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Increasing student performance on the Independent School Entrance Exam (ISEE) using the Gap Analysis approach

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Increasing student performance on the Independent School Entrance Exam (ISEE) using the Gap Analysis approach

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Content Running Head: INCREASING MATH ISEE STUDENT PERFORMANCE 1

INCREASING STUDENT PERFORMANCE ON THE INDEPENDENT SCHOOL
ENTRANCE EXAM (ISEE) USING THE GAP ANALYSIS APPROACH

by
Shanon Etty Sarshar

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

MAY 2013

Copyright 2013 Shanon Etty Sarshar
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2

Acknowledgements
First and foremost, I would like to thank my dissertation chair, Dr. Kenneth Yates.
His unconditional support, wisdom, guidance, and patience were indispensable during
this entire journey, and I would not have made it here without him. I would also like to
greatly thank my boss and 3
rd
grade teacher Valerie Lev, the director at “Education
Express”, for her wholehearted support, guidance, knowledge, and expertise as an
educator. Lastly, I would like to express my gratitude to my dissertation committee, Dr.
Robert Rueda and Dr. Kathy Stowe for their knowledge and supervision.

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Table of Contents
List of Tables 6
List of Figures 7
Abstract 8
Chapter 1: Introduction 9
Background of the Problem 9
Statement of the Problem 10
Purpose of the Study and Guiding Questions 14
Importance of the Problem 14
Chapter 2: Literature Review 17
Introduction 17
The History of Private Schools in the US 18
The Role of Private Schools in the US Education System 19
Standardized Tests Used By Private Schools for Admission 20
Why Do Some Students Perform Poorly on Standardized Tests? 22
Test Preparation Courses and the Effectiveness of These Courses 25
Does Test Preparation Translate into the classroom? 27
Individual Learner Characteristics 28
Cognitive Characteristics 28
Aptitude 28
Cognitive Development 31
Prior Knowledge 34
Affective Characteristics 35
Motivation 35
Social Characteristics 44
Social Capital 44
Role Models 45
Environmental Influences 46
Summary 48
Chapter 3: Methodology 50
Purpose of Inquiry and Guiding Questions 50
Description of the Framework 50
Step 1: Operationalization of the Goal 52
Step 2: Current Performance 53
Step 3: Gap in Performance 54
Step 4: Assumed Causes of the Performance Gap 54
Informal Interviews 54
Learning and Motivation Theory 55
Causes Informed by the Literature 60
Step 5: Validation of the Causes of the Performance Gap 63
Sample and Population 63
Instrumentation and Data Collection 63
Data Analysis 64
Summary 65
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Chapter 4: Results 66
Demographics 66
Study Question One 67
Knowledge and Skills Results 68
Assumed Knowledge Causes 69
Student Survey Results 70
Synthesis of Knowledge Survey 73
Motivation Results 75
Assumed Motivation Causes 75
Motivation Student Survey and Interview Results 76
Synthesis of Motivation Survey and Interview Data 80
Organization Results 84
Assumed Organization Causes 84
Student Survey and Interview Results 85
Parent Survey 88
Synthesis of Organization Survey and Interview Data 91
Comparison of Knowledge & Skills, Motivation, & Organization Results 92
Chapter 5: Solutions & Implementation Plan 94
Study Question Two 94
Knowledge and Skills 94
Knowledge and Skills Results 94
Knowledge Theory 95
Knowledge Principle and Application 96
Summary of Knowledge Solutions 99
Motivation 99
Motivation Results 99
Motivation Theory 100
Motivation Principle and Application 101
Application to ISEE 103
Organizational Barriers 103
Organization Results 103
Organization Theory 104
Organization Principles and Application 105
Implementation 106
Goal Hierarchy for Below-5 Student Stake Holder 109
Summary 111
Chapter 6: Discussion 112
Synthesis of the Results 112
Strengths and Weaknesses of the Approach 113
Recommendation and Implications 113
Evaluation 114
Level 1 Reactions 115
Level 2 Learning 115
Level 3 Transfer 116
Level 4 Impact 116
Limitations 117
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Future Research 117
Conclusion 117
References 119
Appendix A: Below-5 Student Pre-requisite Knowledge Questionnaire 129
Appendix B: Below-5 Student Smiley-Face Motivation & Organization Survey 134
Appendix C: Below-5 Student Motivation and Organization Interview Protocol 136
Appendix D: Parent Organization Survey 138

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List of Tables
Table 3.1 Knowledge types 56
Table 3.2 Summary of assumed causes for knowledge, motivation,
and organization 61
Table 4.1 Knowledge type, knowledge question, and percent
answered correctly 72
Table 4.2 Student motivation questions, motivation constructs,
and means 77
Table 4.3 Student organization questions, organization constructs,
and means 85
Table 4.4 Parent motivation questions, motivation constructs,
and means 89
Table 4.5 Parent organization questions, organization constructs,
and means 90
Table 5.1 Summary of causes, solutions, and implementation
of the solutions 108
Table 5.2 Summary of Education Express’ organizational goal,
short-term goals, cascading goals, and performance goals 109
Table 5.3 Summary of performance goals, timeline and
measurement of performance goals 110

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List of Figures
Figure 1.1 Time schedule for ISEE students 11
Figure 3.1 Gap Analysis Process 51

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Abstract
Using the Gap Analysis problem-solving framework (Clark & Estes, 2008), this study
examined the performance gap experienced by 6
th
grade students on the math sections of
the ISEE (Independent School Entrance Exam). The purpose of the study was to identify
and validate the knowledge, motivation, and organization causes of the students’ low
performance on the ISEE pre-test. The participants in the study were 9 students identified
as scoring below a stanine of 5 (referred to as Below-5 students) on the mathematics
sections of an ISEE pre-test. Quantitative surveys and qualitative interviews were used to
collect data, and data was analyzed using descriptive statistics. The results of the study
found a significant prerequisite knowledge gap (40%), motivational barriers of values and
self-efficacy, and organizational barriers including difficulty with homework completion
and lack of homework support at home. Research based solutions to close the knowledge,
motivation, and organization gaps are recommended. The implications of the study
indicate that in order to achieve a stanine of 5 or higher on the math sections of the ISEE,
Below-5 students will need pre-training in knowledge and skills, a motivation increase in
self-efficacy and values, and organizational resources such as a proper homework
environment and homework help.
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CHAPTER 1: INTRODUCTION
Background of the Problem
The private sector of the American education system and private school
enrollment reflects parents’ desire to seek alternative options for providing their children
with educational opportunities, (Patrinos & Sosale, 2007). A great amount of private
school enrollment is often connected to schools with religious affiliation, but secular
private school enrollment has also increased during the past two decades (Rampell, 2009).
Parents often choose to send their children to private schools because of the higher
academic standards, greater high school graduation rates, better instruction, increased
student safety, and less alcohol and drug abuse (NAEP, 2012). Additionally, independent
school student performance on the National Assessment of Educational Progress (NAEP)
report card in math, reading, and writing was significantly higher in all three areas than
that of public school student performance (NAEP, 2012). Private schools provide better
learning environments, have lower dropout rates, and higher college completion rates
(Bissonnette, 2011).
Although private school enrollment decreased by roughly 13% during the 2009-
2010 school year due to the economic recession and increasingly difficult entrance
requirements, US private school enrollment remains at 10% of the population. Moreover,
the high standards of private schools and difficult entrance requirements cause parents to
seek supplementary academic assistance for their children (Rampell, 2009).

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Statement of the Problem
The increasingly challenging standards of private schools have created a market for
private “enrichment centers” and other test preparation organizations in assisting students
in overcoming private school acceptance barriers. Education Express (EE), an academic
enrichment center established in 1995 in West Los Angeles, strives to teach elementary
and middle school students high-level academic skills that will translate into the
classroom and standardized tests, through small group workshops in a casual atmosphere.
Over the course of the past 17 years, Education Express has been offering students a wide
variety of workshops, such as summer enrichment courses in mathematics, reading, and
writing, creative writing workshops, back-to-school programs, and standardized test
preparation courses.
The administration at Education Express consists of a director, who has a master’s
degree in education and is a credentialed elementary school teacher, and 10 instructors.
Out of the 10 instructors, 6 teachers have masters’ degrees in education, and 4 instructors
had bachelors’ degrees.
One of the main programs at Education Express is the ISEE (Independent School
Entrance Exam) preparation course (the “ISEE Program”). The ISEE is an admissions
exam that is required of students who are entering private middle and high schools across
the nation. The ISEE has three different levels, for students in various grade groups. The
lower level exam is designed for students in 4
th
and 5
th
grade (entering 6
th
grade), the
middle level is designed for students in 6
th
and 7
th
grade (entering 7
th
and 8
th
grade), and
the upper level is designed for students in 8
th
and 9
th
(entering 9
th
and 10
th
grade).
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Additionally, the ISEE contains 5 sections: verbal reasoning, quantitative comparison
(mathematics), reading comprehension, mathematics achievement, and an essay section.
Except of the final essay section, each section of the exam is graded on a stanine score of
1-9.
ISEE students begin the ISEE Program in June, July, or August by taking a 3-hour
practice ISEE Pre-test that was developed by the ERB. In the Fall, beginning in
September, ISEE students begin the 12-week ISEE Program at Education Express. At the
end of the Program, ISEE students take the same 3-hour practice ISEE test that they had
taken over the summer, and, finally, ISEE students take the actual ISEE in November or
December. A time schedule for ISEE students can be found in Figure 1.1.

Figure 1.1: Time Schedule for ISEE Students.

Schedule for ISEE Students:

June / August:
- Take ISEE Pre-Test at EE

September - November:
- 12-week ISEE Preparation Course at EE

November
- Take ISEE Post-Test at EE

November – December
- Take actual ISEE at designated testing site
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Education Express has been offering the ISEE Program since its establishment in
1995. Overall, students who enter the Program have done very well in these courses, and
have been able to boost their ISEE entrance exam scores. In general, student performance
has been above satisfactory, but in 2009, the ERB board, the Educational Records Bureau
that develops the ISEE exam, made several changes to the test. One of these changes
involved increasing the level of difficulty of the content, specifically the math content by
including more advanced geometry and algebra concepts that cover math content for
students in grades 6 through 8 (NCTM, 2012). This change created a new challenge for
ISEE students, and many ISEE students’ mathematic scores declined, in particular for the
elementary age students.
This change in the format of the ISEE exam resulted in a subsequent gap in student
performance on the ISEE exam, and this gap also presented a challenge for Education
Express, especially with respect to the elementary students. Because the level of
difficulty of the math content was made more difficult by increasing the math content
from a 6
th
grade level to an 8
th
grade level, one of the main issues that students face is a
basic skill deficit in the math knowledge needed for the ISEE – many elementary school
students are missing the prior knowledge needed to reach high scores on the exam.
Furthermore, elementary school students’ ability to successfully complete the
mathematics and quantitative reasoning sections of the ISEE may also depend on their
current stage of cognitive development. According to Huitt and Hummel (2003), the
ability to perform algebra requires students to have entered the cognitive stage of
reasoning known as “formal operations”, which usually begins around adolescence. In
the “formal operations” stage, children develop the ability to think abstractly, and no
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longer need concrete objects in order to solve problems. Most of the middle level
students are between the ages of 10-12, and have not yet entered adolescence. This
discrepancy between the level of math presented on the exam, and the level of math that
students are cognitively capable of handling also presents a challenge in the ISEE course.
Additionally, the math content presented on the middle level exam entails very
advanced math concepts involving logic and reasoning skills, computation skills, and
innate number sense at the pre-algebra and algebra level. Many of the students who begin
the ISEE Program at EE lack sufficient prior knowledge to be able to successfully
complete the entire math course curriculum. Without the necessary math knowledge and
skills, the students’ math scores may be below a stanine score of 5, and the majority of
private middle schools require at least a stanine of 5 or higher for admission.
Subsequently, the ISEE students now fall into either the higher performing group (stanine
score of 5 or above), or the “Below-5” group scoring at a stanine of 4 or lower, as
determined by the practice ISEE test students take at the beginning of summer.
After examining the actual ISEE exam results from the past several years, Education
Express has determined that a mathematics intervention may be required to bring the
Below-5 students up to par with the knowledge and skills necessary to successfully
participate in the ISEE Program during the fall and achieve the Education Express goal
that all students successfully achieve a stanine score of 5 or higher on the mathematics
sections of the ISEE exam.

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Purpose of the Study and Guiding Questions
The purpose of this case study is to examine the knowledge and skills, motivation, and
organizational context, culture, and capital causes of the achievement gap between the
Below-5 group (stanine of 4 or lower) and higher performing group (stanine of 5 of
higher) on the math sections of the middle level ISEE exam.
The study questions include:
1. What are the causes of the gap that “Below-5” students have in knowledge and
skills, motivation, organizational context, culture, and capital that affect their
successful achievement of 5 or better on the ISEE Program Post-test?
2. What are the potential knowledge and skill, motivation, and organizational
solutions to address the Below-5 students gaps in achieving a score of 5 or better
on the ISEE Program Post-test?
The Gap Analysis Process Model (Clark & Estes, 2008) will be used as the
framework to identify the causes for students falling below a stanine score of 5 on the
math sections of the ISEE Pre-test. Through analysis of the data from the study questions,
a process will be recommended by which the organization is able to measure and evaluate
the achievement of the organizational goal.

Importance of the Problem
Private or independent schools play a vital role in our country’s educational system.
Private schools compose about 50% of the US school system and there are different types
of private schools. Independent schools provide religious education, may have particular
educational philosophies, or can serve as college preparatory schools.

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Private schools use entrance exams. Because of competitive selection criteria, private
school admission requires standardized testing that assesses student verbal and
mathematical skills. The two main elementary and secondary-level standardized tests in
the United States are the Secondary School Admission Test (SSAT) and the Independent
School Entrance Exam (ISEE). Both the SSAT and ISEE are norm-referenced
standardized tests, composed of two verbal sections, two math sections, and a writing
section. The ISEE is the standardized exam used by the majority of privately controlled
schools in Los Angeles.

This problem is important at the national level because standardized test scores drive
socioeconomic and political decision-making (Phelps, 2005). Additionally, providing
standardized test preparation not only improves the validity of the standardized test
results, but also serves as a gateway into equal educational and professional opportunity
(Phelps, 2005). Students, teachers, and schools will benefit from improved test
preparation programs that meet the needs of all students.
This problem is important at the local level because Education Express aims to help
all students, regardless of their ability level, achieve strong standardized test scores.
Improving the ISEE Program and facilitating access to the curriculum for all students will
help Education Express accomplish its goal of ISEE preparation. Additionally, test
preparation for the mathematic sections is especially important and relevant to students
between the ages of 10-12. There may be a discrepancy between the level of cognitive
development required for successful completion of the math sections of the ISEE exam,
and students’ actual level of cognitive development. The algebraic concepts assessed on
the ISEE require students to have reached the cognitive stage of “formal operations”, in
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16

which students are able engage in abstract thinking without the use of concrete objects
(Huitt et al., 2003). According to Huitt et al. (2003), primary school students often do not
enter “formal operations” prior to adolescence. Knowledge of the discrepancy between
what ISEE students are actually capable of accomplishing, and the content that they are
expected to know will help Education Express in adapting the ISEE course to better fit
the needs of the students. With knowledge of students’ cognitive abilities, Education
Express will be able to make the ISEE math content more accessible to students in the
concrete operational stage, which requires manipulation of concrete objects.

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CHAPTER 2: LITERATURE REVIEW
Introduction
Private schools, which are also referred to as privately controlled or independent
schools, play a major educational role in the United States. Independent schools often
serve the role of providing both secular and religious education (Bissonnette, 2011).
Independent schools exist at different educational levels: elementary school, secondary
school, and higher education.
According to the Private School Universe Survey (PSUS, 2001), there are currently
three types of elementary and secondary private schools: religious schools, which
represent about 49% of private schools, Catholic schools, representing about 30% of
private schools, and nonsectarian schools, or schools that do not apply to a certain
religious belief, which represent about 21% of private schools (PSUS, 2001). Privately
controlled higher education institutions include private colleges and universities (Patillo,
1990). About 50% of higher education institutions are privately controlled. Private
colleges and universities include liberal arts colleges, comprehensive colleges and
universities, specialized institutions, two-year colleges, and distinguished research
universities. Roughly half of these independent higher education systems also have a
religious affiliation (Patillo, 1990).
Both public and private school systems use standardized testing to evaluate,
categorize, and place their students (Phelps, 2005). Standardized test scores are also used
to evaluate educators, schools, and districts. In addition to evaluation and admission roles,
standardized test scores are a main factor in accountability and have been used to hold
various parties accountable for progress and failure. While testing is not required for
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18

admission into public K-12 schools, standardized admission tests are often required for
admission into private middle and upper schools.
This review of the literature will examine the history of private schools in the US,
the role of private schools in our country’s educational system, and the standardized tests
used by private schools for admission. Next, the literature review will examine probable
causes for differences in test scores between students, causes of differences in test scores
for learning disabled children, test preparation courses and the effectiveness of these
course for students and learning disabled students, and then examine the overlap between
standardized test preparation and classroom content. Finally, the review of literature will
examine individual learner characteristics; such as cognitive, affective and social
characteristics of elementary school students that can impact standardized test scores.

The History of Private Schools in the US
The first private schools, Catholic schools opened by missionaries, date back to
the 16
th
century (education.stateunivsity.com). During the colonial period, there was no
distinction between private and public schools and the government was not involved in
the functioning or funding of these schools. In New England, there were “town schools”
that coexisted with private religious schools.
In the 1700 and 1800’s, there were several different types of schools, but there
was still no clear distinction between private and public systems. A diversity of schools
existed – public town schools, charity schools for the poor, and different types of private
schools that families would pay for.
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It was not until 1837, when Horace Mann, president of the Massachusetts senate,
signed the bill creating the Massachusetts board of education, that public schools were
formed. The Massachusetts board of education created a standard, public, and free state-
wide education system in Massachusetts that was open to all children
(education.stateuniversity.com). The purpose of the board of education was to create a
“common school” that would create an American identity for American children. In the
mid 1800’s, during the American Civil War, Catholic schools and other schools with
various religious denominations began to appear.
From about 1939 to 1945, during World War II, there was a big increase in the
establishment of private schools. Many nonpublic or private schools would receive
government funding, but in 1959, this practice was discontinued because it went against
the First Amendment, which called for a separation of “church and state”. During the
1950’s, Catholic schools and other religious schools were the main type of private
schools that existed. Between the 1960’s and 1980’s, there was a large growth in the
number of private schools established, and in 1962, the National Association of
Independent Schools was founded in New York City (education.stateuniversity.com).

The Role of Private Schools in the US Education System
Today, the private school system is well established throughout the nation and the
private school system serves an important role in the US education system. Private
schools serve a religious purpose, and about 80% of private schools in the US have a
religious affiliation (PSUS, 2001). Roughly 20% of US private schools are nonsectarian
schools, secular private school systems, such as Montessori schools or high-achieving
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20

college preparatory schools. Unlike public schools, private school systems do not receive
public funding and have annual tuition costs (Education Week, June 2012).
Additionally, a process of double selection characterizes private schools because the
schools select students and the parents select the schools for their children
(education.stateuniversity.com). Standardized testing is part of the selection process in
private schooling (education.stateuniversity.com). Private schools often have rigorous
academic requirements for students, and students must go through a selection and
admittance process (Education Week, June 2012). Because of the rigorous selection
process for admission into private schools and higher academic standards, the majority of
private schools have various admission requirements, which often include standardized
testing that assesses student verbal and mathematical skills.
Overall, when contrasted with public schools, private schools play a different role
in the US education system. Independent schools provide religious education, may have
particular educational philosophies, or can serve as college preparatory schools. Private
schools at all levels use standardized tests to qualify students for admission.

