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An examination of teachers’ perceived value and knowledge of mathematical development in early childhood settings
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An examination of teachers’ perceived value and knowledge of mathematical development in early childhood settings
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AN EXAMINATION OF TEACHERS’ PERCEIVED VALUE AND KNOWLEDGE OF
MATHEMATICAL DEVELOPMENT IN EARLY CHILDHOOD SETTINGS
by
Jinna Hariri
A Dissertation Proposal 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 2018 Jinna Hariri
2
AN EXAMINATION OF TEACHERS’ PERCEIVED VALUE AND KNOWLEDGE OF
MATHEMATICAL DEVELOPMENT IN EARLY CHILDHOOD SETTINGS
by
Jinna Hariri
A Dissertation Presented
in Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF EDUCATION
USC ROSSIER SCHOOL OF EDUCATION
UNIVERSITY OF SOUTHERN CALIFORNIA
2018
APPROVED:
___________________________________
Pedro Garcia, Ed.D.
Committee Chair
____________________________________
Rudy Castruita, Ed.D.
Committee Member
_____________________________________
Rebeca Andrade, Ed.D.
Committee Member
3
ABSTRACT
The underlying argument of this study is that young children should develop in an engaging
environment that includes a variety of learning opportunities concerning concepts, procedures,
and approaches, all of which will empower their academic preparation necessary for today’s
challenges. National attention has focused on building a foundation in preschool through college
by educating students to excel in STEM careers (Dorph, Shields, Tiffany-Morales, Hartry, &
McCaffrey, 2011). The research showed that young children have the cognitive capability to
learn mathematics through age-appropriate activities, and learning mathematics for
prekindergarten children ages three to five positively affects their later academic achievement.
There is, however, a limited understanding of the nature of teaching mathematics in a preschool
classroom, and what is required to implement positive results. Specifically, the beliefs of early
childhood educators, documented in a review of research, recognizes mathematical instruction as
an influential factor in teacher practice and student learning. The goal of this study was to
provide insight into four areas, including teachers’ beliefs regarding the teaching of mathematics,
as well as teachers’ self-efficacy, knowledge of the mathematical development of
prekindergarten children, and their beliefs as to what extent and frequency they incorporate
mathematics in their preschool classrooms. A mixed method of data collection was designed to
examine the subjective of the study. Quantitative data through a survey and qualitative data
collected from one-on-one interviews. Although the results suggested prekindergarten teachers
value mathematics education in the preschool classroom more than previously known,
participating teachers believe that social and emotional development are their priorities.
4
DEDICATION
I dedicate this dissertation to my father, who instilled in me the confidence and sense of service
that are the cornerstones of my dedication to prekindergarten students.
5
ACKNOWLEDGMENTS
This dissertation would not have been possible without the support of an institution and
several people to whom I am ever indebted. I begin by first expressing my heartfelt gratitude to
the Rossier School of Education at the University of Southern California. The backing of such
an institution made this undertaking all the more feasible.
I express my sincerest gratitude to my dissertation advisor, Dr. Pedro Garcia. His
guidance, leadership, expertise, and dedication throughout this process gave me the fortitude to
endure. Doubtless, I would not have reached the project’s conclusion without his unwavering
support.
I am also grateful to Dr. Rudy Castruita, one of my dissertation committee members. His
engagement in invaluable conversations constituted pivotal moments in the progress of the
dissertation, inspiring me to be meticulous and unflinching in my goal of influencing early
childhood mathematics in such a unique way.
I am thankful to my mentor and dissertation committee member, Dr. Rebeca Andrade.
Her steady support, kindness, and dedication were instrumental throughout this difficult journey.
Furthermore, the process of data collection would not have been as thorough without her
enduring guidance.
A special thank you is reserved to the teachers who actively participated in this study, providing
valuable data and insight. I am also grateful for my prekindergarten students who inspired me to
strive to better early childhood education. This project begins and ends with them in mind, of
course. I am also thankful for Dr. Pouya Alimagham’s friendship and counsel as well as his
ceaseless encouragement.
6
Last but certainly not least, I am deeply appreciative of my family, foremost among them
is my husband, Ferris, and my daughter, Gilda, both of whom never waivered in the patience,
support, and love as I worked to finally make this long-held academic dream a reality. I am also
indebted to my mother, who believed in me all my life, and inspired me by her example—a
testament to female fortitude and resilience. In the end, it was my father, for whom this
dissertation is dedicated and who instilled in me a confidence that is the foundation for any
success that I have enjoyed.
Needless to say, any of the project’s shortcomings are exclusively mine.
7
TABLE OF CONTENTS
List of Tables ...........................................................................................................9
List of Figures ........................................................................................................10
Chapter One: Introduction .....................................................................................11
Statement of the Problem ...........................................................................13
Research Questions ....................................................................................14
Purpose of the Study ..................................................................................14
Significance of the Study ...........................................................................15
Limitations of the Study.............................................................................15
Definition of Terms....................................................................................16
Organization of the Study ..........................................................................16
Chapter Two: Literature Review ...........................................................................17
Introduction ................................................................................................17
Importance of Teaching Mathematics .......................................................19
Knowledge of Mathematical Development ...............................................28
Theoretical Framework ..............................................................................31
Chapter Three: Methodology .................................................................................34
Introduction ................................................................................................34
Restatement of Problem, Purpose, and Research Questions......................34
Design ........................................................................................................37
Instrument ..................................................................................................38
Sample........................................................................................................40
Data Collection ..........................................................................................41
Data Analysis .............................................................................................42
Chapter Four: Data Analysis ..................................................................................43
Introduction ................................................................................................43
Results for Research Question 1 ................................................................50
Results for Research Question 2 ................................................................54
Results for Research Question 3 ................................................................57
Results for Research Question 4 ................................................................60
Summary of the Findings from Quantitative and Qualitative Data ...........62
Discussion ..................................................................................................67
Conclusion .................................................................................................72
Chapter Five: Conclusions .....................................................................................74
Introduction ................................................................................................74
Statement of the Problem ...........................................................................74
Research Questions ....................................................................................75
Theoretical Framework ..............................................................................75
Literature Review.......................................................................................76
Key Findings ..............................................................................................78
Teachers’ Beliefs on Teaching Mathematics .............................................78
Self-Efficacy ..............................................................................................80
The Knowledge of the Mathematical Development of Preschoolers ........81
Frequency of Incorporating Mathematical Concepts in the
Preschool Classroom ......................................................................83
8
Limitations .................................................................................................83
Implications................................................................................................84
Conclusion .................................................................................................89
References ..............................................................................................................90
9
LIST OF TABLES
Table 1. Quantitative Survey Response Rate .........................................................45
Table 2. Age Range of the Participants .................................................................46
Table 3. Work Experience as a Teacher ................................................................47
Table 4. Demographic Data of Participants of the One-on-One Interviews ..........50
Table 5. Perceived Values on Teaching Mathematical Concepts (N=32) .............51
Table 6. Value Dimensions ....................................................................................53
Table 7. Results of Self-efficacy of Preschool Teachers in Helping
Preschoolers Learn Mathematics .............................................................55
Table 8. Assessing Self-Efficacy ...........................................................................56
Table 9. Results from Knowledge of Children’s Mathematical Development ......57
Table 10. Knowledge of Mathematical Development ...........................................58
Table 11. Measuring Instructional Practice Frequency .........................................61
10
LIST OF FIGURES
Figure 1. Highest Degree of the Respondents’ Work Experience .........................48
Figure 2: Highest Degree of the Respondents and Work Experiences ..................49
11
CHAPTER ONE: INTRODUCTION
A primary goal of education is to provide each student with the academic preparation
necessary for life-long learning and personal fulfillment in a challenging and evolving world
(Watt & Linley, 2013). In an era of reform, STEM education is disproportionally lacking
professionals in the United States. Yet, these disciplines are critical in preparing students for the
professions needed in the 21st century in which science and technology are integral components
to the modern economy (Drew, 2011). As such, national attention has focused on building a
foundation from preschool through college in educating students to excel in STEM careers
(Cross, Woods, & Schweingruber, 2009). For instance, in 2009, President Barack Obama
launched the Educate to Innovate Initiative, calling for 100,000 STEM teachers with content
knowledge and proficiencies to train students in science, math, and technology (President’s
Council of Advisors on Science and Technology, PCAST, 2010).
The STEM workforce in the US has grown dramatically during the last decades as the
number of retiring baby boomers increased thereby shifting the country from an industrial to a
technological economy (Drew, 2011). According to data from the Bureau of Labor Statistics
(2007), there will be a need for an estimated 21 million skilled workers in America. The
Department of Commerce (2011 as cited in National Research Council, 2012) reported that
STEM positions are expected to grow 17% by 2018. Consequently, it is necessary to
significantly increase the number of students who enter STEM fields by 34% (PCAST, 2010) in
order to prepare a modern workforce and remain globally competitive.
California in particular has benefitted from a disproportionately large number of STEM
jobs in the nation, and is expecting continued growth in these sectors by about 2.4%.
Additionally, a million California residents retired between 2006 and 2016. Data from the
12
California Council on Science and Technology (CCST) demonstrated that California’s
educational system is underrepresented in terms of the number of qualified, marketable, and
accredited professionals for the 30,000 anticipated positions that will develop by 2018 (CCST,
2007). Such data has raised an enhanced view of educational reform that centers attention on the
value and importance of STEM education (Dorph et al., 2011). Mathematics especially stands
out as a platform that creates knowledge in the understanding of complex natural phenomena
(Copple, 2004).
The investigation and research on STEM education revealed that certain essential
elements require improving STEM education, including the quality of science and math
educators (Drew, 2011). The lack of convinced elements has caused policy stakeholders in early
education to publish declarations concerning the urgency of embracing mathematics in early
childhood curriculum. In 2002, the National Association for Education for Young Children
(NAEYC) proposed a position statement on the nature of these challenges that included
recommendations to promote early childhood mathematics training (Clements & Sarama, 2004).
In doing so, the American education system stands committed to providing students at every
level with the essential skills to excel in mathematics by accepting the wisdom that the most
applicable way to overcome these challenges is to enhance teaching and learning beginning in
the preschool years. Thus, the effective teaching of mathematics requires a cognitive quality of
classroom instruction formed and strengthened with the teachers’ own task values and beliefs
that support mathematical learning as well as a proficiency in the understanding of children’s
mathematical development (Frenzel, Goetz, Lüdtke, Pekrun, & Sutton, 2009). Related evidence
described early childhood teachers’ perceived values to be directly related to classroom
instruction and student achievement in the primary stages (Turner, Meyer, Midgley, & Patrick,
13
2003). There is a need to examine early childhood teachers’ knowledge of early mathematical
development and their outlook related to how mathematics should be taught.
Statement of the Problem
The growing recognition in recent decades that excellence in student performance in
mathematics corresponds to future national prosperity has fueled the drive to improve the
instruction of such an important subject. International and domestic assessments show that
American students fail to reach the level of excellence both nationally and internationally. The
national call for ensuring a solid mathematical foundation for all students demands improved
preparation to increase the number of students for professions that require a high proficiency in
math (Drew, 2011). The National Council of Teachers of Mathematics and the National
Association for the Education of Young Children both confirmed the results of cumulative
research on children’s capacities and learning in the first six years that high-quality, challenging,
and accessible mathematics education for children ages 3 to 6 is not only vital to future
mathematical learning but also contributes to academic achievement in later years. Reform
strategies addressed these challenges with new standards and resources to improve mathematics
education and focus on the mathematical proficiency of Americans with increased attention on
early childhood foundations of mathematical literacy (Cross et al., 2009).
While knowledge and mathematical competence of early childhood teachers are
recognized as important strategies to support a sustainable plan for improving student
achievement in mathematics, there is also a need to understand what preschool mathematics
teaching involves and what is necessary to implement effective mathematical education.
Specifically, the importance of teachers’ beliefs that harness their commitment through which
they facilitate task values in classrooms has not been thoroughly documented or explicitly
14
addressed in teacher training. Most importantly, awareness of measuring teachers’ knowledge of
early mathematical development and how much value they place on teaching mathematics in the
preschool classroom is needed since teachers’ beliefs about teaching and learning mathematics is
a primary asset in providing the foundation for such support.
Research Questions
The research questions listed below have been chosen based on their importance and
relevance to teaching mathematics in the preschool classroom. Attention was given to the
measures and analytical techniques used in investigating teachers’ beliefs, values, and the
knowledge of their students’ development in terms of mathematics. The following questions
guided the study:
1. What are public preschool teachers’ perceived values about teaching mathematics to
preschoolers?
2. How confident are urban public preschool teachers in helping preschoolers learn
mathematics?
3. What is the knowledge level of public preschool teachers regarding the mathematical
development of their students?
4. With what frequency do public preschool teachers believe they incorporate mathematical
concepts in class?
Purpose of the Study
The purpose of this study encompasses three components. The main purpose was to
describe preschool teachers’ beliefs and perceived values about teaching mathematics to
preschoolers. A concurrent objective was to investigate the knowledge of preschool teachers
regarding the mathematical development of students in California public schools. The third goal
15
of this study was to investigate how often teachers’ beliefs are incorporated into teaching
mathematics concepts in class.
Significance of the Study
The significance of this study is measured by the extent of the contribution it will make to
broaden related-education problems, and to contextualize its findings within the body of research
that will foster further research. Further, this study is important as it provides information to
principals and school leaders that will help them foster supportive environments as it provides a
detailed description of preschool teachers’ perceived beliefs as well as their mathematical
knowledge of preschool-age children. Thus, the applicable information illustrated within this
study offers helpful knowledge for its implication in professional development.
Ultimately, teachers’ beliefs and knowledge are intertwined (Manouchehri, 1997),
therefore, professional organizations and schools can incorporate the results of this study’s
formative data to teach educators intervention approaches. The constructive outcome from this
study will enable educational organizations and schools to facilitate a better alignment of
research, practice, and beliefs in order to provide more effective teacher training as it pertains to
the urgent need to embrace mathematics in the early childhood curriculum.
Limitations of the Study
Although the study’s findings are illuminating and add to a deeper understanding of the
role of teachers’ beliefs and values, and how they impact the mathematical development of their
students in preschool classroom settings, there are number of limitations and shortcomings that
need to be addressed in future research. First, the data was drawn from a limited geographic
region. Second, analyses of the current data focused on a small sample. To increase the
16
applicability of the findings and provide transferred conclusions, future research can aim to
gather data from a larger representative sample.
