 118
Teachers at The Academy have the knowledge, skill, and motivation to develop the
spatial awareness lessons, as shown in observations of the original PD, the lesson plan design
session, the lesson plan implementation, and reflective interviews. They developed a sense of
urgency around teaching these lessons beginning with the original PD session, where teachers
wanted to plan the lessons immediately, organizing their lesson plan session for the following
week. All 12 teachers participated in the lessons, even though the teachers discovered early on
that the lessons would be taught on a day when six of the teachers would not be available.
During the lesson design session, teachers helped each other research and develop the plans.
English teachers were incorporated into these STEM-oriented lessons and were eager to
collaboratively develop the students’ spatial awareness vocabulary. Lesson implementation
observations showed compelling and highly interactive hands-on lessons designed around best
practices, including student inquiry and collaborative group learning. Reflective interviews
showed teachers’ excitement about the lessons, their honest critiques of what worked and didn’t
work, and a willingness to continue these lessons through inter-departmental and cross-
departmental planning.
Organizational Support
How are teachers’ knowledge and motivation to develop and implement the spatial
awareness lessons impacted by The Academy’s organizational culture?
Through document analysis, initial survey, and reflective interviews, teachers indicated
that they perceived a high level of support from The Academy’s organizational structures.
Although the principal was involved in the initial PD, the teachers were given complete freedom
in designing and implementing the lessons. The Academy’s principal and leadership team
provided time for lesson plan design, supplies and materials for the lessons, and the logistics for
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 119
the workshops. In reflections, teachers indicated that they needed more time to develop these
lessons at both the departmental and school level. Suggestions for these additional lessons
included developing common vocabulary for spatial awareness and for STEM communication
and developing a school-wide common rubric for scientific and technical writing.
Synthesis
The literature review of the gender achievement gap in STEM revealed that this disparity
was underpinned by a gender gap in spatial awareness, a prerequisite skill for STEM success.
According to the literature, spatial awareness is a skill that can be learned fairly rapidly through
concentrated lessons. This review of literature led the researcher to ask the following questions:
if teachers have the necessary knowledge, motivation, and organizational support, will they be
able to design lessons on spatial awareness? Will the girls benefit from those lessons? Will this
intervention further The Academy’s mission to provide girls a highly rigorous college
preparatory STEM-focused education?
Through qualitative methods including document analysis, survey, observations, and
reflective interviews, this dissertation has detailed a case study in which teachers in The
Academy were exposed to the necessity of developing spatial awareness in girls as a prerequisite
STEM skill. Recognizing this need propelled the teachers to use their knowledge and skills to
develop highly innovative, interactive, collaborative, hands-on spatial awareness lessons that
were delivered to girls through several workshops in one day. Through pre- and post testing of
students and through observation, the teachers noticed growth in the girls’ spatial awareness
skills over the course of the workshop day. The teachers were self-motivated to help students
develop these skills further through additional departmental and school-wide lesson planning.
The Academy leadership team provided the teachers with material and structural support and
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 120
with the freedom they needed to develop the plans without interference. This small case study
validated the literature’s indication that spatial awareness is a necessary skill for girls, that it can
be taught in a relatively short period of time, and that willing teachers who are given framing,
support, and time can develop effective lessons to teach this needed STEM skill.

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 121
CHAPTER FIVE
IMPLEMENTATION AND EVALUATION PLANS
This case study describes the development of innovative lesson plans to teach a vital
prerequisite STEM skill, spatial awareness, to female students within The Academy, a single-
gender public school within a large urban school district. The mission of The Academy, the site
where this study was performed, is to provide girls with a highly rigorous college preparatory
STEM-focused education in an all-girls environment fostering academic excellence, ethical
leadership, and intellectual curiosity. The literature review showed that spatial awareness, a
prerequisite STEM skill, is a key component for STEM course success for females, who are not
often exposed to spatial awareness skill development, and that the skill could be taught in a very
short period of time. Using a framework of Clark and Estes’ (2008) gap analysis as filtered
through an educational environment by Rueda (2011), the study examined the knowledge, skill,
and motivation of the teachers in The Academy to develop and implement lessons to teach
spatial awareness skills, and the organizational structures in place to support the teachers in
innovative curricular design. A teacher and administrator-practitioner frame allowed for
innovation and creativity on the part of the teachers in collaboratively developing the lesson
plans without restriction.
The assumed knowledge and motivational influences for the key stakeholder group
(teachers in The Academy) and the predicted organizational support for the curricular design
process were validated through qualitative methods, including an initial open-ended teacher
survey, document review of school plan and PD plan, observation of the PD session on spatial
awareness, observation of the lesson design sessions, observation of the lesson implementation in
the classroom, and final reflective interviews. The research contained multiple steps and
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 122
methodology to assist in developing a rich and descriptive case study of one practice within an
organization; triangulation of the findings and member checking were used to validate the data.
Based on the literature review and preliminary document analysis, the researcher
developed the initial assumed influences, which were validated and described in Chapter 4. This
chapter organizes its findings and recommendations by the teachers’ knowledge, the teachers’
motivation, and the impact of the school’s organizational structure.
The basis of the implementation and evaluation plan offered in this chapter is the New
World Kirkpatrick Model, based on the original Kirkpatrick Four Level Model of Evaluation
(Kirkpatrick & Kirkpatrick, 2016). The Kirkpatrick Model’s four levels of evaluation are
reaction, learning, behavior and implementation (Kirkpatrick & Kirkpatrick, 2016). The
Kirkpatrick Model was originally designed to evaluate training in business organizations;
because in educational institutions, training and staff development only have purpose if they
result in a positive outcome for student learning, Guskey (2000) added a fifth dimension to the
Kirkpatrick Model that includes teachers’ reaction, teachers’ learning, teachers’ use of new
knowledge and skills, school organization support, and the effect on student learning. This study
examines all five dimensions of Guskey’s (2000) revision of the Kirkpatrick Model, using Clark
and Estes’ (2008) focus on the knowledge, motivation, and organizational factors. This study
also included a feminist and practitioner research frame that focused the research on specific
actions that could result in gains for students. Several of the practices that were implemented
during the course of this innovation research were already in use in the school; some of the
knowledge, motivation, and organizational recommendations that emerged from the study simply
need adjustment or refinement.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 123
Recommendations for Practice to Address Knowledge,
Motivational, and Organizational Influences
Knowledge Recommendations
Based on the literature review, the assumed knowledge influences for this study included
the following: that teachers understand spatial awareness themselves; that teachers know both
that spatial awareness is a prerequisite skill for success for girls in STEM and that it is a
teachable skill; that teachers use CC and NGSS as a basis for instruction; and that teachers know
the elements of lesson design for hands-on, project-based curriculum and specifically for lessons
teaching spatial awareness skills. Table 6 summarizes the Summary of Knowledge
recommendations.
Declarative knowledge solutions, or description of needs or assets. Conceptual
knowledge is a way of categorizing or organizing knowledge (Anderson, Krathwohl & Bloom,
2001). Teachers need to be able to identify power standards in Common Core Math and Next
Generation Science Standards. One of the main tenets of the National Board for Professional
Teaching Standards (NBPTS) is that teachers must have a firm command of their subject area,
including factual information, as well as understanding the major themes and concepts of their
discipline (National Board, 1987). The recommendation is to use data based decision making to
assist teachers in their identification of power standards.
Data based decision making is based on the teachers identification of patterns of student
performance that unveil students' strengths and weaknesses relative to students' learning goals as
well as the selection and planning of instructional strategies and interventions to facilitate student
achievement of learning goals (van Geel, Visscher, & Teunis, 2017). In the case of science and
math teachers, teachers must be well versed in the Common Core Mathematics and Next
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 124
Generation Science Standards, which are the national standards for these subject areas (Common
Core, 2016). The teacher’s ability to translate mathematical and scientific curricular standards
into effective practice is of primary importance to student progress (Krajcik, McNeill, & Reiser,
2008; Spillane & Zeuli, 1999).
Table 6