Standardized Tests Used By Private Schools For Admission
In addition to applications and teacher recommendations, private secondary schools
require students to take a standardized test to assess their basic verbal and mathematic
abilities. The majority of private secondary schools accept either the SSAT (Secondary
School Admission Test) or ISEE (Independent School Entrance Exam) as a form of
admissions exam (Silas & Reed, 2011).
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The SSAT is 2.5 hour long standardized test administered to elementary and middle
school students (www.ssat.org). The SSAT has 2 levels. The lower level SSAT is for
students are currently in grades 5-7 and the upper level SSAT is for students who are
currently in grades 8-11. Additionally, there are 5 timed sections on the SSAT exam. The
first section is 25-minute writing sample where students are asked to agree or disagree
with a topic. There are also two verbal sections. The first verbal section involves
synonym matching questions and analogy questions. The second verbal section is reading
comprehension. There are two mathematics sections and each math section is 30 minutes
long. Finally, the SSAT is scored using percentile ranks.
The ISEE is a 3-hour long standardized test, administered to elementary and
middle school students (isee.org). The ISEE has 3 levels. The lower level ISEE is for
students currently in grades 4-5, the middle level ISEE is for students currently in grades
6-7, and the upper level ISEE is for students in grades 8 and up. There are 5 timed
sections on the ISEE exam. The first section of the exam is verbal reasoning, and is
composed of synonym matching and sentence completion. The second section of the
ISEE is quantitative reasoning, and involves both mathematics questions and comparing
values in two different columns. The third section is reading comprehension, which
involves 7 reading passages, and the fourth section is mathematics. The last section of the
ISEE is a 30-minute essay, and students are asked to respond to one of two questions.
The essay section of the exam is not graded, but is sent to the schools that the student has
applied to as an extension of the student’s application. The ISEE is scored on a stanine of
1-9. Lastly, the ISEE exam is the main standardized test accepted by schools in southern
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22

California; consequentially, many students in southern California may prepare for the
ISEE exam.
In sum, The SSAT and ISEE are standardized tests that are used for admission
into private secondary schools. The two tests are similar in format and assess writing,
verbal, and mathematic abilities. Based on individual school requirements, different
private schools require either the SSAT or ISEE for admission. Because of the prevalence
of ISEE testing in southern California, Education Express offers ISEE test preparation
courses.
Why Do Some Students Perform Poorly On Standardized Tests?

While standardized tests involve content learned in school, these assessments are very
different from an assessment taken at school (NCTM, 2012). Many students perform
poorly on standardized tests, and educators often wonder why certain students have poor
performance on standardized exams. Firstly, the format of standardized exams is often
different form the format of exams taken at school. In school, students must show their
work and demonstrate how they arrived at the answer in order to receive full credit. On a
standardized test, students only receive credit for choosing the correct letter from the
answer choices. Many students have difficulty adjusting to this difference. At school,
students are accustomed to studying for exams that test only one subject at a time.
Standardized tests, on the other hand, assess a variety of subjects in a single exam, such
as verbal ability, reading comprehension skills, and mathematics.
There are additional factors that make standardized tests different from tests
administered in school (NCTM, 2012). Standardized test questions are often phrased in a
confusing manner, and many students may not understand what the question is asking.
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Younger students, such as elementary and middle school students, may have difficulty
taking a timed exam. They may also face difficulty completing a task without teacher
guidance. Furthermore, timed tests may cause anxiety in elementary school age students.
In addition to the difficulties involved in taking a standardized test versus a test
administered at school, the student may have never actually learned the standardized test
content or material in class. The child may have been absent from school the day a
particular math concept was taught, or may not have been paying attention to the teacher
in order to learn the concept. What’s more, standardized tests may assess students on
content that is beyond their grade level, and elementary school students may face
standardized test questions that assess middle school content (NCTM, 2012).
Another probable cause for differences in standardized test scores may be aptitude.
According to Smith and Ragan (2005), individuals have different aptitudes, or abilities to
learn and achieve. Students with lower aptitudes are more likely to have lower
performance on standardized tests. Additionally, many students may have learning
disabilities, a condition giving rise to difficulties acquiring knowledge and skills to the
normal level of students at that same age, but have not been diagnosed with these
disabilities (Scruggs et al., 1986). Students with diagnosed learning disabilities can
receive accommodations during standardized tests, such as extended time. Students who
are not diagnosed with these learning disabilities, however, will not receive the
accommodations they need in order to succeed on a standardized test, and this lack of
diagnosis can result in poorer standardized test performance.
There are also group differences in standardized testing and social stratification,
which can result in differences in student scores (Camara et al., 1999). In addition to test-
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24

taking concerns regarding the nature of standardized exams, there are also racial and
ethnic group differences in standardized test scores. There is a gap between ethnic group
scores, such as Hispanic of African-American students, and Caucasian or Asian student
scores. A student’s socioeconomic status and level of parental education can also affect
scores.
Lastly, the quality of education received at school also affects standardized testing.
Academic preparation at school can directly support standardized test performance, and
many students may not receive all the necessary content knowledge at school in order to
perform well on standardized tests (NCTM, 2012). Because of the discrepancy between
the content knowledge taught at school and content knowledge tested on standardized
exams many families seek additional standardized test preparation.
To summarize the previous literature, the nature of standardized tests is different
from exams administered at school. The expectations of standardized tests, the format,
and the range of subject areas tested on standardized exams are differences that can cause
issues for primary school students. Because students may not receive sufficient
preparation at school, many families may elicit the help of test preparation course.
Varying levels of aptitude may cause differences in standardized test scores, and
undiagnosed learning disabilities may cause students to perform poorly on standardized
tests. The quality of education received at school may also be insufficient;
consequentially, there may be a gap in knowledge between the content on standardized
tests and the content that students have learned at school.

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25

Test Preparation Courses and Effectiveness of These Courses

Because of the discrepancy between content taught at school and content tested on
standardized exams, students often enroll in standardized test preparation courses.
Standardized test preparation is effective because it can increase student scores on verbal,
reading comprehension, and mathematics sections of the exam (Briggs, 2001). Common
subjects that are taught in these courses include organization skills, test-taking strategies,
mathematics, vocabulary-based verbal reasoning skills, and reading comprehension.
Furthermore, teaching students test-taking strategies is worthwhile because test-taking
instruction has been found to improve test scores by one-quarter of a standard deviation
(Phelps, Wahberg, & Stone, 2005).
Moreover, standardized test preparation is important because standardized testing
plays an important role in education and society (Phelps et al., 2005). There is a strong
relationship between the number of high stakes tests students take and mathematics
performance in 8
th
grade. Standardized testing also improves the country’s global
performance. Top-performing countries such as England and Germany use more
systematic control measures like standardized exams, and the United States currently
ranks as one of the lower-performing countries globally. There is a positive correlation
between more standardized testing and higher school exam scores, and benefits of
standardized testing include knowledge acquisition, organization, and motivation (Phelps
et al., 2005).
Preparing students for standardized tests is also valuable because test-taking skills
have real world applications. Phelps et al. (2005) state, “The ability to respond to a
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structured set of questions in a specific format has become a communication skill that is
vital in today’s society”. Test-taking skill translate into real-life situations such as
applying for a job, reporting a car accident, or checking into a hotel. Additionally, higher
standardized test scores are correlated to higher levels of education and higher positions
in the workforce and good performance on standardized tests is one of the main ways to
gain access to the competitive blue-collar job market; students must take these tests in
order to go to college and graduate school and to become lawyers, doctors, entrepreneurs,
or any other type of professional (Phelps, 2005). Standardized tests provide checks and
balances in the education system, as well as quality control, especially for entrance into
the workforce (Phelps, et al., 2005).
Criticisms of standardized testing. Though most academic institutions use
standardized tests, there are also several disadvantages to standardized testing and
standardized test preparation. For example, standardized test prep can affect how much
meaningful learning takes place in the classroom because classroom teachers often end
up “teaching to the test” (Sacks, 2001). The lack of meaningful learning subsequently
does not allow students to acquire important skills and abilities, and greatly reduces
metacognitive knowledge such as critical thinking skills, creative thinking, and problem
solving abilities (Sacks, 2001). Additionally, because standardized tests are often
multiple choice, students are limited in their ability to demonstrate the knowledge that
they possess. Lastly, one major criticism of standardized tests is that they often do not
take diversity into account; socioeconomic status, culture, language, and gender are all
barriers that may prevent a student from succeeding on a standardized test (Sacks, 2001).
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While there are several drawbacks to standardized testing practices, overall,
standardized test preparation is effective because it provides students with missing
content knowledge and test-taking skills that will improve performance. Standardized
tests provide important information about students, which is useful for decision-making,
and test-taking skills have real world applications.

Does test preparation translate into the classroom?
Standardized test preparation courses not only help improve standardized test
performance, by they also teach and reinforce content that students learn in school. (Duke
et al., 1997). There are explicit connections between learning test-taking strategies and
general learning practices. Test-taking strategies also translate into the classroom.
Standardized test preparation teaches students specific test-taking techniques, and uses
the standardized test “as a vehicle to offer a long-term tutorial in vocabulary, reading
comprehension, and math” (Briggs, 2001).
There is also an overlap between standardized test content and school curriculum
because test preparation and classroom instruction go hand in hand (Herman & Golan,
1993). Content knowledge learned at school and classroom instruction can help students
on standardized tests, and standardized test preparation can also reinforce the information
that students learn in school (Duke & Ritchhart, 1997). Moreover, standardized test
preparation is a year-long activity that ideally should be incorporated into classroom
instruction throughout the year for greatest effectiveness (Phelps, 2005).
In sum, there is an overlap between standardized test content and classroom
content. Standardized test preparation is worthwhile because the knowledge and skills
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that students gain will not only help them on the standardized test, but will also help them
learn in the classroom.

Individual Learner Characteristics
When examining knowledge, organizational, and motivational settings, in order to
look for possible causes for learners’ lack of achievement, it is useful to have a
framework for considering learner characteristics in the design of instruction. Smith and
Ragan (2005) provide a framework for analyzing individual learner characteristics.
According to Smith and Ragan (2005), in order to design effective instruction,
instructional design should consider the cognitive, affective, and social characteristics of
learners.
Cognitive Characteristics
Learners differ in their cognitive characteristics, which involve aptitude, stages of
cognitive development, and prior knowledge.
Aptitude. Individuals are born with varying degrees of aptitude, the innate ability
to learn or achieve in a given setting. There is a distinction between a person’s general
aptitude to learn, and specific aptitudes known as aptitude complexes. When designing
instruction, it is important to consider general aptitude because it can help determine how
much time it will take for learners to learn the material and the amount of practice
required for learning (Smith & Ragan, 2005). Aptitude is important because the higher a
student’s general aptitude, the less time and practice it will take to master material.
Aptitude and ability are high correlated to motivation (Ackerman & Kanfer, 2003).
Aptitude complexes are specific abilities in given subjects, such as social complex,
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science and math complex, and cultural complex (Ackerman & Kanfer, 2003). Aptitude
complexes involve personality, ability, and interest, and individuals may vary in their
level of aptitude complex for in various subjects. For example, while some students may
have high science and math aptitude complexes, they may have lower social and
personality complexes. Overall, both general aptitude and aptitude complexes are
cognitive characteristics that allow a student to learn.
Lastly, aptitude or intelligence may be viewed as fixed or malleable (Dweck &
Leggett, 1988). An individual’s beliefs about intelligence also result in different types of
goals and behavior. The entity theory of intelligence states that intelligence is fixed and
uncontrollable; individuals who ascribe to the entity theory believe aptitude cannot be
changed and set performance goals. Conversely, the incremental theory of intelligence
states that intelligence is malleable, increasable, and controllable. Individuals who ascribe
to the incremental theory of intelligence believe that their performance depends on the
amount of effort invested into the task and set mastery learning goals (Dweck et al.,
1988). Finally, individuals with the entity view invest less effort and persistence, but
individuals with incremental view invest more effort and persistence into challenging
tasks.
Aptitude for young learners. Children begin learning before entering elementary
school through early childhood experiences such as pre-school and learning in the home
(Crosnoe et al., 2010). Children receive different amounts of early learning; therefore
they enter elementary school with widely different skill levels in core subjects. These
disparities and differences in skill sets compound over time, and, consequentially,
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children have different ability levels during the schooling process. These early learning
experiences form the basis for the aptitude of young learners in school.
Aptitude for young learners in math. Because young learners receive different
amounts of early learning, individual students enter elementary school with widely
different skill levels in subjects such as math. Children also develop informal mathematic
knowledge during early childhood experiences (Baroody & Ginsburg,1990); this informal
knowledge allows students to enter school ready to learn, and because each student has
different levels of informal knowledge, it will inevitably affect their aptitude in a given
subject. Furthermore, students engage in self-regulated learning to compute math and
individual students have different levels of self-regulation in math; self-regulation can
affect aptitude (Baroody et al., 1990).
Children come to school with a sense of informal mathematics knowledge, which
is based on activities that involve counting. This informal knowledge is the basis for
assimilating formal mathematics taught at school. Moreover, the extent to which children
benefit from formal instruction taught in elementary school depends on their level of
prior knowledge; children will assimilate new information into their existing schemas
(Baroody et al., 1990). If the information that is being taught is too unfamiliar, than they
will be unable to assimilate the information and will loose interest in the task.
Additionally, gaps between a child’s existing informal knowledge and the level of formal
instruction at school will prevent assimilation, and consequentially impede learning
(Baroody et al., 1990). Therefore, children need to have a solid foundation of schemas
and information when entering school in order to be able to assimilate the new
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information they learn; these schemas are built during their early childhood learning
experiences in pre-school and in the home environment.
Additionally, as pointed out by Ackerman et al. (2003), learners have different
aptitude complexes in specific subjects. In particular, the science-math complex is the
aptitude trait that allows learners to excel in both science and math. The science-math
complex is associated with visual perception, spatial ability, logic and reasoning, and
interest. Given this information, middle level ISEE students with higher science-math
aptitude are more likely to score well on the mathematics sections of the ISEE exam.
Additionally, the Below-5 students at Education Express may be entering the ISEE
Program with varying degrees of aptitude in math. If the students are entering the ISEE
Program with varied math ability, then instruction must be designed to accommodate
various ability levels.
Cognitive development. Another major cognitive characteristic to examine is the
cognitive development of the learners. The theory of cognitive development suggests that
the human mind develops in broad stages (Joffrion, 2010). According to Jean Piaget
(1954), a child’s ability to learn is related to the child’s stage of cognitive development,
and there are four stages of development (Joffrion, 2010). The first stage of cognitive
development, the sensory motor stage, lasts from birth to 2 years, and children understand
the world through their senses, engaging in activities such as listening, looking, grasping,
crying, and sucking. In the second stage, or the pre-operational stage of development,
from ages 2 to 7, the child learns how to use language and symbols. The child begins to
use language to represent objects, symbols, and images through words. During the
concrete operational stage, from ages 7-12, the child engages in logical and objective
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thinking, and understands the world through manipulation of concrete objects. Operations
are considered reversible mental actions, and concrete operations are applied to actual
objects (Santrock, 2009). At this stage, it is difficult for children to understand abstract
concepts and hypothetical situations. Finally, between the ages of 12 and adulthood,
children reach the formal operations stage in which they are capable of abstract,
hypothetical, and deductive reasoning skills (Joffrion, 2010).
Additionally, there are also changes in information processing capabilities
throughout the lifespan. For example, memory capacities, thinking abilities, and the
ability to sustain and control attention change and develop from birth to adolescence
(Santrock, 2009).
Cognitive development of young learners. Young learners between the ages of
10-12 fall into the concrete operational stage of cognitive development, during which
they require manipulation of tangible objects (Piaget, 1954). Students in this stage are
capable of concrete, logical thinking, but have a difficult time understanding abstract or
hypothetical concepts. Learners are able to classify and divide objects, categorize objects,
and order objects based on a quantitative dimension such as size or length.
Memory is a central process in children’s cognitive development and memory
improves with age (Santrock, 2009). During middle childhood, there is an increase in
long-term memory, the relatively permanent type of memory that holds large amounts of
information over a long period of time (Santrock, 2009). An increase in long-term
memory allows children to gain new knowledge and use different learning strategies such
as creating mental images and using visualization. Long-term memory also allows
children to build expertise in certain subjects, and existing information in one subject
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facilitates acquisition of more knowledge in that subject (Erricsson, K.A., Charness, N.,
Feltovich, P.J., & Hoffman, R.R., 2006). Furthermore, during middle childhood, children
begin to use more learning strategies, deliberate mental activities that improve processing
of information and learning, such as creating mental images and engaging in elaboration,
or extensive processing of information (Bjorklund, 2008).
Several aspects of thinking also emerge and develop during middle childhood. For
example, critical thinking, which is the ability to think reflectively and productively, as
well as evaluate evidence, emerges during middle childhood. Additionally, creative
thinking, which involves problem solving in novel ways, also emerges during this stage
of development, and children also begin to think scientifically (Rickards, Moger, &
Runco, 2009).
Cognitive development of young learners in math. During the concrete
operations stage of cognitive development (Piaget, 1954), students learn how to perform
basic math functions using tangible objects (Joffrion, 2010). Because of the inability to
engage in abstract thinking, students in this stage of development require manipulatives,
such as blocks, counters, and coins, in order to understand higher order thinking math
concepts, such as volume, surface area, geometry, and algebra (Joffrion, 2010).
Furthermore, the middle level ISEE math sections involve complex math concepts like
algebra (such as solving for a variable, solving for the unknown, inverse operations,
graphing ordered pairs, equation of a line, and slope) and complex geometry (such as
finding surface area, volume, and using the Pythagorean theorem). The discrepancy
between the level of math that ISEE students are cognitively prepared to solve and the
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level of math that is presented on the ISEE exam poses a problem for ISEE test
preparation.
In sum, young learners are in the concrete operational stage of cognitive
development. In this stage, students will face challenges solving more complex math
problems that involve abstract thinking and intangible objects, such as algebra and
higher-level geometry, which are presented on the middle level ISEE exam. The
discrepancy between the middle level ISEE students’ cognitive capability and the level of
cognitive thinking required to complete the middle level math sections presents a
problem for ISEE test preparation and subsequent ISEE student performance.
Prior knowledge
According to Smith and Ragan (2005), prior knowledge, or the amount of
information an individual knows about a certain topic, is one of the most important
characteristics to consider when designing instruction for a group of individuals. The
prior knowledge capabilities are a reflection of learning over time. A student’s prior
learning, or specific knowledge that serves as a pre-requisite for achieving higher
learning, is required not only for learning in school, but also for developing general
knowledge about the world (Smith & Ragan, 2005). The more prior knowledge a learner
has, the easier it will be for that learner to understand more difficult concepts; it is
important for learners to have a solid prior knowledge base in order to build higher order
knowledge.
Prior knowledge of learners in middle childhood. When middle level students
enter the ISEE Program, they usually have a prior knowledge base of 5
th
or 6
th
grade. The
middle level ISEE exam tests knowledge concepts for grades 6-8 (NCTM, 2012).
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Consequentially, middle level ISEE students have a weak prior knowledge base to build
on because, even though students in grades 6 and 7 take the middle level exam, the ISEE
exam is designed to test content that is beyond the knowledge that any middle level ISEE
student would have yet learned in school.
Prior knowledge of young learners in math. Furthermore, a solid prior
knowledge base is essential in the subject of math According to National Council of
Teachers of Mathematics (NCTM, 2012), the mathematics concepts on the middle level
ISEE exam include concepts ranging from 6
th
-8
th
grade. Because the mathematic
concepts presented on the middle level ISEE exam are so advanced, middle level students
often have weak prior knowledge for fractions, decimals, geometry (such as calculating
surface area, volume, and the Pythagorean theorem), and algebra (such as understanding
the coordinate plane, ordered pair, plotting / locating points, x and y-intercepts, slope,
graphing a line, and understanding the equation of a line) (Kennedy, 2008).
Because prior knowledge is most likely learned at school, ISEE students have low
prior knowledge in math. When ISEE students enter the ISEE Program at Education
Express, they have just completed the 5
th
grade. The math content on the ISEE exam
involves math concepts for students between 6
th
and 8
th
grade. This lack prior knowledge
in math may contribute to the Below-5 students inadequate score.
Affective Characteristics
Smith and Ragan (2005) also examine several affective characteristics that
account for individual differences between learners. Additionally, individual learners also
differ in their affective characteristics.
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Motivation. Motivation, the process by which goal-directed activity is instigated
and sustained, is a construct that differentiates learners (Pintrich & Schunk, 2002).
Motivation affects both learning and performance, and is composed of three indices: a)
active choice, choosing to begin the task; b) persistence, continuing to work at a task in
the face of obstacles; and c) mental effort, using correct strategies. Motivation is very
specific to the individual, and is also very specific to the given task or context. The
various affective characteristics of individuals, such as attributions, self-efficacy, values,
beliefs, goal orientation, and self-worth theory all contribute to a student’s overall
motivation to engage in work.
Attributions. Attribution theory states that humans are motivated to understand
themselves and the world around them and that people act like naïve scientists, curious
about the causes of their own and others’ behavior (Weiner, 1979). Causal attributions,
such as effort-based or ability-based attributions, depend on the person’s perception of
causes. There are three dimensions for causal attributions. The stability dimension refers
to how stable the attribution is over time, the control dimension indicates how much
control one has over the cause, and locus is the source of the cause. While effort and
ability are both considered internal causes, they differ in terms of stability and
controllability; ability is considered stable and uncontrollable, but effort is considered
changeable and controllable (Weiner, 2008).
Furthermore, attributions have different locus’ of control and can be either
internal or external. Individuals with an internal locus of control believe that both success
and failure are a result of an internal construct or their innate ability, which cannot be
changed. Conversely, individuals with an external locus of control believe that success
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and failure are a result of an external construct, such as effort, which can be changed.
Failure that is attributed to an internal cause will lead to lowered self-esteem, but failure
that is attributed to effort causes may lead to a feeling of guilt, but will result in increased
effort (Weiner, 2000).
Self-efficacy. Self-efficacy is defined as one’s perceived judgment about his or
her ability to execute actions necessary to achieve a specific goal or level of performance
(Bandura, 1997). It is measured by how people would answer the question, “Can I do this
task?” Self-efficacy is usually specific to tasks or situations and can vary across domains.
According to Bandura (1997), people form self-efficacy beliefs based on verbal feedback
and consequences of their behavior, and self-efficacy focuses on a person’s performance
capabilities, not on the individual qualities of the person (Bandura, 1997; Zimmerman,
2000).
Self-efficacy predicts the three indices of motivation: one’s level of self-efficacy
determines if he or she will choose to begin the task, how much effort will be invested
into the task, and whether he or she will persist at the task in the face of a challenge
(Zimmerman, 2000). Additionally, Basi, Steca, Delle Fave, and Caprara (2007) found
that students with high self-efficacy reported higher academic aspirations and spent more
time on their homework than did students with low self-efficacy. High self-efficacy and
moderate goal setting also enhance motivation and subsequent performance (Bandura &
Locke, 2003). Conversely, low self-efficacy, the perceived lack of capability to take
action required to achieve a desired goal, can have a negative impact on motivation and
cause issues with active choice, persistence, and mental effort (Zimmerman, 2000).
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Values. Wigfield and Eccles’ expectancy-value theory (2000) focuses on
expectations for succeeding at a particular task. According to this theory, an individual’s
choices, persistence, and performance can all be explained by the individual’s beliefs
about how well he or she will do at the task and by how much the person values the task.
Expectancy reveals a person’s judgments about capabilities to accomplish a task and
succeed, and values refer to the different beliefs a person may have about the reasons
why he or she might engage in the task (Wigfield & Eccles, 2000). Expectancies are
based on beliefs about ability. Values are composed of interest in the task, importance of
the task, and utility or usefulness of the task. A person’s expectations for success or
failure, beliefs about ability, and perceived difficulty of various tasks can influence
values.
Additionally, over time, social values are gradually transformed into personal
values, and these personal values impact motivation (Ryan & Deci, 2000). There is a
range of motivation, from amotivation, or lack of motivation, to extrinsic motivation, and
intrinsic motivation, engaging in an activity because it gives one joy. The different types
of motivation reflect the varying degrees to which the value has been internalized, or
taken in by the person, and integrated, transforming the value into one’s own.
Ryan and Deci (2000) claim human beings are motivated to reach goals for
different reasons. They claim that extrinsic motivation is engaging in an activity because
it leads to a separable outcome such as incentives or rewards. Incentives such as praise or
money have the potential to create extrinsic motivation for students and extrinsic
motivation can lead to low self-efficacy (Ryan & Deci, 2000). Intrinsic motivation is
ideal because people who are intrinsically motivated show more interest and confidence
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towards novel tasks. Furthermore, intrinsic motivation causes improved performance and
higher self-efficacy. According to Ryan and Deci (2000), people are driven to fulfill three
innate psychological needs: competence, autonomy, and relatedness. Events that
encourage feelings of competence, such as positive feedback on work, enhance intrinsic
motivation and situations that deter feelings of competence, such as negative feedback on
schoolwork, decrease intrinsic motivation.
Beliefs. Additionally, individuals have different beliefs about their ability. An
individual’s beliefs and values result in different views of intelligence, types of
behavioral responses, goals, and behavior. According to Dweck et al. (1988), a person’s
theory on intelligence influences performance. The entity theory of intelligence views
intelligence as fixed and uncontrollable, and these individuals focus on ability and
adequacy. This theory of intelligence will lead the person into the maladaptive “helpless”
behavior patterns in the face of challenging tasks. Individuals who adapt the “helpless”
response will avoid challenge and lack effort and persistence in the face of obstacles.
Moreover, when “helpless” individuals encounter failure, their performance will worsen,
they will begin using ineffective strategies, and they will make internal attributions for
the failure such as a lack of intelligence, memory, or problem-solving ability (Dweck et
al., 1988). People with the maladaptive “helpless” response have negative cognition,
negative affect, and impaired performance in the face of challenge.
On the other hand, the incremental theory of intelligence views intelligence as
malleable, increasable, and controllable, which will result in the adaptive “mastery
oriented” response (Dweck et al., 1988). In the “mastery oriented” response, individuals
seek challenge, assert more effort and persistence, and maintain improving performance
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in the face of obstacles. Unlike the maladaptive “helpless” response, those with the
adaptive mastery response invest more effort and engage in novel problem-solving
strategies in the face of failure. They also make external attributions for failure and plan
specific strategies to overcome the challenge. Those with mastery orientation have
positive cognition, positive affect, and enhanced performance when they encounter
setbacks.
Moreover, a person’s beliefs and responses also result in different types of goals
(Dweck et al., 1988). Perceiving one’s intelligence as fixed and unchangeable leads not
only to the maladaptive “helpless” pattern of behavior, but it also results in setting
performance goals, in which individuals seek to gain approval of their ability and
competence. On the contrary, perceiving one’s intelligence as malleable will lead to
mastery learning goals, in which the individual is concerned with increasing his or her
competence. Overall, beliefs can influence a person’s cognition, affect, and behavior.
Goal orientation. Goals are cognitive representations of motives. There are two
types of achievement goal orientation, or reasons for engaging in achievement behaviors
(Covington, 2000). In achievement performance-approach orientation, individuals
approach a desired consequence to validate superior ability, whereas in performance-
avoidance orientation, individuals will avoid a negative consequence in order to mask
incompetence. The second type of achievement goal orientation is learning-mastery goal
orientation, in which people will take on challenging tasks for the sake of learning and to
improve their self-confidence.
Values and beliefs also indicate the types of goals a person will set (Dweck et al.,
1988). According to Dweck et al. (1988), there are two types of achievement goals:
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performance goals and learning mastery goals. Attributing outcomes to ability and
perceiving intelligence as fixed and unchangeable will result in setting performance goals,
in which individuals are concerned with obtaining positive evaluations of competence
and avoiding negative evaluations. Performance goals focus on judgments of ability
relative to other people, are ego and ability focused, and are dependent on extrinsic
factors. On the other hand, attributing outcomes to effort and perceiving intelligence as
changeable will lead to mastery learning goals, which involve understanding and learning
information. Mastery goals are task-involved, task-focused, and focus on self-
improvement (Dweck et al., 1988)
Moreover, goal setting is a key motivational process. Goals can influence a
student’s active choice in starting an academic task, and the level of difficulty of a goal
can also predict whether the student will persist at completing it in the face of an
academic challenge. The level of difficulty of goals must also be monitored because
individuals will not choose to begin a task if goals are perceived as too challenging so as
to protect their self-worth (Covington, 2000). Consequentially, Clark and Estes (2008)
describe the importance of “C3” goals: goals that are challenging, clear, and current.
Setting “C3 goals” will foster active choice, mental effort, and persistence (Locke &
Latham, 2002). Furthermore, goals should be short-term and vary among students based
on different levels of knowledge; larger goals should be broken up into smaller goals
because once an individual has accomplished the smaller goals, he or she will have more
self-efficacy in completing the larger task Locke & Latham, 2002).
Motivation of young learners in middle childhood. Motivation is a construct
that differs throughout the lifespan (Santrock, 2009). Students in the developmental stage
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42