Definition of Terms
Knowledge of early mathematical development: age-appropriateness of mathematics
instruction in the preschool classroom (Copley, 2004; Ginsburg et al., 2006).
Beliefs: Beliefs are convictions or assumptions of truth of some statement, idea, or reality
(Colman, 2009). Beliefs are “mental constructs that represent the codifications of
people’s experiences and understanding” (Schoenfeld, 1999, p. 2).
Organization of the Study
This study encompasses five chapters, the first of which includes the study’s overview,
purpose, significance, research questions, and limitations. The second chapter outlines a review
of the literature related to national and global approaches to preschool mathematics education,
teacher professional development, and teachers’ beliefs. Chapter three includes an outline of the
description of the methodology for surveying and interviewing teachers of public preschools in
California, and the data gathering through mixed methods is the focus of chapter four. Chapter
five concludes the study with its evaluated findings, implications, and recommendations for
future research.
17
CHAPTER TWO: LITERATURE REVIEW
Introduction
This literature review highlights key themes that provide national and global attention to
early childhood education, the importance of mathematics in preschool education, teachers’
professional training, and standards for preschool children’s knowledge of mathematical
development. The review begins with an overview of the focus on the mathematical
development of children under the age of six in national and global levels, including a national
early childhood organization that called for supporting early mathematical development, and its
impact on future student academic achievement. When providing details to support this current
challenge, it is important to offer a review of the literature in the following areas: (a) teacher
professional development, (b) beliefs and the impact on student achievement, (c) the ability of
preschool children to learn mathematical concepts, and (d) the National Association for the
Education of Young Children’s (NAEYC) recommended standards for developing mathematical
knowledge in early childhood programs. Additionally, this chapter includes a highlight on the
literature related to understanding early childhood mathematics and the previous research
connected to NAEYC and the position statement of the National Council of Teachers of
Mathematics (NAEYS & NCTM, 2002). These elements provide comprehensive, descriptive
information in response to demands for building a mathematical foundation for preschoolers.
The national policy agenda recognized the importance of mathematics instruction in early
childhood education in providing the fundamentals of mathematics necessary for later grades
(Early et al., 2007). Due to the recognition that participation in the modern world requires
knowledge and competence in mathematics, this policy emphasized implementation of age-
appropriate mathematics curricula that were planned based on research and expertise (NCTM,
18
2002). The American Educational Research Association (AERA, 2005) and the National
Research Council (2009) mandated preschool teachers to integrate more opportunities for
learning mathematics than simply counting and working with shapes. Additionally, the new
national and state standards require the same emphasis as the NAEYC’s joint position with the
NCTM, which announced a statement postulating that high quality mathematics education for
three to six-year-old children is a fundamental requirement for the future learning of
mathematics (NAEYC & NCTM, 2002). Consequently, several federal initiatives, such as Grow
Smart and Good Start, focus on preschool research that are based on mathematics standards and
curriculum guidelines to ensure that children enter elementary school with the necessary
foundation that significantly supports later, more complex growth in mathematics (NAEYC &
NCTM, 2002).
Reflecting on the importance of mathematics education, then-President Bush established
the National Mathematics Advisory Panel (NMAP) in 2008 (Kelly, 2008). The primary goal of
NMAP was to provide evidence-based advice about what concepts educators should teach to
students from Kindergarten to 12th grade, and to suggest professional training for educators.
The NCTM generally recognized the report’s recommendations and called for funding to help in
its implementation, and to conduct further research to advance the methodology of teaching and
learning mathematics.
Further, the Mathematical Sciences Education Board of the Center for Education at the
National Research Council, which developed the Committee on Early Childhood Mathematics
(CECM) and NMAP, brought attention to the instructional core of mathematics in preschool
classrooms in 2009 (Cross et al., 2009). In an effort to utilize the results of the committee’s
investigation of the existing research, NMAP recommended implementing developmental,
19
research-based evidence to improve curriculum, preschool mathematic instruction, and teacher
education (Kelly, 2008).
NMAP addressed certain aspects of early childhood mathematics. Primarily, it posited
that children are capable of attaining substantial knowledge of various mathematical concepts
before entering kindergarten thereby equipping them for later mathematics learning and
achievement (Cross, Woods, & Schweingruber, 2009). Therefore, improving the mathematics
curriculum of preschoolers and kindergarteners became an important goal of early childhood
programs. Accordingly, many states, like South Carolina, New Jersey, Ohio, Virginia,
Wyoming, Texas, and Louisiana have implemented new research-based levels of mathematics
education to enable students to succeed at formal grades (Neuman & Roskos, 2005).
Through a process of quantitative and qualitative metasynthesis, several institutions
found that the early childhood education emphasis creates learning opportunities for children.
The NAEYC (2002), NCTM (2000), the National Research Council (NRC, 2000), the RAND
Mathematics (Hamilton & Berends, 2006), and the Conference on Standards for Prekindergarten
and Kindergarten Mathematics Education (as cited in Clements, Sarama, & DiBiase, 2003) all
supported facilitating cohesive strategies and curricula that improve the quality of mathematics
experiences for young children.
Importance of Teaching Mathematics
The next driving force following the initiatives encapsulates a research-based
understanding that children are more competent to learn mathematics than previously thought
(Ginsburg, Lee, & Boyd, 2008). According to cognitive learning theories, children’s cognitive
skills grow as children learn and begin to apply previously learned information to new concepts.
In other words, the complexity of children’s learning is that new knowledge becomes established
20
as it builds on previously learned evidence (Ginsburg, Lee et al., 2008). Evidence, from learning
theories, suggested that children prior to school-age years demonstrate competence in enduring
mathematical concepts (Clements, Sarama, & DiBiase, 2003). Through an empirical
investigation, Clements and Sarama (2007) compared classrooms that included both state-funded
and Head Start prekindergarten programs to evaluate the efficacy of a preschool mathematics
program (“Building Blocks”), and concluded that early intervention in mathematics teaching to
preschoolers in particular helps children who are at risk academically. Data from observations of
preschool children showed that the building of mathematical concepts occurs in cumulative
ways. For instance, children reasonably incorporate complex mathematics during playtime, and
naturally transfer previous knowledge to novel and more complex situations (Baroody, 2000).
Data from a primary study of several large-scale, longitudinal studies, including the Early
Childhood Longitudinal Study-kindergarten cohort, the National Longitudinal Survey of Youth,
the Infant Health and Development Program, The Montreal Longitudinal Experimental
Preschool Study, examined the relationship between levels of competence and skills during
preschool years and later achievement, and concluded that math skills upon entering formal
grades are most predictive of later academic achievement followed by reading skills and
attention span (Baroody, 2000; Klibanoff, 2006). Nationally recognized professional early
childhood organizations like NAEYC promote high quality education and advocate instruction in
early mathematics that should ensure proficiency in numbers, operations, geometry,
measurement, and algebra concepts (Ginsburg, Lee et al., 2008).
It is important to underline that 70% of all four-year-old children attend an early
childhood program for a year or two (U. S. Department of Education, National Center for
21
Education Statistics, 2008), a reality that highlights significant opportunities for building a
stronger foundation in mathematics for those children.
Global Attention on Mathematic Teaching in Early Childhood Education
The need for students to study Science, Technology, Engineering, and Mathematics
(STEM) over the last few decades has been evident in the increasing demand from technology
employers and the growing role of “tech companies” in economic development. Consequently,
several countries have implicated research, innovation, and implementation (Ainley, Kos, &
Nicholas 2008). Furthermore, the progress of mathematical proficiency of four-year-olds in
countries such as China, Japan, and South Korea promoted interest in proactively supporting
mathematical skills early in life. Countries, such as Australia, established National Quality
Standards for early childhood provisions (Australian Children’s Education and Care Quality
Authority, 2011) and the teaching of mathematical concepts in early years, such as Early Years
Learning Framework for Australia (Department of Education, Employment and Workplace
Relations, DEEWR, 2009) in order to create requirements for teachers to incorporate the new
standards in early childhood pedagogical practice. During the past few years in Germany, early
mathematical education has become an important objective for children ages three to six,
resulting in the establishment of several of programs for preschool children that emphasize
mathematics as a domain of learning skills.
Teacher Training
According to NAEYC & NCTM (2002), launching mathematics’ education during
preschool years not only provides “a sound mathematical foundation for all members of our
society,” (NAEYC & NCTM, 2002, p. 1) but also “to prepare increasing numbers of young
people for [specialized] work that requires a higher proficiency level” (NAEYC & NCTM,
22
2002, p. 1). Through mixed methods of investigation, scholars suggested that a lack of support
for mathematics development in early childhood classrooms is a result of educators not receiving
the necessary education and training to provide instruction and a suitable curriculum to support
cognitive development regarding proficiency in mathematics in children under age six (Copley &
Padron, 1998; Kilpatrick Swafford, & Findell, 2001). Researchers also showed that providing
professional development in mathematics helps educators create a suitable framework
implication that affects instructional practices (Klein, Starkey, Clements, Sarama, & Lyer, 2008;
Thornton, Crim, & Hawkins, 2009), and increases competence in mathematics and enjoyment in
practice (Arnold, Fisher, Doctoroff, & Dobbs, 2002).
Research on assessing the performance of teachers with professional development in
terms of mathematical knowledge demonstrated how higher professional development
determines topics in early childhood education and strategies to meet mathematical curricula
goals. In this regard, Thornton et al. (2009) found that prekindergarten teachers who have
participated in Collaborative, Collegial, and Cooperative Coaching Grant Professional
Development show statistical increases in levels of emphasis placed on mathematics, such as
measuring, geometry, and graphing. In an experimental study with a control group, Arnold et al.
(2002) concluded that children in an experimental group whose teacher received ongoing
professional development showed higher average scores on the Test of Early Mathematics
Ability (Second Edition; TEMA-2) by 3.67 points than the children in the control group whose
teacher had not received professional development. The latter group showed an average
improvement of only 0.84 points. Samara, Clements, Starkey, Klein, Wakeley (2008) examined
the impact of professional development on teachers’ practices by using the classroom
observation method thereby focusing on classroom interaction and instruction in experimental
23
and control groups. They reported that the experimental group, whose early childhood teachers
had professional development in teaching mathematics, had a higher mean of 3.6 than the control
group with a score of 2.8. The study also reported that the experimental group had more minutes
per week devoted to math instruction (257 vs. 151) (Sarama & Clements, 2009a).
Concerning the impact of professional development on teachers’ practices in early
childhood classrooms, Starkey, Klein, and Wakeley (2004) examined scores on mathematical
knowledge among a control group and an experimental group of children from low-income and
middle-income families. The results of the study showed that children’s scores from both low-
income and middle-income families in the experimental group improved significantly more than
the children in the control group (Starkey et al., 2004).
Furthermore, scholars investigating preschool education also suggested that children who
participated in high quality, early childhood education not only showed increased intelligence
and social development but also demonstrated mathematics achievement that persisted up to age
21 (Ramey & Ramey, 2004). Magnuson, Ruhm, and Waldfogel (2007) used a longitudinal study
of preschool to first grade in order to determine the mathematical gains in preschoolers of low-
income families who attended high-quality public preschools, and likewise concluded that
mathematics achievement is noticeable as a result of the relative contributions of changes in the
academics achieved in high-quality preschools.
Teachers’ Values
Research showed that teachers’ beliefs act as a powerful tool that directly impacts their
practices and willingness to adopt new teaching strategies (Hofer, 2001). In this regard, scholars
investigated the teachers’ beliefs to understand their impact and effectiveness as well as how
their values could improve (Donovan & Bransford, 2005). There are several different but related
24
definitions of “beliefs” in the literature, but one of the primary definitions refers to personal
convictions, philosophies, or opinions about the context of education (Czerniak, Lumpe, &
Haney, 1999). Another definition refers to an individual’s mix of subjective knowledge and
feelings about a certain object or person (Thompson, 1992) that guides a person’s thinking and
performance processes. Furthermore, beliefs viewed in the context of the cognitive process have
been described by concepts like mental representation, feeling, and functional role (Bogdan,
1986). From a psychological perspective, there seems to be agreement that beliefs play a role in
one’s cognition and behavior.
As such, the examination of the impact of teachers’ beliefs about their work indicates that
a coherent set of views forms the teachers’ curriculum ideology that generates patterns when
developing and implementing their teaching course content (Stodolsky & Grossman, 1995). In
Woods’ (1996) study of English as a second language, teachers revealed that perceived values
established the notion that belief, knowledge, and judgment influence teachers’ classroom
behavior. In a closer look at the beliefs of teachers and their influences on their practices in the
classroom, data from the 21 fourth- through sixth-grade teachers showed their behaviors were
aligned and supported by their beliefs (Stipek, Givvin, Salmon, & MacGyvers, 2001).
Moreover, the research also demonstrated that teachers’ beliefs and values regarding content and
pedagogy have a significant effect on the direction of their development, preparation, and
implementation of lessons (Kulinna, Silverman, & Keeting, 2000; Pajares, 1992). In their
quantitative study, Richards, Gallo, and Renandya (2001) showed that teachers’ beliefs are
central to teacher training programs, and modifications in teachers’ notions led to changes in
teachers’ practices, individual improvement, and the student learning process. Changes in
25
teachers’ beliefs occur in multiple-dimensional ways and are fostered by personal factors as well
as by the professional contexts in which they work (Richards et al., 2001).
Scholars argued that teachers’ perceived values about curriculum and instruction impact
the quality of their focus on providing meaningful learning activities (Frykholm, 2004; Stipek et
al., 2001), concluding that the congruence in teachers’ beliefs and the current, demanding
mathematic standards regulate teachers’ behaviors to create optimal mathematics instruction in
classrooms thereby fostering learning opportunities for students (Stipek et al., 2001).
For instance, Kowalski, Pretti-Frontezak, & Johnson (2001) hypothesized that teachers’
beliefs are consistent with their willingness to teach certain subjects. A questionnaire was used
to elicit responses from 470 Head Start teachers to quantify the degree to which teachers’ beliefs
impacted teaching social and emotional development, mathematics skills, and early literacy. The
statistics indicated that teachers in both special education and early childhood public preschools
focused on social-emotional skills, which is important for preschool children to learn. Data from
this study also showed that 24 teachers believed that mathematics was the least important subject
matter to teach. The author concluded that only focusing on social-emotional development in
preschool classrooms does not provide opportunities for exploration and acquisition of
mathematics and early literacy (Kowalaski, 2001).