Summary of Knowledge Influences and Recommendations

Assumed knowledge
influence
(D, P, or M)*
Cause, Need, or Asset
Validated
Yes, High
Probability,
or No
(V, HP, N)
Priority
Yes, No
(Y, N)
Principle and citation
Context-specific
recommendation
Teachers are able to
identify power
standards in the CC
Math and NGSS (D)
Y N Conceptual knowledge
is a way of categorizing
or organizing
knowledge (Anderson et
al., 2001)
Provide
information on
data-based
decision-making
to assist teacher
identification of
power standards
Teachers are familiar
with the concept of
spatial awareness and
the connection to the
STEM gender
achievement gap (D)
N Y Knowledge is often in
the form of new and
important concepts, vital
processes, and current
theories (Clark & Estes,
2008)
Provide
information on the
concept of spatial
awareness and the
connection to the
STEM gender
achievement gap.
Provide SRI as
basis to assess
teacher skills
Teachers are able to
apply principles of
hands-on, project-
based lesson planning
to the development of
spatial awareness
lessons (P)
Y Y Procedural knowledge is
the subject-specific
method of performing a
task, including criteria
for appropriate use of
the method (Anderson et
al., 2001).
The synthesis of content
knowledge and
Provide a job aid
that contains the
steps needed to
apply hands-on,
project-based
lessons plans to
spatial awareness
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 125
Assumed knowledge
influence
(D, P, or M)*
Cause, Need, or Asset
Validated
Yes, High
Probability,
or No
(V, HP, N)
Priority
Yes, No
(Y, N)
Principle and citation
Context-specific
recommendation
pedagogy forms a
second kind of
procedural knowledge,
that of content
pedagogy, or the
application of pedagogy
to the specific subject
field by the teacher
(Shulman, 1986)
Teachers are self-
reflective of their
teaching practice
during and after
teaching the spatial
awareness lessons
(M)
Y Y Metacognitive
knowledge is the
awareness of one’s own
cognition and cognitive
processes (Anderson et
al. 2001).
For teachers,
metacognition is a vital
skill, as it is related to
the transfer of
knowledge to the
student (Pintrich, 2002)
Provide journals
and writing
prompts for
teachers to
practice self-
reflection. Model
self-reflective
writing at PD
meetings
Teachers demonstrate
interest in their
subject matter and are
aware that their
modeling of engaged
practices increases
student engagement
(M)
Y Y Modeling to-be-learned
strategies or behaviors
improves self-efficacy,
learning, and
performance (Denler,
Wolters, & Benzon,
2014)
Provide PD for
teachers on
modeling practices
that target student
engagement
*D = declarative knowledge; P = procedural knowledge; M = metacognitive knowledge
Teachers must be familiar with the concept of spatial awareness and the connection to the
STEM gender achievement gap (D). Spatial awareness involves the ability to think and reason
through the transformation of mental pictures (Casey, Nuttall & Pezaris, 2011). The skill of
spatial awareness is one of the most important prerequisite skills to STEM course success
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 126
(Hegarty, 2014: Kersh et al., 2008, National Council, 2000). Tests of cognitive ability,
specifically mechanical reasoning, and spatial awareness show a difference between males and
females, with males consistently showing higher levels of spatial awareness than females (Voyer,
D., Voyer, S., & Bryden, 1995). Knowledge is often in the form of new and important concepts,
vital processes, and current theories (Clark & Estes, 2008). This suggests that teachers need to
be provided with information on the concept of spatial awareness and the connection to the
STEM ender achievement gap.
Results of studies on spatial awareness prompted the National Council of Teachers of
Mathematics in 2000 to add to the Table of Standards and Expectations for Kindergarten through
2
nd
grade an entire section on developing visualization, spatial reasoning and geometric modeling
(National Council of Teachers of Mathematics, 2000). If trained, teachers can incorporate the
teaching of visual-spatial awareness in math and science through age appropriate visual, active
learning, and computer graphics imaging activities (Mathewson, 1999). When teachers
consciously develop spatial ability in girls through mathematics, science, computer coding and
hands-on skills, the male advantage in spatial awareness can be neutralized (Mathewson, 1999).
Procedural knowledge solutions, or description of needs or assets. Procedural
knowledge is the subject-specific method of performing a task, and it includes knowledge about
the criteria for appropriate use of the method (Anderson et al., 2001). For teachers, the synthesis
of content knowledge and pedagogy forms a second kind of procedural knowledge—that of
content pedagogy, or the application of pedagogy to the specific subject field by the teacher
(Shulman, 1986). Math and science content pedagogy dictates that teachers should develop
project-based lesson plans for spatial awareness lessons. NGSS require that most lessons have
project-based elements (Next Generation Science Standards, 2016). Given this context, the
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 127
researcher recommends providing teachers at The Academy with a job aid (a written checklist)
containing the steps necessary to apply project-based lesson plans could help teachers effectively
develop these types of lesson plans.
Spatial awareness can be learned, often in a relatively short period of time (Feng et al.,
2007; Moè, 2016; Uttal, Meadow et al., 2013). Several studies demonstrate that spatial
awareness can be enhanced by allowing students to manipulate 3D physical objects, sketch 3D
objects, or manipulate 3D objects in space via a digital platform (Uttal, Miller & Newcombe,
2013; Sorby, 2009). Ideally, spatial awareness lessons progress from sketching and drawing 3D
objects to translating 3D objects into 2D descriptions or drawings (Sorby, 2009). The results of
this study thus indicate that providing teachers with job aids that offer specific examples of the
progression of skill development will be beneficial.
Metacognitive knowledge solutions, or description of needs or assets. Metacognitive
knowledge is the awareness of one’s own cognition and cognitive processes (Anderson et al.,
2001). Teachers use metacognition in their reflections on their teaching practices during and
after teaching the spatial awareness lessons (M). Teachers must be self-reflective, because
teachers’ attitude toward their subject matter is one of the most important factors in girls’
sustained interest in science and math (Heaverlo et al., 2013). And metacognition is a vital skill
for teachers, because it is related to the transfer of knowledge to the student (Pintrich, 2002).
Therefore, this study’s findings suggest that self-reflection should be encouraged for teachers,
both by providing journals and writing prompts for self-reflection and by modeling self-
reflective writing in PD meetings.
Reflection helps teachers to analyze and reform their teaching practices, and it is
therefore standard for teachers to reflect on their educational practice (Danielson, 2011;
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 128
Danielson & McGreal, 2000). In pedagogical reflection, the teacher reflects on educational
goals, theoretical assumptions, and the relationship of theory to teaching practice (Larrivee,
2008). One method for reflective practice is journal writing (Larrivee, 2000). This study’s
findings indicate that The Academy should provide journals and other tools of reflective practice
for teachers in order to support their own critical examination of the spatial awareness lessons.
It is also important that teachers demonstrate interest in their subject matter and are self-
aware that their modeling of engaged practices increases student engagement (M). Indeed,
classroom climate and teacher modeling are one important predictors for female students’
success in science and math classes (Beilock et al., 2010; Fouad et al., 2010). Modeling to-be-
learned strategies or behaviors improves students’ self-efficacy, learning, and performance
(Denler, Wolters, & Benzon, 2014). This study’s findings thus indicate that teachers should be
provided with PD activities that focus on the teacher modeling practices that target student
engagement.
These modeling practices are especially important for math and science teachers. In math
classes where teachers have high levels of content knowledge and demonstrate low levels of
math anxiety, female students have higher test scores (Beilock et.al., 2010). Similarly, female
students are more efficacious in math and science courses when provided with female teachers or
other female math and science role models (Burkam et.al., 1997). Heaverlo (2011) found that
three specific teacher behaviors were associated with improving success in science and math for
girls: willingness to provide encouragement, willingness to answer questions, and setting high
expectations for students. Thus, the findings of this study indicate that teachers should be
provided with PD on teacher modeling techniques specific to math and science education.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 129
Motivation Recommendations
Clark and Estes (2008) suggest that there are three indicators of motivation in task
performance: choice, persistence, and mental effort. Choice means going beyond intention to
actually begin the task; persistence means continuing to pursue a goal in the face of distractions;
and mental effort means seeking and applying new knowledge to solve a novel problem or
perform a new task.
The literature review identified three key motivational factors, goal orientation, interest,
and self-efficacy, as influencing The Academy teachers’ ability to perform the central tasks
examined: to recognize and evaluate student skills in spatial awareness, to creatively and
collaboratively develop spatial awareness lessons, and to implement the innovative lesson plans
in the classroom.
These motivational influencers were validated through observations of lesson design
sessions, observations of lesson implementation in the classroom, and reflective interviews after
the lesson implementation (see Table 7).
Table 7