of middle childhood face particular motivation challenges in attributions, self-efficacy,
values, beliefs, and goal orientation.
Attribution. During middle childhood, students will attribute academic outcomes
to ability or to effort (Caraisco-Allogiamento, 2008). Students who attribute grades to
ability, which is an internal, uncontrollable, and stable dimension, are more likely to
develop learned helplessness, the belief that the student will receive negative outcomes
despite the amount of effort he or she exerts. Students who make external attributions for
grades, such as effort-based attributions, are more likely to invest more effort into school.
Overall, attributions during middle childhood affect active choice, persistence, and
mental effort.
Self-efficacy. Self-efficacy beliefs, which are important predictors of performance,
tend to drop between middle childhood and adolescence, especially between late
elementary school and the beginning of secondary school (Parajes & Graham, 1999).
This drop in self-efficacy impacts performance, and many middle childhood students are
in this exact stage of development, with lower self-efficacy.
Values and beliefs. Wigfield and Eccles (2000) state that an individual’s
expectations for success and the value they place on succeeding are factors that influence
motivation. During middle childhood, children’s values and beliefs change. As children
get older, they begin to value certain academic tasks less than others and this change is
based on perceived utility and experiences of success and failure (Wigfield & Eccles,
2002). Students in late elementary school also face a decline in competence beliefs, and
their expectations for success are very sensitive to success and failures they experience at
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43

that time (Wigfield & Eccles, 2002). Additionally, competence beliefs are related to tasks
that they value, and competence beliefs also influence children’s interests.
Goal orientation. A child’s goal orientation also evolves during middle childhood.
Goal orientation can affect classroom engagement and subsequent achievement outcomes
for students in late elementary school (Meece, Blumenfeld, & Hoyle, 1988). Late
elementary school students who set mastery goals have shown more learning and
understanding of information than students who set performance goals. On the contrary,
performance oriented students in middle childhood work towards gaining recognition,
pleasing the teacher, and reducing the amount of effort invested.
Motivation of middle childhood learners in math. Motivation in math also
changes during middle childhood. One of the main constructs in motivation is self-
efficacy (Bandura, 1997). As mentioned, students in middle childhood tend to have a
drop in their self-efficacy beliefs, and self-efficacy is especially important for
mathematics performance. Particularly, math self-efficacy beliefs decline during the
transition from middle childhood into adolescence, which is the exact transition stage that
middle level ISEE students are in. For 6
th
grade students, self-efficacy beliefs in math
will predict student performance on standardized tests and achievement exams (Parajes &
Graham, 1999). Furthermore, math self-efficacy beliefs are a stronger predictor of math
performance than previous performance in math and the influence of self-efficacy on
mathematics performance is as strong as aptitude or general mental abilities (Parajes &
Graham, 1999). At any ability level, students who have higher math self-efficacy beliefs
are more accurate in math computations and show greater persistence than students with
low math self-efficacy beliefs. Additionally, higher ability students have stronger
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perceptions of self-efficacy, particularly in math, which has important implications for
weaker math students.
For example, there is a decline in math competence beliefs in middle childhood,
beginning in late elementary school and continuing into secondary education (Wigfield &
Eccles, 2002). The value that students in middle childhood place on math also decreases
during the transition from elementary school to secondary school (Parajes et al., 1999).
Mastery goal orientation in mathematics, which involves fully understanding various
math concepts, leads to greater learning (Mecce et al., 1988).
In summary, the changes in student self-efficacy, values, beliefs, and importance
of goal orientation are all factors that should be considered in identifying causes of
achievement gaps in mathematics for middle level ISEE students and designing and
implementing instruction to close these gaps.

Social Characteristics
According to Smith and Ragan (2005), there are also differences in social
characteristics between learners, such as varying social capital, role models, and
environmental influences.
Social capital. Individuals come from different home and school environments
with varying degrees of social support to foster learning. The term “social capital” is used
to describe the degree and quality of forms of social support in a young person’s
interpersonal network (Stanton-Salazar, 1997). A person’s networks consist of family,
friends, and teachers, and these networks are important because they provide structure,
security, and motivation. Social capital can be provided at home through family, through
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peers or role models, or at school through teachers and instruction (Stanton-Salazar,
1997). For example, active parental roles and helpful social networks are forms of social
capital (Goddard, 2003). Social capital at home and instructional support at school are
strong indicators of educational success for elementary school students (Stanton-Salazar,
1997). Students who have more capital at home and more support at school also perform
better on standardized tests. Moreover, students from communities with high levels of
social capital are more likely to have helpful social networks and positive resources
(Ainsworth, 2002).
Enrolling children in private school can also be viewed as a form of social capital.
The amount of social capital that middle level ISEE students are provided in their home
environments can affect their success in the ISEE Program and on the ISEE exam
Role models. Models are very influential on people’s behavior (Bandura, 1997).
Models influence motivation by inhibiting certain actions and disinhibiting other actions.
An effective model is perceived as competent, credible, similar, enthusiastic, positive,
fair, and supportive. Additionally, self-efficacy beliefs are derived from watching models
(Bandura, 1997). Zimmerman (2000) states that learning is enactive, learning through
experience, or vicarious, learning by observing models. Thus, vicarious learning
composes much of the self-knowledge people have about themselves. Likewise, learned
helplessness, attributing failure to causes that one has no control over, can be induced
through modeling. Bandura (1997) claims that vicarious failure experiences produce
learned helplessness and in the Zimmerman et al study (1981), modeling affected the
children’s level of self-efficacy, confidence, and persistence in completing the impossible
task. Role modeling has positive effects on student motivation. Because of the
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importance of vicarious learning, learning by seeing role models, role models are very
important in social contexts, such as home and school environments. Mentors are also
important because they can demonstrate proper social discourse, and parents can serve as
mentors (Stanton-Salazar, 1997).
Role models in math for young learners. Role models have similar effects for
students in middle childhood or late elementary school. Additionally, parental effects on
student math achievement have also been found to be important (Crane, 1996). Students
who had parental support in math demonstrated stronger math scores than students
without parental math role models.

Environmental influences. Smith and Ragan (2005) also state that environmental
influences can impact individual learners. A learner’s environment consists of home and
school. An important environmental influence would be the context and nature of a
learner’s home environment. Having a quiet place at home to study, uninterrupted time to
do homework, and academic support at home can all contribute to a student’s academic
success. Having support from parents or mentors at home to engage in work can impact a
student’s academic outcome.
Environmental influences for young learners. The environment can also
influence learners by assisting students to develop learning strategies. Bjorklund (2008)
states that individual’s use learning strategies, deliberate mental activities that improve
processing of information, to facilitate learning. Learning strategies can help students
store information in their long-term memory, the permanent and relatively unlimited
memory storage (Santrock, 2009). Learning strategies require work and effort, and during
middle childhood, learners begin to use more of strategies such as mental images, which
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involves creating imagery to improve memory, and elaboration, thinking of examples and
personal associations in order to make information meaningful (Scheider, 2004; Kellogg,
2007). Children in middle childhood often require instruction to understand how to use
learning strategies (Santrock, 2009).
What’s more, Dembo and Seli (2004) found that learning strategies help students
improve their time management, learn higher-level content knowledge, develop critical
thinking skills, and ask for support outside the classroom. Employing learning strategies
involves self-regulatory learning; the ability to take control of one’s learning and change
certain aspects of one’s behavior when necessary. Self-regulatory learning involves
establishing learning goals, monitoring progress towards those goals, monitoring
understanding of concepts, asking for help when needed, and changing the learning
environment in the face of distraction (Dembo & Seli, 2004). Self-regulation can be
taught in both the school and home environment.
Environmental influences for young learners in math. A learner’s school and
home environments also have an effect on the student’s achievement in math. According
to Crane (1996), home environment plays an important role in elementary school students’
achievement in math. In the Crane (1996) study, elementary school students who had
supportive home environments, such as a quiet place at home to study, uninterrupted time
to do homework, and parental support, showed improvements in math exams, and
improved by three-fifths of a standard deviation.
In summation, learner characteristics must be considered when examining
knowledge and skills, motivation, and organizational gaps in performance. Cognitive,
affective, and social characteristics of learners should also be considered when examining
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gaps, and individual learner characteristics must be considered when designing
instruction.
Summary
As indicated by the review of current literature, private schools currently play an
important role in our country’s system of education and there are three distinct categories
of private schools: catholic schools, religious schools, and nonsecretarian schools such as
Montessori schools or college-preparatory schools. Private schools can serve a religious
purpose or other purposes and, consequentially, have rigorous entrance requirements.
Standardized testing is part of the admissions process to private schools. The main
standardized test used by private secondary schools in southern California is the
Independent School Entrance Exam (ISEE). Students perform differently on standardized
tests because of differences in format between the types of exams taken at school and
standardized exams, the variety of subjects tested on a standardized exam, test anxiety,
and differences in aptitude. Test preparation courses can help students improve their
performance on standardized tests by providing them with test-taking skills to help them
succeed on standardized exams. In addition to test-taking strategies, there is an overlap
between standardized test content and content learned in school. Consequentially,
preparing for standardized tests will also help students do better at school, and content
learned in school will also help students do better on standardized exams. Lastly,
individual learner characteristics, including cognitive, affective, and social characteristics
must be considered when designing instruction for students.
The literature review indicates that there are several knowledge, motivation, and
organization variables to consider when designing intervention. Firstly, research indicates
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that individual student differences in aptitude and a student’s beliefs or views of aptitude
as fixed or malleable may cause differences in standardized test scores (Ackerman &
Kanfer, 2003; Dweck & Legett, 1988). Thus, aptitude and beliefs will be assumed causes
for examination. Moreover, the literature also suggests that student prior knowledge can
affect academic success, and a lack of prior knowledge in math will also be considered an
assumed cause for Below-5 student performance (Smith & Ragan, 2005). A student’s
cognitive development can also impact the pupil’s ability to succeed at certain levels of
math, and cognitive development is another assumed cause that will be examined
(Joffrion, 2010). As indicated by the literature review, motivation is a construct that
impacts student performance, and motivation will consequentially be another assumed
cause for Below-5 student performance. Lastly, the literature suggests that providing
students with proper support in the home environment can help foster student
achievement; therefore the students’ home environment will be examined to see if it is
affecting Below-5 student performance on the ISEE (Dembo & Seli, 2004).
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CHAPTER 3: METHODOLOGY
Purpose of Inquiry and Guiding Questions
The purpose of this case study was to examine the knowledge and skills,
motivation, and organizational context, culture, and capital causes of the achievement gap
between the Below-5 group (stanine of 4 or lower) and higher performing group (stanine
of 5 of higher) on the math sections of the middle level ISEE exam.
The study questions included:
1. What are the causes of the gap that “Below-5” students have in knowledge and
skills, motivation, organizational context, culture, and capital that affect their successful
achievement of 5 or better on the math sections of the ISEE Program Post-test?
2. What are the potential knowledge and skill, motivation, and organizational
solutions to address the Below-5 students gaps in achieving a score of 5 or better on the
math sections of the ISEE Program Post-test?
Description of the Framework
The framework for the methodology in the current study was the Gap Analysis
Problem Solving Approach (also referred to as GAP or GAP Analysis) (Clark & Estes,
2008; Rueda, 2011). The GAP analysis model of improved institutional performance
examines three key variables: 1) knowledge and skill deficits, 2) organizational issues,
and 3) motivation. According to the GAP approach, institutions first set global and
cascading goals, examine current performance, identify gaps in performance, hypothesize
and validate how KMO impact those gaps in performance, create solutions, implement
those solutions, and evaluate the effectiveness of those solutions. The steps in the GAP
Analysis process are listed below in Figure 3.1.
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Both quantitative and qualitative methods were used for the GAP Analysis model
in this study. In order to determine knowledge gaps, quantitative data were used by
looking at artifacts, such as secondary data from pre-training test that had already been
collected. In order to determine organizational and motivation gaps, qualitative data such
as student interviews and periodic motivation surveys and were used.