The review of the above studies suggested that preschool teachers play a significant role
in preschoolers’ educational context, and that their perceived values and beliefs are effective
resources in preschool that directly impact the quality of education. The literature review also
suggested that preschool teachers’ mathematics implementation that align with NAEYC and
NCTM standards will be influenced by teachers’ beliefs and values about the mathematics
curriculum. Accordingly, if teachers do not believe in teaching mathematics concepts to
26
preschool children, then they may not implement the mathematics instructional methods in their
classrooms. Consequently, school administrators and teacher training programs need to
investigate teachers’ beliefs in designing effective teacher training and professional development
programs that address the needs of the preschool children in the area of mathematics.
Teachers’ Self-Efficacy
Implementation of a mathematics curriculum is a complex process in which teachers hold
their established beliefs about the quality and effectiveness of their teaching. Ample evidence
shows that teachers’ beliefs about teaching and learning are critical in determining successful
integration and providing learning opportunities (Fraivillig, Murphy, & Fuson, 1999; Frykholm,
2004; Stipek et al., 2001).
Another approach that researchers used to evaluate teachers’ beliefs stems from cognitive
theory whereby teachers’ self-efficacy is conceptualized as teachers’ beliefs in their ability to
plan, create, arrange, and carry out actions that lead to attaining their teaching goals. According
to Bandura (1997, 2006), teachers’ self-efficacy is an influential source of instructional context
since their perceived values are directly related to creating and fostering physical and mental
effort as well as persistent behaviors required to attain instructional goals. A number of studies
showed that teachers’ self-efficacy beliefs influence student achievement in several ways
(Cousins & Walker, 1995). Teachers with high self-efficacy become more actively engaged in
providing adequate teaching methods that encourage student autonomy and reduce custodial
control (Cousins & Walker, 1995; Schunk, Pintrich, & Meece, 2014). Notably, teachers with
high self-efficacy also show responsibility for students with learning problems (Schunk et al.,
2014).
27
Tschannen-Moran and Hoy (2001) noted that a high sense of self-efficacy has a strong
influence on the capability to bring about desired outcomes of student engagement and learning
in every educational setting. The literature demonstrated that teachers’ self-efficacy increases if
they believe that student achievement and behavior can be changed by education (Schunk et al.,
2014).
According to Skaalvik and Skaalvik (2007), the level of teachers’ self-efficacy is not only
related to their willingness to organize and execute a course of action necessary to bring about
the desired results but it is also interconnected to content knowledge and teachers’ acquired
training (Pajares, 2002). On this subject, Skaalvik and Skaalvik (2007) added that self-efficacy
beliefs also determine teachers’ ability to reconcile their pedagogical values while seeking
practical solutions to issues and problems in their professional lives.
According to Aerni (2008), a teacher with a high level of self-efficacy not only
demonstrates a strong instructional commitment to student learning but also shows adjustment in
instructional methods and materials presented in class to trigger student achievement. Desimone
(2009) found the positive relationship between teachers’ beliefs and knowledge directly related
to the quality and effectiveness of mathematics teaching. Desimone also added that teacher
education programs are a significant and crucial influence on altering teachers’ beliefs and
fostering critical values in instruction.
It is worth noting that the theories that explain motivation as an internal thought process
of confident individuals who initiate an action, and persist on a task that unites goal-oriented
behaviors with cognitive theories on the important role of self- efficacy beliefs include planning,
organizing, rehearsing, monitoring, making decisions, solving problems, and assessing progress
(Schunk et al., 2014). Indeed, self-efficacy controls human functioning by impacting cognitive,
28
motivational, affective, and selection processes (Bandura, 1986). The cognitive theory used in
the fields of psychology, education, and communication focused on how individuals acquire
knowledge in a social context. In his social cognitive theory, Bandura (1999) distinguished
learning as a process best understood through the behavioral model, the consequence of the
modeled behavior, the learner’s internal cognitive process, and the learner’s perceived self-
efficacy (Schunk et al., 2014). From a social cognitive theory perspective, self-efficacy beliefs
for performing a task are a key motivational factor that influences a teacher’s task choices, effort,
persistence, and achievement.
Although there are several studies on teachers’ perceptions, values, and self-efficacy, the
examination of preschool teachers’ self-efficacy is at a preliminary level. Researching teachers’
beliefs and perceptions could provide both a new focus on teacher education programs as well as
professional development, which are necessary to optimizing the teaching and learning of
mathematics in preschool classrooms. The NAEYC and NCTM’s position on early childhood
mathematics stated that the mathematics knowledge of most early childhood teachers in terms of
utilizing a comprehensive approach to mathematics education is not available to all teachers
(NAEYC & NCTM, 2002, p. 2). Assessing teachers’ confidence will add to the limited research
in early-childhood mathematics’ education and provide information for professional
development to strengthen mathematical proficiency among preschool children.
Knowledge of Mathematical Development
Numerous studies have thoroughly investigated children’s mathematical development
thereby providing information on the developmental progression of children’s mathematical
understandings (Baroody, Lai, & Mix, 2006; Clements & Sarama, 2007). Much of the literature
on enhancing children’s mathematics’ development suggested that teachers must have a
29
complete understanding of mathematical concepts (Ma, 1999). In doing so, teachers must
consider children’s mathematical development including the cognitive ability and consideration
of the prior knowledge of the child (Clements, 2001). Consequently, the research in this area
posited that teachers must master instructional methods that facilitate and enhance classroom
pedagogy (Baroody, Lai, & Mix, 2006; Seo & Ginsburg, 2004). Additionally, researchers
studying the factors that affect the quality of mathematics instruction in a preschool classroom
concluded that teachers’ beliefs about preschool children’s age-appropriateness of mathematics
education is a major factor in developing and deepening the conceptual understanding of
mathematics in preschool children (Lee & Ginsburg, 2007).
Teachers’ knowledge of mathematics is related to their knowledge and understanding of
mathematical concepts and their awareness of the process by which children learn mathematics.
Scholars who studied teachers’ knowledge in planning and providing age-appropriate instruction
identified several harmful misconceptions that preschool teachers have formed about
mathematics teaching in preschool classrooms, such as: (1) the belief that young children are not
ready for mathematics; (2) mathematics is for intelligent individuals with specific mathematics
genes; (3) simple numbers and shapes are the only essential mathematical concepts for
preschoolers; (4) young children are not cognitively ready for mathematics; and (5) language and
literacy are more important than mathematics for preschoolers (Lee & Ginsburg, 2009). The
results of the study suggested that these misconceptions develop from teachers’ beliefs about
teaching mathematics and the lack of information on preschool children’s cognitive abilities to
learn mathematical concepts. Such mistaken beliefs resulted from teachers’ outlook, and can be
addressed with professional development, once the consequential misconceptions are recognized.
30
The available research on mathematics development of preschool children showed how
teachers’ beliefs about the age-appropriateness of mathematics instruction are aligned with
teachers’ supporting behavior (Sarama & Clements, 2009a). By focusing on children’s
developmental readiness for mathematics in preschool, Ginsburg and Golbeck (2004) concluded
that preschool children acquire designated mathematics skills in numbers, operations, algebra,
and cardinality. Correspondingly, a number of studies show that children are capable of
substantive mathematical understanding (Ginsburg & Amit, 2008; Klein, Starkey, Deflorio, &
Brown, 2011; Sarama & Clements, 2009a).
In 2009, the NAEYC released a new report of its Developmentally Appropriate Practice
in Early Childhood Programs book (Copple & Bredekamp, 2009) demonstrating how
developmentally-appropriate standards are important guides in curriculum development and
teaching, defining teachers’ roles in planning, and implementing the learning concepts. The new
version of developmentally-appropriate practice emphasized the necessity of teachers’
knowledge of children’s development and learning that considers children’s age, development
status, and the social and cultural contexts, all of which factor into the teacher’s outlook when
establishing challenging experiences and goals (Copple & Bredekamp, 2009). The NAEYC
report on Developmentally Appropriate Practice in Early Childhood Programs specifically
highlighted the role of teachers’ knowledge of children’s learning development.
The above review of the literature showed that three kinds of knowledge are significant
for teaching mathematics: knowledge of mathematics; knowledge about how children develop in
the domain of early mathematics; and knowledge of impactful instructional approaches. The
literature review also suggested that building upon teachers’ prior knowledge and their
understanding of preschool children’s mathematical development are essential to effective
31
mathematics education in a preschool classroom. Additionally, while research has increased
knowledge on mathematics teaching in preschool classrooms, and supported the belief that
knowledge of children’s mathematical development is continuous thereby influencing teachers’
implementation of mathematics instruction in a preschool classroom, teachers’ understanding of
mathematical development has not been measured rigorously.
Theoretical Framework
It is important to highlight that the conceptual theory for this study was based on two
major educational approaches that have dominated the current literature on enhancing knowledge
acquisition: constructivism and cognitive load theory (Jonassen 1999; Loyens & Gijbels 2008;
Taber 2006; Vygotsky, 1978). Such a focus also underlies the role of teachers’ beliefs in
children’s mathematical development. Constructivist approaches shared a common philosophy
that provided the learner with skills and support including scaffolding, coaching, and modeling
that encourage learners to actively process and construct the new knowledge (Decker, Decker,
Freeman, & Knopf, 2009). In constructivism approaches, the role of the teacher was to develop
a classroom culture that places emphasis on learner participation in intellectual activities which
is important in guiding, shaping, and expanding student thinking (Ball, 1989; McDiarmid, 1989).
The second and most modern educational approach accounts the ultramodern view on human
cognitive architecture and focused on utilizing principles and techniques for optimizing learners’
cognitive resources identified as cognitive load effects (Sweller, Ayres, & Kalyuga, 2011).
According to the cognitive load theory, which explained instructional design implications of
human cognitive architecture (Sweller, 1988) and the manner in which new information was
presented to learners (Mayer, 2010), the human cognitive structure has three main components:
sensory memory, working memory, and long-term memory (Sweller, 2004). Further, the theory
32
places emphasis on facilitating the acquisition of knowledge in long-term memory with a
characteristic of unlimited capacity for storing information through a working memory with
limited capacity in keeping data received from sensory motors (Kirschner, Paas, & Kirschner,
2009). The theory generated instructional principles that stress a notion that since working
memory has a limited capacity, instructional methods should avoid overloading it with additional
activities that do not directly contribute to learning. This load is categorized as intrinsic load by
focusing on the complexity of learning tasks (Kirschner et al., 2009) and an extrinsic load as
determined by the manner the task is presented (Mayer, 2011). The process of learning,
introduced by the cognitive load theory, placed a strong emphasis on instructional guidance that
promotes efficient learning as the most beneficial (Sweller, 1988). The result of the knowledge
and understanding of teachers in providing meaningful learning is the provision of appropriate
cognitive processing during learning. This provision includes selecting relevant materials that
reduce the intrinsic and extrinsic load and increase German load, organizing the new material,
and integrating it with prior knowledge of the learner (Mayer, 2010). These theories highlight
the important role of teacher knowledge and beliefs in facilitating learning, organizing the
information, and integrating it with prior knowledge of the learner. Such a conclusion
underscores the factors that affect the quality of education students receive, highlighting the
importance of understanding how beliefs impact instruction and the role of teacher as a facilitator
or inhibitor of knowledge.
Each of these facets affects preschool teachers’ application of mathematics concepts and
standards mandated by NAEYC and NCTM. By focusing on teachers’ perceived values,
confidence in teaching mathematics concepts in preschool classrooms, and knowledge of
children’s mathematical development, there is a possibility to promote a teacher’s capacity to
33
positively affect the mathematical learning of students by determining the prerequisites
necessary for teachers’ successful preparation and professional development.
Chapter three will explain the methods and procedures for the current study,
encompassing the rationale for the design of the self-report instrument and the procedures,
results, and statistical analyses of each part of the development. Validity and reliability measures
are addressed along with details regarding preschool teachers who participated in the study and
completed each phase of the investigation.
34
CHAPTER THREE: METHODOLOGY
Introduction
This chapter includes a description of the design of the study, the participants of the
research portion, the instruments used to conduct the research, data collection procedures, and
the method of data analysis.
Restatement of Problem, Purpose, and Research Questions
This study explored preschool teachers’ beliefs, values, confidence, and the knowledge of
mathematical development of children in public schools spanning three school districts in
southern California. Using a mixed method of quantitative and qualitative methods, the
investigation examined teachers’ beliefs and knowledge in terms of the mathematical
development of children.
The literature review underlined research in early-childhood mathematics’ education, and
highlighted a need for information regarding the teaching of mathematics at a preschool level.
The historical review on mathematics reform both nationally and globally indicated that there is
an urgent need to foster preschool children’s understanding of mathematics. Studies on teaching
and learning the processes of mathematics illustrated that: (a) early childhood teachers must
integrate mathematics education in children’s everyday play activities (Ginsburg, Lee et al.,
2008; McCray & Chen, 2012); (b) preschool children’s mathematics’ education
requires preschool teachers who are not only experts in pedagogical content knowledge but are
also able to recognize children’s mathematical development knowledge and the process of
learning (McCray & Chen, 2012); (c) show how children learn mathematical concepts during the
preschool years (Pajares & Miller, 1994); and (d) there are strong relationships between teacher
knowledge and beliefs in terms of their educational behavior in the classroom.
35
Data from the literature review also categorized a range of beliefs influencing
mathematics instruction in the preschool classroom (Copley, 2004; Ginsburg, Kaplan et al.,
2006) including the teacher’s beliefs and values regarding mathematics acquisition, age
appropriateness of mathematics education, and teacher comfort in mathematics instruction that
provides a foundational support for an effective context for learning mathematics (Balfanz, 1999;
Bredekamp & Copple, 1997; Copley & Padron, 1998; Greenes, Ginsburg, & Balfanz, 2004; Lee
& Ginsburg, 2007).
Examining preschool teachers’ beliefs represents a narrow lens through which to view the
instructional values and beliefs of teachers and how they impact students’ achievements in
mathematics. The information on preschool teachers provides valuable insight for the design of
novice teacher-training courses and in-service professional development programs as well as
field supervision.
The purpose of this study encompassed four components. The primary purpose was to
describe preschool teachers’ beliefs and perceived values about teaching mathematics to
preschoolers. A concurrent objective was to investigate the knowledge of preschool teachers
regarding the mathematical development of students in California public schools. The third goal
was to examine teachers’ self-efficacy beliefs or their confidence in teaching mathematics to
preschoolers, and how they directly impacted student development and the implementation of
mathematics curricula in preschool classrooms. The fourth goal focused on investigating the
frequency of incorporating teaching mathematics concepts in preschool classrooms.