Summary of Motivation Influences and Recommendations

Assumed
motivation
influence
Cause, Need, or
Asset
Validated
Yes, High
Probability,
No
(V, HP, N)
Priority
Yes, No
(Y, N)
Principle and citation
Context-specific
recommendation
Teachers
demonstrate interest
in teaching in their
curricular area
(Interest)
Y Y Activating and building
upon personal interest
can increase learning
and motivation (Schraw
& Lehman, 2009).
Provide
opportunities such
as leading PD, for
teachers to share
their interest in
their curricular
area.

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 130
Assumed
motivation
influence
Cause, Need, or
Asset
Validated
Yes, High
Probability,
No
(V, HP, N)
Priority
Yes, No
(Y, N)
Principle and citation
Context-specific
recommendation
Teachers act as
STEM role models
for their students
(Modeling)
Y Y Model values,
enthusiasm and interest
in the task (Eccles,
2006).
Female students are
more efficacious in math
and science courses
when provided with
female teachers or other
female math and science
role models (Burkam et
al., 1997).
Provide increased
opportunities for
teachers to model
learning, interest
and involvement in
their subject area.
Teachers actively
teach and display
growth mindset
techniques.(Self-
Efficacy)
Y Y Learning and motivation
are enhanced when
learners have positive
expectations for success
(Urdan & Pajares,
2006).
Teachers who actively
teach the concept of
growth mindset to
students and incorporate
growth mindset in their
teaching practice
increase student
achievement particularly
in math and science
(Blackwell et al., 2007;
Schmidt et al., 2015).
Provide
opportunities for
teachers to reflect
upon their teaching
of and personal
growth in growth
mindset teaching
practice with
targeted feedback
from model
teachers.

Interest. According to Schraw and Lehman (2009), activating and building upon
personal interest can increase learning and motivation. Because one of the key elements in high-
quality teaching is teacher enthusiasm (Bowen, 2016; Brophy & Good, 1986; Feldman, 2007),
teachers must demonstrate interest in teaching in their curricular area. Teacher interest can be
increased by teacher-led PD, which can have a large impact on both teachers’ effectiveness and
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 131
their continued interest in their subject matter (Borko, 2004; Wilson, 2013). Teacher interest in
their subject matter is crucial, because teacher attitude is the most important factor in girls’
sustained interest in science and math (Heaverlo et al., 2013). Positive teacher attitudes are
conveyed by willingness to provide encouragement, willingness to answer questions, and high
expectations (Heaverlo et al., 2013). Teachers can sustain or increase their own in interest in
their subject matter by working in groups to evaluate teaching practices in a supportive
atmosphere (Reiser et al., 2017). Teachers feel more efficacious in their teaching practice when
they develop their professional practice through collaboration and self-reflection (Turner,
Warzon, & Christensen, 2011). Therefore, this study’s findings indicate that The Academy
should provide opportunities for teachers to collaborate, to lead PD, and to self-reflect in order to
support teachers’ curricular interest in their subject matter.
Modeling enthusiasm. If teachers model enthusiasm, interest and values in a task,
student engagement increases (Eccles, 2006). This teacher modeling is particularly important for
females in STEM courses, as gender role identity may inhibit the development of cognitive
ability in highly gender-typed domains such as math and science (Nash, 1979; Sherman, 1967;
Signorella et al., 1989). One of the most important factors in STEM success for females is the
exposure to female faculty with high interest in and enthusiasm for STEM subjects (Beilock et
al., 2010; Li, 1999). As Burkam et al. (1997) have showed, female students are more efficacious
in math and science courses when provided with female teachers or other female math and
science role models. It is therefore important for teachers, particularly female STEM teachers, to
model for their students their enthusiasm for STEM subjects.
Teacher influence is extremely important in sustaining girls’ STEM interest. Heaverlo,
Cooper, and Lannan (2013) surveyed a sample of 591 middle and high school girls about their
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 132
experience in math and science courses. Of the five hypothesized predictors for sustained
interest in STEM (family STEM interest, extracurricular STEM activities, teacher interest in
STEM, race or ethnicity as a factor, and region of residence), only teacher influence was a
significant predictor for sustained interest in STEM courses. The study found that teachers who
communicate high expectations, make connections with real-life STEM activities, and discuss
career paths in STEM have greater impact on girls’ continued interest in STEM (Heaverlo et.al.,
2013). These findings imply that The Academy teachers should be provided with increased
opportunities to model learning, interest, and involvement in their subject area.
Self-efficacy and growth mindset. Urdan and Pajares (2006) found that learning and
motivation are enhanced when learners have positive expectations for success, and that belief in
one’s ability is correlated with positive outcomes. The concept of growth mindset builds on
belief’s relationship to ability; the foundation of growth mindset is that intellectual ability is not
fixed, but can be cultivated and developed through application and instruction, and that all
people can learn if given the support and materials needed for learning to occur (Dweck, 2006).
Recent studies show that teaching students about growth mindset can mitigate some of
the effects of the gender achievement gap in math and science (Dar-Nimrod & Heine, 2006;
Leslie et al., 2015; Schmidt et al., 2015); teachers who actively teach students about growth
mindset to students and incorporate growth mindset in their teaching practice increase student
achievement, particularly in math and science (Blackwell et al., 2007; Schmidt et al., 2015).
Techniques for using growth mindset in the classroom include praising for process and
portraying challenges and mistakes as highly valued in the educational process (Dweck, 2014).
These and other professional practices can be fostered by teacher peer observations that include
feedback about technical and classroom management skills and about professional growth and
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 133
change (Peel, 2005). This suggests that teachers at The Academy should be provided with
opportunities to receive targeted feedback from model teachers about how they teach and apply
growth mindset teaching practices.
Organizational Recommendations
According to Clark and Estes (2008), organization and stakeholder goals are often not
achieved due to a lack of resources (most often time and money) or because stakeholder goals
are not aligned with the organization’s mission and goals. The work of Gallimore and
Goldenberg (2001) sheds more light on how stakeholder goals come to diverge from
organizational goals. They separate cultural models, or the observable beliefs and values shared
by individuals in groups, from cultural settings, or the settings and activities in which
performance occurs (Gallimore & Goldenberg, 2001). These studies, taken together, indicate
that resources must align with processes and cultural models must align with cultural settings
throughout the organization’s structure for the mission and goals to be achieved.
In the case of education, there are several types of barriers to achieving organizational
goals. Oftentimes the material resources needed to achieve organizational goals are unavailable
or misused (Clark & Estes, 2008). And there is sometimes a lack of attention to the
organizations social and cultural context, which makes it difficult to effect change (Rueda,
2011). However, in any organization, change can occur when new social and cultural climates
are created and maintained (Schneider et al., 1996).
True advancement in education requires bold leadership, collaboration, and innovation.
At The Academy, where the mission is to provide girls with a highly rigorous college
preparatory STEM-focused education in an all-girls environment fostering academic excellence,
ethical leadership, and intellectual curiosity, the organizational structure must encourage a
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 134
culture of collaboration, innovation, and leadership. The organizational influences at The
Academy, reported in Table 8, have been validated through initial survey, observations of PD,
and observation of lesson planning sessions.
Table 8