Figure 3.1: Gap Analysis Process

The steps of the Clark and Estes (2008) Gap Analysis Process Model are:
Step 1: Goals: Identify and operationalize measurable organizational goals.
Step 2: Current Performance: Quantify the current achievement at each level.
Step 3: Gaps: Determine gaps between goals and current performance.
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Step 4: Causes: Hypothesize and validate empirically how each of three causes
(knowledge and skills, motivation, organizational culture) impact the proposed
gap.
The following steps of the Clark and Estes (2008) Gap Analysis Process Model will be
discussed in Chapters Four, Five and Six of the dissertation and will not be incorporated
into this methodology chapter.
Step 5: Solutions: Plan systemic and individual gap-closing solutions.
Step 6: Implementation: Implement systemic and individual gap-closing solutions.
Step 7: Evaluate and modify solutions for continual improvement.

Step 1: Operationalization of the Goal
In order to help students who are not performing up to par on the ISEE, Education
Express has set the following performance goals. The current global goal of the
institution is that all students will receive a stanine score of 5 or better on math sections
of the November ISEE Post-test administered at Education Express because this will
indicate that they are ready to succeed on the December ISEE exam.
A complete GAP Analysis would include examination of all the stakeholders. A
stakeholder would be any person that is concerned with the achievement of the
organization’s global goal, such as administration, teachers, parents, and students. For
the purpose of this study, the students as stakeholders were the focus of this study. The
other stakeholders are also discussed as needed to support student achievement of their
goal.
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Each stakeholder can have individual goals, and within each stakeholder there can
be cascading goals. For the purpose of this study, the cascading goals selected for this
study are concerned with student achievement on the math sections of the ISEE exam.
The cascading goal addressed in this study is for the Below-5 group of students to
achieve a score of at least a 5 on the math sections of the ISEE exam. The next cascading
goal is for the Below-5 students to achieve the required knowledge and skills and learn
the various math topics necessary to receive a score of 5 or higher.
Goal for Below-5 students in mathematics. When examining ISEE student
performance in the past and when considering the difficult level of the math content on
the ISEE exam, the current goal of the organization is to provide students who are
identified as falling below a stanine score of 5 on the ISEE math sections on the ISEE
Pre-test with pre-training so that all students, including these Below-5 students, will get a
score of 5 or better on the post-ISEE Program training test in November. The overall goal
of the organization is that all students receive a score of 5 or higher in post-training so
that they will receive a score of 5 or higher on actual ISEE exam administered in
November each year.
Step 2: Current Performance
The second step in the GAP Analysis process involves examining current
performance. Every year, roughly 100 middle level students enter Education Express for
ISEE test preparation, and each year about 10 students receive a stanine score below 5 on
the ISEE in December. Furthermore, the Below-5 students are often identified at the
beginning of the test preparation course through data collected from the Pre-test that
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ISEE students take before the actual course in June or August. The data from the Pre-test
also informs the current gap in performance.
Step 3: Gap in Performance
Step 3 in GAP Analysis requires identifying gaps in performance. As indicated by
test data, roughly 10% of students at Education Express fall in the Below-5 category. If
the knowledge, organization, and motivation causes of the gap that Below-5 students face
is not addressed, then the current gap will continue and is likely to get wider as academic
standards continue to become increasingly challenging. Thus, by analyzing causes of
gaps, appropriate solutions must be created to close the current gap.
Step 4: Assumed Causes of the Performance Gap
The fourth step in GAP Analysis is to hypothesize assumed causes of
performance gaps (Clark & Estes, 2008). Individuals often jump to solutions regarding
assumed causes of performance gaps (Rueda, 2011; Clark & Estes). Therefore, in order to
avoid error, the following section examines all the assumed causes based on informal
interviews, learning, organization, and motivation theory, and the Chapter 2 literature
review. These assumed causes are identified so that they can then be validated (Rueda,
2011). A summary of these causes can be found in Table 3.2.
Informal Interviews
Based on teacher observations over the past several years by this researcher and
other faculty, many of the lower performing students who fall into the “Below-5” group
of students, are unable to perform up to par in the course because they lacked the basic,
prior knowledge required to perform the higher level math on the ISEE. Several
interviews with the Director of Education Express also validated the observation that
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students were missing important prior knowledge. In particular, the specific content areas
where ISEE students faltered were: identifying factors versus multiples, working with
positive and negative integers, calculating perimeter, area, surface area, volume, and
several pre-algebra concepts (inverse operations, graphing points, coordinate plane,
graphing a line, slope). The interviews with the Director of Education Express and the
observations of student performance in the fall preparation course resulted in a 50-item
survey assessing the basic prior knowledge that students needed to have in order to
perform the higher-level ISEE math.
Learning and Motivation Theory
Learning. In addition to interviews, learning or knowledge causes may be
another imperative cause for gaps in student ISEE performance based on a review of
learning theory. Using the National Council of Teachers of Mathematics (NCTM)
standards, the ERB (2009) outlines the following topics on the mathematics sections of
the ISEE: numbers and operations (which includes whole numbers, decimals, fractions,
and percents), algebraic concepts, geometry, measurement, data analysis, and probability.
According to Anderson and Krathwohl’s (2001) revised taxonomy for learning,
the above concepts that are on the ISEE exam involve different knowledge types.
Knowledge and learning involve four different types of knowledge: factual knowledge,
the basic elements that students need to know in order to solve a problem, conceptual
knowledge, the relationship between basic elements within a category that allow them to
work together, procedural knowledge, the ability to use skills, techniques, and methods,
and metacognitive knowledge, which is the knowledge of one’s cognition (Anderson &
Krathwohl, 2001). Table 3.1 categorizes the NCTM standards into each knowledge type.
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Table 3.1
Knowledge Types

Type of Knowledge Concepts on ISEE
Factual Knowledge of the terms
- Whole numbers
- Integers
- Prime numbers
- Fractions, decimals, percents

Understanding the relationship between decimals,
fractions, and percents

Data analysis
- Ability to read a graph / chart

Knowledge of ordered pairs on a graph (x, y)

Conceptual Identifying:
- Integers
- Factors versus multiples
- Least common multiple
- Greatest common factor
- Decimals, fractions, percents

Geometry – knowledge of theories:
- Perimeter, area, surface area, volume
- Pythagorean theorem

Understanding the relationship between decimals,
fractions, and percents

Algebraic concepts:
- Knowledge of inverse operations
- Knowledge of variables
- Knowledge of ordered pairs

Procedural Rounding:
- Whole numbers
- Decimals
- Fractions
- Percents
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Estimating

Adding subtracting, multiplying, and dividing
decimals

Adding subtracting, multiplying and dividing
factions

Adding, subtracting, multiplying, and dividing
mixed numbers

Problems involving percent:
- “Percent of” problems
- Calculating discount
- Calculating sales tax

Data analysis
- Ability to use a graph to find information
- Central tendency: mean, median, mode,
range, minimum value, maximum value

Probability

Geometry – applying theories:
- Perimeter,
- Area: quadrilateral, triangle, circle
- Surface area of three dimensional figures
- Volume

Applying inverse operations

Algebraic concepts:
- Solving for the unknown
- Solving for variables
- Locating an ordered pair
- Plotting a point on a graph using an ordered
pair

Calculating the slope of a line

Metacognitive - Setting goals
- Selecting effective strategies
- Monitoring progress towards goals
- Evaluating their progress
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- Explaining how they achieved their goals

Motivation. Motivation is another construct that greatly affects ISEE student
performance. According to Mayer (2011), motivation is the learner’s contribution to the
process of learning and necessary for meaningful learning to occur. There are 3 different
indices of motivation: a) active choice, which involves choosing to begin the task, b)
persistence, or continuing to engage in the task even in the face of challenge, and c)
mental effort, which involves using the correct strategies to problem solve (Pintrich,
2003; Pintrich & Schunk, 2002.)
Additionally, motivation involves several underlying psychological and
environmental constructs that are also related to the three motivation indices. Values,
self-efficacy, attributions, mood, and goals also affect an individual’s motivation (Clark
triangle, 2005; Pintrich, 2003). Values involve interest in the given task, the important the
individual views the task to be, and the perceived utility or usefulness of the task
(Wigfield & Eccles, 2000). Values can also indicate a person’s expectations for success
or failure on a given task. Values are important because they affect all three indices of
motivation, and according to the CANE model of motivation (Clark, 1998), active choice,
persistence and mental effort are driven by value and interest in the task. Self-efficacy, an
individual’s beliefs about his or her ability achieve a specific goal, also drives all three
indices of motivation (Bandura, 1997). What’s more, an individual’s attributions, or
belief about control and stability of novel or negative events, can be attributed to internal
or external causes (Weiner, 2000). External attributions and environmental factors affect
choice, persistence in the face of challenge, and mental effort (Weiner, 2000). A student’s
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mood, which involves affect and emotion, also connects to all three indices. Lastly,
mastery goals, engaging in learning in order to master the concept, versus performance
goals, engaging in learning to meet a certain level of performance, also affect each of the
three motivation indices (Bandura & Locke, 2003).
Teacher observations indicate that middle level ISEE students suffer from all
three indices on the math sections of the ISEE exam; therefore the underlying causes
were examined. Because all these psychological and environmental factors influence
three indices of motivation, they were included as assumed causes for any validated
indicator of lack of choice, persistence mental effort.
Organization. Several possible organizational issues could also contribute to the
gap in ISEE student performance. One aspect of the Program organization is that the
majority of the ISEE classes are held on the weekends when students are not attending
school. This scheduling of ISEE courses may deter students from dedicating time and
effort into studying. Many elementary school students may dislike having to spend their
weekends in a classroom rather than dedicating their weekends to leisure activities. This
organizational aspect may be contributing to the current. Gap.
According to Gallimore and Goldenberg (2001), cultural models and cultural
settings are another aspect of organization that also affect student performance. Cultural
models are shared mental schemas between a group of people that dictate values,
interactions, behavior, cognitions, and affect. Cultural models often go unnoticed because
they are substantial part of the environment and these models are found at home or in the
community (Gallimore et al., 2001). Cultural models affect behavior at school, and each
ISEE student comes from a different background with various cultural models.
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Additionally, cultural models impact context, which may include when or where
homework is completed, how much time or emphasis is placed on studying, and parental
involvement. ISEE students may
Another important aspect of organization involves cultural settings, everyday
events that occur within a cultural context. Cultural settings include daily activities, such
as bedtime, homework time, and leisure time. Cultural settings involve the home
environment, and ISEE students all come from different cultural settings. A student’s
home environment impacts academic performance, and many ISEE students may be
coming from an environment involving high pressure to succeed or the opposite, a setting
characterized by disinterest in the student’s success. These various organizational,
cultural, and contextual components all have an impact on the “Below-5” student
performance on the ISEE exam.
Causes Informed by the Literature
According to the literature, there are several causes that may be contributing to
the current Below-5 student performance gap on the math sections of the middle level
ISEE exam. Firstly, differences in aptitude and ability may result in different scores on
standardized exams (Ackerman & Kanfer, 2003). Additionally, the difference between
the format of exams students are accustomed to taking in school and the breadth and
scope of standardized exams can also result in poor test scores (NCTM, 2012).
An important cause that was discovered in the literature review was the cognitive
development of learners (Santrock, 2009). The majority of middle level ISEE students
may still be in the concrete operation stage of cognitive development, which requires
manipulation of tangible objects, but the middle level ISEE exam involves math concepts
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that require formal, abstract thought, which many of these students are not yet capable of
(Piaget, 1954). Thus, an inappropriate level of instruction for the cognitive level of the
learner is another assumed cause. Along the same lines, because the math sections of the
middle level ISEE exam cover math content for students in grades 6 to 8, many Below-5
students may have weak prior knowledge in math to tackle the difficult content presented
on the exam (Smith & Ragan, 2005; NCTM, 2012).
The individual and cognitive characteristics that are suggested by the literature
reveal motivation as another assumed cause for gaps in Below-5 student performance.
The Below-5 ISEE students often face issues with active choice, persistence, and mental
effort (Pintrich, 2003; Pintrich & Schunk, 2002). Furthermore, many Below-5 students
may lack social capital, or social support in their home environments (Stanton-Salazar,
1997), 7. Below-5 students may lack appropriate role models in math or have poor
environmental influences (Bandura, 1997; Smith & Ragan, 2005). Lastly, lack of a proper
home learning environment can be cause for lack of student achievement, and
consequentially, students home environment should also be considered a possible cause
for poor student achievement (Dembo & Seli, 2004).
Summary. A summary of the sources of assumed causes categorized as
Knowledge, Motivation, and Organization is found in Table 3.2.
Table 3.2
Summary of Assumed Causes for Knowledge, Motivation, and Organization

Sources / Causes Knowledge Motivation Organizational
Processes

Informal Interviews

Students are missing
prior knowledge

Studying for the
exam is optional

Do not persist in the
Classes are held
during the
weekends

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face of challenge

Invest minimal
effort into class and
homework
assignments

Students are in class
with peers and
prefer to socialize
during class

Theory

Knowledge types:
- Factual
- Conceptual
- Procedural,
- Metacognitive
3 indices:
1) Active choice
2) Persistence
3) Mental effort

- Values
- Self-efficacy
- Attribution
- Mood
- Goal orientation
- Incentives
- Models

Organizational
barriers in
homework
environment
(Clark & Estes,
2008).
Literature

Different aptitudes &
varied ability
(Ackerman &
Kanfer, 2003)

Cognitive
Development (Piaget,
1954)

Prior Knowledge
(Smith & Ragan,
2005)

Motivation (Pintrich
& Schunk, 2002)

Context &
environment (Smith
& Ragan, 2005)

Lack of role models
Attribution
(Weiner)

Self-efficacy
(Bandura)

Values (Wigfield &
Eccles; Ryan &
Deci)

Malleable versus
entity beliefs about
ability (Dweck,
1988)

Goal orientation
(Zimmerman, Lock
& Latham, Clark &
Estes, 2008)

Self-worth
Cultural models
& cultural
settings
(Gallimore &
Goldenburg,
2001).
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(Bandura, 1997)

(Covington, 2000)

Step 5: Validation of the Causes of the Performance Gap
The above list of assumed causes proposed in Table 3.2 were used to validate to
create a knowledge and skills questionnaire and survey that was distributed to a Below-5
sample population at Education Express.
Sample and Population
The sample and population of the study was 6
th
grade students between the ages
of 11 and 12 in the greater Los Angeles area who attend Education Express for ISEE
preparation. The population size of Below-5 students was 37 out of 104 middle-level
ISEE students, and the sample size of the study was 9 students (n = 9). Additionally,
there were a total of 10 middle-level ISEE instructors at EE.
Instrumentation and Data Collection
Knowledge causes. Once the Below-5 students were identified based on the ISEE
pre-test in June, they were given a 40-item math questionnaire to identify the exact math
concepts and pre-requisite math skills they need to learn in order to be able to tackle the
advanced-level math in the ISEE preparation course and on the exam. In order to
examine knowledge causes for Below-5 student performance, students who are identified
as falling into the Below-5 group were given a 40-item math questionnaire to determine
the content knowledge in math that they are missing. The current goal is set because
Education Express can identify a knowledge and skills gap based on the pre-test students
take in June. The exact knowledge and skills that ISEE students need, however, were not
identified until they took a 40-item survey of basic math concepts. Additionally,
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Education Express has not identified the motivation and organizational issues that may be
responsible for the gap in ISEE math performance. Goal is that all the students get a 5 or
better in post-training so that they will do 5 or better on actual ISEE exam.
Organizational causes. A survey was given to Below-5 parents asking about the
students’ home learning environment and role models in the home in order to triangulate
data. The survey asked parents to see if they are providing the proper home learning
environment for their children.
Motivation causes. In order to determine Below-5 student motivation, the Below-
5 group of students were given weekly smiley face surveys at the end of every class
asking them about value, interest, importance, and utility. Using a smiley face Likert
scale, the motivation survey asked students to rate their interest in the subject, their value
for engaging in the ISEE preparation, how important they believe studying for the ISEE
exam is, and how useful they found the ISEE preparation course. Additionally, student
interviews were also used to assess motivation and to triangulate the data.
Data Analysis
Several strategies were used to analyze survey, interview, and document data. The
unit of analysis of this inquiry project was Education Express. The purpose of this inquiry
project suggested the use of a quantitative and qualitative methodology to investigate the
causes for Below-5 student performance on the math sections of the middle level ISEE
exam. The various data collected from the quantitative and qualitative methodology, such
as questionnaires, surveys, and interviews, informed propose solutions to the director and
administration of Education Express. The focus is to understand the Below-5 student gap
even in the face of standardized test preparation.
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For the survey results, descriptive statistics were used to identify the basic
features of the data, and included the mean.
For the qualitative data collected through the semi-structured interviews and focus
groups, the text of the transcripts were coded using symbols that represent the categories
of knowledge and skills, motivation and organization to capture and analyze relevant
information and guide the identification of causes with additional granularity.
Summary
In sum, both quantitative and qualitative methods, such as a knowledge
questionnaire, student interviews, and motivation and parent surveys, were used for the
purpose of the inquiry to identify the knowledge and skill, motivation, and organizational
causes for Below-5 student performance on the math sections of the ISEE Post-test. The
methodology followed the Gap Analysis Process Model (Clark & Estes, 2008, Rueda,
2011) by establishing goals, determining gaps, identifying assumed causes and validating
causes of the under achievement of the Below-5 group in the ISEE Program.
To address the second study question of identifying the potential knowledge and
skill, motivation, and organizational solutions to address the Below-5 students gaps in
achieving a score of 5 or better on the math sections of the ISEE Program Post-test, the
following steps of the Clark and Estes (2008) Gap Analysis Process Model will be
discussed in Chapters 4, 5 and 6 of this dissertation.
Step 5: Solutions: Plan systemic and individual gap-closing solutions (Chapter 5).
Step 6: Implementation: Implement systemic and individual gap-closing solutions
(Chapter 5).
Step 7: Evaluate and modify solutions for continual improvement (Chapter 6).
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CHAPTER 4: RESULTS
Education Express has set achievement goals to enable Below-5 students to score
a stanine of 5 or higher on the math sections of the ISEE Post-test. The Clark and Estes
(2008) Gap Analysis Process Model was used as the framework for this study. According
to the framework, knowledge and skills deficits, motivation, and organizational barriers
all contribute to the Below-5 student gap in math achievement, and each of the three
areas were examined.
Quantitative research methods in the form of a student knowledge questionnaire,
student motivation surveys, and parent home organizational surveys were used to capture
data. Additionally, to supplement the quantitative data and offer more detail, qualitative
student interviews at the end of 2 math lessons were also used to provide data.
Data analysis suggested the perceived gaps in Below-5 student knowledge and
skills, motivation, and organizational barriers that may need to be closed in order to help
Below-5 students to achieve the organizational goal of scoring a stanine of 5 or higher on
the math sections of the ISEE Post-test.
Demographics
The participants of the study were nine 6
th
grade students, ages 10-12, who attend
both public and private elementary schools in the greater Los Angeles County. While,
overall, their socioeconomic backgrounds do vary, the majority of Below-5 students
come from middle-class families who are enrolling their children in the private school
system. In additionally, 10 ISEE instructors participated in this study.