The literature review demonstrated the need to study the teachers’ beliefs, therefore,
teachers from four districts were asked to specify their beliefs and knowledge by providing
answers to the following research questions:
36
1. What are public preschool teachers’ perceived values about teaching mathematics to
preschoolers?
2. How confident are urban public preschool teachers in helping preschoolers learn
mathematics?
3. What is the knowledge level of public preschool teachers regarding the mathematical
development of their students?
4. With what frequency do public preschool teachers believe they incorporate mathematical
concepts in class?
The review of the literature showed there is an urgent call for the implementation of
mathematics instruction in early childhood programs (Clements & Sarama, 2004). The policies
and requirements are rooted in the understanding that the learning process of mathematics and
early skills in mathematics provide the foundation for later learning (Geary, 2000). Scholars
investigated the teaching and understanding of mathematics for elementary, middle, and
secondary students (Blanton & Kaput, 2005; Farmer, Hauk, & Neumann, 2005; Kosko &
Norton, 2012; Nicol & Crespo, 2005). Additionally, there are several studies that focus on child
development theories as they relate to preschool children developing mathematical concepts
(Baroody, 2000; Pepper & Hunting, 1998; Hunting, 2003). One key concern in teaching
mathematics in early childhood programs is that teachers vastly underestimate the mathematical
capabilities of the young children in their care (Copple, 2004). Teacher training programs do not
have mathematics preparation training to meet the needs of their children (Baroody, 2004;
Ginsburg, Lee et al., 2008). Consequently, teachers make decisions that influence children’s
mathematical understanding regarding age-appropriate mathematical tasks. Although teachers
teach mathematics and their self-efficacy, beliefs, and values are fundamental in the
37
implementation of mathematics curricula in preschool programs (Maier, Greenfeld, & Bulotsky-
Shearer, 2013), researchers put less consideration on preschool teachers’ beliefs, self-efficacy,
and their knowledge of preschool students’ development in mathematics. Furthermore,
measuring teachers’ beliefs is beneficial in developing the knowledge and skills of preschool
teachers to effectively teach mathematics in preschool classrooms, and for providing information
on teachers’ beliefs and knowledge of preschool children’s development of mathematical
concepts (Ginsburg, Lee et al., 2008). Such information will help delineate necessary changes in
teachers’ professional development for the long-term goal of building a strong foundation in
early-childhood mathematics’ teaching.
Design
According to Creswell (2014), conveying the nature of an inquiry using a strong methods
procedure starts with studying the latest methodology in research. The published research has
incorporated mixed-methods approaches in social and human sciences because of their strength
in drawing data from quantitative and qualitative approaches (Creswell, 2014). Thus, a mixed-
methods approach that triangulates the findings provides a sophisticated and complex manner by
which to examine the consistency of the findings with the current literature, and quantitative and
qualitative data that the researcher selected for this study. This mixed methodology approach
has been used to maximize the strength of quantitative research by providing descriptive
information from public schools paired with the power of the qualitative inquiry method to
produce an in-depth exploration drawn from the language of qualitative inquiry.
The qualitative part of this research attempted to provide a clear understanding of the
rendering of teachers’ beliefs by reporting information and quotations from actual face-to-face
conversations. According to Creswell (2014), credible qualitative research usually uses
38
purposive rather than random sampling strategies after formulating preliminary questions. The
qualitative portion of this investigation encompassed personal interviews with five teachers,
allowing them to express their beliefs and how they felt about teaching mathematics.
Instrument
For the purposes of this study, the quantitative data was collected through a questionnaire
which was generated as a cross-sectional survey by which data might be reported using
descriptive statistics in alignment with Fink (2012). Most importantly, a survey was the
appropriate technique for this study since the beliefs of teachers needed to be collected directly
from the teachers. Additionally, the survey was administered via an online questionnaire that
teachers at the three regions completed alone and online at their convenience.
By administrating the Teachers’ Perceived Values Survey, an original questionnaire, the
study obtained significant information in terms of the quality of knowledge and beliefs held by
teachers serving in elementary public schools regarding children’s mathematical development.
The researcher of this study used a set of questions based on four principles that guided their
structure.
The primary guiding principle was to choose a set of statements that represented values
and features deemed necessary in determining the teachers’ values regarding teaching
mathematics in preschool classrooms. The second guiding principle was to develop constructs
that distinguished between the dimension of confidence and level of self-efficacy in teaching
mathematics concepts. The third guiding principle focused on teachers’ knowledge related to
their students’ mathematical development. The final guiding principle was dedicated to
discerning teachers’ current practice in mathematics education.
39
The beliefs spectrum consisted of 10 items and solicited information regarding teachers’
beliefs that identified their academic and professional opinions toward teaching mathematics’
concepts in preschool classrooms. This information would assist researchers and professional
development designers at public schools to create goals and values that enhance teachers’
personal theories of teaching. According to cognitive load and constructivist theories, teachers’
personal attitudes of teaching are central to task-improving innovation in classroom (Schunk et
al., 2014).
The construct for teachers’ self-efficacy contained 10 items, while the construct for
teachers’ knowledge of their students entailed 10 items. Lastly, the construct for measuring
teachers’ beliefs about incorporating mathematical concepts in the classroom encompassed five
items. In this regard, the survey used a Likert-type scale ranging from “strongly disagree” to
“strongly agree.” The survey was embedded in Question Pro in February, 2017. The invitation
was then sent to teachers at public schools by e-mail via research associates.
The included items of knowledge on the mathematical development of preschool-age
children were organized around topics and critical components that connect preschool students to
mathematical concepts, and they can be integrated as part of early childhood daily activities.
The included items in Knowledge of Mathematical Development of Students (KMDS) were also
supported with research and current early childhood age-appropriate cognitive processing in the
field.
The last items on the survey included five questions that formed the core of the
questionnaire and collected information about classroom instructional practices and the level of
emphasis teachers placed on incorporating certain skills and mathematics concepts in their daily
40
plan with preschoolers. The information offered explanations on the frequency of teaching
mathematical concepts in the preschool classroom.
The validity of the instrument refers to the degree to which a study accurately reflects or
measures the research hypothesis that the researcher is attempting to measure (Fink, 2012).
While reliability is concerned with the accuracy of the actual measuring instrument or procedure,
validity is concerned with the study’s success at measuring what the researcher set out to
measure. Furthermore, construct validity traditionally has been used to demonstrate that a
survey is measuring the construct it claims to be measuring (Zohrabi, 2013). To sustain
construct credibility and ensure how well the instrument transforms the concept that the
researcher intends to measure, the researcher of the present study considered face validity and
content validity. Face validity is a type of test in which the researcher asks whether or not the
test appears to measure what it intends to measure. As a check on content validity, survey items
were sent to a professor of child development and other experts to obtain suggestions for
modification. Accordingly, the questions adequately covered the domain being measured and
were representative of the larger domains of value and promotion.
Sample
The researcher of the current study acknowledged the rich resource of information that
can be obtained from practitioners who are responsible for serving preschoolers in public
elementary schools and were invited to voluntarily complete a survey focusing on their
perceptions and knowledge of children’s mathematical development. For quantitative and
qualitative phases of the current study, the units of analysis were female and male teachers
serving in public urban schools in California.
41
According to Pallant (2013), a sufficient sample size for a quantities inquiry is the
minimum of individuals that share a common experience participating in a similar context. The
number of participants for the current study, of which the purpose was to make inferences about
the preschool teacher population from the sample, originally entailed 62 teachers from the target
population.
For the qualitative part of the study, the researcher made an initial phone call to each
targeted teacher. The researcher introduced herself, explained the purpose of the interview, and
gave assurances about anonymity and confidentiality. The one-on-one interviews were
conducted with five preschool teachers who serve in urban public schools and who were willing
to be interviewed. After an appointment was made with each teacher, the interviews took place
at schools where the teachers serve.
Data Collection
The design of a research study defines the systematic measurement, description, and
assessment of the sample (Pallant, 2013). In the current study, preschool teachers serving in
urban, public elementary schools were the sample of the study; therefore, data collection focused
on 50 full-time teachers. According to Creswell (2014), it is important for researchers of social
science to follow the six steps, including the identification of the research problem, the review of
the literature, the clarification of the research’s purpose, the collection of data, the analysis and
interpretation of the data, and the evaluation of the research. Shadowing the six steps, the
current study employed and included quantitative data collection from a survey that applies
electronic questionnaires.
For the quantitative part of the study, an invitation with a link to the instrument was
emailed to participants in southern California districts. In order to achieve a high response rate, a
42
contributing factor to reliable results (Creswell, 2014), follow-up procedures included email
reminders as needed.
The nature of the qualitative part aligned with Creswell (2014) criteria that explained the
researcher as a “key instrument” that gathers data through interviews in the field with subjects
who experience the issue under investigation. This is especially important and relevant since the
researcher in the entire process of qualitative approach focused on learning the outlook that the
participants hold. According to Creswell, qualitative researchers must place special emphasis on
developing a multifaceted picture of the problem under consideration. As such, the researcher of
the current study personally interviewed the teachers, gleaning multiple perspectives and
identifying possible factors in teaching mathematics in preschool classrooms. An electronic
voice recorder was used for recording the process to make analogue recordings more
comfortable and to allow the researcher to concentrate on the participants during the interviews
rather than transcribing.
Data Analysis
Statistics for Process of Social Sciences (SPSS) software was used to address the
descriptive research questions. According to Salkind (2014), descriptive analysis is an
appropriate approach to outline the basic features of the data in a quantitative study since it
provides clear summaries about the samples and measures. Teachers had to spend approximately
15 minutes reading the cover letter and completing the questions, questions that included simple
instructions that were designed to provide a range of information on various aspects important to
the process of teaching mathematics in preschool classrooms.
The content analysis for the information collected via qualitative data collection included
summarizing, highlighting, and coding to make sense of the data collected.
43
CHAPTER FOUR: DATA ANALYSIS
Introduction
This chapter is a presentation of the findings from a mixed study comprised of a
quantitative survey completed by 32 preschool teachers serving in public schools. The results
included the response rates of the online surveys, the respondents’ demographic information, the
research findings from compiled and analyzed data, and an analysis of the qualitative data
collected from one-on-one interviews with five teachers who are serving in preschool and
prekindergarten transition classrooms.
Numerous research studies showed that mathematics education for preschool children
builds a foundation for later academic achievement and excellence in science, technology,
engineering, and math (Campbell, Ramey, Pungello, Sparling, & Miller-Johnson, 2002; National
Research Council & Mathematics Learning Study Committee (NRC & MLSC, 2001); Peisner-
Feinberg et al., 2000; Schweinhart & Weikart, 1997). The research documented the
understanding of teachers’ beliefs assists early childhood education and influences the reform
movement in mathematics (Handal & Herrington, 2003). However, there is limited
understanding of what preschool mathematics education entails and what is required to
successfully implement it.
Purpose of the Study
The purpose of this study was to provide insight into the four central beliefs of teachers in
order to understand and improve early-childhood mathematics’ education in California public
preschools. In the current study, preschool teachers’ beliefs regarding the instructional practices
of mathematics are explored in the areas of (a) teachers’ perceived values on teaching
mathematical concepts, (b) teachers’ self-efficacy beliefs in helping preschoolers learn
44
mathematics, (c) teachers’ knowledge of the mathematical development of their students, and
(d) teachers’ beliefs regarding the frequency of implementation of mathematical concepts in the
preschool classroom.
Data collected through electronic surveys and interviews verify the research findings
asserted by the researcher. The following research questions were addressed:
1. What are public preschool teachers’ perceived values about teaching mathematics to
preschoolers?
2. How confident are urban public preschool teachers in helping preschoolers learn
mathematics?
3. What is the knowledge level of public preschool teachers regarding the mathematical
development of their students?
4. With what frequency do public preschool teachers believe they incorporate mathematical
concepts in class?
Quantitative Survey Response Rate
Based upon the selection criteria postulated in this study, 62 preschool teachers serving
public preschools qualified to participate in the quantitative data collection. The survey report
from Questionpro shows that 54 individuals started and 32 fully completed the Teachers’
Perceived Values Survey. Twenty-two participants did not fully address the questions.
Consequently, the researcher had to make a decision regarding how to handle the missing data.
For the purpose of conducting this study, the researcher used listwise deletion for handling the
missing data. According to Vogt and Johnson (2015) listwise deletion is a statistical method for
handling missing data in which an entire record is excluded from analysis if any single value is
45
missing. Table 1 illustrates the number of participants in the Teachers’ Perceived Values
Survey.
Table 1
Quantitative Survey Response Rate
Measure Number Invited
to Participate
Number
Participated
%
Participated
Teachers 62 32 51
Quantitative Demographic Data
Demographic data from the participants were collected in the survey, such as age,
number of years teaching, and gender. The data from the quantitative part of the study revealed
that all participants were female teachers, which was not a surprise. Indeed, the number of early
childhood educators who responded to the survey were female, and the presence of a significant
proportion of women teachers, particularly in early childhood education, is a long-standing
phenomenon that characterizes the schooling culture of the educational system with a gender
imbalance in favor of women (Decker et al., 2009).
The U. S. Department of Education (2016) reported 44% of early childhood teachers are
under 40 years old. The reported ages of the respondents, the majority of which were under 40,
mirrored this national trend. Table 2 presents the age range of the participants.
Statistical reports in 2011-12 demonstrated that 56% of preschool teachers have a
master’s or higher degree (U. S. Department of Education, 2016). These figures are not in
keeping with national trends for preschool teachers and the current study. Of the study’s 32
respondents surveyed, 21 individuals (65.6%) hold a four-year college degree. The survey also
46
indicated that seven of the respondents’ (or 21.9%) highest educational achievement is a master’s
degree. Four respondents (12.5%) completed a two-year college education.
Table 2
Age Range of the Participants
Age Frequency Valid % Cumulative %
Under 25 1 3.1 3.1
25-29 7 21.9 25.1
30-39 12 37.5 62.5
40-49 7 21.9 84.4
50-59 4 12.5 96.9
60 + 1 3.1 100.0
The increasing number of years in which teachers have held their positions demonstrated
a corresponding increase in their validity, not only regarding their responses to classroom
challenges, but also positively affecting their students’ achievements (Friedrichsen, Abell,
Pareja, Brown, Lankford, & Volkmann, 2009). Thus, the researcher looked for those who had
been in their current position for a significant amount of time. In regards to teachers’ work
experiences, the national average of work experience is about one to five years
(U. S. Department of Education, 2016) which is supported by the statistical outcomes of the
current survey that clearly illustrated that 34.4% of the participants have three to five years of
experience.