Summary of Organizational Influences and Recommendations

Assumed
organizational
influence
Cause, Need, or
Asset
Validated
Yes, High
Probability,
No
(Y, HP, N)
Priority
Yes, No
(Y, N)
Principle and citation
Context-specific
recommendation
Teachers and
administrators
collaborate as a
team (CM)
Y Y Team leadership is an
organizational
structure in which
members share
common goals, are
interdependent, and
must work collectively
to achieve their goals
(Northouse, 2015).
Team leadership
results in greater
productivity, better
use of resources, better
decisions, problem-
solving, and greater
innovation
(Northouse, 2015)
Provide
opportunities for
teachers and
administrators to
make collaborative
decisions regarding
major processes and
policies, keeping the
collaborative model
in the forefront
Teachers and
administrators use
innovative practices
such as questioning
and using mistakes
as powerful
learning
opportunities (CM)
Y Y The mainstays of
disruptive innovation:
associating,
questioning,
observing,
networking, and
experimentation (Dyer
et al., 2013).
Fruitful innovation
requires a unique
capacity to capitalize
on fears and doubts
Provide
opportunities for
teachers to learn
disruptive
innovation
techniques and
observe innovative
administrators
modeling practices
such as questioning
and learning through
mistakes
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 135
Assumed
organizational
influence
Cause, Need, or
Asset
Validated
Yes, High
Probability,
No
(Y, HP, N)
Priority
Yes, No
(Y, N)
Principle and citation
Context-specific
recommendation
along the way,
changing the doubts to
new opportunities for
innovation (Belsky,
2016).
The organizational
structure provides
authentic leadership
opportunities for
teachers (CS)
Y Y Leadership for
innovation in an
organization is
dependent on instilling
a genuine desire in the
hearts and minds of
others to take
ownership in their
work and act together
motivated by a shared
purpose (Belsky,
2016).
Provide an emerging
leaders pipeline and
encourage
distributed
leadership
opportunities for
teachers throughout
the school.
Continually keep the
vision and mission
of the school (to
provide
opportunities for
girls in STEM) at
the forefront of all
decision-making

Collaboration
Collaborative leadership, often termed team leadership, is an organizational structure in
which members are interdependent, share common goals, and must work collectively to achieve
their goals (Northouse, 2015). Team leadership results in greater productivity, better use of
resources, better decisions, better problem-solving, and greater innovation (Northouse, 2015).
Team leadership, a relatively new concept for education, developed in the 1990’s from research
on effective schools and school leadership (Leithwood, Begley, & Bradley Cousins, 1990;
Leithwood & Montgomery, 1982). Team leadership in education includes distributing
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 136
leadership widely across multiple roles and multiple people in order to improve student
outcomes (Camburn, Rowan, & Taylor, 2003).
When teachers and administrators work as a team, student outcomes improve and school
improvement processes are more sustainable over time (Hallinger & Heck, 2011; Robinson,
Lloyd, & Rowe, 2008). Teachers report that participating in a collaborative culture increases job
satisfaction and commitment to the school (Dauksas & White, 2010). The building of
collaborative culture is important for teacher motivation and school-wide innovation, but is
equally important to student achievement (Ronfeldt et al., 2015). These findings indicate that it
is important for the teachers and administrators at The Academy to establish team leadership and
to make collaborative decisions about major processes and policies, always keeping the
collaborative model in the forefront.
Innovation
In any organization, innovation and creativity are vital to successful performance
(Anderson, Potočnik, & Zhou, 2014). Disruptive innovation commences with questioning the
basic tenets of a company, using the innovation techniques of associating, questioning,
observing, networking, and experimentation (Dyer et al., 2013). Innovation skills are not inborn;
two thirds of innovation techniques can be learned by practicing and honing innovation skills
(Dyer et al., 2013). Fruitful innovation requires a unique capacity to capitalize on fears and
doubts by reframing the doubts as new opportunities for innovation (Belsky, 2016).
Educational organizations seeking innovation and change should be grounded in a
philosophy of growth mindset. A growth mindset is one that is not fixed or predetermined, but
that allows for the capacity to grow through hard work and resiliency (Dweck, 2006). With
growth mindset, experimentation, mistakes, and evaluation are seen as integral parts of the
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 137
learning process (Dweck, 2006). Innovation involves a continuous cycle of design: innovating,
prototyping the innovation, seeing the innovation in practice, then reassessing and refining the
innovation (Dyer et al., 2013). The cycle of design can be seen as an application of growth
mindset, helping teachers to develop as innovators by learning and practicing the skills of
disruptive innovation. In order to develop a school culture of innovation, teachers must be
encouraged to develop innovative practices such as questioning and using mistakes as powerful
opportunities to learn. These findings indicate that to develop a culture of innovation at The
Academy, administrators must provide opportunities for teachers to learn disruptive innovation
techniques and must themselves model disruptive innovative practices for teachers; they must
also ensure that growth mindset is part of the school’s culture of innovation in order to encourage
teachers to experiment and innovate.
Teacher Leadership
Curriculum planning was once thought to be a task only for the experts, but teachers are
now seen as professional educators with distinct knowledge bases and professional expertise.
This attitude was codified in two reports on teaching in 1986, the Holmes report and the
Carnegie report (Carnegie Forum, 1986: Holmes Group, 1986), and today, the teacher is
positioned as a curriculum developer and a refiner of practice in both national and state standards
for the teaching profession (National Board, 2016). Teacher leadership is no longer just a
function of positions held outside the classroom, but is deeply embedded in the practice of
teaching (Ash & Persall, 2000). In their role as teacher–leaders, teachers work collaboratively to
improve teaching and learning; design learning; and engage in school-related research and
review of best practices (Ash & Persall, 2000).
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 138
Crucially, administrators provide the context and conditions for innovation for these
teacher–leaders (Ash & Persall, 2000). Leadership for innovation in organizations depends on
instilling a genuine desire in the hearts and minds of others to take ownership in their work and
act together, motivated by a shared purpose (Belsky, 2016). The principal must be able to
inspire a shared vision, enable teachers as leaders, model the way, and lead from the heart (Israel
& Fine, 2012). These findings indicate that at The Academy, the principal must continually keep
the vision and mission of the school (to provide opportunities for girls in STEM) at the forefront
of all decision-making; encourage distributed leadership opportunities; and provide an emerging
leaders pipeline to develop teacher leadership.
Integrated Implementation and Evaluation Plan
Implementation and Evaluation Framework
This implementation and evaluation plan was grounded in the New World Kirkpatrick
Model which is based on the original Kirkpatrick Four Level Model of Evaluation (Kirkpatrick
& Kirkpatrick, 2016). This model suggests that evaluation plans should start with the goals of
the organization and work backward; by doing so, the “leading indicators” that bridge
recommended the organization’s goals with recommended solutions are both easier to identify
and more closely aligned with organizational goals. The “reverse order” of the New World
Kirkpatrick Model allows for a sequence of three other actions: (a) first, developing solution
outcomes that focus on assessing work behaviors; (b) next, identify the indicators that will show
that learning occurred during implementation; and (c) finally, identify indicators for
organizational members’ satisfaction with implementation strategies. Designing the
implementation and evaluation plan in this manner forces connections between the immediate
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 139
solutions and the larger goal and solicits proximal “buy in” to ensure success (Kirkpatrick &
Kirkpatrick, 2016).
Organizational Purpose, Need, and Expectations
The mission of The Academy is to provide girls with a highly rigorous college
preparatory STEM-focused education in an all-girls environment. The organizational
performance goal is to have 100% of the girls enrolled in The Academy on target by 2018 to
graduate with the STEM skills necessary for A–G eligibility. To reach that goal, the students’
performance in CC Mathematics and NGSS standards must improve. Mathematics and science
teachers view spatial awareness as a prerequisite skill for mathematical reasoning, geometric
understanding, measurement, and graphing (Hegarty, 2014; Kersh et al., 2008; National Council,
2000). There is a noted difference between men and women in the skill of spatial awareness as
measured by the Vandenberg and Kuse measurement (Geiser et al., 2008; Maccoby & Jacklin,
1974; Voyer et al., 1995). However, spatial awareness can be learned, often in a relatively short
period of time (Feng et al., 2007; Moè, 2016; Uttal, Meadow et al., 2013). Therefore, this study
had three goals: to develop the innovative practice of deliberately teaching spatial awareness to
girls; to explore the knowledge and motivation of the key stakeholder group, the teachers, to
collaboratively plan and deliver the spatial awareness skills curriculum; and to examine the
impact of The Academy’s organization in supporting the development of the lessons.
Kirkpatrick level 4: Results and leading indicators. Table 9 shows the Kirkpatrick
Model Level 4 Results and Leading Indicators for the organizational goal. It gives outcomes
(both internal and external), metrics, and methods used to decrease the STEM gender
achievement gap (the key stakeholders, the teachers, developed lessons and taught the skill of
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 140
spatial awareness to female students in a single-gender school, with support from school
administration).
Table 9