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Study Question One: What are the causes of the gap that “Below-5” students
have in knowledge and skills, motivation, organizational context, culture, and
capital that affect their successful achievement of 5 or better on the ISEE Program
Post-test?
The quantitative data results in the form of student knowledge, motivation, and
organization surveys, and parent organization surveys, provided information about the
magnitude of existing gaps. Once the Below-5 students were identified after the ISEE
Pre-test, they were given a 40-item knowledge survey to determine knowledge gaps.
Below-5 students were also given a motivation and organization “smiley-face” survey at
the end of lesson 10 in the ISEE Program to assess motivation and home organization
factors. The smiley-face survey assessed the motivation constructs of student interest,
utility, importance, effort, and self-efficacy. The smiley-face survey also asked students
about organizational constructs, such as ISEE classes being held on the weekend, and if
Below-5 students had a quiet place at home to do ISEE homework. The parent
organization survey asked parents about parent motivation constructs, importance and
utility, regarding their children’s ISEE homework, and the organizational constructs of
having a quiet place at home for students to do their ISEE homework, and having a
credible model that students could ask for help from if they needed help with ISEE
homework.
The qualitative data results in the form of student interviews expanded on the
quantitative student surveys and provided more detail regarding motivation, and
organization causes. Students were interviewed individually during their snack time in
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between classes. Over the course of 3 lessons, each of the 9 students was interviewed in
their math class during break time. A job aid with 8 open-ended interview questions was
created to facilitate the student interviews, and each student was asked each of the 8
questions. 5 interview questions assessed student motivation, and 3 interview questions
asked students about organizational factors at home. Student responses were written
down in short hand and the responses were then analyzed and coded.
Descriptive statistics, including means and an analysis of the means were used to
analyze the results.

Knowledge and Skills Results
The Anderson and Krathwohl (2001) framework for knowledge was used to
assess Below-5 student knowledge. Applying Anderson and Krathwohl’s (2001) revised
taxonomy for learning, the math concepts presented on the ISEE exam involve four
different types of knowledge: factual knowledge, the basic elements that students need to
know in order to solve a problem, conceptual knowledge, the relationship between basic
elements within a category, procedural knowledge, the ability to use skills, techniques, or
methods, and metacognitive knowledge, which is the knowledge of one’s cognition
(Anderson & Krathwohl, 2001).
The review of literature also pointed to several assumed causes, such as the
importance of prior knowledge (Smith & Ragan, 2005), cognitive development (Joffrion,
2010;Piaget, 1954), and different aptitudes or ability (Smith & Ragan, 2005; Ackerman
& Kanfer, 2003).

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Assumed Knowledge Causes
There were several assumed knowledge and skill causes for the Below-5 student
gap in performance. Based on informal interviews with the director of Education Express,
a lack of prior knowledge was one assumed cause. Prior knowledge is specific knowledge
that serves as a pre-requisite for achieving higher learning and facilitates learning more
advanced concepts (Smith & Ragan, 2005). Below-5 students may be missing the four
different types of prior knowledge necessary to succeed on the ISEE: factual, conceptual,
procedural, and metacognitive knowledge (Anderson & Krathwohl, 2001). A 40-item
knowledge survey was used to validate the assumed cause of low prior knowledge. A
copy of the student knowledge survey is included in Appendix A.
Furthermore, the cognitive development of middle level ISEE students was
another assumed cause for the knowledge and skills gap. The majority of the Below-5
ISEE students are assumed to still be in the concrete operations stage of cognitive
development, during which students learn how to perform basic math functions by using
tangible objects and are unable to engage in abstract thinking required for higher order
math without the use of manipulatives such as blocks or counters (Piaget, 1954; Joffrion,
2010). Advanced math concepts, such as volume, surface area, geometry, and algebra,
that are assessed on the ISEE require abstract thinking (Joffrion, 2010). The assumed
cause of cognitive development was also assessed in the 40-item knowledge survey in
items 9,10, and 11, which assessed “order of operations” required for algebra, item 15,
which asked students to find volume, item 16, which assessed surface area, items 21, 26,
and 28-30, assessing the relationship between fractions, decimals, and percents, and item
27, which was a fraction word problem.
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Lastly, another assumed cause involved differences in aptitude and ability (Smith
& Ragan, 2005). Because children receive different amounts of early learning, they enter
school with different skill sets, and these differences compound over time, resulting in
different levels of ability (Crosnoe et al., 2010). Aptitude can result in different levels of
ability in subjects such as math. Consequentially, the 40-item questionnaire also assessed
Below-5 student aptitude in math by determining their skill set in the pre-requisite math
knowledge.

Student Survey Results
Once Below-5 students were identified, they were given a 40-item knowledge
questionnaire that identified the basic, pre-requisite math knowledge necessary for
successful completion of the ISEE Program. The knowledge questionnaire assessed basic
math vocabulary (sum, difference, product, quotient, mean), prime numbers, factors,
multiples, order of operations, geometry (perimeter, area, surface area, volume) with
quadrilaterals, triangles, and circles, angle measures, place value, computation with
decimals, fractions, and percents, and basic probability.
Descriptive statistics were calculated for the knowledge data and the mean test
score for the 9 Below-5 students was m = 0.60. A score of 1.00 on the pre-requisite
knowledge questionnaire would indicate that Below-5 students had all the necessary prior
knowledge that is required to successfully complete the ISEE Program at Education
Express and subsequently score a stanine of 5 or higher on the ISEE, which indicates a
clear gap in Below-5 knowledge.
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Factual knowledge. The questions involving factual knowledge on the
knowledge survey involved identifying math terms such as “product”, “prime number”,
fractions, decimals, and percents, and identifying the relationship between fraction,
decimal, and percent. Additionally, knowledge of acute, right, and obtuse angle types and
place value of decimals were also assessed.
The results of the knowledge survey show that the majority of Below-5 students,
about 55%, were missing the factual knowledge of prime numbers.
Conceptual knowledge. The conceptual knowledge on the survey involved
listing factors, prime factors, multiples, and understanding the relationship between
decimals, fractions, and percents. Furthermore, Below-5 students were also assessed on
their knowledge of geometry formulas, such as perimeter, circumference, area of
quadrilaterals, triangles, circles, surface area, and volume.
According to the results of the knowledge questionnaire, 55% of Below-5
students are missing conceptual knowledge of prime factors, and 100% of the students
are missing conceptual knowledge about the relationship between decimals and fractions.
Procedural knowledge. Several aspects of procedural knowledge were assessed
in the knowledge survey. Below-5 students were asked to apply math terms, such as sum
and product to solve problems. They were also asked to add, subtract, multiply, and
divide decimals, fractions, and mixed numbers, and to find perimeter, area, surface area,
and volume. Lastly, students were asked three basic probability questions for rolling a
number cube.
Overall, the bulk of missing prior knowledge was procedural knowledge. The
main areas of missing procedural knowledge are as follow: order of operations [question
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#9 – 6/9 (66%), question #10 – 8/9 (88%), question #11- 9/9 (100%)], circumference
[question #13 – 9/9 (100%)], area [question #14 – 9/9 (100%)], surface area [question
#16 – 9/9 (100%)], dividing with decimals in the divisor [question #25, 9/9, (100%)],
word problem with fractions [question #27 – 9/9 (100%)], comparing fractions [question
#31 - 9/9, (100%)], multiplying mixed numbers, [question #36, 7/9, (77%)], and dividing
fractions [question #37, 8/9, (88%)].
Metacognitive knowledge. During the knowledge survey, Below-5 students were
asked to select appropriate strategies to solve each problem, and to self-monitor progress
towards completing the knowledge survey.
Table 4.1 provides an item analysis of knowledge types on the knowledge survey
(Anderson & Krathwohl, 2001) and the mean score for each item.
Table 4.1
Knowledge Type, Knowledge Question and Percent Answered Incorrectly

Knowledge
Type
Knowledge Question Percent of students that
answered question
incorrectly

Factual

1 – Identifying the term “product”
5 – Listing examples of prime numbers
17 – Identifying right angle
18 – Identifying acute angle
19 – Identifying obtuse angle
20 – Knowledge of decimal place value

*Question #5 – 5/9 (55%)

Question #20 – 2/9 (22%)
Conceptual

3 – Listing factors
4 – Listing factors
6 – Listing prime factors
26 – Converting decimal to fraction
28 – Converting decimal to percent
29 – Converting percent to decimal
30 – Converting percent to decimal

*Question #6 – 5/9 (55%)
*Question #26 – 9/9
(100%)
Question #28- 2/9 (22%)
Question #29 – 2/9 (22%)
*Question #30 – 6/9
(66%)
Procedural 1 – Calculating “product”
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2 – Calculating “product”
7 – Listing multiples of a number
8 – Identifying Least Common
Multiple
9 – Order of operations
10 – Order of operations
11 – Order of operations
12 – Calculating perimeter
13 – Calculating circumference

14 – Calculating area
15 – Calculating volume
16 – Calculating surface area
21 – Writing decimal as fraction
22 – Adding decimals
23 – Multiplying decimals
24 – Dividing decimals
25 – Dividing decimals
27 – Fraction word problem
31 – Comparing fractions
32 – Adding fractions
33 – Adding mixed numbers
34 – Subtracting fractions
35 – Multiplying fractions
36 – Multiplying mixed numbers
37 – Dividing fractions
38 – Probability
39 – Probability
40 – Probability

Question #7 – 2/9 (22%)
Question #8 – 3/9 (33%)

*Question #9 – 6/9 (66%)
*Question #10 – 8/9
(88%)
*Question #11- 9/9
(100%)
*Question #13 – 9/9
(100%)

*Question #14 – 9/9
(100%)
Question #15 – 3/9 (33%)
*Question #16 – 9/9
(100%)
*Question #21 – 9/9
(100%)

Question #23 – 1/9 (11%)
Question #24 – 1/9 (11%)
*Question #25 – 9/9
(100%)
*Question #27 – 9/9
(100%)
*Question #31 – 9/9
(100%)

Question #33 – 2/9 (22%)

*Question #36 – 7/9
(77%)
*Question #37 – 8/9
(88%)

Metacognitiv
e

- Selecting effective strategies
- Monitoring and evaluating
progress towards set goals

Note: Items with asterisk (*) indicate a knowledge gap & an area of concern

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Synthesis of Knowledge Survey
Overall, the knowledge mean for the 9 Below-5 students was m = 0.60 (60%),
when the mean should be m = 1.00 (100%), which would demonstrate that Below-5
students are entering the ISEE Program with sufficient prior knowledge to succeed. Yet
the results indicate a 40% gap in prior knowledge. In particular, the results of the
knowledge survey reveal that Below-5 students are mainly missing factual knowledge of
prime numbers, conceptual knowledge of prime factors, and procedural knowledge in
order of operations, circumference, area, surface area, and computation with decimals,
fractions, and percents. The evident gap in knowledge indicates a clear need for
knowledge and skills acquisition in factual, conceptual, and procedural knowledge in
math prior to beginning the ISEE Program so that Below-5 students will be able to
successfully advance through the ISEE Program at Education Express.
Validation of Data. The knowledge survey validated the assumed cause of low
prior knowledge because of the 40% discrepancy between Below-5 students existing pre-
requisite knowledge and the amount of pre-requisite knowledge necessary to successfully
enter the ISEE Program at Education Express. Additionally, the knowledge survey also
validated the assumed cause of cognitive development; on average, about 85% of the
students missed items 9, 10, 11 involving “order of operations”, 100% of students missed
item 16 involving surface area, 100% of Below-5 students missed the fraction word
problem, and 66% percent of students missed the fraction word problem in item 30.
Lastly, the range of scores on the knowledge survey confirmed the assumed cause of
differences in aptitude and ability: the lowest score on the survey was 42.5% and the
highest score was 72.5%.
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Solutions to address the gaps in conceptual and procedural knowledge will be
provided in Chapter 5, based on the appropriate assessments for each knowledge
dimension (Anderson & Krathwohl, 2001).

Motivation Results
Assumed Motivation Causes
According to informal interviews, there were several presumed causes of the
current gap in performance that Below-5 students face. The first assumed cause was that
Below-5 students do not see the importance of studying for the ISEE because the ISEE is
an optional exam. The three indices of motivation, active choice, persistence, and mental
effort, were another assumed cause because Below-5 students often do not complete
ISEE homework assignments, do not persist in the face of challenge, and often use
incorrect strategies to solve math problems. Additionally, another presumed cause was
that students invest minimal effort into class work and homework assignments.
Motivation theory also provided several assumed causes, such as the three indicators of
motivation, active choice, persistence, and mental effort, and several underlying
constructs of motivation, such as values and self-efficacy. The researcher set out to
validated these assumed causes through student surveys and interviews. A copy of the
student “smiley-face” survey is included in Appendix B and a copy of the student
motivation interview job aid is included in Appendix C.

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Motivation Student Survey and Interview Results
Survey. The student smiley-face surveys involved a Likert scale using smiley
faces from 1 to 4 smiley’s. 4 smiley’s indicated that the student completely agreed with
the statement, and 1 smiley indicated that the student completely disagreed with the
statement.
The first survey question assessed student interest in studying for the ISEE exam
and was not statistically significant (Interest1 m = 3.44). Question 2 assessed student
interest in the math lesson and was statistically significant (Interest2 m = 3.11). The third
question assessed student’s perceived utility value towards the math lesson and was not
statistically significant (Utility m = 3.56). Question 4 assessed how important they
believed each math lesson to be in helping them improve their performance on the ISEE
and was also not significant statistically (Importance1 m = 3.89). Question 5 asked
students about how much effort they invest into doing their homework at school (School
effort m = 3.89), versus how much effort they invest into doing their ISEE homework,
which was borderline statistically significant (ISEE effort m = 3.67). The final motivation
item on the survey asked students about their self-efficacy or confidence in being able to
complete ISEE homework and was highly significant (Self-efficacy m = 3.44).
Table 4.2 provides the question, the motivation construct and means for each
question type for the motivation survey items. Question 2 has the lowest mean on the
Likert scale (Interest2 m = 3.11), followed by interest in studying for the exam (m = 3.44)
and invested effort in the ISEE (m = 3.44). Questions 2 (interest), 6 (effort), and 7 (self-
efficacy) are statistically significant. Among the motivation constructs, interest and self-
efficacy have the lowest means.
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Table 4.2
Student Motivation Questions, Motivation Constructs, and Means (Descending Order by
Means)

Question Question Construct Mean
4. I think it is important to learn the math concepts in
today’s lesson because they will help me do better
on the actual ISEE exam.
Importance 3.89
5. I always try my best when I do my homework for
school.
Effort 3.89
6. I always try my best when I do my ISEE
homework.
Effort 3.67
3. Today’s math lesson was useful because it taught
me information that will help me do better on the
ISEE exam.
Utility /
Interest
3.56
7. I am confident that I can complete this week’s
ISEE math homework.
Self-
Efficacy
3.44
1. As of today, I am interested in studying for the
ISEE.
Interest 3.44
2. I thought today’s math lesson was interesting. Interest 3.11

When examining the data, the survey results show that the main motivation
barriers involved interest in the daily math lesson (m = 3.11), interest in studying for the
exam (m = 3.44), and self-efficacy in completing math homework (m = 3.44). Below-5
students’ utility value towards the ISEE Program was high (m = 3.56). Additionally, the
survey asked students about effort invested into school assignments versus effort
expended on ISEE homework in order to understand if Below-5 students invest the same
amount of effort into the ISEE Program; students showed that they spent slightly less
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effort on ISEE homework (mean = 3.67) than they did on their homework for school (m
= 3.89).
Interview. Over the course of 3 lessons, the Below-5 students were also
individually interviewed during snack time at Education Express to gain more
information regarding their motivation to complete the ISEE Program. Out of the 8
interview questions, 5 questions assessed motivation. Question 1 assessed interest and
asked students if they found the math lesson to be interesting, and what part of the lesson
they thought was most interesting. The majority of the students, 6 out of 9, said that they
did find the lesson to be interesting. One student stated, “I thought the process of
elimination strategy was interesting,” and another student commented that the strategies
were “good and useful.” Students also said that the “math tricks” they learned were
helpful, and that the review of math terms also helped them. Another student commented
that the math lesson was interesting because she felt like math was not her strong suit and
the lesson helped the student work on a this weakness. One student stated, “The math
lesson was sort of interesting, I already knew a lot of the things we went over so I felt
bored, but the teacher was funny.” Of the 9 Below-5 students interviewed, 3 said that
they did not find the math lesson to be interesting. One student said, “There was not
enough enthusiasm,” another student noted that she felt bored during the lesson, and
another student said, “I did not feel like the math lesson was that important.” Overall, the
majority of students interviewed said they did find the math lesson to be interesting;
consequentially, the assumed cause of lack of interest was not a cause that was validated
by the student interviews.
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Question 2 asked students if they were motivated to complete their ISEE
homework and why. Only 3 out of the 9 students said that they enjoyed doing their ISEE
math homework. One student said that she was motivated to do her ISEE homework
because she knew it would help her prepare for the ISEE. Another student said that the
doing the ISEE math homework helped her learn, and the last student said, “The
homework doesn't take very long so I don’t mind.” The majority of the Below-5 students
who were interviewed, 6 out of 9 students, said that they were not motivated to do their
homework. One student responded, “No, I am not because it is homework,” and another
student said, “No because I don't have a lot of time because I have to get my school work
done.” One student stated, “It feels like I have to get it done, so I do it even though I
don’t want to,” and another student commented, “I know I should do it, but I don't always
want to. I usually do it because I have to.” Lastly, one Below-5 student noted, “I’m sort
of motivated to do it. I have to do it on the weekend after I get schoolwork done.”
Question 2 in the interview pointed out and confirmed that students valued doing their
homework for school over doing their ISEE homework.
Question 5 assessed importance and asked students if they thought it was
important to study for the ISEE and why. While one student mentioned, “The teachers at
EE make it seem like the test is not a big deal,” all of the students stated that they felt it
was important to study for the ISEE and provided very rich responses. Two students
stated that it was important because it would help them get into a “good middle school.”
Another student said, “ I think it’s important because my parents want me to do better on
the ISEE and some of the stuff we learn I also learn in school, so it also helps me do
better in math class.” One Below-5 student said, “The thing is that everyone takes the test
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so it’s necessary in one way to study for it. It’s important to study for the test the same
way that it’s important to study for a school test. You want to show off what you know.”
Yet another student confirmed the importance of studying for the ISEE and compared
himself to his peers. He said, “I think it is because I know some friends who didn't study
because they thought it was the same as the standardized test we take every year at school,
and he really struggled on it.”
Moreover, another student said, “Yes, because I want to get a good grade, and I
don't want to go into the test not know anything because everybody else who goes into
the test does (know things).” One Below-5 pupil mentioned, “Yes, because you want to
get into other schools. It’s a big factor so you want to do well and excel and go ahead of
other students.” Lastly, another student stated, “I do because I do my homework and now
I’m doing much better. If I had those scores I wouldn’t get into any of the schools I
wanted.” As was evident from the interview data, the assumed cause that students did not
think it was important to study for the ISEE exam was not an actual cause, and was not
validated by the student interviews.
Question 7 examined value and asked students if they had value for taking the
ISEE course at Education Express. Undividedly, all of the Below-5 students interviewed
stated that they found the course to be extremely valuable. One student said, “It’s not
even a question!” Another student stated, “Sometimes we go over hard problems and then
I understand them so it’s worthwhile,” and another pupil said that the ISEE course taught
her more about time management skills. As a result, because all the Below-5 students
valued taking the ISEE Program, value is an assumed cause that was not validated by the
data.