Data analysis of the current study delineated that respondents with 16 to 20 years of
teaching experience as well as respondents in their first year of their teaching position did not
have an education level lower than a two-year college degree. The participants with 16 to 20
years of teaching experience and participants in their first year of teaching reported the highest
47
number of master’s degree holders. This aligns with research that found longer retention of
teaching positions to be significantly associated with having health insurance, disability
insurance, and pension coverage, all of which is attainable with higher educational degrees
(Holochwost, DeMott, Buell, Yannetta & Amsden, 2009). Table 3 and Figure 1 provide a
visualization of the participants’ work experiences. Figure 2 presents detailed results regarding
the association between work experience and teachers’ education levels.
Table 3
Work Experience as a Teacher
Years of Work
Experience
Frequency
Valid % Cumulative %
This is my first year
2 6.3 6.3
1-2 years
3 9.4 15.6
3-5 years
11 34.3 50.3
6-10 years
2 6.3 56.3
11-15 years
5 15.6 71.9
16-20 years 9 28.1 100.0
48
Figure 1: Highest Degree of the Respondents’ Work Experience
49
Figure 2: Highest Degree of the Respondents and Work Experiences
Qualitative Demographic Data
To identify aspects related to mathematical education in preschool classrooms more
deeply, it was necessary to approach it from different vantage points; therefore, an invitation was
sent to preschool teachers serving in public preschools. Five teachers who ensured the
representation of the entire population were selected for in-depth interviews. Table 4 details the
demographic profile of each teacher who participated in a qualitative interview.
50
Table 4
Demographic Data of Participants of the One-on-One Interviews
Teachers Gender Age Education Work Experience
Teacher A
Female 30-39 BA & C* 5 years
Teacher B
Female 40-49 MA 18 years
Teacher C
Female 50-59 MA 16 years
Teacher D
Female 40-49 MA & MS 25 years
Teacher E Female 50-59 ED 30 years
* Note: Also, a one-year MA w/credential teaching
Results for Research Question 1
What are public preschool teachers’ perceived values about teaching mathematics to
preschoolers?
Research question 1 produced results underscoring that all of the participants valued the
mathematical concepts taught in a preschool classroom and believed that initiating such learning
is particularly beneficial for daily activities, but they believed prekindergarten students are not
ready to be taught mathematical concepts.
The result for perceived values of teaching mathematics in a preschool classroom does
not align with the literature review. Lobman, Ryan, and McLaughlin (2005) also concluded
from eight focus group meetings with administrators, teachers, and professional development
providers in which all failed to discuss mathematics when they spontaneously reviewed the
relevant subject matters for preschoolers. Additionally, the Blevins-Knabe, Austin, Musun,
Eddy, and Jones (2000) study regarding early childhood teachers classified mathematics as less
important than literacy.
51
None of the teachers who participated in the current survey believed that prekindergarten
students are ready to learn mathematical concepts in preschool. While 50% of participants of the
current study believed that math is abstract for preschoolers, 59% of participants believed that
children could learn mathematical concepts without the help of teachers. In high-quality
mathematics’ education for 3 to 6-year-old children, educators are responsible for deliberately
providing a range of age-appropriate experiences and high instructional teaching (National
Association for the Education of Young Children and National Council of Teachers of
Mathematics, 2002, p. 4). This raises inquisitiveness for further investigations through
qualitative data collection regarding the approaches employed by the teachers who agreed with
the belief that children can learn mathematical concepts without the help of the teachers. What
are the possible intentional and planned instructions that provide learning mathematical concepts
for preschoolers without the help of teachers?
Table 5
Perceived Values on Teaching Mathematical Concepts (N=32)
Questions % SD* % SWD* % SA* % SWA* % A*
Mathematics
is Significant
38.7 22.6 38.7
Thinking
Through
3.1 3.1 6.3 87.5
Math without
Help
6.3 34.4 3.1 40.6 15.6
Mathematics
is Abstract
25.0 37.5 15.6 18.8 3.1
Preschoolers
Ready
94.4 5.6
52
Table 5 (Cont’d.)
Questions % SD* % SWD* % SA* % SWA* % A*
Math is Vital
40.6 9.4 50.0
Math as a
Daily Activity
43.8 3.1 53.1
Note*: SD = Strongly Disagree, SWD = Somewhat Disagree, SA = Strongly Agree, SWA = Somewhat Agree, and
A = Agree.
The results from quantitative data also supported that, although teachers value the
learning of mathematics, the implication of mathematics learning depends on their priorities.
Task value, or believing in the importance of a given task, is more than the conception of what is
desirable within every individual (Schunk et al., 2014). Valuing the teaching of mathematical
concepts guides cognition, motivation, and behavior navigates teachers’ instructional choices,
persistence, and actual performances (Ball, 1993; Cobb, Wood, Yackel, & McNeal, 1993; Eccles
& Wigfield, 2002; Fennema, Franke, Carpenter, & Carey, 1993; Thompson, 1992; Wood, Cobb,
& Yackel, 1991). Placing a special emphasis on teaching mathematical concepts influences
teacher engagement in using mathematical strategies that enhance student enquiry skills and
rational thinking by modeling as well as actively engaging students in activities that will assist
them to construct mathematical concepts, (Ball, 1993; Cobb et al., 1993; Fennema et al., 1993;
Lampert, 1991; Thompson, 1992; Wood et al., 1991). Thus, the coding of teachers’ values
focused on the importance of the subject matter, motivation to engage children, and stimulus of
modeling thinking.
The three codings of measuring the strength of the teachers’ agreement regarding the
importance of teaching mathematics to preschoolers, along with descriptions and examples, are
listed in Table 6.
53
Table 6
Value Dimensions
Coding Meaning Example of Teachers Statements
Math as Subject Matter Understanding Why I know that the basic math skills
Mathematics Matters teachers provide in early childhood
set the building blocks for their
entire academic careers.
Modeling Thinking Teaching Rational Teachers should guide children in
Thinking seeing the connection of ideas with
mathematics as well as knowledge
throughout the day and problem-
solving thinking.
Engaging Children Constructing Math There are many ways that children
Concepts could learn math themselves, for
instance blocks, time, or measuring
in the science area.
______________________________________________________________________________
The results for the question regarding the perceived values, “What are public preschool
teachers’ perceived values about teaching mathematics to preschoolers?” show that all five
teachers value mathematical concepts in preschool classrooms as they pertain to the role of
mathematics in early childhood education and their part as educators in presenting mathematics
to preschoolers. For instance, Teacher B affirmed:
I understand how important mathematics is in education. I know that the basic
math skills teachers provide in early childhood education set the building blocks
for their entire academic careers. Without learning math skills, like counting,
math concepts, and like adding, children are not prepared to move into secondary
school. I understand that math plays an important role in children’s future and as
one of predictive of successive academic outcomes, but math is not our priority.
Previous qualitative studies showed that preschool teachers are not aware of the current
rigorous demand on early childhood math education, and they explicitly agreed that
54
young children should be engaged in mathematical learning. However, the implication of
mathematics learning depends on their priorities (Lee, & Ginsburg, 2007)
Results for Research Question 2
How confident are urban public preschool teachers in helping preschoolers learn
mathematics?
This study’s second research question sought to determine the nature of preschool
teachers’ confidence in teaching mathematical concepts to preschoolers and teachers’ judgments
about whether they have the capability to perform a particular activity. The results show that,
although teachers express confidence in their teaching, their confidence does not stand alone.
Teachers explained their needs for resources and support to enhance children’s engagement and
an enlightened effect that leads to student success. The statistical data from the range of 18.8%
to 56.3% indicated that 39% of the respondents on average are confident in teaching
mathematical concepts to preschoolers, and 34.1% of participants are not confident in terms of
goal setting.
The results of the current study, which examined the teachers’ self-efficacy, support
previous research that suggested some of the more powerful influences on the development of
teacher efficacy include mastery experiences during student-teaching and the induction year
(Hoy, 2000). In the current study, 27 teachers (84.4% of the participants) had teaching
experience between 3-20 years. Table 7 outlines the results of the factor analysis in terms of the
self-efficacy beliefs of respondents.
55
Table 7
Results of Self-efficacy of Preschool Teachers in Helping Preschoolers Learn Mathematics
Questions % SD* % SWD* % SA* % SWA* % A*
Confident in
Teaching
Math
48.4 9.7 41.9
Confident in
Setting Goals
3.1 3.1 21.9 6.3 65.6
Confident in
Assessment
6.3 31.3 6.3 56.1
Confident in
Everyday
Activities
46.9 3.1 50.0
Note*: SD = Strongly Disagree, SWD = Somewhat Disagree, SA = Strongly Agree, SWA = Somewhat Agree, and
A = Agree.
Teachers’ perceived capabilities as well as their judgments of their teaching abilities
influence their performance in a designated level (Bandura, 1993, 1997), central motivational
variables in social cognitive theory that factor into their professional accomplishments and
planning for the future, especially when they encounter difficulties (Zee & Koomen, 2016). The
motivational impact of self-efficacy can lead to outstanding performance (Schunk et al., 2014).
According to Bandura (1982), when self-efficacy is high, individuals will actively engage in
assignments that foster the development of their skills with exceptional outcomes. Incorporating
Bandura’s (1995) behavioral and affective reactions of different levels of self-efficacy and
outcomes provides a systematic assessment for evaluating the participants’ self-efficacy. Table 8
depicts the coding used to assess teachers’ self-efficacy.
56
Table 8
Assessing Self-Efficacy
Coding Behavior/ Affect Example of Teachers’ Statement
High Self-Efficacy Persistent High-Cognitive
Enjoyment
Teachers must encourage
children to communicate, explain
their thinking, as well as interact
with important mathematics in a
deep and sustained way.
Low Self-Efficacy Apathy, Withdrawal, Self-
Devaluation
The results demonstrated that participants generally show confidence in their teaching.
For example, Teacher A stated:
I am confident in teaching any subjects since I love teaching, but I wish I had
some type of training, like resources, workshops, educational materials.
Providing professional development in mathematics is not only about training.
Workshops also have a positive effect on teachers’ instructional practices and not
only give competence in mathematics but they also increase enjoyment of
teaching too. Workshops on activities, like geometry and graphing, could
increase children’s time engagement in learning mathematics.”
The findings also showed that teachers with more experience are increasingly confident.
Teacher B explained,
As far as limitation, I do not focus on limitation. I never had any training for teaching
math in my life. I wish I had. But I focus on how I can help children. I am confident in
teaching math. I have learned through experience that problem-solving thinking should
be actively introduced to preschoolers through a variety of appropriate experiences.”
Such insight aligns with the literature review, positing that teachers’ years of experiences is an
important factor in their self-efficacy level. Specifically, teachers who have 13 or more years of
experience exhibit stronger self-efficacy (Takunyaci & Takunyaci, 2014), and show higher levels
of planning and adopting new ideas (Jerald, 2007). Additionally, research identified a second
57
factor, often called general teaching of efficacy, which becomes obvious in teachers that strongly
believe in their ability to reach difficult children (Hoy, 2000).
Results for Research Question 3
What is the knowledge level of public preschool teachers regarding the mathematical
development of their students?
The results for research question 3 demonstrated that while all of the teachers agreed with
children’s ability to learn the numbering of objects and measuring lengths and weights, 12.2% of
teachers believed that prekindergarten students are incapable of learning to divide 12 cookies
among two people and learn to compare shapes.
Data from the survey shows that 12.2% of teachers believed that prekindergarten students
are incapable of learning to divide 12 cookies among two people and learn to compare shapes.
Table 9
Results from Knowledge of Children’s Mathematical Development
Questions % SD* % SWD* % SA* % SWA* % A*
The Number of
Objects
38.7 12.9 48.4
Dividing 12 Fish
Crackers
3.1 9.4 12.5 34.4 40.6
Measuring
Lengths/Weights
48.4 12.9 38.7
Comparing
Shapes
6.3 28.1 9.4 56.2
Note*: SD = Strongly Disagree, SWD = Somewhat Disagree, SA = Strongly Agree, SWA = Somewhat Agree, and
A = Agree.
58
Over the last decade, child development scientists and psychologists studied in-depth
children’s mathematical development and explicitly delineated facts and domains about the
developmental progression of children’s mathematical learning (Baroody et al., 2006; Sarama &
Clements, 2009b). Teacher’s knowledge of these domains, or understanding what preschoolers
are capable of learning, impacts the pedagogy needed to support mathematical constructions and
goals that young children develop as a foundation for later academic achievement (Duncan et al.,
2007; NAEYC & NCTM, 2002; NRC & MLSC, 2001; Romano, Babchishin, Pagani, & Kohen,
2010). The mathematical domain covered for coding the current study is derived from the most
important themes and standards in preschool mathematics that help teachers in the
implementation of developmentally challenging and attainable mathematical goals (Clements,
2004). Furthermore, such themes are representative of the developmental progression by experts
in the field of cognitive development (Baroody et al., 2006; Clements & Sarama, 2009).
Table 10 represents the domains and operations included in this study along with descriptions
and examples.
Table 10
Knowledge of Mathematical Development
Coding Description Example of Teachers’
Statement
Verbal Counting Articulating the Number They began to understand that
Sequence cardinal numbers, for example,
one, two, and three, refer to quantity
and ordinal numbers.
Counting/Numerosity Determining Numerosity Children are capable of learning to
count and sort. This is the first step.
59
Table 10 (Cont’d.)
Coding Description Example of Teachers’
Statement
Addition and Subtraction Adding or Taking Away They practice addition and
subtraction at playtime. ‘I have three
crayons; you have two. Do you want
me to give you one? Now, you have
two, and I have two crayons.’
Division Fair Sharing They could learn to divide a set of
items in a primary level, like ‘one for
me and one for you.’
Measuring/Waiting Validity of Length or When they have snacks, for example,
Weight example, celery, they develop
informal measurement systems that
help them compare the length of
celery. ‘Mine is longer than yours.’
______________________________________________________________________________
The results of the qualitative data also support that participants possess the knowledge of
mathematical development of their preschoolers. Teacher B explained,
Children learn numbers and basic numbers. Children develop other mathematical
concepts informally through discovery. For example, children are naturally
interested in the shapes around them. They observe and talk about the shapes of
signs, buildings, and other objects.