Outcomes, Metrics, and Methods for External and Internal Outcomes

Outcome Metric(s) Method(s)
External Outcomes
District awareness of spatial
awareness lessons as a best
practice.
Increase in spatial awareness
lessons over time
District level PD on best
practices in spatial awareness
lessons
Parent awareness of spatial
awareness as a prerequisite
skill for STEM success
Pre- and post-intervention
survey at parent PD session
Parent PD on spatial
awareness
Increase in math and science
scores on SBAC tests
Data from interim and final
SBAC assessments
Prepare for testing and teach
to standards
Internal Outcomes
Teacher awareness of the
importance of developing
spatial awareness skills in
female students
Agenda items on PD and
departmental agendas on
teaching spatial awareness
Teacher reflection and
evaluation of PD on the
gender spatial awareness gap
Teacher collaboration on
lesson plans by department
and grade level
Departmental and grade-level
meeting agendas and rubric of
observation of collaboration
techniques
Develop rubric of observation
for collaboration. Use rubric
to measure collaborative
techniques in departmental
and grade-level meetings
Increase in number of
lessons on spatial awareness
delivered
Increase in written lesson plans
and observable lessons on the
topic of spatial awareness
Classroom observations
Support for the development
of collaboratively designed
lessons by the
administration of the school
Paid PD sessions focused on
the collaborative development
of lesson plans
Schedule times and payment
for teachers to collaborate
Increase in grades in math,
science, and computer
science
Data from 5,10,15, and 20-
week grades
Use standards-based grading
to reflect standards growth
over semester

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 141
Kirkpatrick Level 3: Behavior
The stakeholders of focus were the teachers in The Academy. The first critical behavior
was that teachers needed to understand the urgency of teaching spatial awareness as a
prerequisite STEM skill for girls. The second critical behavior was that teachers needed to
collaborate to develop lesson plans for spatial awareness. The third critical behavior was that
teachers needed to deliver the lesson plans during classroom instruction. The fourth critical
behavior was that teachers needed to evaluate the effectiveness of the collaboratively developed
lesson plans in teaching the spatial awareness skills to students. Specific metrics, methods, and
timing for each of these outcome behaviors appear in Table 10.
Table 10

Critical Behaviors, Metrics, Methods, and Timing for Teachers

Critical behavior Metric(s) Method(s) Timing
1. Teachers must
understand the urgency of
teaching spatial awareness
as a prerequisite STEM
skill for girls
Teacher discussion
during and evaluation
of PD on spatial
awareness and girls
STEM success
PD
Professional
discussion
Early in the
school year
(August /
September)
2. Teachers must
collaboratively develop
lesson plans for spatial
awareness
Written lesson plans
Collaboration rubric
Collaboration
during scheduled
and non-scheduled
PD time
Prior to teaching
spatial awareness
lessons
3. Teachers must deliver
the collaboratively
designed lesson plans
during classroom
instruction
Observation rubric Peer observation During lessons
4. Teachers must evaluate
the effectiveness of the
collaboratively developed
lesson plans in teaching the
spatial awareness skills to
students.
Self-reflection
Results of student
performance on SRI
pre- and post-lessons
Written journals
Results on pre- and
posttests
Prior to and after
delivering
lessons
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 142

Required drivers. Teachers needed the support of The Academy administration in the
form of time and support for developing and delivering the spatial awareness lessons. Table 11
shows the recommended drivers for administrations’ support of critical behaviors.
Table 11

Required Drivers to Support Teachers’ Critical Behaviors

Method(s) Timing
Critical behaviors
supported (1, 2, 3,4)
Reinforcing
Provide information on the concept of spatial
awareness and the connection to the STEM
gender achievement gap
Prior to developing
spatial awareness
lessons
1, 2, 3, 4
Provide information on data-based decision-
making to support teacher identification of
power standards
Annually 1
Provide a job aid that contains the steps needed
to apply project-based lesson plans to teach
spatial awareness
Prior to developing
spatial awareness
lessons
2
Develop collaborative lesson plan rubric Prior to teaching
spatial awareness
lessons
2
Provide time for collaborative lesson planning Ongoing 2
Provide journals and writing prompts for
teachers to practice self-reflection. Model self-
reflective writing at PD meetings
After spatial
awareness lesson
delivery
4
Provide PD for teachers on modeling practices
that target student engagement
Monthly 1, 2, 3, 4
Encouraging
Provide increased opportunities for teachers to
model learning, interest, and involvement in
their subject area
Monthly 2, 3, 4
Collaboration and peer modeling during
faculty meetings
Weekly 2, 3, 4
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 143
Method(s) Timing
Critical behaviors
supported (1, 2, 3,4)
Provide opportunities for teachers to reflect
upon their teaching of and personal growth in
growth mindset teaching practices, with
targeted feedback from model teachers
Monthly 1, 2, 3, 4
Peer-to-peer observation Weekly 2, 3, 4
Rewarding
Administrator praise, in meetings and written
notes to teachers
Every two weeks 1, 2, 3, 4
Financial compensation for PD sessions after
regular hours
Twice annually 1, 2, 3, 4
Provide an emerging leaders pipeline and
encourage distributed leadership opportunities
for teachers throughout the school
Ongoing 1, 2, 3, 4
Monitoring
Teachers use department- and grade-level
meetings to review progress in testing
indicators, such as spatial awareness tests and
SBAC scores
Yearly 1, 2, 3, 4
Teachers and administrators review progress in
grades in STEM courses
Every 10 weeks 2, 3, 4
Teachers monitor through peer-to-peer
observations
3–4 times a year 1, 2, 3, 4