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Lastly, question 8 discussed utility value of the ISEE Program, asking students
how they thought the ISEE Program would help them improve their scores on the actual
ISEE. All of the students interviewed felt that the ISEE Program would help them in one
way or another. One student said that the math strategies she learned during ISEE math
class were very useful, and she also stated, “Going over the math concepts in class helps
me practice how to do them for the real test.” Another student said that the ISEE Program
“helps me do better in math because the math is really hard.” Students said that the math
strategies, or “tricks” they learned, and the “tips” teachers gave them would help their
performance on the actual exam. They also said that practicing the math concepts in class
made them “easier,” helped them learn new concepts, feel less stressed, and feel
comfortable going into the test. Therefore, all the students found utility value in the ISEE
Program; consequentially, utility value was an assumed cause for the performance gap
that was not validated by the data collected.
Synthesis of Motivation Survey and Interview Data
A few common themes appeared from the survey and interview data. Below-5
students felt that the ISEE math classes were useful. They valued the ISEE Program and
understood that it would help them perform better on the ISEE in the winter. Some
students felt that ISEE math class was not interesting, and when compared to schoolwork,
students invested less effort into their ISEE homework. As a whole, students also felt that
ISEE math class helped them learn strategies and concepts that would help their
performance on the actual exam.
Validation of data. When examining the assumed motivation causes, several of
the causes were validated by the collected data. The survey results confirmed that Below-
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5 students struggle with self-efficacy in math and self-efficacy towards doing their math
homework. A lack of self-efficacy affects the three indicators of motivation; low self-
efficacy affects active choice because many students may not feel like they are capable of
beginning their homework, persistence because a lack of confidence in their ability may
cause Below-5 students to give up in the face of challenge, and incorrect mental effort to
solve homework problems. Furthermore, as revealed by the survey and interview data,
Below-5 students lacked motivation to complete their weekly ISEE homework. Many
students pointed out that their schoolwork came first and ISEE homework came second,
which often lead to students not completing their weekly ISEE math homework. What’s
more, Question 2 in the interview pointed out and confirmed that Below-5 students
valued doing their homework for school over doing their ISEE homework. All three
indices of motivation are related to Below-5 students’ lack of motivation to complete
ISEE homework; this revealed issues with active choice to begin the task, persisting in
doing their homework despite challenges, and using correct mental effort.
Consequentially, interest in math lessons, self-efficacy, and motivation to complete ISEE
homework is an assumed cause that was validated by the student interviews.
During the survey and interview process, a divergence between the quantitative
and qualitative data appeared. Firstly, though interest in the math lesson was the survey
item with the lowest mean, the interview data revealed that, overall, students did find the
math lesson to be interesting because they were able to learn information that they found
useful. There are several possible explanations for this divergence (Patton, 2002).
Students may have felt intimidated by the researcher during the interview process and
may not have felt comfortable saying that they did not find the math lesson to be
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interesting. Another explanation could be that while the Likert scale on the quantitative
survey forced students into one of four categories, the interview allowed students to
express their feelings and communicate what aspects of ISEE class they did or did not
find to be interesting. Consequentially, because of the divergence, interest in class work
is an assumed cause that will be considered validated.
Additionally, several of the assumed causes were not validated by the data. For
example, though it was thought that Below-5 students did not think it was important to
study for the ISEE, both the survey and interview data revealed that students thought it
was very important to study for the exam. Of all the motivation survey items, importance
had the highest mean. . The underlying motivation construct of value was another
assumed cause that was not validated by the interview data because Below-5 students
said that they valued the ISEE Program a lot. Lastly, the assumed cause of utility value
was also negated by the interview data because all of the students understood that being
in the ISEE Program would undoubtedly help them improve their performance on the
actual ISEE.
When examined as a whole, student’s qualitative and quantitative data showed
that students struggled with interest in math lessons, self-efficacy, and motivation to
complete their ISEE homework. These results indicate that interest and self-efficacy,
active choice in completing homework, and the three indices of motivation will be the
major motivation constructs to address in order to improve Below-5 student motivation.
Solutions to address interest, self-efficacy, and homework completion will be addressed
in Chapter 5.

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Organization Results
Assumed Organization Causes
There were several assumed organizational causes for the Below-5 gap in
performance on the ISEE. One possible cause may be that ISEE classes are held on the
weekends, and Below-5 students prefer not to be in class on the weekend during their free
time. Another assumed cause is that students are in class with peers and prefer to
socialize during class rather than participate and complete class work.
Moreover, as revealed by the literature, cultural models and cultural settings are
an important component of organization, and can impact Below-5 student performance
(Gallimore & Goldenburg, 2001). Cultural models are shared cognitions between a group
of people that dictate values and behavior, and cultural models are often found at home.
Cultural models, such as parents, can affect behavior at school and behavior at ISEE class.
They can also affect context such as when and where homework is completed and how
much time is dedicated to studying. Consequentially, the data collected also attempted to
determine parent beliefs about their children successfully completing the ISEE Program
and to better understand the cultural models that Below-5 students have at home; because
Below-5 student parents were also given a parent survey because students may be
indirectly receiving negative messages at home (Hara & Burke, 1998).
What’s more cultural settings involve the home environment and include daily
activities, such as homework time. Below-5 students’ cultural settings, particularly their
home environment and where they complete ISEE homework, was another assumed
cause that was set out to be validated by the data. Accordingly, Below-5 parents were
also given parent surveys to determine if the parents as cultural models depict negative
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messages regarding the ISEE Program, which therefore impacts Below-5 students, and to
gain a better understanding of Below-5 students’ home setting. The student survey and
interview set out to validate these assumed organizational causes.

Student Survey and Interview Results
Survey. The student smiley-face survey also assessed organizational constructs,
using the 1 to 4 Likert scale. Question 8 asked students if they like taking ISEE prep
classes during the weekend and was statistically significant (Weekend m = 3.00, p
= .004). Question 9 asked students if they have a quiet place at home to do their ISEE
homework, which was also statistically significant (quiet m = 3.33, p = .002). The final
organization question on the smiley face survey asked students if they have a credible
model at home to help them with ISEE math homework and was found to be statistically
significant (model m = 2.89, p = .003).
Table 4.3 provides the question, the organization construct, means, and
significance level for each question type for the student survey items.
Table 4.3
Student Organization Questions, Organization Constructs, and Means (Descending
Order by Means)

Question Question Construct Mean

9. I have a quiet place at home where I can do
my ISEE homework.
Quiet place to
study
3.33
8. I like taking ISEE classes during the
weekend.
Weekend 3.00
10. If I have a question about my ISEE
homework, there is someone at home that I
can ask about it.
Model / Support 2.89

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The overall mean for student organization was m = 3.07. All of the organization
variables, including timing of the ISEE class, a quiet place to do homework, and
homework support at home, were found to be statistically significant The results of the
quantitative student survey pointed to possible challenges with the timing of the ISEE
class, a quiet place to do homework, and homework support in math at home, and
validated the assumed organizational causes .The qualitative interview provided insight
into these possible issues.
Interview. Of the 8 questions on the interview job aid, 3 questions examined
Below-5 student organizational factors. Question 3 asked students if they had a quiet
place at home to study. More than half of the students interviewed, 5 out of 9, said that it
was challenging finding time to do ISEE math homework because their homes were
rarely quiet. One student responded, “ It’s difficult because my younger siblings are
always running around, so it’s hard.” Another Below-5 student said, “Our house isn’t that
big so you can hear someone at the other end of the room; if I switch places, its not
always as comfy.” Several students mentioned that loud noises in the house, such as
siblings turning on loud music or television presented a barrier against doing their
homework. One student described, “Our house isn’t always quiet. We have guests over
all the time, and if we don’t have guests, my sister always turns on the TV really loud, so
it’s tricky.” Other students said that they found regular disturbances in the house to also
be interfering. A student commented, “We have a dog and he’s always barking.
Sometimes I hear my mom washing dishes or talking to my brother so I can’t always
concentrate.” The student interview confirmed the assumed cause that finding a quite
place at home to do homework was an organizational barrier.
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Question 4 of the interview asked students about the amount of homework
support they received at home, and if there was someone to ask if they did not understand
a math problem. The majority of the students said that they did not have someone at
home who could help them with their math homework. One student said that the person
was not always available. She responded, “My dad can help me, but he’s not always
home, so not always.” The greater part of the Below-5 students said that their parents
often did not understand the math homework. One girl replied, “ Mom and dad offer to
help, but they don't always understand the questions, so if I have a question, I don't
always have someone to ask.” Another student reported, “My parents try to help, but
sometimes the homework confuses them, too!” Several students commented that their
parents often did not apprehend the math homework themselves. A Below-5 student said,
“No, my mom rarely understands the math homework, and my brother can’t always help.”
Furthermore, one student said that her parents were not good at math themselves, so she
felt very little support in doing her math ISEE homework. She said, “My mom isn’t really
good at math, so not really.” Some parents provided incorrect support. One child
answered, “Sometimes my mom, but the answer isn’t always right.” Lastly, one child
said, “I always ask mom, but she always tells me to email teacher.” Consequentially, one
of the biggest organizational barriers that students faced was that they did not feel like
they had support in math homework at home, and if they had questions about any math
assignments, their parents or siblings were not able to help them. The student interview
confirmed that the lack of a capable math model at home was one of the biggest
organizational issues that Below-5 students faced.
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Question 6 asked students if they enjoyed taking ISEE classes on the weekend.
Half of the students said that, overall, they did not enjoy coming into Education Express
over the weekend. One student commented on the timing of ISEE lessons, “Yes, but it’s
difficult sometimes because it’s in the middle of the day.” Another student mentioned
that she preferred engaging in other hobbies during her free time, “There are a lot of
activities over the weekend, but sometimes I have to come here instead.” One Below-5
student explicitly said, “I don't enjoy it, but I know I have to come.” The other half of
Below-5 students said that, overall, they did not mind coming into Education Express and
enjoyed the environment. One student commented, “Yeah, to be honest, because in the
morning I usually don't do anything so instead of wasting time at home, I come to
Education Express. If it was after school it would be stressful.” Another Below-5 pupil
said, “I do, its fun coming here and I like the snacks.” Other students mentioned that they
thought the ISEE classes were fun and that they enjoyed having something to do on the
weekend.
Overall, the results of the survey and interview reveal that most students often did
not have a quiet place at home to study, and more importantly, that the lack of homework
support at home often prevented them from completing their ISEE homework. Moreover,
some students disliked coming to Education Express during their free time on the
weekend. The student interview data confirmed the three assumed organizational causes:
the timing of the ISEE class on the weekend, the lack of a quiet place at home to study,
and the lack of a competent adult that could help them with math homework or answer
questions, and the timing of the ISEE class on the weekend.
Parent Survey
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Parent beliefs. Parents serve as role models at home, and provide their children
with both positive and negative social cues; therefore, to better understand the
organization gap, the researcher also surveyed parents about their beliefs to better
understand the kinds of messages they may be giving students (Hara & Burke, 1998).
Because parents serve as cultural models and provide cultural settings, Below-5 student
parents were also given a parent survey because they may inadvertently be
communicating negative messages to their children, which will consequentially impact
Below-5 student performance (Hara & Burke, 1998). The parents of Below-5 students
were also asked to fill out a parent survey about their child’s home environment. The
parent organization survey also assessed the amount of support parents provided their
children with in completing the ISEE Program at Education Express. A copy of the
parent organization survey is included in Appendix D.
The first survey item asked parents about how important they thought it was for
their children to do their weekly math homework and was not statistically significant
(Importance m = 3.89, p = .293). The second item on the parent survey asked parents
about their utility value for ISEE homework, their beliefs in the connection between
completing weekly homework assignments and ultimate success on the ISEE exam and
was approaching statistical significance (utility m = 3.67, p = .052).
Table 4.4 provides the question, the motivation construct, and the means for each
question type for the parent survey items.
Table 4.4
Parent Motivation Questions, Motivation Constructs, and Means (Descending Order by
Means)

Question Question Construct Mean

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1 I think it is important for my child to do his /
her ISEE homework.
Importance 3.89
2 Completing weekly ISEE homework
assignments will help my child do well on the
ISEE test.
Utility 3.67

The overall mean for parent motivation was m = 3.78. Parent utility towards the
ISEE course was the only parent motivation construct that had borderline significance (p
= .052). The results of the parent survey indicate that parents have high motivation in
supporting their children through the ISEE Program at Education Express because they
understand it’s importance and utility.
Parent organization. The parents survey also asked parents about their child’s
home environment and assessed the amount of support parents provided their children
with in completing the ISEE Program at Education Express. The third parent item on the
parent organization survey asked parents about the amount of support they offer their
children in completing ISEE homework by reminding students to complete the weekly
assignments and was not statistically significant (Support m = 3.78, p = .126). Question
4 asked parents if their children have a quiet place at home to study and was statistically
significant (Quiet m = 3.44, p = .006). Question 5 asked whether there is an adult at home
that their children can ask questions about math homework and was very statistically
significant (model m = 2.33, p = .001).
Table 4.5 provides the question, the organization construct, and the means for
each question type for the parent survey items.
Table 4.5
Parent Organization Questions, Organization Constructs, and Means (Descending Order
by Means)

Question Question Construct Mean

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3. As a parent, I support my child by reminding
my child to do his / her ISEE homework.
Support 3.78
4. My child has a quiet place at home to do
ISEE homework
Quiet 3.44
5. I feel that I am able to help my child with
basic math problems if he / she needs it.
Role
Model
2.33

The results from the organization questions of the parent survey showed that
students lacking a quiet place at home to do homework was significant (p = .006) and that
most parents did not feel like they could effectively answer questions that their children
had about math homework, which was very significant (p = .001). The results point to
these two factors, a place to study and support, to be major organizational barriers.

Synthesis of Organization Survey and Interview Data
The results of the survey and interview confirmed that the that Below-5 students
often did not have appropriate cultural settings, or a quiet place at home to study, which
consequentially would lead to a gap in homework, and consequentially a gap in
performance on the ISEE. More importantly, that the lack of competent cultural models
and homework support at home often prevented Below-5 students from completing their
ISEE homework. Parents also confirmed that they did not feel competent to help their
children with their ISEE homework, which points to a clear deficit in Below-5 student
organizational support. A divergence occurred when students were asked about coming to
Education Express during their free time on the weekend. While the survey item that
asked students about coming to EE on the weekend had the second to lowest mean,
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Below-5 students were divided in their interview responses. About half of the students
reported that they did not enjoy coming to ISEE class on the weekend, but the other half
of students reported that they did enjoy coming to EE on the weekend. Consequentially,
because of this divergence, the data will be considered as having confirmed the assumed
organization cause of ISEE classes being held on the weekend. Solutions to closing the
organizational gap in performance will be provided in Chapter 5.
Validation of data. Overall, the student and parent data validated the three
assumed organizational causes for the Below-5 student performance gap: the lack of
cultural settings, a quiet place at home to study, the lack of competent cultural models at
home to provide help with homework, and that many Below-5 students did not enjoy
having ISEE class over the weekend.

Comparison of Knowledge and Skills, Motivation, and Organization Results
There were several differences between the knowledge and skills, motivation, and
organization results. Firstly, there was a very large, distinct prior knowledge gap of about
40% (m = 0.60). Below-5 students are missing crucial knowledge, such as conceptual
knowledge of prime numbers, and procedural knowledge of area, surface area, and the
relationship between fractions, decimals, and percents. The gap in knowledge also
represents a stage of formal cognitive development that Below-5 students have not yet
reached. In order to succeed during the ISEE Program, students that are identified as
being Below-5 on the ISEE Pre-test will need increase their level of prior knowledge in
math before starting the Program.
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Furthermore, while the three indices of motivation, active choice, persistence, and
mental effort, also play a role in the current performance gap, the quantitative and
qualitative data showed that Below-5 student motivation was much higher than expected.
The overall mean for student motivation, including student interest, utility, importance,
effort, and self-efficacy was m = 3.57 on a scale of 1 to 4, which indicates that Below-5
students are motivated to complete the ISEE Program at Education Express. The main
motivation constructs that need to be addressed include interest, value, utility, and self-
efficacy.
Finally, the analysis of data also shows that several organizational barriers must
also be addressed to close the Below-5 student performance gap. The overall mean for
student organization was m = 3.07, and the overall mean for parent beliefs and
organization was m = 3.78. Students need a quiet place at home to study and complete
ISEE math homework, and Below-5 pupils also need a competent adult who can answer
questions and assist them if they come across any challenges in reviewing and practicing
the math concepts. One of the main organizational barriers was that students do not feel
like they have a credible model at home to help them with ISEE math homework
questions. Lastly, the timing of ISEE classes on the weekend also presented an
organizational challenge for about half of the Below-5 students, and this organizational
issue must also be addressed in order to close the performance gap.

Knowledge and Skills, Motivation, and Organization Solutions
Chapter 5 will examine recommended solutions to close the knowledge,
motivation, and organization gaps that were found at Education Express.
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CHAPTER 5: SOLUTIONS AND IMPLEMENTATION PLANS
The purpose of the study is to examine the knowledge and skill, motivation, and
organization barriers that are contributing to the current gap in Below-5 student
performance on the ISEE Post-test. The discussion of this question addresses the
remainder of the Clark and Estes (2008) GAP process. Chapter 5 will draw upon learning
and motivation research to suggest implications for solutions to close the knowledge and
skills, motivation, and organizational gaps that exist for Below-5 students.

Study Question Two: What are the potential knowledge and skill, motivation, and
organizational solutions to address the Below-5 students’ gaps in achieving a score
of 5 or higher on the ISEE Program Post-test?