Teacher B, who also clarifies her knowledge of the mathematical development of preschoolers,
noted,
Let’s say preschoolers are capable of learning problem-solving. Mathematic
concepts is a broad [term] and could entail many models. Yes, children are
capable of learning to count, sort, and measure. This is the first step. They can
learn to add and take away items, too.
It is important to note that there is no previous qualitative study on teachers’ knowledge of the
mathematical development of preschool children.
60
Results for Research Question 4
With what frequency do public preschool teachers believe they incorporate mathematical
concepts in class?
The statistical data and one-on-one interviews for Question 4 demonstrated that preschool
teachers give high priority to social and emotional development. The majority of teachers
surveyed (72%) incorporated mathematics in the prekindergarten curriculum; 72% of teachers
interviewed believed that a higher priority is given daily to social and emotional learning as well
as reading domains than the teaching of mathematics, however, 28% of participants agreed with
incorporating mathematics in the prekindergarten curriculum but not every day.
The research supported the point that early mathematical knowledge develops primarily
in social settings with mathematics content, concrete activities, and scaffolding by a more
competent adult, typically the teacher (Decker et al., 2009; Starkey & Cooper, 1995), on a
regular base. A mathematically competent person is more likely to lead the child to construct
more complex mathematical procedures or abstract mathematical representations than the child
can learn alone or with the child’s peers (Radziszewska & Rogoff, 1991). It is clear that
conceptually grounded learning for each child occurs within the zone of proximal development
and that teachers need training to scaffold children well in this zone (Decker et al., 2009).
Moreover, the curriculum activities across the school year should coincide with the teaching plan
and goals.
To explore the frequency of participants’ incorporating mathematical concepts in
preschool classrooms, the coding focused on goal-setting. Schunk et al. (2014) stated goals that
refer to establishing quantitative or qualitative standards of performance influence teachers’
expanded efforts and persistent behaviors. According to Clark and Estes (2008), it is necessary
61
to reduce challenges by focusing on creating clear goals, breaking tasks into manageable parts,
providing procedural advice, creating success to ability, monitoring closely, and giving feedback,
all of which are crucial to addressing high-quality education. Thus, the coding for assessing the
frequency of teachers’ instructional practices focused on daily goals for formal and informal
instruction, as depicted in Table 11.
Table 11
Measuring Instructional Practice Frequency
______________________________________________________________________________
Coding Description Example of Teacher Statement
______________________________________________________________________________
Daily goals for informal Plans for facilitating We practice math every day, like
instruction in math activities for informal counting 1-10 during washing hands.
acquisition of math
skills
Daily goals for formal Plans for facilitating Today, we had a craft activity that
instruction activities for formal children made and accipiter with
acquisition of math circles.
skills
______________________________________________________________________________
The results from teachers’ interviews also showed that although teachers recognize the
importance of learning mathematical concepts in terms of children’s academic achievement, and
endorse learning math concepts in preschool classrooms, they do not rate mathematics as a high
priority and show greater emphasis on using direct, highly-structured teaching approaches on a
daily basis.
Teacher A explained why she prioritizes other developmental goals over mathematics
learning,
Math is not my priority. The priority is social, emotional development. I believe
we have behavioral and socializing problems that should be addressed. Also,
62
social emotional learning is a valuable skillset that helps with social and
interpersonal skills and cognitive regulation, too. Language is another area that I,
as a preschool teacher, work on continuously.
Such results align with the previous qualitative research, concluding that teachers
spend less classroom time on mathematics (Early et al., 2007; Pianta & La Paro, 2003).
Children’s early mathematical experiences play a significant role in the development of
their informal knowledge of mathematics and serve as a foundation for their cognitive
development. In this descriptive study, the teachers’ pedagogical beliefs regarding
incorporating mathematics in everyday activities, which answers the fourth research
question, parallels the outcome of previous studies in which preschool and kindergarten
educators belief that to be ready for academic success in formal school, prekindergarten
children need to be healthy and socially and emotionally competent. Furthermore, they
hold that the acquisition of basic mathematics knowledge and skills is not significantly
important (Lin, Lawrence, & Gorrell, 2003; Piotrkowski, Botsko, & Matthews, 2001).
Summary of the Findings from Quantitative and Qualitative Data
Results for Research Question 1
What are public preschool teachers’ perceived values about teaching mathematics to
preschoolers?
The data analysis demonstrated that all participants value the mathematical concepts
taught in a preschool classroom and believe in fostering preschool children’s mathematical
knowledge. The quantitative data results showed that 100% of the participants recognized the
importance of learning mathematical concepts in preschool classrooms as a significant subject.
Interview data also supported the point that preschool teachers believed learning math skills at a
63
young age is invaluable for children’s development and later academic success. Teacher C, for
instance, opined,
Learning math skills at a young age is invaluable for the development and growth
of children in our schools. Math skills taught in early childhood education are the
foundation children need to succeed in kindergarten, school, and beyond.
This result is inconsistent with the literature review, which noted that preschool teachers’
beliefs regarding the teaching of mathematics have been only measured across early childhood
classrooms through observation and specific intervention (Copley, 2004; Ginsburg, Kaplan et al.,
2006; Sarama, DiBiase, Clements, & Spitler, 2004). These observations and studies postulated
that early childhood educators believe preschoolers need to be healthy, socially and emotionally
competent, but teaching math is not essential (Lin et al., 2003; Piotrkowski et al., 2001).
Although teachers expressed their belief that early mathematics education is important
for preschool children, the majority of all teachers who participated in the survey believed that
preschool children are not ready for learning math.
While 50% believed that math is too abstract for prekindergarten children, 59%
expressed that children could learn math without the help of their teachers. Interviews with
teachers also showed three out of five teachers described their beliefs on pedagogical practice
and learning mathematics concepts without the help of teachers. According to Teacher A:
Children learn numbers and basic numbers. Children develop other mathematical
concepts informally through discovery. For example, children are naturally
interested in the shapes around them. They observe and talk about the shapes of
signs, buildings, and other objects.
Such points corresponded with the previous studies that investigated the teaching
practices of mathematics by preschool teachers, with a rationale that preschool teachers
empathically believe informal teaching is superior to formal teaching either for different reasons
64
or because they believe that this is the only way preschoolers learn (Graham, Nash, & Paul,
1997).
Results for Research Question 2
How confident are urban public preschool teachers in helping preschoolers learn
mathematics?
Seventy-two percent of teachers expressed confidence in teaching mathematical concepts
while 6.2% of teachers reported low confidence in setting goals in the prekindergarten
classroom. The results from the one-on-one interviews with prekindergarten teachers also
confirmed that teachers show confidence in their teaching ability. However, the confidence does
not stand alone. Teachers explain their needs for resources and support to enhance children’s
engagement and an enlightened effect that leads to students’ success. Teachers’ statements
showed that their confidence is not driven by academic skills in mathematics; it is established
either by experience or love of teaching. In this regard, Teacher C, for example, explained,
I am a very confident teacher in my knowledge and my ability to deliver
information to children. However, I strongly believe to implement an effective
mathematical knowledge, I need specific methods and curricula to help remedy
this problem.
Such an outlook corresponded with the literature review that concluded teachers who
believe in their motivation and personal ability generally possess high self-efficacy (Hoy, 2000).
The teachers’ lack of confidence in setting goals for teaching mathematics in preschool
classrooms is also similar to the previous studies that showed early childhood teachers found
setting goals with the aim of mathematical proficiency uncomfortable and challenging (Copley,
2004).
65
Results for Research Question 3
What is the knowledge level of public preschool teachers regarding the mathematical
development of their students?
The majority of the surveyed participants understood that prekindergarten students have a
normal cognitive capability of concepts development, problem-solving, and acquisition of
particular mathematical skills and concepts. The results from the survey also delineated that
12.2% of teachers disagreed with the idea that prekindergarten students with normal cognitive
capability of concept development can learn to divide 12 crackers between two individuals.
The results from the one-on-one interviews also demonstrated that four out of five
teachers supported children’s abilities in verbal counting, determining numerosity, addition and
subtraction, and measuring. According to Teacher A,
They observe and talk about the shapes of signs, buildings, and other objects.
Also, when children have snacks, for example, celery, they may develop an
informal measurement system that helps them compare the length of celery
pieces.
Although the studies covering teachers’ knowledge of the mathematical development of children
helped to contribute to the literature on effective practices (Clements et al., 2003), the majority of
researchers investigating teachers’ qualifications focused on the content knowledge of teachers,
not their knowledge of children’s development. Platas’ (2013) quantitative study on the
measurement of childhood teachers’ knowledge of early mathematical development, the only
study in this area, with 346 pre and in-service preschool teachers, showed preschool teacher
classroom experience and completion of a course in mathematical development form their
knowledge of mathematical development of their students.
66
Results for Research Question 4
With what frequency do public preschool teachers believe they incorporate mathematical
concepts in class?
The results revealed that the majority of teachers surveyed, 72%, incorporated
mathematics in the prekindergarten curriculum, and 72% of interviewed teachers placed a higher
priority on social and emotional needs and reading domains in their classrooms than on
intellectual or academic activities related to mathematical learning. Furthermore, 28% of the
teachers incorporated mathematical concepts in learning activities, such as in art and dramatic
play, but not on a daily basis. The one-on-one interviews also affirmed that all teachers include
mathematics learning in preschool curricula. Teacher C, for instance, stated
Children learn math through all kinds of simple hands-on activities and any group
art and dramatic play. I also use small groups for exploring shapes and building
patterns. I ensure that all children leave the preschool classroom with a rich
foundation in preparation for kindergarten. First and most importantly, parents
should work with their children in social and self-regulation behaviors. Then, I
wish for resources that guide me for a special curriculum.
Teacher A explained why she prioritizes other developmental goals over mathematics learning,
Math is not my priority. The priority is social, emotional development. I believe
we have behavioral and socializing problems that should be addressed. Also,
social emotional learning is a valuable skillset that helps with social and
interpersonal skills and cognitive regulation, too. Language is another area that I,
as a preschool teacher, work on continuously.
This parallels the previous research that showed preschool teachers’ instruction and
techniques assist children in primarily learning and focusing on social and emotional
development and that teachers spend less time on mathematics (Early et al., 2007; Lee &
Ginsburg, 2007; Pianta & La Paro, 2003).
67
Discussion
The study presented in this chapter provided an invaluable window onto mathematics
teaching in the preschool classroom, and addresses a gap in the literature on teachers’ values on
teaching mathematics to prekindergarten children and teachers’ knowledge of mathematical
development of preschoolers. Limited studies are measured only by observing preschool
teachers’ beliefs about teaching mathematics to preschoolers. Thus, it is important to explore the
possible explanations for the views teachers hold that are preliminary or different from previous
studies.
Possible explanation for teachers’ beliefs about teaching mathematics to
preschoolers. The first interview question asked, “What are public preschool teachers’ beliefs
about teaching mathematics to preschoolers in general?” and the results are clear-cut. Preschool
teachers value the importance of mathematics for preschoolers while they hold different views
for preschool education. The teachers tended to agree that embedding mathematics education is
relevant to individual development of children, but they were concerned about their students’
social, emotional, and undeveloped readiness.
Several factors affect this view, including the involvement of teachers in government-
funded preschools that are responsive to the standard-based accountability movement and have
now actively focused on literacy and mathematics (Neuman & Rockes, 2005; The White House,
2003). For instance, Head Start outcome reports include literacy and mathematic achievement
(Head Start Bureau, 2001). Correspondingly, some publicly-funded preschools have adopted
curricula that enhance mathematics to meet the new standards (Schweinhart, 2003). Thus,
teachers, who value mathematics’ education in preschool, work in the context of a new
framework and standards that influence their traditional beliefs. They adopt a contemporary
view and internalize the caution and warning of the importance of mathematics.
68
The second possibility is that the level of teacher education might influence their beliefs.
In fact, the majority of participants (87.5%) in the survey hold bachelor and master degrees, and
all teachers who volunteered for the one-on-one interviews have master degrees (see Table 4).
Doubtless, teachers’ knowledge has a profound influence on constructing their values and
pedagogical beliefs (Fang, 1996; Villegas-Reimers, 2003).
One factor involving teachers’ concerns about the readiness of their students can be
related to the need of children from a low socio-economic background, a background that often
negatively affects relatively poor mathematics and literacy achievement even during preschool
and kindergarten years (Denton & West, 2002; Fry, R., 2007; Lee & Burkam, 2002).
Learning occurs naturally when all students are fluent in the language of instruction,
whether English or otherwise (Garrison & Kerper Mora, 1999). One factor involves teachers’
concerns about the preschoolers’ readiness, which can partially be associated with the challenge
of providing new concepts in a language that all students can understand, an issue in California
since the majority of classrooms include students at various levels of English proficiency (García
& Frede, 2010; McCardle, Mele-McCarthy, Cutting, Leos, & D’Emilio, 2005). In fact, Teacher
D expressed a concern about ELL students who not only create challenges for preschool teachers
when covering mathematical concepts in a comprehensible language but also prompt teachers to
sometimes lower expectations that deny equal access to mathematical skills and reasoning.
While they value teaching mathematics to preschoolers, teachers’ concerns include one
possible factor that involves the preschool children’s ability to self-regulate their behavior,
emotions, and attention. Children indeed exhibit individual differences in their ability to self-
regulate (Blair, 2002). The research showed that school-readiness is supported by a range of
skills that fall under the rubric of “self-regulation” (Blair, 2003; Diener & Kim, 2004; Duncan et
69
al., 2007; Eisenberg, Fabes, Guthrie, & Reiser, 2000; Raver, 2002), such as a preschooler’s
ability to manage her emotions when facing frustrating or distressing situations (Schultz, Izard,
Ackerman, & Youngstrom, 2001), and process new information and develop learning strategies.
These issues have been documented as connected to their self-regulation of attention (Blair,
2002; Fantuzzo, Perry, & McDermott, 2004; Howse, Lange, Farran, & Boyles, 2003;
McClelland, Morrison, & Holmes, 2000; Zelazo, Müller, Frye, & Marcovitch, 2003). In fact, in
their one-on-one interviews Teachers A, B, and C expressed concern over children’s ability to
manage and modulate emotions, attention, and behavior in their preschool classrooms.