Organizational support. There are three necessary components for innovation in an
organization: the people, the processes, and the philosophy of innovation (Dyer et al., 2013). For
innovation to thrive, the people on the team must have a balance of discovery- and delivery-
driven skills (Dyer et al., 2013). Discovery-driven skills are those that innovate by questioning
current practices, observing and networking innovative designs, and producing an experimental
design that is then prototyped (Dyer et al., 2013). Delivery-driven skills are the planning and
implementing skills that realize the prototype and analyze it (Dyer et al., 2013). Both of these
skills must exist in a company for it to have a culture of innovation (Dyer et al., 2013). At The
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 144
Academy, a culture of innovation was signaled by the organization’ support of the teachers’
internal process of discovery, use of design, prototyping, and refining of design. The Academy
needed to provide the material needed for the design process (Dyer et al., 2013). Innovative
design requires leaders who are not only supportive but have a deep personal interest in the
innovation, so The Academy leadership needed to be invested in the teachers’ development of
the spatial awareness lessons (Dyer et al., 2013).
In order for teachers to develop the spatial awareness lessons, they first needed to be
trained on spatial awareness and its importance to female students’ success in STEM courses.
The Academy administration supported this learning by developing a PD session that taught the
skills and developed the teachers’ sense of urgency about teaching the spatial awareness skills to
their students. The Academy supported the teachers’ development of the spatial awareness
lessons by providing them with the time to develop the lessons and by providing extra pay for
after school or Saturday planning time. Additionally, to support the development of a culture of
innovation at The Academy, the administration needed to be part of the collaboratively
developed lessons, because cultures of innovation require that all organization members
participate in the innovative processes (Dyer et al., 2013).
As the teachers moved forward to deliver the lessons, the administration provided
additional support in the form of materials necessary for the lessons and release time for
teachers’ participation in peer review. The administration further supported the teachers by
providing time for reflection and discussion of best practices during follow-up PD sessions.
Finally, it will be important to the evaluation process for administration and teachers to monitor
the students’ grades and SBAC scores to assess whether the spatial awareness lessons are having
the desired effect of raising the scores.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 145
Kirkpatrick Level 2: Learning
Learning goals. After completing the training and collaborative development of lesson
plans, The Academy teachers were able to do the following:
1. Explain the elements of spatial awareness skills (D)
2. Collaboratively develop spatial awareness lessons (M)
3. Evaluate their own and other teachers’ spatial awareness lessons (M)
4. Indicate confidence that they could teach spatial awareness lessons (Confidence)
5. Value collaborative planning of the lessons (Value)
6. Recognize the importance of the spatial awareness lessons to female STEM student
success (Commitment)
Program. The learning goals listed in the previous section were achieved through PD,
several collaborative lesson planning sessions, peer-to-peer observation, and a final evaluation
session. Teachers participated in PD on spatial awareness, where they took the SRI assessing
their own skill in spatial awareness and the principal led discussion on the results of the SRI.
Then the principal and science department chair presented research on the gender STEM
achievement gap and its connection to the prerequisite skill of spatial awareness. This
presentation built urgency for The Academy, an all-girls STEM school, to address spatial
awareness and laid out the role of the teachers in building the skill across the curriculum.
Teachers were asked to develop their own lessons to teach spatial awareness to students using
the school’s existing collaborative design model. Teachers observed the spatial awareness
sessions and practiced peer-to-peer evaluation of these lessons through a process already in place
at the school. After peer review was complete, teachers participated in an evaluation session to
determine the best practices to use as a school. Ongoing evaluation will occur as teachers and
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 146
administrators look at SBAC and grade reporting data to evaluate the success of the lessons, and
teachers and administrators will continue to refine and evaluate the lessons in light of this data.
The cycle of ongoing evaluation and refinement of lesson plans is shown in Figure 9.

Figure 9. Cycle of evaluation.
Components of learning. It is often necessary to demonstrate declarative knowledge
before applying the knowledge to solve problems; learning should be evaluated for both the
declarative and the procedural knowledge being taught. Learners should also value their training
as a prerequisite to using their newly learned knowledge (attitude); they must be confident that
they can succeed in applying their knowledge and skills (confidence) and committed to using
them on the job (commitment). Table 12 lists the evaluation methods and timing for these
components of learning.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 147
Table 12

Components of Learning for the Program

Method(s) or Activity(ies) Timing
Declarative Knowledge: “I know it.”
Knowledge checks during initial PD. Use of spatial
awareness indicator to illustrate skill
During PD
Knowledge checks through discussions, “pair,
think, share,” and other individual/group activities
Periodically during PD and
documented via observation notes
Procedural Skills: “I can do it right now.”
Application of spatial awareness skills to lesson
planning
During collaborative lesson planning
session
Quality of the feedback from peers during group
sharing
During collaborative lesson planning
sessions
Evaluation of lessons During peer-to-peer observation
Attitude: “I believe this is worthwhile.”
Instructor’s observation of participants’ statements
and actions demonstrating that they see the benefit
of what they are being asked to do
During the PD lesson and
collaborative planning session
Discussions of the value of collaboratively designed
lessons
During collaborative planning
sessions and peer-to-peer observations
Confidence: “I think I can do it on the job.”
Peer-to-peer observation Following collaborative lesson plans
Discussions following peer-to-peer observation During follow-up evaluation session
Commitment: “I will do it on the job.”
Discussions following peer-to-peer observations During follow-up evaluation session
Reflection on lesson plans After lesson plan delivery

Kirkpatrick Level 1: Reaction
Reaction is the degree to which participants find the training favorable, engaging and
relevant to their jobs (Kirkpatrick and Kirkpatrick, 2016). For this multi-tiered training, there
were two main points where reaction by teachers could be ascertained: first, during the initial PD
session, and second, during evaluation of the lesson plans during the evaluation session. Table
13 shows the components measured to ascertain the teachers’ reactions to the program.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 148
Table 13

Components to Measure Reactions to the Program

Method(s) or Tool(s) Timing
Engagement
Observations of participation during initial PD During initial PD
Observation of participation during collaborative
design sessions
During collaborative design
session
Observation of trainee engagement of teacher during
delivery of lessons
During lesson delivery
Observation of participation during evaluation session During evaluation session
Relevance
Observations of engagement during collaborative
design sessions
During collaborative design
sessions
Observation of discussion during evaluation session During evaluation session
Continual delivery of spatial awareness lessons After evaluation session
Customer Satisfaction
Brief pulse-check with teachers during discussion
(ongoing)
At end of initial PD, collaborative
session and evaluation session
Notes from evaluation session During evaluation session
Teacher sharing of reflective journal entries During evaluation sessions