Knowledge and Skills
Knowledge and Skills Results
Below-5 students were given a 40-item knowledge questionnaire to assess their
prior knowledge in math. The results of the knowledge survey demonstrate that there is a
substantial gap in Below-5 student pre-requisite knowledge. The knowledge survey
validated the assumed cause of low prior knowledge because of the 40% discrepancy
between Below-5 students existing pre-requisite knowledge and the amount of pre-
requisite knowledge necessary to successfully enter the ISEE Program at Education
Express. Additionally, the knowledge survey also validated the assumed cause of
cognitive development; on average, about 85% of the students missed items 9, 10, 11
involving “order of operations”, 100% of students missed item 16 involving surface area,
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100% of Below-5 students missed the fraction word problem, and 66% percent of
students missed the fraction word problem in item 30. Lastly, the range of scores on the
knowledge survey confirmed the assumed cause of differences in aptitude and ability: the
lowest score on the survey was 42.5% and the highest score was 72.5%. Consequentially,
the main gaps in knowledge were in conceptual and procedural knowledge types, as well
students’ level of cognitive development.
Knowledge Theory
Cognitive theory. According to cognitive theory of learning, learning is better
facilitated when new information is connected to a learner’s prior knowledge (Mayer,
2011). Additionally, students will have an easier time learning when new information fits
into and is connected to the learner’s existing mental structures, known as mental
schemas. Cognitive theory stresses the importance of prior knowledge in successful
learning. Based on the results of the pre-requisite knowledge assessment, the main gaps
in Below-5 student prior knowledge involved conceptual and procedural knowledge
types, and cognitive development.
Conceptual knowledge. Conceptual knowledge is knowledge of the relationship
between basic elements within a category that allow them to work together (Anderson &
Krathwohl, 2001). Additionally, conceptual knowledge includes knowledge of
classifications and categories, knowledge of principles, and knowledge of theories,
models and structures (Anderson & Krathwohl, 2001). Examples of conceptual
knowledge on the ISEE include knowledge of prime numbers and formulas for
calculating area and surface area. In addition to cognitive theory, which implies tying
new information to prior knowledge, Skinner’s reinforcement theory suggests that
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learning involves a change in behavior, and behavior is caused by stimuli found in a
learner’s environment (Skinner & Green, 2004). Adjusting stimuli and the learner’s
environment will result in learning. Furthermore, in order to change behavior, Skinner et
al. (2004) suggest using reinforcement to promote desired behaviors.
Procedural knowledge. Furthermore, procedural knowledge is the knowledge of
“how to do something” (Anderson & Krathwohl, 2001). It is the ability to use skills,
techniques, and methods to solve a problem, and knowledge of when to use appropriate
methods (Anderson & Krathwohl, 2001). Cognitive theory suggests that in order to
facilitate the acquisition of procedural knowledge, it must be connected to students’ prior
knowledge, and must fit into existing mental structures. Additionally, procedural
knowledge is acquired through demonstration and use of worked examples (Anderson &
Krathwohl, 2001).
Cognitive development. According to Piaget (1954), students that are in the
concrete operations stage of cognitive development require manipulation of tangible
objects in order to understand and learn abstract concepts such as surface area and
algebra (Joffrion, 2010).
Knowledge Principle and Application
Conceptual knowledge. There are several methods for teaching conceptual
knowledge, such as showing relationships between concepts and how concepts are
categorized and organized and by using prior knowledge to build new knowledge
(Anderson & Krathwohl, 2001). According to Nesbit and Adesope (2006), having
students create concept maps, a diagram that is used to organize information by showing
the relationships among concepts, will facilitate conceptual knowledge acquisition. In the
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study, elementary school students used concept maps in subjects such as science and
math to facilitate learning (Nesbit et al., 2006). The results of the post-test measured
student recall and transfer, and the results of the study showed that using concept maps
resulted in increased knowledge retention.
What’s more, according to Skinner et al. (2004), students must be provided with
practice and reinforcement in order to learn conceptual knowledge, using methods such
as using flash cards.. As a result, Below-5 students should use concept maps and
reinforcement methods such as flash cards in order to acquire missing conceptual
knowledge.
Procedural knowledge application. Additionally, there are several methods for
instructing procedural knowledge. Procedural knowledge taught by demonstration of how
to carry out procedures and by the use of worked examples (Anderson & Krathwohl,
2001). What’s more, students can learn procedural knowledge through observing teacher
demonstrations. Hallet, Nunes, & Bryant (2010) found that learning the procedural
knowledge of adding fractions was facilitated when students were provided with both
verbal instructions and demonstration. The researchers found that students who were
provided with teacher demonstrations outperformed the control group of students who
were only provided verbal instructions (Hallet et al., 2010). What’s more Below-5
students should be provided with practice and constructive feedback during ISEE class in
order to build math skills (Bransford, Brown, & Cocking, 2004). Consequentially,
Below-5 students should be provided with demonstrations of how to solve problems that
involve procedural knowledge, such as finding area, surface area, and solving for
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variables, and then be provided with the opportunity to practice each math skill while
receiving feedback from the ISEE instructor.
Cognitive development application. In order to learn the abstract math concepts
on the ISEE, students that are in the concrete operations stage of cognitive development
will need guidance and instruction to facilitate the cognitive development (Burs & Silbey,
2000). Burns et al. (2000) indicate that instructors can help facilitate cognitive
development by using several teaching strategies. Firstly, multiple ways of representing a
mathematical solution can foster cognitive development (Burns et al., 2000).
For example, hands-on experiences and activities are critical at this stage of a
child’s cognitive development because they provide students with a medium to make
theoretical ideas concrete and tangible (Burns et al., 2000). Consequentially, the use of
materials such as blocks and shapes can facilitate abstract knowledge acquisition, as well
as providing students with a touchable method of testing and confirming their reasoning.
Furthermore, in order to teach algebra, teachers can refer to concrete situations or
they can create word problems to represent the situation. For example, in order to
represent the equation “x + 5 = 12”, teachers can create a word problem: “Tony had a
certain number of cards. His sister gave him 5 cards. Tony now has 12 cards. How many
cards did he begin with?” Creating word problems will allow students to develop
reasoning skills, which are mental processes involved in evaluating any kind of argument,
and these reasoning skills lead to the abstract stage of cognitive development (Burns et al.,
2000; Anderson, 1990). Lastly, teachers should show multiple ways of finding the same
solution in order to foster cognitive development (Burns et al., 2000).

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Summary of Knowledge Solutions
Overall, in order to build prior knowledge, the results of the knowledge survey
indicate that Below-5 students will require pre-training before entering the ISEE Program
in the Fall. The pre-training course should focus on the acquisition of conceptual
knowledge through the use of concept maps and reinforcement and procedural
knowledge through the use of demonstration. In order to teach surface area, teachers can
use blocks and manipulatives to create a connection between concrete and abstract
concepts. In order to learn abstract concepts, Below-5 students will need to use tangible
objects to solve surface area, fractions word problems, and algebra. Below-5 students will
need to use tangible objects in order to learn abstract concepts such as finding surface
area and algebra.
Motivation
Motivation Results
The results of the student motivation survey and interviews show several
motivation causes for the performance gap. Below-5 students struggled with interest in
math lessons, lacked self-efficacy in their ability to complete ISEE homework, and also
lacked motivation to complete their ISEE homework. These results indicate that the
underlying constructs of values and interest, and self-efficacy, which affect the visible
three indices of motivation (active choice in completing homework, persistence, and
mental effort), will be the major motivation constructs to address in order to improve
Below-5 student motivation.

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Motivation Theory
According to motivation theory, there are three visible indicators of motivation: a)
active choice in beginning a task, b) persistence in the face of challenge, and c) mental
effort, or using correct strategies. (Clark, 1998; Pintrich & Schunk, 2002). The three
visible motivation indices are driven by underlying constructs, such as values and self-
efficacy, and affect both learning and performance.
Values. Expectancy-value theory states that an individual’s choices, persistence,
and performance can all be explained by an individual’s expectancy, beliefs about how
well he or she will do at the task, and by value, the different beliefs a person may have
about the reasons for engaging in a task (Wigfield & Eccles, 2000). Additionally, values
are composed of interest, importance, and utility; consequentially, the validated cause of
interest in ISEE class falls under the category of value. A person’s expectations for
success or failure, beliefs about ability, and perceived difficulty of various tasks can
influence values (Wigfield & Eccles, 2000). Value affects all three indices of motivation
because the more value a student has for a task will ensure active choice in completing
homework, persistence in the face of challenge on homework, and using correct mental
effort and strategies on a task.
Self-efficacy. Self-efficacy, perceived judgments about one’s ability to execute
necessary actions to achieve a specific goal or level of performance, is another underlying
motivation construct that affects performance (Bandura, 1997). Self-efficacy is task and
domain specific and can vary between across different realms. Self-efficacy can be low in
one domain, but very high in another domain. Furthermore, self-efficacy beliefs are based
on feedback and outcomes of behavior, and focus on the individual’s performance
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(Bandura, 1997; Zimmerman, 2000). Self-efficacy predicts the three indices of
motivation: one’s level of self-efficacy determines if he or she will choose to begin the
task, how much effort will be invested into the task, and whether he or she will persist at
the task in the face of a challenge (Zimmerman, 2000).
Motivation Principle & Application
Values. Interest is an aspect of student values, and values and interest affect
active choice, persistence, and effort; students who are interested in a particular domain
are more likely to choose to begin the task, pursue engaging in the task in spite of set
backs, and invest effort into the activity (Simpkins, Davis-Kean, & Eccles, 2006).
Bernero (2000) conducted a study attempting to generate more student interest in math
lessons and to make math more enjoyable through the use of cooperative learning. In
cooperative learning, students work in groups to collectively accomplish academic
learning goals and, at the same time, practice and develop social skills in order to
successfully accomplish a given task. Students were assigned roles within the group,
which created a sense of responsibility toward the team and the completed work.
Assigned roles also improved student behavior (Bernero, 2000). Students were asked to
complete individual and group reflections about the cooperative learning. The results of
the study indicated that the use of cooperative learning not only created more interest in
math, but students also felt that it made math more enjoyable. Additionally, cooperative
learning also improved student self-esteem and self-efficacy.
Self-efficacy. Self-efficacy affects all three indices of motivation; students with
high self-efficacy are not only more likely to attempt new tasks, but they also invest more
effort and are likely to persist longer in the face of difficulties (Bandura, 1997). Bandura
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(1997) provides several strategies for increasing self-confidence and subsequently
increasing self-efficacy. Firstly, students must be assured that they are competent and
capable of learning the math material being taught. Next, students must be taught
learning strategies, such as self-recording, having students keep a record of their own
behavior, and self-reinforcement, having students choose their own reward for
completing a task, that will allow them to become more effective, self-regulated learners.
Siegle and McCoach (2007) conducted a study on increasing student mathematics self-
efficacy. The study attempted to determine if modifying instructors’ teaching strategies
would increase students’ mathematics self-efficacy. The teaching strategies that were
implemented include providing frequent, constructive teacher feedback, setting specific,
concrete goals that include specific performance standards, and using similar models that
demonstrate the desired math skill and desired level of performance as a form of social
comparison (Siegle et al., 2007). Prior to the intervention, students were given Student
Mathematics Survey to assess self-efficacy before treatment, and the Math Achievement
Test to assess math achievement. Students were also administered the same measures
after the treatment. The difference between pre-test and post-test self-efficacy ratings was
found to be statistically significant. The results of the study suggest that the intervention
was effective for students across all ability level and demonstrate that teachers can
modify their instructional strategies, which can result in increases in their students’ self-
efficacy (Siegle et al., 2007).

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Application to ISEE
A lack of values and interest and low self-efficacy were assumed motivation
causes that were validated by the data, and also directly influence the Below-5 student
issue of active choice to begin ISEE homework assignments. In order to solve issues with
interest in math lessons, ISEE instructors can incorporate activities that involve
cooperative learning into each math class. Cooperative learning will not only create
interest, but it will also increase student self-efficacy and confidence towards
implementing the knowledge they learn and thus completing ISEE related assignments
(Bernero, 2000). Additionally, guided practice, rehearsal, and scaffolding during lessons
will also enable students to strengthen skills and increase their self-efficacy towards
achieving more challenging tasks (Bandura, 1997). Setting challenging but doable goals
will allow students to monitor their own progress, and as they accomplish each goal, their
level of self-efficacy will increase (Clark & Estes, 2008). Lastly, giving students credible,
effort-based feedback will also increase levels of self-efficacy (Clark & Estes, 2008).

Organizational Barriers
Organization Results
The results of the organizational data confirmed the assumed organizational cause
that Below-5 students often did not have a quiet place at home to study. More importantly,
that the lack of homework support at home often prevented Below-5 students from
completing their ISEE homework. Parents also confirmed that they did not feel
competent to help their children with their ISEE homework, which points to a clear
deficit in Below-5 student organizational support. The results of the quantitative survey
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indicated that most students did not enjoy coming to EE on the weekends for ISEE class,
and about half of the students in the interview confirmed that that they did not enjoy
coming to ISEE class on the weekend. Overall, the student and parent data validated the
three assumed organizational causes for the Below-5 student performance gap: the lack of
a quiet place at home to study, the lack of someone at home to ask for help with
homework, and that many Below-5 students did not enjoy having ISEE class over the
weekend.
Organization Theory
Importance of homework. Homework, which is defined as “as tasks assigned to
students by schoolteachers that are meant to be carried out during non-instructional time”,
is an effective and important instructional tool that propels academic achievement
(Bembenutty, 2011). Homework also has a positive effect on middle school student
learning and is meant to enhance students’ learning experiences. According to Ramdass
& Zimmerman (2011), homework plays an important role in developing students’ self-
regulation strategies. Two aspects of homework completion are also very critical: the
importance of having a quiet place at home to study, and the importance of having
parental support and role models in homework completion (Ramdass & Zimmerman,
2011).
Self-regulatory learning strategy. Homework completion touches on a range of
self-regulatory issues (Xu & Corno, 2003). According to Zimmerman (2002), creating a
quiet place at home to study is a self-regulatory learning strategy. Self-regulated learning
involves the use of strategies for planning, monitoring, and assessing progress towards
reaching a specific learning goal. Self-regulated learners select, structure, and create
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environments that optimize learning (Zimmerman, 2002). Self-regulatory strategies can
also be taught and monitored in the classroom (Jennkins, 2009).
Cultural settings and cultural models. What’s more, students must complete
homework in the proper environment. A significant aspect of a proper homework
environment involves a quiet place without distractions (Xu & Corno, 2003). Xu and
Corno (2003) found that one of the advantages of having quiet place at home to study is
more accurate completion of homework Additionally, parent role models are critical in
setting up a proper homework environment at home and parent help in homework
completion is very important (Xu & Corno, 2003). More than important than offering
help with homework content, parental homework support is especially important for
motivation, emotional coping, task focus, and persistence in the face of challenge (Xu &
Corno, 2003). A lack of role models at home model makes it challenging for students to
effectively complete their homework in the proper environment.
Organization Principles and Application
Self-regulatory learning strategy. Research suggests that Below-5 students
would benefit from self-regulated learning strategy instruction in math achievement in
order to be able to create a proper place to study (Jenkins, 2009). In 2009, Jenkins
conducted a study examining the extent to which explicit self-regulated learning strategy
instruction impacted students’ learning behaviors and subsequent mathematics
achievement on standardized tests. In the study, mathematics instructors weaved into
their instruction self-regulatory strategy development. Math teachers supported students
in articulating steps and thoughts towards problem solving, helped students develop a
process for analyzing mistakes, checking their work, helped students learn how to
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effectively use their resources, such as class notes, and teaching students strategies to
review for tests (Jenkins, 2009). Most importantly, math teachers guided students in how,
when, who they should ask for help when they do not know how to solve a problem. The
results of the study showed that students with explicit self-regulatory learning strategy
instruction had significantly higher standardized test scores than students who did not
receive the instruction (p = .03). Consequentially, in addition to creating a quiet,
appropriate setting for students to study, Below-5 students would also benefit from self-
regulatory learning strategy instruction.
Homework support class. The results of the parent organization survey
demonstrated that Below-5 student parents did not feel capable in providing their children
with homework help. According to Beck (1999), academically struggling students can
benefit from attending homework support classes. In his qualitative study, he found that
students who were considered to be “at-risk” of failing school benefited from after-school
homework programs. During the intervention, students were able to dedicate extra time
after school to “hone their skills” in the presence of a competent adult that would provide
them with academic support and additional time on task (Beck, 1999). Consequentially,
Education Express will provide “homework help” classes after school for students who
are struggling with homework completion and that do not have someone at home that can
help them answer questions.
Implementation

In order to integrate the knowledge, motivation, and organization solutions, an
implementation plan will be put into effect. Firstly, in order to close the current
knowledge gap, students who are identified as falling “Below-5” after the ISEE Pre-test
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in June will go through a math pre-training course during June, July, and August to teach
them the necessary prior knowledge needed to succeed in the ISEE Program during the
Fall. The math pre-training course will be held twice a week at Education Express, and
the content knowledge will be geared towards ISEE test preparation.
Additionally, in order to keep students motivated, ISEE instructors will
incorporate cooperative learning during ISEE classes to create interest, values, and
increase self-efficacy (Bandura, 1997; Bernero, 2000). Below-5 students will also be
taught self-regulatory strategies during ISEE class so that they are able to create a space
and time at home to be able to complete ISEE homework (Jenkins, 2009). Education
Express will also create a “homework help” class on Thursday afternoons during the
ISEE Program so that students have a quiet place to do homework and cultural models,
such as ISEE math teacher, to provide homework help. The Thursday “homework help”
class will create the appropriate cultural settings for students to effectively complete their
ISEE math homework and Below-5 students can use ISEE teachers as appropriate
cultural models (Gallimore & Goldenberg, 2001; Xu & Corno, 2003).
Lastly, the solution to the organizational barrier of ISEE classes being held on the
weekends would be to offer the same ISEE classes after school during the week. Below-5
students and parents will be offered both the week-day and weekend option for ISEE
classes in order to satisfy all students, and they will be able to choose when to take ISEE
class. The implementation plan just described along with causes and solutions can be
found in table 5.1.

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Table 5.1
Summary of Causes, Solutions, and Implementation of the Solutions

Knowledge &
Skills
Motivation Culture/Context/Capital/Policy
Causes Conceptual
knowledge

Procedural
knowledge

Cognitive
Development

Aptitude / Ability

Lack values /
interest in
math lessons

Low Self-
efficacy
- Cultural setting: lack of quiet
place to do homework

- Cultural Model: lack of
support / adult to ask for
homework help

- ISEE classes are held on the
weekends

Solutions Conceptual
knowledge – use
concept maps &
reinforcement
such as flash
cards

Procedural
knowledge – use
demonstration &
worked examples

Cognitive - Use
tangible objects
for abstract
concepts to
facilitate learning
and guide
cognitive
development

Students need
pre-training in
pre-requisite
knowledge in
order to
successfully
complete the
ISEE Program in
Use
cooperative
learning to
create interest
in math class
& to create
self-efficacy


Modify
teaching
strategies to
include
providing
frequent,
constructive
teacher
feedback, goal
setting, and
use of similar
models that
demonstrate
the desired
math skill and
level of
performance.

- Teach students self-regulation
strategies to complete
homework

Offer homework help class

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109

the fall

Aptitude / Ability

Implementation Offer pre-training
program over the
summer for
Below-5 students
identified after
Pre-Test in June.

Incorporate
tangible objects
in formal
operations lessons
such as surface
area, Pythagorean
theorem, and
algebra.
Incorporate
cooperative
learning into
ISEE lessons

Have ISEE
teachers
modify
teaching
strategies to
use strategies
that foster
self-
regulatory
skills and self-
efficacy
Incorporate self-regulation
strategies in every ISEE class

Offer Thursday homework help
class

Offer ISEE classes during the
week after school so that
students can pick weekday or
weekend classes.

Goal Hierarchy for Below-5 Student Stake Holder
In order to facilitate suggested the implementation plan, a goal hierarchy was
created to enable Below-5 students to achieve the overall performance goal of scoring a
stanine of 5 or higher on the math sections of the ISEE exam. Table 5.2 summaries the
organizational goal, cascading goals, and performance goals for Below-5 students.

Table 5.2
Summary of Education Express’ Organizational Goal, Short-term Goals, Cascading
Goals, and Performance Goals

Organizational Goal: Below-5 Students will increase their math ISEE scores to a
stanine of 5 or higher.

Knowledge Motivation

Organization
Goal 1:
Below-5 students
will receive a stanine of 5 or
Goal 2: Below-5 students
will choose to complete
Goal 3: Below-5
students will complete
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110

higher on the ISEE Post-test
in November.

ISEE course work, and
persist and apply mental
effort towards completion
of the fall ISEE Program.

their weekly ISEE
homework at home
without the help of an
adult as measured by a
parent report.

Cascading Goal 1:
Below-5 students will
achieve a stanine of 5 or
higher on the math sections
of the practice test during
lesson 10 of the ISEE
Program.
Cascading Goal 2:
Below-5 students will
choose to begin, persist, and
apply mental effort to
complete the pre-training
course with 100% accuracy.

Cascading Goal 3:
Below-5 students will
complete their math
homework without the
help of the instructor
during the Thursday
“homework-help” class
with 90% accuracy.
Performance Goal 1:
Below-5 students will
demonstrate proficiency in
mathematical concepts by
achieving a score of 95% or
higher on the pre-requisite
knowledge assessment
during the summer training
program.

Performance Goal 1:
Below-5 students will
choose to begin, persist, and
apply mental effort towards
completing all ISEE
homework assignments.

Performance Goal 1:
Below-5 students will
complete their math
homework with the help
of the instructor during
“homework-help” class
with 95% accuracy.

Performance Goal 2:
Below-5 students will
complete surface area and
algebra ISEE class
problems with the use of
manipulatives with 90%
accuracy during the summer
training program.

Performance Goal 2:
Below-5 students will be
able to explain the value of
completing their ISEE
homework assignments.

Performance Goal 2:
Below-5 students will
be complete in-class
math activities on their
own with 95% accuracy
by lesson 3.

Table 5.3 summarizes the suggested performance goals and how completion of
those goals will be measured.

Table 5.3
Summary of Performance Goals, Timeline and Measurement of Performance Goals

Stakeholder Performance Goal Goal Measure
Knowledge Performance Goal 1: Below- Below-5 students will re-take the 40-
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5 students will demonstrate proficiency in
mathematical concepts by achieving a
score of 95% or higher on the pre-requisite
knowledge assessment during the summer
training program.

item knowledge questionnaire at the
end of the summer training program in
August.
Knowledge Performance Goal 2: Below-
5 students will complete surface area and
algebra ISEE class problems with the use
of manipulatives with 90% accuracy during
the summer training program.

ISEE instructor will demonstrate
procedure, monitor class progress, and
check student worksheet for accuracy.
Motivation Performance Goal 1: Below-
5 students will choose to begin, persist, and
apply mental effort towards completing all
ISEE homework assignments.
ISEE instructors will check students’
ISEE homework for completion each
week during ISEE class.

Motivation Performance Goal 2: Below-
5 students will be able to explain the value
of completing their ISEE homework
assignments.

Below-5 students will be asked to
write a self-reflection describing the
value of completing ISEE homework
at the end of the first ISEE lesson.
Organization Performance Goal 1:
Below-5 students will complete their math
homework with the help of the instructor
during “homework-help” class with 95%
accuracy.
The ISEE math instructor will lead the
homework-help class by going
through each homework problem on
the board and answering questions.
Instructor will check students’ math
homework for accuracy.

Organization Performance Goal 2:
Below-5 students will be complete in-class
math activities on their own with 95%
accuracy by lesson 3.
The ISEE math instructor will monitor
the students’ progress during math
class and check class work for
accuracy.

Summary
The proposed solutions to close the Below-5 student gap in knowledge,
motivation, and organizational barriers were discussed in this chapter. Chapter 6 will
provide a discussion of the Gap Analysis, including an evaluation plan to assess the
effectiveness of the suggested solutions.
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CHAPTER 6: DISCUSSION
Using the Clark and Estes (2008) Gap Analysis Process framework, the purpose
of the study was to examine the knowledge and skill, motivation, and organization
barriers that contributed to the gap in Below-5 student performance on the math sections
of the ISEE Post-test.
The study questions included:
1. What are the causes of the gap that “Below-5” students have in knowledge and
skills, motivation, organizational context, culture, and capital that affect their
successful achievement of 5 or better on the ISEE Program Post-test?
2. What are the potential knowledge and skill, motivation, and organizational
solutions to address the Below-5 students gaps in achieving a score of 5 or better
on the ISEE Program Post-test?

Synthesis of the Results
The results of the gap analysis revealed that, on average, there was 40%
knowledge gap in the pre-requisite knowledge required to successfully complete the
ISEE Program. The gap analysis also showed that Below-5 students lacked the
motivational constructs of value and interest in the math lessons and had low self-
efficacy towards completing ISEE assignments. Lastly, the organizational barriers at
Education Express involved the lack of a quiet place at home for Below-5 students to
complete their ISEE homework and the timing of ISEE classes during the weekend.

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Strengths and Weaknesses of the Approach
There are several strengths to the Gap Analysis approach. Firstly, Gap Analysis
goes beyond action research and instills a performance framework for problem solving. It
also provides concrete solutions to close deficits and provides measurable results.
Additionally, when compared to the Positive Deviance approach, Gap Analysis looks at
aspects of organizations that can be fixed and improved, thus bettering the organization’s
performance.
While there are several benefits to using the Gap Analysis model, there are also a
number of weaknesses to the approach that should also be considered. Firstly, conducting
a Gap Analysis takes time, and in order to conduct a complete Gap Analysis, one must
look at all the stakeholders involved. The current gap analysis only examined one
stakeholder, the students. Additionally, Gap Analysis assumes a deficit approach towards
organizational performance, which can deter employee confidence and can also
subsequently cause a decrease in the institution’s level of performance. When taken as a
whole, however, the Gap Analysis approach was chosen because it aims to improve
institutional performance by ameliorating existing deficits.

Recommendation and Implications
As a solution to close the knowledge gap, Education Express will offer a
knowledge pre-training course over the summer for Below-5 students that are identified
after the ISEE Pre-test in June. The summer pre-training course will cover prime numbers
and factors, circumference, area, surface area, and computation with decimals, fractions,
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and percents. Additionally, during the pre-training course and the ISEE Program,
instructors will incorporate the use of tangible objects when instructing concepts that
involve formal operations, such as surface area.
As revealed by the literature, the solutions to close the motivation gap were to
incorporate cooperative learning into each ISEE lesson in order to create student interest.
ISEE teachers will also modify teaching strategies during ISEE lessons to use strategies
that foster self-regulatory skills and subsequently foster self-efficacy in students.
The proposed solutions to close the organization gap were to incorporate self-
regulation strategies in every ISEE class so that Below-5 students will learn how to create
the proper homework environment at home and to also offer a homework-help class on
Thursday afternoon.

Evaluation
In order to evaluate the effectiveness of the proposed solutions to close the
Below-5 student performance gap, an evaluation plan will be created for Education
Express. According to Kirkpatrick (2006), there are four levels of evaluation when
assessing the success of an intervention and suggested solutions. The first level of
evaluation assesses participant reactions and motivation, followed by level 2, which
assesses learning or performance. The third level of evaluation assesses transfer or
behavior, and the final level of evaluation examines impact and if the performance gap
has been closed (Kirkpatrick, 2006). Once the knowledge, motivation, and organization
solutions have been implemented to close the Below-5 student performance gap, the
suggested evaluation plan will be put into effect using the four levels of evaluation.
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Then describe how you would use an evaluation system to assess the impact of your
solutions on the gap at all four levels: In italics, describe the results you would expect to
see at each level of evaluation, if the implementation of your solution was effective
Level 1 Reactions. According to Kirkpatrick (2006), the first level of evaluation
should measure the participants’ reactions to the training and their motivation. Assessing
how the Below-5 students felt after the intervention program is important because a
participant’s initial reactions are important for learning results. In order to conduct a level
1 assessment, Below-5 students will be given a four-column satisfaction chart with star
stickers to rate their reactions to training. Using a Likert scale of 1 to 4 stars, students
would rate their satisfaction with the ISEE pre-training course, interest in ISEE classes
during the ISEE Program, self-efficacy towards completing ISEE assignments, and how
satisfied they were with their homework environment. Below-5 students will be asked to
fill out the chart 4 times during the 12-week course. {Expected results: If the intervention
is successful, we would expect to see 4 star stickers in the knowledge, motivation, and
organization columns of the chart.}
Level 2 Learning. At the second level of assessment, instructors assess the how
much students have learned as a result of the intervention and if participants are
performing differently as a result of the intervention (Kirkpatrick, 2006). In order to
conduct a level 2 evaluation, the ISEE instructors will administer the 40-item knowledge
questionnaire once Below-5 students go through the summer pre-training, just before
entering the ISEE Program in the Fall, to assess how much students have learned.
{Expected results: The expected level of performance on the knowledge survey after the
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summer pre-training course would be above 90%, a 30% increase from the Below-5
student average of 60%.}
Level 3 Transfer. Kirkpatrick’s level 3 of assessment measures transfer and
seeks to determine if learners are able to apply the knowledge and skill acquired through
training to other environments (Kirkpatrick, 2006). In order to measure transfer,
Education Express will examine Below-5 students math scores at their elementary school
to determine if they are able to transfer the ISEE math knowledge they learn at Education
Express to the classroom setting. {Expected results: Research and learning theory
suggest that standardized test preparation teaches and reinforces content that students
learn in school (Duke et al., 1997). If Below-5 students successfully learn the math
knowledge at Education Express, then they will be able to apply the knowledge to their
school setting, which will improve their performance in math at school.}
Level 4 Impact. Kirkpatrick’s fourth level of evaluation examines the impact of
the intervention. In particular, a level 4 evaluation determines whether the institution was
indeed able to close the performance gap. Education Express would apply the
recommended knowledge, motivation, and organization solutions to the succeeding group
of Below-5 students who enter EE the following academic year. {Expected Results: EE
would monitor their progress and subsequent ISEE performance, and if the students who
were identified at scoring below a stanine of 5 on the math sections were able to score a
stanine of 5 or higher, it can be concluded that the intervention had a positive impact.}

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Limitations
There were several limitations to the current study. Firstly, the researcher was an
instructor at the site of the study, and because the researcher was a part of the
organization, the study may not have been as objective (Patton, 2002). Additionally, the
small sample size used in the study may not be a good representation of the entire
population of middle level ISEE students. The fact that the study was conducted only at
one site also has limitations because it is possible that the Below-5 student gaps are
particular to the site and do not exist in other places. Lastly, the difference in age between
the Below-5 students was another limitation because a 10-year old Below-5 student’s
cognitive development may differ from a 12-year old Below-5 student’s cognitive
development (Joffrion, 2010); thus, age is a limitation for assessing cognitive
development.
Future Research
Areas for future research would involve conducting a Gap Analysis to examine
the other stakeholders at Education Express, such as Below-5 student parents or ISEE
instructors. Furthermore, another possible area for future research could involve
expanding the current Gap Analysis and conducting a Cognitive Task Analysis on the
various components of the knowledge required for the ISEE. Future research may also
examine differences in performance based on the age of the Below-5 students between
the ages of 10-12.
Conclusion
The current gap in performance at Education Express was a result of a change
made in 2009 to the format of the math sections of the ISEE. In 2009, when the ERB
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increased the level of difficulty of the math content on the exam, a subsequent gap in
student knowledge was created. This resulted in a gap in performance at Education
Express, as each year a handful of students, also known as the “Below-5” students, would
not receive satisfactory scores on the math sections of the ISEE, consequentially limiting
their eligibility into private middle schools.
The Clark and Estes (2008) Gap Analysis model was the framework that was used
for the study, which examined the knowledge and skill, motivation, and organization
barriers that contributed to the gap in Below-5 student performance on the math sections
of the ISEE Post-test. The Gap Analysis model examined the knowledge, motivation, and
organization causes for the gap, and provided solutions in each of those areas to close the
gap. The results of the study found that there was a vast knowledge gap of 40%, a
motivational gap in interest and self-efficacy, and an organizational gap in homework
completion and timing of the ISEE classes.
The implications of the case study show that, not only do knowledge and skills
impact performance, but both motivational and organizational barriers also play a
significant role in academic fulfillment, and that these two areas must also be considered
in order to raise academic scores. The current case study can apply to similar gaps in
math performance in elementary school, as prior knowledge, motivation, and
organizational factors impact student performance regardless of the context or
environment. When taken as a whole, the current Gap Analysis of Below-5 student
performance on the math sections of the ISEE is a valuable case study, as it can serve as a
model for closing academic gaps in various other institutions.
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APPENDIX A
Below-5 Student Pre-requisite Knowledge Questionnaire

Name: ___________________________

ISEE Pre-training Assessment

Directions: Please answer the
following questions. If you do not know
what the answer is, please leave the
question blank.

1) What is the product of 35 and
46?
___________________________

2) The product of 22 and 57 is:
___________________________

3) What are the factors of 12?
___________________________

4) What are the factors of 36?
___________________________

5) Please list 3 examples of prime
numbers:
___________________________

6) Which of the following are the
prime factors of 24?
a. 1, 2, 3, 4, 6, 8, 12
b. 1, 2, 3, 4, 6
c. 1, 2, 3
d. 2, 3

7) The first 10 multiples of 12 are:
___________________________

8) What is the least common
multiple for 6 and 8?
___________________________
___________________________

9) 60 x 40 = ___________
8

10) What is the product of 21 and 36
divided by 4? (189)

___________________________

11) 2(3 + 4) – 10 / 2 - PEMDAS

___________________________

12) Please find the perimeter for the
following shape:

12
in.

INCREASING MATH ISEE STUDENT PERFORMANCE

129

Perimeter = _______________

13) What is the circumference of a
circle with a radius of 5 inches?

Circumference =

_________________________

14) Please find the area for the
following shapes

a. Quadrilateral

11 yds

Area = ____________________

b. Triangle

8 cm

15 cm

Area = ____________________

c. Circle

Area = ____________________

5
in

8 yds
7
cm

INCREASING MATH ISEE STUDENT PERFORMANCE

130

15) Please find the volume for the
following shape:
a. Cube

3 in.

3 in.

Volume = ____________________

16) What is the surface area of the
cube?

3 in.

3 in.

Surface Area = ____________________

17) How many degrees are in a right
angle?
a. 180
b. 100
c. 90
d. 45

18) How many degrees are in an
acute angle?
a. More than 90
b. Less than 90
c. 180
d. 45

19) How many degrees are in an
obtuse angle?
a. More than 90
b. Less than 90
c. 180
d. 45

For questions 20-21, please refer to the
following decimal:

0.136

20) What is the place value of the
underlined digit?
a. Tenths
b. Hundredths
c. Thousandths

21) How can the decimal be written
as a fraction?

3 in.
3 in.
INCREASING MATH ISEE STUDENT PERFORMANCE

131

22) 4.59 + 6.072 =

____________________

23) 1.3 x 5 =

____________________

24) 5.75 ÷ 5 =

_____________________

25) 36.44 / .4 =

____________________

26) How can you represent 0.08 as a
fraction?

____________________

27) David took a Wordly Wise test at
school and answered 18 out of 20
questions correctly. What
percent did he receive on the
test?

________________________
28) 0.3 is what percent?
a. 3%
b. 30%
c. 60%
d. .3%

29) How can 40% be written as a
decimal?

____________________________

30) 5% is equivalent to which
decimal?
a. 0.5
b. 0.05
c. 5.00
d. 50.0

31) Jonathan and Talia had lunch at
CPK. Jonathan ate 3 out of 6
slices of his pizza, and Talia ate 4
our of 7 slices of her pizza. Who
ate more pizza?

______________________________

______________________________

32) 2/5 + ¾ =

_______________________

33) 1 ¾ + 2/3 =

_______________________

INCREASING MATH ISEE STUDENT PERFORMANCE

132

34) ¾ - ½ =

_______________________

35) ¾ * 4/9 =

_______________________

36) 1½ x 3 ⅝ =

_______________________

37) ¾ ÷ 1/6 =

_______________________

38) What is the probably of rolling a
6 when rolling a number cube (a
die)?

_______________________

39) What is the probability of rolling
a prime number when rolling a
number cube (a die)?

_______________________

40) What is the probability of rolling
an odd number when rolling a
number cube (a die)?

_______________________

INCREASING MATH ISEE STUDENT PERFORMANCE

133

APPENDIX B
Below-5 Student Smiley-Face Motivation & Organization Survey

Name: ____________________ Date: ____________________

Lesson _____

Directions: Please color in the number of smiley faces that express how you feel. 4
smiley faces mean you completely agree, 1 smiley face means you completely disagree.



        
I completely do not
agree
I do not agree I agree I completely agree

1. As of today, I am interested in studying for the ISEE.

   

2. I thought today’s math lesson was interesting.

   

3. Today’s math lesson was useful because it taught me information that will help
me do better on the ISEE exam.
   

4. I think it is important to learn the math concepts in today’s lesson because they
will help me do better on the actual ISEE exam.

   

5. I always try my best when I do my homework for school.

INCREASING MATH ISEE STUDENT PERFORMANCE

134

   

6. I always try my best when I do my ISEE homework.

   

7. I am confident that I can complete this week’s ISEE math homework.

   

8. I like taking ISEE classes during the weekend.

   

9. I have a quiet place at home where I can do my ISEE homework.

   

10. If I have a question about my ISEE homework, there is someone at home that I
can ask about it.

   

INCREASING MATH ISEE STUDENT PERFORMANCE

135

APPENDIX C
Below-5 Student Motivation and Organization Interview Protocol

Name: ____________________

Date: ____________________

Lesson _____

1. Did you find today’s math lesson to be interesting? What part of the lesson was
most interesting?

2. Are you motivated to complete your ISEE math homework?

3. Do you have a quiet place at home to study?

4. Do you have someone at home that you can ask questions if you do not
understand a problem?

INCREASING MATH ISEE STUDENT PERFORMANCE

136

5. Do you think it is important to study for the ISEE exam?

6. Do you enjoy coming to Learning Encounters on the weekends?

7. Do you find value in taking this course at Learning Encounters?

8. How do you think the ISEE course will help you succeed / improve your score on
the actual ISEE?

INCREASING MATH ISEE STUDENT PERFORMANCE

137

APPENDIX D
Parent Organization Survey
Name: ____________________

Child’s Name: ____________________

Date: ____________________

Directions: Please fill out the following survey on a scale of 1 to 4. A score of 4
indicates that you strongly agree with the statement, and a 1 indicates that you strongly
disagree with the statement.

1 2 3 4
Strongly disagree

Disagree

Agree

Strongly agree

1. I think it is important for my child to do his / her ISEE homework.

1 2 3 4

2. Completing weekly ISEE homework assignments will help my child do well on
the ISEE test.

1 2 3 4

3. As a parent, I support my child by reminding my child to do his / her ISEE
homework.

1 2 3 4

4. My child has a quiet place at home to do ISEE homework.

1 2 3 4

5. I feel that I am able to help my child with basic math problems if he / she needs it.

1 2 3 4

Abstract (if available)

Abstract Using the Gap Analysis problem-solving framework (Clark & Estes, 2008), this study examined the performance gap experienced by 6th grade students on the math sections of the ISEE (Independent School Entrance Exam). The purpose of the study was to identify and validate the knowledge, motivation, and organization causes of the students’ low performance on the ISEE pre-test. The participants in the study were 9 students identified as scoring below a stanine of 5 (referred to as Below-5 students) on the mathematics sections of an ISEE pre-test. Quantitative surveys and qualitative interviews were used to collect data, and data was analyzed using descriptive statistics. The results of the study found a significant prerequisite knowledge gap (40%), motivational barriers of values and self-efficacy, and organizational barriers including difficulty with homework completion and lack of homework support at home. Research based solutions to close the knowledge, motivation, and organization gaps are recommended. The implications of the study indicate that in order to achieve a stanine of 5 or higher on the math sections of the ISEE, Below-5 students will need pre-training in knowledge and skills, a motivation increase in self-efficacy and values, and organizational resources such as a proper homework environment and homework help.

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Asset Metadata

Creator Sarshar, Shanon Etty (author)

Core Title Increasing student performance on the Independent School Entrance Exam (ISEE) using the Gap Analysis approach

School Rossier School of Education

Degree Doctor of Education

Degree Program Education

Publication Date 05/03/2013

Defense Date 03/04/2013

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

Tag Education,educational psychology,gap analysis,OAI-PMH Harvest,standardized test preparation,standardized tests

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Yates, Kenneth A. (committee chair), Rueda, Robert (committee member), Stowe, Kathy (committee member)

Creator Email shanon.sarshar@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-250584

Unique identifier UC11288167

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Legacy Identifier etd-SarsharSha-1650.pdf

Dmrecord 250584

Document Type Dissertation

Rights Sarshar, Shanon Etty

Type texts

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

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

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