According to Teacher C,
I understand and believe in teaching mathematics. But the challenge is, first and
most importantly, children come to school showing different social, emotional,
and behavioral regulation levels. Some come with undeveloped self-control
associating with impulsive, emotion, attention, and behavior regulatory. I think
parents have power to help children learn to manage their behaviors. These kids
come from different socioeconomic backgrounds.
Mathematics is abstract. There are several reasons that prekindergarten teachers think
mathematics is abstract and are not motivated to focus on teaching math. One explanation is
related to the type of training they received, which historically, placed a strong emphasis on
social, emotional development. In particular, researchers documented that such belief is rooted
in the misconception that children cognitively are not ready to learn math concepts (Clements &
Sarama, 2007). This idea may relate to teachers’ knowledge based on the Piaget theory that
children ages 2-6 are in the stage of preoperational thinking and are not capable of learning
abstract concepts (Ginsburg, Pappas, & Seo, 2001; Lee & Ginsburg, 2007). Also, the instruction
of early childhood educators regarding mathematics instruction is traditionally limited to rote
learning of procedures and arriving at the correct answers (Pianta et al., 2005). These teachers
believed that mathematics is too difficult and instructions are not developmentally appropriate
70
for preschoolers. Little attention is given to problem-solving procedures that are associated with
the teachers’ assisting students to construct a deep understanding of mathematical concepts.
Possible explanation for the teachers’ high self-efficacy report. Much empirical
research has focused on preschool teachers’ self-efficacy. However, no studies examined the
teachers’ self-efficacy regarding the teaching of mathematics to preschoolers. As described in
the results section, the majority of teachers reported a high self-efficacy level in their ability to
teach mathematics to their students. Hoy (2000) stated although teachers’ high self-efficacy can
be rooted in their past successes or failures in teaching children, other factors can also have an
impact, such as the school’s socioeconomic level, student achievement levels, and mastery
experiences during student-teaching and the induction year. Another possible explanation is that
collective efficacy beliefs also shape the normative environment of the school, and influence
both teacher’s behavior and confidence (Hoy, Sweetland, & Smith, 2002). There is a possibility
that participants of the current study developed a complementary construct known as the
collective teacher self-efficacy, which Goddard, Hoy, and Hoy (2000) described as “the
perceptions of teachers in a school that the efforts of the faculty as a whole will have a positive
effect on students.” Collective efficacy leads teachers to be more persistent in their teaching
efforts and develop confidence in their ability (Hoy et al., 2002; Pfaff, 2000).
Possible explanation on teachers’ knowledge of mathematical development of
preschoolers. One possible explanation for largely reporting knowledge of the mathematical
development of preschoolers can be connected to the experiences of teachers. The only existing
study on the measurement of early childhood teachers’ knowledge of mathematical development
shows that their preschool teacher classroom experiences and the completion of a course in
mathematical development form their knowledge of the mathematical development of their
71
students (Platas, 2013). Only two participants of the current study are in their second year of
their teaching practice.
The current study does not exam teachers’ professional training in teaching mathematics,
but there is also a possibility that the teachers who participated in the survey received some type
of training in teaching mathematics. None who participated in one-on-one interviews had any
training or completed a course in mathematical development. In fact, the interviewed teachers
expressed a need for training in teaching mathematics in early childhood classrooms. As such,
studies focusing on preschool teachers’ training on mathematics instruction show that
approximately 80% of preschool to third grade preparation programs in New Jersey’s four-year
colleges offer coursework that focused on literacy. In contrast, only 16% offered coursework
that emphasized mathematics, 74% included mathematics education only as a part of a
comprehensive early childhood education course, and 10% did not offer mathematics education
at all (Lobman et al., 2005).
Possible explanations for teachers’ beliefs on incorporating mathematical concepts
in preschool classrooms. One explanation for teachers’ beliefs against incorporating
mathematics’ concepts in the prekindergarten curriculum everyday is that teachers may not be
prepared or trained to adequately teach mathematics to children. A current teacher review of
teacher preparation concluded that math coursework pedagogy in teacher preparation is missing
(Early et al., 2007). Some of the participants completed their university education at a time
when mathematics was not emphasized, and the current U. S. Department of Education was not
yet merged. A second possible explanation is that the teachers did not receive sufficient support
to implement mathematics effectively (Early et al., 2007). Early childhood professionals need to
understand that early childhood teachers do not receive adequate support in terms of the
72
teachers’ training in mathematics instruction, the children’s cognitive architecture, learning
processes, curricula, methods of assessment, and pedagogy, especially as they related to teaching
a highly diverse population (Barnett, 2003; Cgohchran-Smith, Cgohchran-Smith, & Zeichner,
2005).
Conclusion
Collecting, analyzing, and integrating quantitative data, including a survey and
qualitative data, and involving one-on-one interviews, all showed that preschool teachers value
teaching and learning mathematics concepts but are concerned about the children’s readiness.
The results show that while preschool teachers demonstrate high self-efficacy, some are not
confident in setting goals to pursue teaching mathematics to preschoolers. The one-on-one
interviews supported the quantitative results that in preschool classrooms the instructional time is
dedicated to social-emotional issues rather than math. At the same time, it is proven that
preschoolers are capable of more abstract and sophisticated skills related to causal reasoning
(Connor, Morrison, Petrella, 2004; Gottfried & Gelman, 2005; Harris, German, & Mills, 1996;
La Paro, Siepak, & Scott-Little, 2009).
Overall, the results of the study indicated that the implementation of early-childhood
mathematics’ education faces distinct challenges. It is obvious that there is a gap in the current
practice, and the mandated standards need improving through professional development and the
education of preschool teachers.
Teacher A explained why she prioritizes other developmental goals over mathematics
learning,
Math is not my priority. The priority is social, emotional development. I believe
we have behavioral and socializing problems that should be addressed. Also,
social emotional learning is a valuable skillset that helps with social and
73
interpersonal skills and cognitive regulation, too. Language is another area that I,
as a preschool teacher, work on continuously.”
74
CHAPTER FIVE: CONCLUSIONS
Introduction
This chapter provides a summary of the study, including the statement of the problem, the
purpose of the study, research questions, a brief review of the literature, and the methodology
applied, as well as the key research findings and the subjective responses of the participants.
Mathematics education has been recognized in the national agenda as part of an urgent
need to improve scientific and technical literacy (Cross et al., 2009). There is a particular focus
on the persistently low mathematics performance of students, especially in terms of the
disparities that exist in the early academic years. Recognizing the increasing importance of
learning mathematics in early years, the Mathematical Science Education Board for Education at
the National Research Council established the committee on Early Childhood Mathematics. The
Committee developed science-based mathematics learning objectives relevant to instruction,
curriculum, and teacher education. Although the Committee confirmed the capacity of children
to learn and become competent in mathematics, the investigation of the current standards in the
early childhood setting, in particular, prekindergarten classrooms, shows that children are not
receiving sufficient guidance in mathematics. High-quality mathematics for children ages three-
five enhances their intellectual thinking and improves later achievement. However, much
remains in terms of understanding what preschool mathematics education involves.
Statement of the Problem
By focusing on improving teaching and learning mathematics in the preschool classroom,
it has become apparent that teachers’ competence, knowledge, and beliefs are recognized as
important factors in supporting a sustainable plan for children’s achievement in mathematics.
Limited research has focused on how teachers’ beliefs shape their instructional values in the
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classroom. The purpose of the present study was to address this gap in the literature and
understand more comprehensively the nature of teaching and learning mathematics in the
preschool classroom and, particularly, to determine what is necessary to implement effective
mathematical education. This is especially important since it is now thoroughly documented that
teachers’ beliefs and commitment facilitate task values in classrooms.
Research Questions
The following research questions guided the study:
1. What are public preschool teachers’ perceived values about teaching mathematics to
preschoolers?
2. How confident are urban public preschool teachers in helping preschoolers learn
mathematics?
3. What is the knowledge level of public preschool teachers regarding the mathematical
development of their students?
4. With what frequency do public preschool teachers believe they incorporate mathematical
concepts in class?
A mixed method of data collection was designed to examine the subjective responses of
the study’s participants. Quantitative data, through launching a survey in QuestionPro, provided
descriptive and inferential statistics, whereas, qualitative data collected from one-on-one
interviews produced meaningful data that postulated descriptive detail on teachers’ beliefs to
address the research questions.
Theoretical Framework
There are two major educational approaches that have dominated the current literature on
enhancing knowledge acquisition: constructivism and cognitive load theory (Jonassen, 1999;
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Loyens & Gijbels, 2008; Vygotsky, 1978). The cognitive load theory explained human cognitive
architecture (Sweller, 1988) and the manner in which new information should be presented to
learners (Mayer, 2011). According to this theory, instructional guidance that promotes learning
in a meaningful way requires providing appropriate cognitive processing, including selecting
relevant materials that reduce cognitive loads, as well as organizing the new material and
integrating it with the prior knowledge of the learner (Mayer, 2011). Constructivist approaches
share a common philosophy by providing the learner with skills and support, including the range
of possible educational goals that a learner can attain with instruction. Inherent to both
approaches is the role of the teacher in organizing the information and integrating it with the
learner’s prior knowledge.
Furthermore, in both educational approaches, teachers’ beliefs have been seen as
powerful directives in student-teacher social negotiation. According to Rene Thom (1973 as
cited in Golafshani, n.d., The Impacts of Teachers’ Conceptions of Mathematics on Their
Instructional Practices, para. 4), the world-famous French mathematician, “all mathematical
pedagogy, even if scarcely coherent, rests on a philosophy of mathematics (p. 204),” which is
rooted in teachers’ beliefs about the nature of the subject. Thus, there exists a framework of
beliefs in mathematics and mathematics pedagogy at any level.
Literature Review
Importance of mathematics. Today, learning math is vital and is among the important
goals for young children. In the last decade, there was a significant amount of research on early
childhood mathematics. First and most importantly, the increase in women’s participation in the
workforce demands high-quality education since about 59% of 4-year-old children spend their
day outside the home (U. S. Census, 2003). Sixty percent of the prekindergarten children in the
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United States attend publicly-funded preschools. Second, the revision of new policies has also
shaped early childhood education policies. The National Education Goals of 1990, the
reauthorization of Head Start and No Child Left Behind of 2001 are policies to strengthen early
learning (National Research Council, 2009). Finally, in an era of reform, science, technology,
engineering, and mathematics (STEM), mathematics education is disproportionally lacking
among professionals in the United States (Drew, 2011), while American students lack
mathematics competence and skills in national and global assessments. Thus, the major reason
for promoting accountability is closing the achievement gap.
The National Research Council, with the help of their committee members including
child development scientists, educational psychologists, psychologists, mathematicians, and
experts from early childhood education, synthesized research from the last 30 years and
examined the evidence about the acquisition of mathematics from prekindergarten to 8th grade.
The NRC report concluded that learning mathematics is important during the early childhood
years for building a foundation that is associated with continued academic achievement
(Clements & Sarama, 2014; Connor, Morrison, & Petrella, 2004; Connor, Morrison, &
Slominski, 2006). The latest investigation on preschoolers’ cognitive capacity reported that
prekindergarten children are capable and intuitively eager to learn mathematical concepts (Geist,
2009; Seo & Ginsburg, 2004). Researchers suggested that providing preschoolers with high-
quality mathematics that enhance the preschoolers mathematical thinking and competence
facilitates mastery of new, developing skills and the sharpening of already existing ones
(Baroody, 2003; Jordan, Kaplan, Ramineni, & Locuniak, 2009).
Beliefs. Focusing on enhancing the quality of mathematics education in early childhood
education, it is important to understand the nature of teaching and learning mathematics by
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examining how teachers view and address mathematics. Broadly construed, human psychology
is the study of human behavior that, through theories, explains the nature and causes of human
behavior. Behaviorism or behavior analysis described human behavior as a function of the
environment; educational psychology, on the other hand, focuses on learning and teaching from
both cognitive and behavioral perspectives that, through cognitive, neuroscience, motivation,
self-regulation, and self-concept theories, described the thinking and learning processes and
factors involved in learning. From educational psychology, perspective belief is firmly rooted in
the cognition (Immordino-Yang, 2015; Zimmerman, & Schunk et al., 2014) that influence
human behavior.
Reviewing literature reveals the gap of preschool teachers’ beliefs on teaching
mathematics, their self-efficacy beliefs in teaching mathematics, their beliefs of children’s
learning capabilities, and their beliefs on the practice of mathematics.
Key Findings
The key findings from the data analyses were summarized and presented in order of
research questions and in line with the relevant literature in Chapter 4.
Teachers’ Beliefs on Teaching Mathematics
Teachers’ beliefs and values have been well-documented, demonstrating how their
perceptions and judgments affect their practices (Bransford & Donovan, 2005). The current
study explored specific types of preschool teachers’ beliefs in order to make the teaching of
mathematics in the preschool classroom feasible and useful to the overall approach to education.
The results from the mixing of qualitative and quantitative data showed that, although all
teachers value building intuitive foundational knowledge and skills in mathematics for pre-
79
kindergarten students, they are more concerned with children’s social and emotional readiness.
Conversely, mathematics is not their primary goal.
In 2002, early childhood education began to emphasize new standards, highlighting the
need for prekindergarten mathematics education (Clements & Sarama, 2004; NAEYS & NCTM,
2002). Education builds cognitive and effective foundations for student readiness in
kindergarten as well as later academic achievement (Cross et al., 2009). One effect of these
recommended new practices, emphasizes STEM skills and mathematics competence, an
approach that was supported by statistical data and one-on-one interviews. Teacher F, for
instance, affirmed.
I am aware that early childhood teachers traditionally paid inadequate attention to
mathematics in preschool classrooms, and now I am aware that investing in
mathematics learning makes children learn more as time goes on.
However, the participating prekindergarten teachers are concerned with their students’
social and emotional readiness, therefore, mathematics is not their primary goal. Teacher A
attested to this concern: “Math is not my priority. Children’s social and emotional development
are my priority.”
Preschool teachers routinely make decisions about how to proceed with instructional
goals in all subjects. Elements are selected or omitted from the lesson in accordance with
teachers’ beliefs about their relative importance. Normally, these elements are then taught to
students in a fashion that is informed by teachers’ beliefs regarding age-appropriate methods of
educational presentation. While 50% of teachers believe that math is too abstract for
preschoolers, 59% of participants held the opinion that children can learn mathematical concepts
without the help of teachers.
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The beliefs documented in the current study about the nature of mathematics in the
preschool classroom are closely aligned with previous observations. It is important to note that
the studies about preschool teachers’ beliefs regarding the teaching of mathematics in preschool
classrooms is very limited. Blevins-Knabe et al. (2000) as well as Musun-Miller & Blevins-
Knabe (1998) and Ginsburg, Lee et al. (2008) found that mathematics was not the priority of
educators in the early childhood setting.
Self-Efficacy
In the current study, self-efficacy, the cornerstone of social cognitive theory, is another
crucial point of investigation in terms of preschool teachers’ thought processes. Self-efficacy,
the belief in one’s abilities to accomplish anticipated outcomes, vigorously affects a teacher’s
behavior, motivation, and, ultimately, success or failure (Bandura, 1997). Teacher self-efficacy
is a teacher’s perceived capability to impart knowledge and to influence student learning
(Guskey & Passaro, 1994).
The results from the quantitative studies showed that teachers reported confidence in their
teaching ability, while 6.2% reported low confidence in setting goals in teaching mathematics to
preschoolers. The results from the one-on-one interviews also supported the point about
teachers’ confidence in their teaching competence, while they desire training in teaching high-
quality mathematics instruction. Their statements indicated that their confidence is not because
of their mathematics skills; rather it is rooted either in experience or love of teaching. In this
regard Teacher C stated, “Through experiences, I have learned to overcome any challenges and
make differences. I am confident in teaching since this is my job.”
The one-on-one interviews also demonstrated that confidence does not appear in a
vacuum. Teachers talk about the need for resources and support, which are important to
81
fostering enjoyment and progressive effects that lead to positive outcomes of children. In this
vein, Teacher B stated, “I never had any training for teaching math in my life. I wish I had. But
I focus on how I can help children. I am confident in teaching math.” Teacher A likewise
added,
I love teaching, but I wish I had some type of not training, like resources,
workshops, educational materials. Providing professional development in
mathematics is not only about training. Workshops also have a positive effect on
teachers’ instructional practices and not only give competence in mathematics but
they also increase enjoyment of teaching too. Workshops on activities, like
geometry and graphing, could increase children’s time engagement in learning
mathematics.
Although there is no research covering preschool teachers’ self-efficacy in terms of
teaching mathematics, the results of teachers’ self-efficacy is supported by the literature review
that explained teachers’ years of experience are an important, influential factor in their self-
efficacy level. Specifically, the teachers who have 13 or more years of experience in teaching
exhibit stronger self-efficacy (Takunyaci & Takunyaci, 2014) and show higher levels of effort,
persistence, planning, and organizing for new ideas (Jerald, 2007). Additionally, the research
identified a second factor, often called general teaching of efficacy that becomes obvious in
teachers who strongly believe in their ability to reach difficult children (Hoy, 2000).
The Knowledge of the Mathematical Development of Preschoolers
The results for research question three demonstrated that while all of the teachers agreed
with children’s ability to learn the numbering of objects and measuring lengths and weights,
12.2% of teachers believed that prekindergarten students are incapable of learning to divide 12
cookies among two people and learn to compare shapes. The results of the one-on-one
interviews also supported that
preschoolers are capable of learning problem-solving. Mathematics concepts are
a broad term and could entail many models. Yes, children are capable of learning
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to count, sort, and measure. This is the first step. They can learn to add and take
away items, too.
Teachers who believed that preschool children are not capable of learning to divide 12
cookies among two people are not aware of learning trajectories across these ages. Learning
trajectories show how goals are coherent to and build on each other and provide hierarchical
ways for mathematics teaching to develop related understandings that can help all children move
forward (Clements & Sarama, 2014; Sarama & Clements, 2009a). This outlook also emphasized
the individual learning trajectories that each preschooler needs to cross.
While studies on teachers’ knowledge of the mathematical development of children help
contribute to the literature on effective practices (Clements et al., 2003), the majority of
researchers who examined teachers’ qualifications focused on their content knowledge, not their
knowledge of children’s development. Platas’ (2013) quantitative study focusing on the
measurement of early childhood teachers’ knowledge of early mathematical development is the
only study in this area, entailing 346 pre- and in-service preschool teachers. The study
demonstrated that preschool teachers’ classroom experience and completion of a course in
mathematical development formed their knowledge of the mathematical development of their
students. The quantitative part of the current study did not investigate preschool teachers’
training in completing a mathematical development course. However, the majority of the
teachers in the one-on-one interviews reported work experiences ranging form 3-20 years. It is
important to note that The Cronbach reliability test was utilized since the KMD was an original
survey conducted by researcher. The results for the KMD reliability test showed the alpha =
0.76, which indicates the inventory was reliable.
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Frequency of Incorporating Mathematical Concepts in the Preschool Classroom
The results showed that the majority of teachers, 72% agreed on incorporating
mathematics in the preschool classroom, while 72% of the survey’s participants place a higher
priority on social and emotional needs as well as reading in their classrooms than the intellectual
or academic activities related to mathematical concepts. Furthermore, 28% of the teachers
believed in incorporating mathematical concepts in learning activities, such as art and dramatic
play, but not on a daily basis. The one-on-one interviews also provided that all teachers agree
that they should include mathematics learning in their preschool curricula. However, their
formal, early-childhood training emphasized the social and emotional development.
Additionally, their training never prepared them to teach effective mathematics, especially as
they relate to current standards. Teacher A highlighted such beliefs.
Math is not my priority. The priority is social, emotional development. I believe
we have behavioral and socializing problems that should be addressed. Also,
social emotional learning is a valuable skillset that helps with social and
interpersonal skills and cognitive regulation, too. Language is another area that I,
as a preschool teacher, work on continuously.
Given these distinctions, the results specify that although teachers agree on incorporating
mathematics in the preschool classroom, mathematics pedagogy is not a priority, and the
possibility of taking advantage of teachable moments in mathematics is not included in everyday
activities. This attitude was supported by the previous research, concluding that preschool
teachers’ instruction and techniques assist children primarily in fostering social and emotional
development and that teachers spend less time on mathematics (Early et al., 2007; Lee &
Ginsburg, 2007; Pianta & La Paro, 2003).
Limitations
The present results significantly expand upon previous research by documenting the
nature of mathematics teaching in the preschool classroom. Such results specifically explored
84
prekindergarten teachers’ beliefs in teaching mathematics to preschoolers as well as teacher’s
self-efficacy, confidence, the knowledge of mathematical development of preschoolers, and the
implications of incorporating mathematics concepts in publicly funded, early childhood settings.
It was acknowledged that replicating these results is desirable, given that the current findings
represent data from a small sample size. Stronger confidence in findings, however, necessitates
replication in a larger sample to assist with external validity. Moreover, although the participants
of the current study are from diverse public schools in terms of the type of school and the
different social economic backgrounds of the students, the data from the quantitative and
qualitative part of the study revealed that all of the teacher-respondents were female. This shows
that the current study failed to capture the thoughts of the men who go through the processes of
masculine participation in the preschool environment. Additionally, the sample was limited to
teachers working in public preschools in California and presumably adhere to the state’s early
childhood mathematics learning standards.
Implications
Implementation of further research. There are several implications that can be drawn
from this study. First, the nature of mathematics teaching in a preschool classroom must be
examined in all types of publicly funded, early childhood settings, such as Head Start. Head
Start teachers and assistant teachers are an essential portion of the preschool teacher population,
serving publicly-funded preschools and playing important roles in early childhood education.
Indeed, approximately 907,000 preschool-age students attend Head Start (Administration for
Children and Families, 2008a), and about 57,000 teachers serve in Head Starts preschools
(Administration for Children and Families, 2008b). Thus, the aggregate results that also
considered a sample of these teachers would represent a meaningful, insightful addition to
85
understanding mathematics teaching in preschools. In addition, researchers could extend the
investigation about which preschoolers do and do not receive various types of mathematics.
Furthermore, research in this area could also consider a closer examination of teachers’
perspectives of preparation, pedagogical knowledge, and their needs for professional
development. Duplicating the study and assessing the dependent variables with the recruitment
of a large sample of participants would draw a firmer conclusion.
Moreover, while the results provide an impetus for further examination of mathematics
teaching in the preschool classroom, it leaves several unanswered questions requiring additional
investigation. In particular, future research should more thoroughly investigate in what
developmental areas preschool children are not ready to receive mathematics education in the
prekindergarten classroom, and what resources might help to overcome these obstacles. A
longitudinal approach, which would assess the effect of resources and responses of over two or
more time periods, would enable researchers to evaluate teachers’ attitudes and their impact on
their practices. Additionally, further research should examine what amount and type of
mathematics learning opportunities preschool teachers can optimally use to build a foundation
for kindergarten children. Lastly, giving mathematics lessons and activities to all
prekindergarten children, as outlined in professional and state standards, requires teacher
understanding and implementation of mathematics experiences. Further research will provide
new insight concerning the best approaches and methods about mathematics practices in the
preschool classroom.
Implementation of practice. The current study recommends developing the values and
knowledge of prekindergarten teachers since they can play a vital role teaching mathematics to
86
prekindergarten children. The review of the study’s results reveals the need for professional
development for teaching mathematics in the following areas:
a. Science-based professional development that educates preschool teachers with the latest
educational theories is especially important in light of the current study, which found that
teachers believe math is abstract and teaching the subject is not their priority. For
instance, professional development that focuses on cognitive load theory, the human
learning process, and the way instruction should be represented might help teachers to
modify their traditional Piagetian notions that children ages two to six are not cognitively
ready to learn mathematics;
b. Professional development that addresses mathematics knowledge as well as mathematics
education to elevate the quality of the teachers’ mathematics knowledge and their self-
efficacy is vital. For example, prekindergarten teachers will be more active in the
implementation of NCTM and NAEYC if they more accurately understand how their
views and training negatively impact children’s learning mathematics and the ability for
young children to learn mathematics. Particularly, as noted before, prekindergarten
teachers have strong beliefs that they lack key elements of contemporary, early-childhood
education. Professional training could influence teachers’ pedagogical beliefs that
traditional education focusing on the “whole child,” including emphasis on social and
emotional development, can also include contemporaneous educational approaches that
engage preschool children in mentally appropriate mathematics, which is essential to
developmentally appropriate instruction (National Association for Education of Young
Children as cited in Copple & Bredekamp, 2009; National Mathematic Advisory Panel,
2008);
87
c. Professional development that focuses on a teaching orientation by centering a
conceptual instructional approach helps preschool teachers meaningfully interpret
mathematical principles and implement educational goals on problem-solving tasks
involving reasoning activities through which teachers actively facilitate, monitor, and
assess the learning progress of the children. Such professional development helps
teachers provide the intentional teaching of mathematics that helps preschoolers advance
beyond their intuitive mathematics (Ginsburg, Kaplan et al., 2006). Results from
qualitative and quantitative data showed prekindergarten teachers believe that children
learn mathematics through informal learning and, some believe, without the help of
teachers. These findings provide evidence that administrators may advocate and increase
informal math instruction through which children’s mathematical thinking naturally
develops. However, these stimulating conditions should not be set without well-crafted
teacher and children-based interactions (Lantz, Nelson, & Loftin, 2004; Schuler &
Wolfberg, 2000). Thus, teachers should receive professional development or the
coaching necessary for such purposeful interactions (Brown & Freeman, 2001; Kuschner,
2001);
d. Professional development in early childhood mathematics that helps teachers plan
specific organized curriculum, or instruction that guides student acquisition of
mathematics and enhances teacher content knowledge on teaching math is likewise
foundationally important (Ginsburg, Lee et al., 2008). The results of the one-on-one
interviews explicitly showed the desire of teachers for training in mathematics
instruction, particularly in the area of curricula with carefully sequenced mathematical
experiences in the classroom. Studies showed that such professional training not only
88
improves the overall quality of teaching (Blau, 2000; Zaslow, Tout, Maxwell, & Clifford,
2004) but can also enhance children’s learning in specific mathematical domains
(Clements & Sarama, 2008). For example, a curriculum that engenders mental processes
for geometry learning in the preschool classroom, including partial use of geometric
attributes and mental strategies to synthesize composite shapes, could help teachers
follow the activities in sequence of identifying, recognizing, solving shape puzzles on
specific computer programs to advance mental effort in memory (Clements & Sarama,
2004; Sarama, Clements, & Vukelic, 1996).
e. Professional development that focuses on helping prekindergarten teachers to value,
promote, and provide mathematics in the everyday context of preschool is instrumental.
For example, The Big Math for Little Kids curriculum (Balfanz, Ginsburg, & Greenes,
2003) provides storybooks to present key concepts of number, shape, pattern,
measurement, operations on the numbers, and space. Activities are also organized to
offer problem-solving thinking, conceptual mathematics learning, and discovery for each
day of the school year (Ginsburg, Lee et al., 2008).
Another necessary implication of the current study is to increase resources that help
teachers overcome classroom obstacles, including improving children’s problems related to self-
regulation, cognition, language, and behavior. Notably, providing human resources in the
preschool classroom helps teachers to respond to the students’ additional adult assistants to fully
participate in classroom activities (Decker et al., 2009). Teacher F explained,
Assistance and resources could/should be provided either formally by having an
adequate number of qualified assistant teachers or informally by creating help
through volunteers, so the prekindergarten teachers’ training can be implemented
within the curriculum and their teaching can be adequately assessed. When I was
in Pasadena, I resolved all problems in a short time because there were four adults
and 16 students. Although the children were not ready and we had language,
89
cognitive, self-regulation, and other behavioral problems, having help in the
classroom allowed me to use the art of teaching. Lack of help in the classroom, in
particular the prekindergarten classroom, kills teacher’s creativity no matter what
she wants to teach.
Conclusion
Understanding the nature of teaching mathematics in the early childhood setting is
important as mathematics is one of the most critical educational factors in terms of children
exceling in science, technology, and mathematics. From the points of view of cognitive and
behavioral learning theories, teachers play a central role in the school context and exert
enormous influence in prekindergarten learning. Accordingly, the teachers’ beliefs have a
powerful influence on education and shape classroom practices (Stipek et al., 2001). Improving
the mathematics education in preschool classrooms is not possible without considering the
teachers’ beliefs and values in teaching mathematics. Virtually, there was a gap in research on
prekindergarten teachers’ beliefs. The current study provides insight into understanding
prekindergarten teachers’ beliefs involving teaching mathematics, delineating the necessity for
the implementation of effective mathematics teaching in the preschool classroom.
90
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Hariri, Jinna Gisoo
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An examination of teachers’ perceived value and knowledge of mathematical development in early childhood settings
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