Evaluation tools.
Immediately following the program implementation. After the initial PD session on
spatial awareness connecting the skill to the STEM gender achievement gap, teachers were
surveyed to ascertain their Level 1 engagement, the relevance of the PD, and their customer
satisfaction with the PD.
Teachers’ Level 2 knowledge, skills, attitude, confidence, and commitment were
ascertained by an open-ended survey after the collaborative lesson plan session. (See Appendix
A for surveys 1 and 2).
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 149
After program implementation. Approximately one month after the spatial awareness
lessons were implemented, a blended open-ended survey was conducted to ascertain teachers’
level of commitment to continuing to develop the spatial awareness lessons (Level 1), and their
confidence in and value of continued implementation of the lessons (Level 2; see Appendix B for
open-ended survey).
Data Analysis and Reporting
According to Kirkpatrick & Kirkpatrick (2016), data analysis must be based on three
questions: (a) Does . . . meet expectations? (b) If not, why not? (c) If so, why? For this research
study, it is important to assess whether the spatial awareness training and collaborative lesson
planning led to effective lessons in spatial awareness for the students. Did the initial training
develop the teachers’ sense of urgency to develop the lesson plans? Were the lesson plans
developed in a collaborative, efficient manner? Were the applied lesson plans effective in
teaching spatial awareness skills? If the answer to these questions is yes, how can this case
study’s findings be translated for use in other schools? If there were problems with any aspect of
the training, lesson plans or delivery of lesson plans, which of these might be altered to be more
effective?
The ultimate goal of the training was to meet the organizational stakeholder goal: to
enable Academy teachers to deliberately teach the prerequisite STEM skill of spatial awareness
to female students. The steps to meeting that goal were, first, the initial PD training on spatial
awareness, and second, the building of teachers’ sense of urgency to transfer their learning to the
classroom by collaboratively developing and delivering lessons on the subject to their students.
Initial interview and survey data reveal that teachers were unaware that spatial awareness was a
prerequisite skill for STEM success, and they did now know that it is a skill that can be taught in
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 150
a relatively short period of time. The teachers had already demonstrated success in collaborative
lesson planning, which is an integral part of the school cycle of improvement.
To deliver the results after administering the immediate and delayed instruments, a chart
will be developed showing teachers the impact of their development and delivery of spatial
awareness lessons. This chart will include three learner outcomes after the delivery of the
lessons: the percentage improvement of the number of students who successfully passed the SRI
spatial awareness indicator; the percentage increase in students with passing math grades (A–C)
and the percentage of increase in students with passing science grades (A–C); and the percentage
of students meeting or exceeding standards on the SBAC mathematics tests. The sample data
chart is shown in Figure 10.

Figure 10. Sample data chart.
Summary
The New World Kirkpatrick Model (2016) is comparable to the classic education
planning method of backward planning. The Kirkpatrick Model begins planning for training
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 151
with the end product in mind, and Level 4 Results are measured by examining the degree to
which the targeted outcomes resulted from the training in Levels 1, 2, and 3. Backward planning
begins with a learning outcome, often one tied to a state standard of what a student should know
or be able to do (Wiggins & McTighe, 2005), and teachers plan lessons and strategies that will
lead to that desired end result. The New World Kirkpatrick Model asks the trainer to examine
whether the training met expectations and why it did or did not; teachers who use the backward
lesson plan model continually review the learning targets and adjust lessons along the way based
on the data to make sure that all learning targets are being met. But the Kirkpatrick Model and
the backward planning model are different in one significant way. Unlike training in business,
where the training sessions tend to be brief and short lived, teachers’ training is continuous, as it
is the main focus of the work. The Kirkpatrick Model’s training questions can help educators to
become more focused, and it would therefore be a good model to introduce in teacher PD
sessions.
Strengths and Weaknesses of the Approach
The Clark and Estes (2008) gap analysis model was originally developed for business as
a way to assess the gap between an organization’s goal and its performance. Gap analysis
examines the three processes critical to achieving the business goal: people’s knowledge,
motivation, and the organizational barriers to achieving the goal (Clark & Estes, 2008). The
approach, as applied by Rueda (2011) to education, allows schools to analyze performance gaps
with a focus on increasing student performance. Gap analysis was useful in initially designing
this study; the gap in student skills and the intentional teaching of spatial awareness to students
were identified using gap analysis. However, the method fell short in analyzing the solution to
the problem, which was an innovative practice. Gap analysis seeks to “remedy the human causes
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 152
behind performance gaps” in organizations (Clark & Estes, 2008); it is not designed to assess
innovations.
The study’s conceptual frame was feminist research, which comes out of a rich tradition
of research for social change; it seeks to examine and address inequity, paying special attention
to women’s lives and the differences in women’s experience based on race, economic position,
and global context (Hesse-Biber, 2013). Feminist research is oriented toward equity and action,
and the other study frameworks, administrator-practitioner research and teacher-practitioner
research, are firmly rooted in the feminist social action tradition (Anderson & Jones, 2000). This
study, which was steeped in the feminist research tradition, was designed around practitioner
action research. This framework allowed the teachers to take the primary role in the researching
spatial awareness lessons and ensured that they had the freedom to design the lessons. This also
allowed the researcher, who is also the principal of the school, to participate through
administrator action research, which allowed for support of both the teachers’ organic and
collaborative lesson design and the teaching of the lessons. In this case study of a small unique
organization, the practitioner research framework enabled the teachers to become invested in the
study and the outcomes for students, and their involvement in designing the lessons enabled
innovation. The process of lesson design and the lessons themselves can be duplicated in other
settings, but it is the teachers’ innovation that is important to the study.
Limitations and Delimitations
This research was conducted in a very small, unique environment. The Academy is the
first public single-gender school in OCSD. It has only been in existence for two years.
Although the school is one of the most geographically, racially, and economically diverse
schools in the OCSD, the families chose the school because their daughters were interested in
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 153
STEM. Additionally, the teachers were recruited for the school based on their willingness to
participate in building the school and doing additional work, including developing innovative
lessons. The school is grounded in a philosophical framework of mastery learning, growth
mindset, and standards-based grading. All of these factors might have skewed the data collected.
However, this study was not designed for replication; it was designed to provide a rich
description of one innovative practice within a particular environment—a practice that yielded
positive results. The teachers’ sense of urgency and collective involvement in designing the
lesson plans and the positive outcome for teacher collective self-efficacy and student
performance are unique to this particular study within this particular environment.
The size of the study is also a factor. The initial teacher population for the study was 14,
narrowed by two medical leaves to 12 teachers. Only 9 teachers participated in the initial survey,
which is not a representative sampling. Additionally, because of the teacher–practitioners’
design of the lesson delivery, only six teachers participated in lesson delivery and the follow-up
reflective interview.
Finally, the purpose of the study was to teach spatial awareness to girls in order to build
the prerequisite skill for STEM success. The teachers indicated in the reflective interviews that,
to effectively continue to build these skills, they would need more time and collaboration
between departments. Although the model of lesson delivery designed by the teachers—
workshops throughout the day—was very effective, the teachers were concerned about retention
and deepening of the skill. They felt that additional lessons would need to be developed to
continue the work started in the one-day workshop. To fully understand the impact of the spatial
awareness lessons on student achievement in STEM courses, the students would need to be
followed through their course selection and STEM achievement through a longitudinal study.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 154
Future Research
This research, which examined the innovative practice of designing and implementing
lessons on the prerequisite STEM skill of spatial awareness within a particular organization over
a short time frame, provides a rich description of one example of teachers displaying self- and
collective efficacy in building an innovative curriculum. The research also describes the
importance of teaching the prerequisite skill of spatial awareness to girls, and it shows one model
of successful instruction in the skill. The lesson design model and the lessons themselves could
be duplicated in other schools interested in providing workshops on spatial awareness for their
students.
Because of the practitioner action research frame used, teachers intend to continue to
develop these lessons through interdepartmental collaboration. This research within this
organization can be deepened by following the continued development of the lessons, the lesson
implementation, and the effect on the student population. This would also require a longitudinal
study of the students involved as they take higher level STEM courses, which would need to take
into account the many variables affecting success in those courses.
This study is not intended to be duplicated, but research into teaching the prerequisite
STEM skill of spatial awareness, particularly to female students, needs to be continued. As the
literature review made clear, many studies have articulated the need for this skill and the absence
of opportunities for female students to practice the skill in traditional public schools, but very
few studies have examined the process of actually teaching the skill. This would be an important
area of further research.
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 155
Conclusion
In the United States today, there is a wealth of jobs in STEM fields that cannot currently
be filled by qualified STEM college graduates. Women, and particularly women of color, are a
huge untapped resource for these jobs. But somewhere along the STEM educational pipeline,
girls, particularly girls of color, fall out. There are many reasons for this situation: teacher and
parent bias, lack of encouragement to take honors and AP courses, stereotype threat, and lack of
preparation for STEM courses. A key component of STEM course success is spatial awareness,
or the ability to mentally rotate objects in space. This skill is developed by preschool play with
construction toys, Lego, and building blocks. Girls are less likely to play with these toys, and
they therefore arrive in elementary school lacking a prerequisite skill for math and science course
success. Although teachers of mathematics and science recognize that this is an important skill
to teach, very few schools deliberately teach this skill. This research has examined what happens
when teachers collaboratively develop lesson plans to deliberately teach girls the prerequisite
STEM skill of spatial awareness.
This study, which was conducted in a small single-gender public school with a diverse
population, aimed to reduce the gendered educational gap in the teaching of the prerequisite
STEM skill of spatial awareness by deliberately teaching the skill to girls. Based on the findings
from the gap analysis conducted (Clark & Estes, 2008) and on principles of action research, the
researcher educated teachers about the existence of the skill gap and gave them free rein to
develop lesson plans to address the gap. The teachers chose to collaboratively develop
innovative hands-on lessons to be delivered in a one-day workshop. Teachers were invested in
and enjoyed the workshops, and pre- and post-intervention testing of students showed an
increase in skills. However, teachers felt that this was just a start; they wanted to continue to
SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 156
collaborate across and within departments to develop further lessons that would reinforce these
skills throughout middle school, with the aim of preparing the girls to take higher level STEM
classes in high school. The teachers’ self- and collective efficacy in working to provide a clear
pathway to STEM success mirrors the vision of the school, and it validates the study’s purpose:
to provide instruction in the prerequisite STEM skill of spatial awareness to girls, particularly
girls of color. If other schools encourage their teachers to collectively develop lessons to address
this prerequisite skill, we might eventually diminish the spatial awareness gender gap. And if
this and other schools address the other barriers to STEM success for girls (teacher bias, parent
bias, student bias, lack of access to AP classes), fewer girls will fall out of the STEM
educational-and-career pipeline, and more girls will be able to take advantage of the open market
in highly creative and lucrative STEM jobs. Addressing the prerequisite STEM spatial
awareness gap is only the beginning.

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 157
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APPENDIX A
SPATIAL REASONING INSTRUMENT
1. Spatial Visualization (answer = C)

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 187
2. Mental Rotation (Answer = C)

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 188
3. Spatial Visualization Answer = C

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4. Mental Rotation (answer = B)

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 190
APPENDIX B
SURVEY INSTRUMENT
Email Invitation:
Dear Academy Teacher
My name is Liz Hicks and I am a graduate student in the Rossier School of Education at the
University of Southern California. I am conducting research on the STEM gender achievement
gap. I am inviting you to participate in this research study by completing this survey. The
survey will take approximately 10 minutes to complete. There is no compensation for
responding nor is there any known risk. The information you share will be kept confidential and
will only be used as an aggregate. Participation is voluntary and you may decide not to complete
the survey at any time, or choose to skip any question you don’t feel comfortable answering. I
appreciate your time and willingness to help in this research on the STEM gender achievement
gap.
Questions:
1. How do you feel about teaching in an all-girls school? (RQ3)
2. Is it different from teaching in a co-ed school? Can you explain the difference? (RQ3)
3. As a teacher, do you feel that you are a role model for STEM? Explain.(RQ 2)
4. Do teachers participate in professional development delivery ?(RQ2&3)
5. What do you know about spatial awareness? (RQ 1&2)
6. Please write what you like best about your school. (RQ 3)
7. Please write what you like least about your school. (RQ 3)
8. How do you feel about growth mindset as a frame for your school? (RQ 2&3)
9. What is one thing you would do to improve your school (RQ 2&3)
10. Do you believe spatial awareness is an important skill to teach girls interested in STEM?
(RQ1 &2)

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 191
APPENDIX C
OBSERVATION PROTOCOL

Teacher__________________________________ Room _________
Date________ Amount of students _____ Time started _____
1. Describe the classroom environment (seating configuration, technology available,
bulletin board and other displays, student work with rubrics) (RQ1&2)
2. Describe the lesson design: (RQ 1&2)
a. Start- does the teacher explain about spatial awareness anytime during the lesson?
Is the pretest given (first section only)?
b. What is the main activity? Describe.
c. lecture? small group? pair share? technology used?
d. Exit ticket or activity? Is the post test given (last section only)?
3. Describe the teacher actions: (RQ1&2)
explanations? check ins? circulation?
4. Describe the student activity: (RQ 1&2)
peer to peer? teacher to student?
5. Verbatim—record verbatim for teacher questioning, student teacher interaction, student-
to-student interaction, and small group discussion where possible.

Observation by _______________________________ Time ended _____

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 192
APPENDIX D
INTERVIEW PROTOCOL

Hello. My name is Liz Hicks and I am a graduate student in the Rossier School of
Education at the University of Southern California. I am conducting research on the
STEM gender achievement gap, and the effect of teachers on the gap. Because you are a
teacher of STEM courses in an all-girls school, and are part of the collaborative teacher
team that developed and delivered the lesson plans to teach spatial awareness to the sixth-
grade students at your school, I am inviting you to further participate in the research by
participating in this post lesson plan delivery interview. This interview will take
approximately 20 minutes to complete and we can meet at a time and place that is
convenient for you. You will be given an Amazon gift card for your participation in the
research study. It is hoped that by reflecting on your teaching practice before and after
your innovative lesson design you might assist other teachers with innovative design.
The information you share will be kept confidential. Participation is voluntary and you
may refuse to participate at any time. I appreciate your time and willingness to help in
this research on the STEM gender achievement gap. This research can help girls to
become more successful in STEM, and I know you are passionate about making things
better for girls in our society. Thank you in advance for your participation in the
interviews.

SPATIAL AWARENESS AND THE STEM GENDER ACHIEVEMENT GAP 193

Interview Questions:
1. Please describe for me the lesson you taught on spatial awareness. (RQ 2)
2. Do you feel that you had the necessary support, time, supplies and information
from the school to plan the spatial awareness lessons? (RQ3)
3. How did you decide on the elements of the lessons for teaching spatial awareness
to your students? (RQ2)
4. Did you feel prepared to teach the lesson? (RQ2)
5. How did you feel the lesson went? (RQ2)
6. In reflecting on the lesson, what might you change, keep or enhance? (RQ2)
7. What further support might you need from the school to continue teaching spatial
awareness lessons? (RQ3)
8. Are there other things you would like to discuss about the lesson? (RQ2)

Abstract (if available)

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Asset Metadata

Creator Ackerman-Hicks, Elizabeth L. (author)

Core Title An exploration of the effect of the development of spatial awareness as a prerequisite science, technology, engineering, and math (STEM) skill on the STEM gender achievement gap: an innovation study

School Rossier School of Education

Degree Doctor of Education

Degree Program Organizational Change and Leadership (On Line)

Publication Date 04/09/2018

Defense Date 01/29/2018

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag OAI-PMH Harvest,secondary instruction,spatial awareness,STEM gender gap

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Hyde, Corrine (committee chair), Crawford, Jennifer (committee member), Ott, Maria (committee member)

Creator Email ela9670@lausd.net,elackerm@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-3139

Unique identifier UC11670742

Identifier etd-AckermanHi-6172.pdf (filename),usctheses-c89-3139 (legacy record id)

Legacy Identifier etd-AckermanHi-6172.pdf

Dmrecord 3139

Document Type Dissertation

Rights Ackerman-Hicks, Elizabeth L.

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA