Singapore Math ii
COMPARATIVE EDUCATION: A STUDY OF THE EFFICACY OF THE SINGAPORE
MATH APPROACH IN A FIFTH GRADE CLASSROOM
A project submitted
by
Jessica Lynn Stephens
to
LaGrange College
in partial fulfillment of
the requirement for the
degree of
EDUCATION SPECIALIST
in
Curriculum and Instruction
LaGrange, Georgia
July 22, 2011
Singapore Math iii
Abstract
This action/evaluation research investigated the efficacy of the Singapore Math methods
in relation to fifth grade Georgia Criterion Reference Competency Test math scores in the
domain of measurement to the subjects’ fourth grade CRCT math scores in the domain of
measurement. Various methods were used in this research project to answer the three focus
questions and to analyze the data. The data for this research was collected by CRCT assessments,
student surveys, a reflective journal, and an interview. The results of this study showed that the
implementation of the Singapore math methods in the teaching of measurement made no
significant differences in the students’ fourth grade CRCT results in the domain of measurement
to the students’ fifth grade CRCT results in the domain of measurement. However, there was a
gain in overall achievement from the students’ fifth grade math CRCT scores compared to the
fourth grade math CRCT scores.
Singapore Math iv
Table of Contents
Abstract .......................................................................................................................................... iii
Table of Contents ........................................................................................................................... iv
Lists of Tables ..................................................................................................................................v
Chapter 1: Introduction ...................................................................................................................1
Statement of the Problem .....................................................................................................1
Significance of the Problem .................................................................................................1
Theoretical and Conceptual Frameworks ............................................................................3
Focus Questions ...................................................................................................................5
Overview of Methodology ...................................................................................................6
Human as Researcher ...........................................................................................................7
Chapter 2: Review of the Literature.................................................................................................8
Singapore Math ....................................................................................................................8
United States Math .............................................................................................................11
Supporters of Singapore Math ...........................................................................................13
School Improvement ..........................................................................................................15
Implementing Change ........................................................................................................15
Summary of Literature Review ..........................................................................................16
Chapter 3: Methodology ................................................................................................................17
Research Design.................................................................................................................17
Setting ................................................................................................................................17
Subjects and Participants ...................................................................................................18
Procedures and Data Collection Methods ..........................................................................18
Validity/Reliability/Dependability/Bias/Equity.................................................................21
Analysis of Data .................................................................................................................23
Chapter 4: Results ..........................................................................................................................26
Chapter 5: Analysis and Discussion of Results .............................................................................30
Analysis..............................................................................................................................30
Discussion ..........................................................................................................................35
Implications........................................................................................................................36
Impact on School Improvement .........................................................................................37
Recommendations for Future Research .............................................................................38
References ......................................................................................................................................39
Appendices .....................................................................................................................................42
Singapore Math v
List of Tables
Tables
Table 3.1.
Data Shell …………………………………………….…………………………19
Table 4.1
Dependent t-test ………………………………………………………………...26
Table 4.2
Chi square test …………………………………………………………………..27
Singapore Math 1
CHAPTER 1: INTRODUCTION
Statement of the Problem
This study will explore the achievement gap in African American elementary students
compared to non - African American students, and the incorporation of the Singapore math
methods as a comparative education design to increase student achievement in fifth grade math.
A problem identified from statewide mathematic assessments is the percent of African American
students not meeting grade - level standards is consistently greater than Whites and other subgroups, including English language learners. Yueng and Conley (2008) stated, “research based
on test results from the National Assessment of Educational Progress conducted since the 1970s
showed a substantial lag in achievement of Black students vis-a`-vis their White counterparts”
(p. 303). Additionally, Phillips, Crouse, and Ralph (1998) stated, “these disparities had been
observed to exist before children enter kindergarten, widen as they move through elementary and
middle schools, and persist into adulthood” (p. 303).
Significance of the Problem
Poor achievement in math leads to problems and concerns not only for the individual and
his or her future, but additionally for the nation and its economic growth rate. Welsh, Nix, Blair,
Bierman, and Nelson (2010) stated, “there are substantial achievement gaps between middleincome children and low-income children at school entry that widen over time and contribute to
serious disparities in learning difficulties, educational attainment, and long-term employment
potential” (p. 43). Research has found that delays in school readiness are often experienced by
culturally diverse children or children growing up in poverty. One of the groups that
compromise the culturally diverse learners is African Americans. Low achievement in math
Singapore Math 2
“…presents a challenge for a society that demands at least minimal math competency for success
in formal schooling, daily living, and employment” (Proctor, Floyd, & Shaver, 2005, p. 1).
In the 2008 publication from the Thomas B. Forham Institute Education Olympics, The
Games in Review, Ballard, Palmieri, and Winkler (2008) stated, “although the strengths of the
U.S. economy and its higher-education system offer some hope for the future, the situation at the
K-12 level should spark concerns about the long-term outlook for the U.S. economy, which
could eventually have an impact on the higher-education system as well” (p. 3). Additionally, as
cited by Ballard et al., Hanushek and his colleagues Jamison, Jamison, and Woessman, looked at
student performance on twelve math and science standardized international tests as a measure of
cognitive skills among those entering the workforce:
Though the analysis was complicated, Hanushek’s key finding was simple: The level of
cognitive skills of a nation’s students has a large effect on its subsequent economic
growth rate. He also found that more years of schooling, previously thought to be the
major advantage that other countries had over the U.S., only boosted the economy when
it was tied with student learning. In other words, “It is not enough simply to spend more
time in school; something has to be learned there.” (Ballard et al., 2008, p. 2)
It is important as educators to identify all under-achieving students in math and move them to a
level of proficiency where they can be successful not only in their education, but additionally in
their future economic world. Therefore, the purpose of this study will be to identify the specific
areas where African American elementary students are low achievers: numbers and operations,
measurement, geometry, algebra, and data analysis and probability. Additionally, this study will
determine if there is a specific trend within the data areas or if low achievement is evident in all
Singapore Math 3
mathematical areas. In relation to these research findings, the Singapore math method will be
used to increase student achievement in fifth grade math in the domain of measurement.
Theoretical and Conceptual Frameworks
This research project strongly conveys the theory of constructivism. Powell and Kalina
(2009) stated, “an effective classroom, where teachers and students are communicating
optimally, is dependent on using constructivist strategies, tools and practices” (p. 241). Within
constructivism there is cognitive constructivism dependent on Jean Piaget’s theory and social
constructivism dependent on Lev Vygotsky’s theory. Piaget and Vygotsky were both advocates
of inquiry-based instruction. Within this type of instruction, students perceive a problem,
construct a mental model to solve the problem, and then formulate a solution (Pass, 2004, p.
110). Furthermore, Powell and Kalina (2009) defined the differences between cognitive and
social constructivism:
In cognitive constructivism, ideas are constructed in individuals through a personal
process, as opposed to social constructivism where ideas are constructed through
interaction with the teacher and other students. While they are fundamentally different
both types will ultimately form overall constructivism or constructed learning elements
for students to easily grasp; the main concept being that ideas are constructed from
experience to have a personal meaning for the student. (p. 241)
This research project related and incorporated the elements of the cognitive constructivism
theory.
Within the cognitive constructivism theory, a student’s individual thought needs to be
acquired in content or subject areas to actually understand the material instead of just being able
to recite it. Powell and Kalina (2009) stated, “promoting classroom situations and activities that
Singapore Math 4
promote individual learning is required” (p. 242). Referring to Piaget’s theory of cognitive
development stated, “humans cannot be given information, which they immediately understand
and use; instead humans must construct their own knowledge” (Powell & Kalina, 2009, p. 242).
For students to be successful in elementary mathematics, they have to learn how to develop their
own knowledge of the content and not merely memorize the rules. From a cognitive
constructivist perspective, Larochelle, Bednarz, and Garrison (1998) stated, “it is reasonable to
characterize learning as a problem solving process in which children reorganize their
mathematical activity in an attempt to resolve what they find problematic within their worlds of
experiences” (p. 71).
Integrating the cognitive constructivist theory into an elementary mathematics classroom
strongly coincides with the second tenet of the LaGrange College Education Department’s
(2010) Conceptual Framework, exemplary professional teaching practices. The undergirding
knowledge base of this tenet includes the thoughts by Delpit and Kincheloe stating, “we believe
that teachers must link the life histories of their students to the content taught in classrooms, so
that their students can make deep, meaningful personal connections” (LaGrange College
Education Department, 2010, p. 5). Additionally, this tenet focuses candidates on
interrelationships between society and its institutions on one hand and issues of race, ethnicity,
gender, and social class on the other. Furthermore, this tenet incorporates methods characterized
by differentiated instruction, since all students do not learn in the same way or the same rate.
(LaGrange College Education Department, 2010)
Within the second tenet of the LaGrange College Education Department’s (2010)
Conceptual Framework, there are two competency clusters that relate to this thesis: instructional
skills and assessment skills. The instructional skills “advocate differentiated instructional
Singapore Math 5
processes that begin with teaching for conceptual understanding, move to presentation of new
knowledge, and then give learners an extended period during which they can apply this new
information in active, meaningful, and cooperative ways” (LaGrange College Education
Department, 2010, p. 7). The assessment skills include understanding and using formal and
informal assessment strategies to evaluate and ensure continuous intellectual, social, and
physical development of students. In addition, students are involved in self-assessments that
help them “become aware of their strengths and needs and that encourages them to set personal
goals for learning” (LaGrange College Education Department, 2010, p. 7). In response to
student feedback, strategies are monitored and adjusted.
With regards to the National Board of Professional Teaching Standards (NBPTS),
instructional skills are directly linked to Proposition Two which states, “teachers know the
subjects they teach and how to teach those subjects to students” (LaGrange College Education
Department, 2010, p. 12). The assessment skills are directly linked to the NBPTS Proposition
Three. This proposition states that, “teachers are responsible for managing and monitoring
student learning” (LaGrange College Education Department, 2010, p. 12). The instructional
skills are related to Element 1C of the NCATE 2000 standards. This element focuses on the
professional and pedagogical knowledge and skills for teacher candidates. The instructional
skills are related to Element 1D of the NCATE 2000 standards. This element focuses on student
learning for teacher candidates.
Focus Questions
After identifying the specific mathematical areas where 5th grade African American
elementary students perform poorly, the purpose of this study was to see if the implementation of
Singapore Math 6
the Singapore math method increased student achievement in fifth grade math in the targeted
areas of difficulty. The following focus questions were used to guide the research for this study:
1. Did the International Singapore Math approach positively affect fifth grade math
student achievement?
2. How do learners feel about the International Singapore Math approach?
3. How well did the International Singapore Math change process work in relation to
fifth grade math achievement?
Overview of Methodology
As part of this research project, a pilot study incorporated the Singapore math method as
a comparative education design to increase student achievement in fifth grade math. Kubow and
Fossum (2007) stated, “comparative education draws on multiple disciplines… to examine
education in developed and developing countries” (p. 6). Kubow and Fossum continue by
stating, comparative education “… encourages us to question our educational systems and to
examine how societal values influence our attitudes toward how we educate” (p. 6).
This study took place in a Title I elementary school in Troup county Georgia. The
subjects in this study were 5th grade math students. The participants included two 5th grade math
teachers and a principal. The first focus question used quantitative instruments including the
math CRCT results. These quantitative data were analyzed using a dependent t-test. The second
focus question was answered with surveys, which were analyzed using the Chi-square test. To
answer the third focus question, qualitative data were collected through interviews and a
reflective journal, which were analyzed by coding for themes.
Singapore Math 7
Human as Researcher
I have taught the past twelve years in a Title 1 school. During this time, I have seen a
change in regards to the increased emphasis on testing and how it relates to student achievement.
In response to this increased emphasis, I have learned how to analyze and disaggregate data from
school benchmarks, state wide assessments, and teacher observations to increase student
achievement. Additionally, I have served on my school’s leadership team as grade - level team
leader for the past six years. One of the duties of serving on the school’s leadership team was to
participate in the development of the School Improvement Plan. Data analysis and targeting
academic areas of weakness throughout the school was a key component of the School
Improvement Plan. Participating in the above data analysis situations has provided me with the
background knowledge to complete this research project.
Singapore Math 8
CHAPTER 2: REVIEW OF THE LITERATURE
Reviewing literature on a topic under investigation provides the opportunity to learn what
is already known about the topic. The research provided in this chapter is from what other
researchers have already discovered and will provide current information to understand my topic.
Comparative education examines education in developed and developing countries. Wilson
(2003) defined comparative education as “an intersection of the social sciences, education and
cross-national data to test propositions about the relationship between education and society and
between teaching practices and learning outcomes” (p.15). Comparative examination often leads
to an analysis of the role that education plays in an individual and national development.
Furthermore, comparative education inspires us to question our educational systems and to
observe how societal values influence our attitudes toward how we educate (Kubow & Fossum,
2007, p. 6).
To help struggling students, it is beneficial to look at other countries educational systems.
Little (2009) stated, “comparison studies from recent commissions and reports have focused on
student results. Students in the United States are not performing as well in math as students in
many other countries” (p. 3). Additionally from recent national test scores, the United States
remains academically behind most of the developed world. Therefore we, as educators, can
observe educational systems from other countries that have been successful in educational
attainment and study and implement those strategies into our educational system and classrooms.
Singapore Math
Through the years, Singaporean students have consistently outranked United States’
students in mathematics. According to the 2003 Trends in International Mathematics and
Singapore Math 9
Science Study, Singaporean students ranked first in the world. Scores for United States students
were among the lowest of all industrialized countries. Hammond (2010) stated:
This accomplishment is even more remarkable given that fewer than half of Singapore’s
students routinely speak English, the language of the test, at home. Most speak one of
the other official national languages of the country – Mandarin, Malay, or Tamal – and
some speak on of several languages or dialects. (p. 181)
Ginsburg, Leinwand, Anstrom, and Pollock (2005) stated Singaporean students are “more
successful in math than their U.S. counterparts because Singapore has a world-class mathematics
system with quality components aligned to produce students who learn mathematics to mastery”
(p. 13). Additionally, Ginsburg et al. (2005) stated:
The components of Singapore math include Singapore’s highly logical national
mathematics framework, mathematically rich problem-based textbooks, challenging
mathematics assessments, and highly qualified mathematics teachers whose pedagogy
centers on teaching to mastery. Singapore also provides its mathematically slower
students with an alternative framework and special assistance from an expert teacher.
(p. 13)
Singapore math highlights the development of strong number sense, excellent mental
math skills, and a deep knowledge of place value. The curriculum is built on a progression from
concrete experience, using manipulatives, to a pictorial stage and finally to the abstract level.
This sequence gives students a concrete understanding of basic mathematical concepts and
relationships before they start working at the abstract level. Singapore math incorporates a
strong emphasis on model drawing, a visual approach to solving word problems that helps
students organize information and solve problems in a step-by-step manner. Concepts are taught
Singapore Math 10
to mastery, then later revisited but not re-taught. Ginsburg et al. (2005) stated Singapore math
“… covers a relatively small number of topics in-depth and carefully sequenced grade-by-grade,
following a spiral organization in which topics presented at one grade are covered in later grades,
but only at a more advanced level” (p. 15).
Singapore math textbooks offer clear, straightforward presentations of the mathematical
concepts and topics outlined according to the national framework. Additionally, the textbooks
provide numerous problem sets and explain mathematical concepts primarily through problems
that illustrate concepts from a variety of different perspectives. Ginsburg et al. (2005) stated
“this approach accords with research affirming the value of problem-based learning, which
requires students to work through extensive problem sets that include routine and non-routine
applications in a wide variety of real-world contexts” (p. 39). Furthermore Singapore textbooks
feature mathematical explanations that begin with physical examples or picture representations
and only later build up to more abstract concepts. This technique is particularly helpful to
students who have difficulty understanding abstract mathematics. Singapore textbooks also use
pictures to develop heuristics that are predominantly useful in helping students visualize how to
break down and attack complex problems.
Singapore and the United States assessments greatly differ. Singapore’s assessments are
administered chiefly for the purposes of pupil accountability and placement. Singapore does not
have a common, annual exam at most primary grades. However, mathematics achievement is a
major component of the grade 4 exam given at the end of grade 4, the PSLE given in grade 6,
and the O-level exam typically given in grade 10. In addition to using assessments for individual
pupil placement and accountability, Singapore uses grades 6 and 10 scores to reward high -
Singapore Math 11
performing schools that achieved better than expected performance on value-added measures of
school outcomes. Ginsburg et al. (2005) stated:
The value-added measure of school performance quantifies the school’s contribution to
student outcomes. This is necessary and desirable, because simple comparisons of the
average outcomes of pupils at a school are not a good measure of school effectiveness;
they do not account for differences in the entry performance levels of students. (p. 66)
United States Math
The United States mathematics system does not have similar features with the Singapore
math system. The United States mathematics system lacks a centrally identified core of
mathematical content that provides a focus for the rest of the system. Its traditional textbooks
emphasize definitions and formulas, not mathematical understanding. The United States
mathematical assessments are not particularly challenging and too many United States teachers
lack sound mathematics preparation. Ginsburg et al. (2005) stated:
At-risk students often receive special assistance from a teacher’s aide who lacks a college
degree. As a result, the United States produces students who have learned only to
mechanically apply mathematical procedures to solve routine problems and who are,
therefore, not mathematically competitive with students in most other industrialized
countries. (p. 13)
In the United States there is no single approach to the mathematic curriculum. Most
curriculum decisions in the United States are made at the local or state level. In Singapore, the
Ministry of Education determines what will be taught nationwide. Therefore, certain elements of
the Singapore approach are distinctly different from what’s typical in the United States.
However, the United States mathematics system has some features that are an improvement on
Singapore Math 12
Singapore’s system, markedly an emphasis on 21st century thinking skills, such as reasoning and
communications, and a focus on applied mathematics. However, if United States students are to
become successful in these areas, they must begin with a strong foundation in core mathematics
concepts and skills, which, by international standards, they presently lack. Additionally, the
United States places a greater emphasis on applied mathematics, including statistics, probability,
and real word problem analysis. The United States mathematics frameworks stress data analysis
and probability, while the Singapore framework treats statistics in a strictly theoretical way
(Ginsburg et al., 2005).
In the United States, textbook design is more difficult than that of Singapore. United
States textbook publishers cannot organize their textbooks for a single mathematical framework.
Instead they must accommodate the standards of fifty states. Ginsburg et al. (2005) stated,
“textbooks in the United States have been criticized for being thick in pages but thin in
mathematics content, but publishers have little choice because of the need to cover the
mathematical topics from standards in a multistate market” (p. 40). Overall, the United States
textbooks do a considerably much worse job than the Singapore textbooks in explaining the
mathematical concepts that students need to learn. Since the mathematical concepts in these
textbooks are often weak, the presentation becomes more mechanical than is ideal.
Unlike Singapore, the United States has a great deal of testing. However, the testing is at
the state level rather than the national level. Therefore, United States assessments serve as a
high-stakes accountability function. No Child Left Behind (NCLB) accountability provisions set
national conditions that drive the states’ accountability provisions. However, NCLB’s method to
accountability is considerably different than Singapore’s. Ginsburg et al. (2005) stated, “NCLB
provisions focus on holding schools accountable for student performance; in contrast,
Singapore Math 13
Singapore’s assessment system places greater emphasis on student performance for purposes of
placement”(p.67).
Supporters of Singapore Math
Supporters of Singapore math feel that it addresses one of the difficulties in teaching
math, in that all children learn differently. In comparison to the most common math programs in
the United States, Singapore math allocates more time to fewer topics, ensuring that children
master the material through detailed instruction, questions, problem solving, and manipulatives.
In 1998, the amount of content covered by the national Singapore syllabi was cut by 10 to 30%
to allow for more project work and independent learning (Tsuneyoshi, 2005). Supporters of
Singapore math like that ideally students do not move on to a new topic until they have
thoroughly learned a topic. Educators express that slowing down the learning process gives
students a solid math foundation on which they can build increasingly complex skills, and it
makes it less likely that they will forget and have to be re-taught the same thing in later years.
Additionally, educators have observed with Singapore math that the pace can accelerate by
fourth and fifth grades, putting students as much as a year ahead of students in other math
programs as they grasp complex problems more quickly (Ginsburg et al., 2005).
As stated above, one of the principles teachers like about Singapore math is the ideas of
teaching to mastery, “teach it and if they don’t get it they will get a chance again next year”
(Ginsburg et al., 2005, p. 150). However, some teachers feel pressure to move on at a faster pace
and not achieve the mastery Singapore math requires before moving on. Another added appeal
to Singapore math is that it has largely skirted the math wars of recent decades over whether to
teach traditional math or reform math. Singapore math has often been defined by educators and
parents as a more balanced methodology between the two, blending old-fashioned algorithms
Singapore Math 14
with visual representations and critical thinking. Hammond (2010) stated in regards to
Singapore education, “this spirit of creativity and innovation is visible throughout the schools,
which are encouraged to engage both students and teachers in experiential and cooperative
learning, action research, scientific investigations, entrepreneurial activities, and discussion and
debate (p. 6)”.
Teachers like Singapore math because it provides higher level mathematical content and
higher level thinking (Ginsburg et al., 2005). Additionally, Singapore math text clearly presents
concepts using pictures, numbers, and words through multi-step, multi-concept, and multi-strand
problems. Furthermore teachers liked how the challenging word problems empower students to
become critical thinkers and that algebraic concepts are introduced at an earlier age than with
United States mathematics.
In the North Middlesex Regional School District of Massachusetts, a study implementing
Singapore math into public classrooms, teachers noticed that the Singapore textbooks:
offer a deeper treatment of mathematical topics that returns to a topic only to teach it with
more depth. The teachers also like the books’ visual explanations that concretely
explained abstract concepts and the numerous multistep problems, differences we also
noted between Singapore and United States textbooks. (Ginsburg et al., 2005, p. 152)
From this study, teachers in the United States feel they will need specially tailored professional
development to successfully use the Singapore textbooks as other research indicates.
Additionally, teachers feel:
The difficulties of students with weak mathematics preparation or those who have not
been exposed to Singapore’s curriculum in prior grades have to be addressed, as do the
lack of real-world examples in the books, the lack of alignment between the Singapore
Singapore Math 15
textbooks and state frameworks, and the unfamiliar language and phrases used in the
textbooks. (Ginsburg et al., 2005, p. 152)
School Improvement
School improvement is a data-driven, research based framework that defines goals and
objectives to improve student learning and for selecting and implementing strategies to improve
the instructional and organizational effectiveness of a school. The most effective school
improvement plans are not unyielding prescriptions for day-to-day action, but rather are guides
for ongoing improvement in critical areas. A successful plan implements action steps,
establishes timelines, and indentifies outcome measures to monitor and evaluate success.
As stated by Schmoker (1999):
School improvement is not a mystery. Incremental, even dramatic, improvement is not
only possible but probable under the right conditions. We have to acknowledge that
people work more effectively, efficiently, and persistently when they work collectively,
while gauging their efforts against results. (pp. 1-2).
If a plan is to become a significant resource and guide for school improvement, then it must be
built and owned by all stakeholders. These include teachers, support staff, school leaders,
students, families, district officials, community members, and business organizations.
Implementing Change
The research of Elbousty and Bratt (2010) has shown that resistance to school
improvement and the change process comes in two forms. One active form is when the teacher
rejects the very idea of working collaboratively, and one passive form is when the teacher
chooses to work only with one or two colleagues while excluding others. Elbousty and Bratt
stated:
Singapore Math 16
Teachers who resist actively express a sense of frustration about fairness and equity,
stating that collaboration with colleagues causes more work for them and does not
necessarily remedy difficulties. Such feelings of unfairness, no matter how large or
small, pose significant threats to the development of the learning community. (p. 7)
Therefore, in a democratic institution, as a public school must be, teachers must truly accept
plurality and differing opinions and seek consensus opportunities among those with whom they
disagree (Elbousty & Bratt, 2010).
Although resistance does occur during school improvement and the change process, when
teachers work together, they share different perspectives and practices that make a collaborative
environment useful and productive. To translate school improvement plans into results, school
leaders must understand the power of shared leadership, the implications of change, and how to
ensure that everyone takes responsibility for implementing improvement plans. Some of the
improvement plans can be to look at how to manage personal transitions of change, the keys to
creating cultures committed to continuous improvement, and how to ensure all stakeholders play
a role in school improvement efforts.
Summary of Literature Review
By acquiring an in-depth knowledge base of one or more topics, one can provide the
opportunity for others to learn what is already known about that topic or topics. Within this
chapter specific research-based knowledge that pertains to each of the study’s focus questions
were discussed to benefit others in gaining knowledge of this content matter. In conclusion, this
research provided the most current and relevant information to understand my research project
and the components of it.
Singapore Math 17
CHAPTER 3: METHODOLOGY
Research Design
In my research project I used a combination of action research design and evaluation
research design. Hopkins (2008) stated, “action research combines a substantive act with a
research procedure; it is action disciplined by enquiry, a personal attempt at understanding while
engaged in a process of improvement and reform” (p. 47). Evaluation research is completed to
determine the effectiveness of a program or curriculum. Action research develops something
new, whereas evaluation research appraises the quality of the innovation. The action research
process was used for this project to identify a need, collect information and resources, prepare
the project, and to introduce and implement the project. Additionally, the evaluation research
process was used to monitor procedures and reactions, identify strengths and shortcomings of the
project, and appraise the project’s ongoing and long-term results (Charles & Mertler, 2002).
Setting
The study took place in a rural elementary Title I Distinguished School in Troup County.
Students attending this school came from diverse communities including both rural and urban
populations. This school comprised of 298 students in Pre K through fifth grade. The student
body included 48% Caucasian, 37% African American, 3% Hispanic, 5% Asian, and 5%
Interracial. Three percent of the student body received instruction in a class for the gifted, 6%
received special education instruction, and 6% were English Language Learners. Sixty-five
percent of the students at this school participated in the free and reduced lunch program. This
study site was selected because it was where I taught. Permission to conduct the study was
granted by the school’s principal, the county school system, and LaGrange College’s
Institutional Review Board.
Singapore Math 18
Subjects and Participants
The subjects in my pilot study were fifth grade math students, divided into an
experimental group and a control group. The experimental group consisted of one White female,
four White males, three African American females, and four African American males. The
control group consisted of six White females, two White males, five African American females,
and four African American males. The students in the experimental group were chosen because
they were fifth grade students who scored level one on their Mathematics CRCT in fourth grade.
The students in the control group were chosen because they were fifth grade students who scored
level two on their Mathematics CRCT in fourth grade.
The participants in the pilot study were the school’s principal and two fifth grade
teachers. The principal was chosen because she was in charge of the curriculum and data. She
has been the principal at this school for three years. One of the fifth grade math teachers was
chosen because she co-taught in my experimental math group. She has taught fifth grade for
seven years. The other fifth grade math teacher was chosen because she was the teacher for the
control group. She has taught fifth grade for four years.
Procedures and Data Collection Methods
Throughout this paper, I will be referring to the data shell in Table 3.1 below and the
three focus questions used to guide the research. Various methods were used in this research
project to answer the three focus questions and to analyze the data. The data for this research
were collected by CRCT assessment, student surveys, a reflective journal, and an interview.
Singapore Math 19
Table 3.1 Data Shell
Focus
Question
Literature
Sources
Did the
International
Singapore Math
approach
positively affect
fifth grade math
student
achievement?
Ginsburg, A.,
Leinwand, S.,
Anstrom, T., &
Pollock, E.,
(2005)
Hammond, L.,
(2010)
Tsuneyoshi, R.,
(2005)
How do learners
feel about the
International
Singapore Math
approach?
Ginsburg, A.,
Leinwand, S.,
Anstrom, T., &
Pollock, E.,
(2005)
Hammond, L.,
(2010)
Schmoker, M.,
(1999)
Elbousty, Y., &
Bratt, K., (2010)
Ginsburg, A.,
Leinwand, S.,
Anstrom, T., &
Pollock, E.,
(2005)
Schmoker, M.,
(1999)
How well did the
International
Singapore Math
change process
work in relation
to fifth grade
math
achievement?
Type:
Method,
Data, Validity
Method:
Assessment
CRCT
How are these
data analyzed?
Rationale
Quantitative:
Pre and post
tests using
dependent ttests.
Effect Size r
Quantitative:
Determine if
there are
significant
differences
Method:
Survey
Quantitative:
Chi square test
Data:
Nominal
Cronbach’s
alpha
Quantitative:
Determine if
there are
significant
differences
Type of
Validity:
Construct
Method:
Interview
Reflective
Journal
Data:
Qualitative
Qualitative:
Coded for
themes
Data:
Interval
Type of
Validity:
Content
Qualitative:
Look for
categorical and
repeating data
Type of
Validity:
Nominal
I used Singapore math methods with my experimental group to teach measurement as
required by the Georgia State Performance Standards over a two week period. Implementing
Singapore math methods involved students solving problems, thinking deeply, sharing ideas, and
learning from one another. Student conceptual, procedural, and factual understandings were
acquired through problem solving and carefully structured practice. As a result, students learned
Singapore Math 20
how to think deeply and appreciate mathematics. The following are the Singapore math
strategies that were used for the pilot study:

Model drawing and an emphasis on the concept of part-whole that precedes the
teaching of model drawing

Mental Math: Techniques encourage understanding of mathematical properties
and promote numerical fluency

Daily activities to build on teacher-directed lessons

“Look and talks” to build understanding of mathematical language

Number bonds, ten frames, and place value charts

The connection of pictures, words, and numbers
Each subject’s fourth grade CRCT math test results were compared with the results of the fifth
grade CRCT math test to determine if there was a significant difference between the scores
between the fourth grade results and fifth grade results in the domain of measurement. Student
surveys (see Appendix A) were administered after the completion of the pilot study. Using a
three choice response scale, the student surveys asked questions regarding how the students felt
about the Singapore math approach and how successful the students felt in math after the
implementation of the Singapore math method. A reflective journal was used on a daily basis
after implementing the Singapore math methods in class. For the reflective journal, a set prompt
of questions (see Appendix B) were used to provide consistency. The journal provided
qualitative data which increased the dependability of the research through consistent data
collection and a controlled setting. The validity and reliability was maximized through
consistent data gathering and daily entries based on answers to prompt questions. An interview
with the school’s principal was conducted on the change process (see Appendix C). These
Singapore Math 21
results were coded for themes aligned with whether Singapore math methods positively affected
student performance on the Math CRCT from his or her fourth grade math CRCT results to his
or her fifth grade Math CRCT results in the domain of measurement.
Validity/Reliability/Dependability/Bias/Equity
The validity, reliability, dependability, and bias of an action research project are crucial.
As a researcher, there are certain procedures that take place to ensure the validity, reliability, and
dependability of data as well as the minimization of bias and the concern for equity. Focus
question one stated “Did the International Singapore Math approach positively affect fifth grade
math achievement?” For this focus question, quantitative interval data was used to determine if
there were significant differences in academic achievement in the domain of measurement.
CRCT math scores were used to show content validity and it was assured by using CRCT pre
and post – tests. CRCT results were deemed appropriate by the Troup County School System to
provide reliable and valid data, because it encompasses all areas of fifth grade Georgia
performance standards. The parallel correlation of the test scores showed reliability. The testretest reliability provided by the correlation of scores from different time periods spoke to the
reliability of my research. It was the assumption of the researcher that state-mandated
assessments were designed to eliminate unfairness, offensiveness, and disparate impact.
Focus question two, “How do learners feel about the International Singapore Math
approach?” quantitative data were used to determine if there were significant differences.
Ordinal data were gathered using student surveys to show construct validity. To show reliability,
a Cronbach’s alpha was calculated for the survey’s internal consistency. Dependability of the
data was ensured by consistently collecting the data and a controlled setting for the survey was
Singapore Math 22
provided. The student survey questions were reviewed for bias by the county school system as
well as the IRB. The analysis of the data showed no disparate impact from the innovation.
Focus question three, which is “How well did the International Singapore Math change
process work in relation to fifth grade math achievement?” qualitative data were gathered
through an interview with the principal of the school and through a reflective journal. The
journal provided qualitative data which increased the dependability of the research through
consistent data collection and a controlled setting. The validity and reliability were maximized
through consistent data gathering and weekly entries based on answers to prompt questions.
Content related validity was shown through the interview questions and the questions were
controlled for bias. Dependability of data were ensured by recording the interview with an
audiotape. The bias in the qualitative data was minimized through the review of items by peer
fifth grade teachers. There was attention given to the review of items for offensiveness,
unfairness, and disparate impact. With a thorough item per item review, bias was eliminated.
The data were analyzed by coding for themes to determine if there were any emerging, recurring,
or dominant themes that occurred.
Equity was assured during the research study through an equity audit. Skrla, McKenzie,
and Scheurich (2009) stated, “equity audits are a systematic way for school leaders-principals,
superintendents, curriculum directors, teacher leaders-to assess the degree of equity or inequity
present in three key areas of their schools or districts: programs, teacher quality, and
achievement” (p.3). The school that provided a home for this research endeavor was privileged
to have several systems in place that promoted educational equity.
Instruction was dictated by
curriculum pacing guides set forth by the district and aligned to state standards. Professional
development was focused on best practices for quality teaching as well as differentiated
Singapore Math 23
instruction. The fifth grade team collaborated daily to create common instruction, materials, and
assessment. All teachers in the on the team were highly qualified. There was much focus at the
district level on moving toward county-wide assessments to ensure equity.
Analysis of Data
Interval data were collected to determine if the Singapore Math approach positively affect
fifth grade math student achievement by comparing the experimental group’s fourth grade CRCT
scores to the group’s fifth grade CRCT scores in the domain of measurement. A dependent t-test
was used to analyze the data to determine if there was a significant difference between the means
from one group tested twice. The decision to reject the null hypotheses was set at p<.05.
Additionally, the effect size was measured using an Effect Size r. A small effect size ranged
from 0.1 to 0.23; a medium effect size ranged from 0.24 to 0.36; and a large effect size was set
for any value 0.37 or higher.
To determine how learners felt about the Singapore Math approach, ordinal data was
collected using student survey. A Chi-square test was used to analyze the student survey to show
significance. Salkind (2010) defines a Chi-square as “an interesting nonparametric test that
allows you to determine if what you observe in a distribution of frequencies would be what you
would expect to occur by chance” (p. 312). The rationale was to determine which questions
were significant and which questions were not significant. The significance level is reported at
the p < .05, p < .01 and the p < .001 levels. To determine reliability a Cronbach’s alpha was also
computed.
To assess how well the Singapore Math change process worked in relation to fifth grade
math achievement qualitative data was used. After an interview with the principal from the
school where the study took place, interview responses were coded for themes to look for
Singapore Math 24
categorical and repeating data that would show recurring, dominant, or emerging themes. The
reflective journal was analyzed by coding as well.
In order to assess the validation, credibility, transferability, and transformational concepts
for this entire study, a holistic approach of analysis was under taken. Two types of validity are
consensual validity and epistemological validity. Consensual validity was confirmed with
faculty approval. Eisner (1991) calls the faculty review process ‘Consensual Validation,’ an
agreement among competent others that the description, interpretation, evaluation and thematic
are right. Epistemological validity occurred when the results were compared to the literature.
Denzin and Lincoln (1998) describe the cycling back to your literature review as
‘Epistemological Validation,’ a place where you convince the reader that you have remained
consistent with the theoretical perspectives you used in the review of the literature.
Credibility is a concept defined as triangulation. Credibility was ensured in this study
through the use of multiple data sources. Eisner (1991) calls this process ‘structural
corroboration,’ where a confluence of evidence comes together to form a compelling whole.
Embedded within Eisner’s definition are the concepts of fairness and precision. To be fair, one
must state that one plans to present alternative (opposing) perspectives with which one may not
particularly agree. This was done by presenting alternative perspectives in the literature review
as well as selecting participants in the data collection process who have opposing views. To be
precise, one must state how one will present a tight argument, a coherent case, and have strong
evidence to assert judgments. Eisner refers to precision as ‘rightness of fit.’
Once credibility was established, this study had transferability. Transferability makes the
claim that the study is useful for others to apply to different situations. Eisner (1991) calls this
process ‘referential adequacy’ where perception and understanding by others will increase
Singapore Math 25
because of this research. Transformational ability is also referred to as ‘catalytic validity’
(Lather as cited by Kinchloe & McLaren, 1998). Catalytic validity is the degree to which the
researcher anticipates his or her study to shape and transform the researchers’ participants,
subjects or school. The evidence of catalytic validity was seen when the results of the study
were examined to determine significance and meaningfulness.
Singapore Math 26
CHAPTER 4: RESULTS
Within this chapter, the results and findings of the research on the efficacy of the
Singapore math approach will be presented and organized by focus question. The first focus
question states, “did the International Singapore Math approach positively affect fifth grade math
achievement?” The quantitative results for the first focus question were gained through the use
of a dependent t-test using students’ math CRCT scores from fourth grade and students’ math
CRCT scores from fifth grade in the measurement domain. The null hypothesis for the test was
that there would be no significant difference between the fourth grade CRCT math scores and the
fifth grade CRCT math scores in the domain of measurement. Additionally, to determine the
magnitude of the difference, the effect size was measured for each t-test using an Effect Size r.
Where a small effect size ranges from 0.1 to 0.23; a medium effect size ranges from 0.24 to 0.36;
and a large effect size is set for any value 0.37 or higher.
Table 4.1 Dependent t-test: 2010 and 2011 CRCT Scores in the domain of measurement
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean
Difference
Df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
t(11) = 0.60, p < .05
2010 CRCT
Measurement
50.41
147.54
12
-0.70
0
11
0.60
0.28
1.80
0.56
2.20
2011 CRCT Measurement
46.33
177.88
12
Singapore Math 27
As shown in Table 4.1, the CRCT scores in the domain of measurement did not show a
significant difference during the fifth grade year as compared with the CRCT scores in the
domain of measurement during the fourth grade year. The statistical dependent t-test does not
show significance with the obtained value of 0.60 not exceeding the critical value of 2.20, and,
therefore, the null is accepted. An Effect Size r value of 0.16 indicates a small effect size in the
difference.
The second focus question states, “how do learners feel about the International Singapore
Math approach?” The quantitative results for the second focus question were gained from
student surveys. These quantitative results were analyzed using a Chi-square test and Cronbach’s
alpha. The Chi-square test was used to determine if the observed distribution of frequencies was
what was expected to occur by chance. The rationale was to determine which questions were
significant and which questions were not significant. The significance level is reported at the p <
.05, p < .01 and the p < .001 levels.
Table 4.2: Chi-Square Statistic for Student Math Survey
Survey Items
n=12
Item 1
Survey Question
Did you like math when using Singapore math
methods?
Item 2
Do you feel better about math after using the
Singapore math methods?
Item 3
Would you like to use the Singapore math
methods again when learning math?
Item 4
Did you like the hands-on activities that were
used to teach measurement?
Item 5
Do you still feel like you need more help with
measurement?
* p<.05, **p<.01, ***p<.001
Χ
10.5**
10.5**
13.5**
24 ***
3.5
The results of the Chi-square statistic for the Student Math Survey in Table 4.2 also
highlighted several significant items. Questionnaire items 1, 2, 3, and 4 were all found to be
Singapore Math 28
highly significant when p < .05, .01, and .001, meaning that there were a high percentage of
students that answered a certain way on these questions. However, item 5 was not significant at
all, which means that there was no significant difference on these questions between what was
observed in the answers and what would have been expected to occur by chance.
To determine the internal consistency reliability of the items on the Student Math Survey,
the Cronbach’s alpha test was conducted using the survey responses. According to Salkind
(2010), “[internal consistency reliability] is used when you want to know whether the items on a
test are consistent with one another in that they represent one, and only one, dimension,
construct, or area of interest” (p. 147). For the Student Math Survey, the computations gave a
Cronbach’s alpha of 0.28. Therefore, this survey showed a moderate level of internal
consistency reliability using the results of the Cronbach’s alpha test which may indicate that the
trends were different among the questions.
The third focus question states, “how well did the International Singapore Math change
process work in relation to fifth grade math achievement?” The qualitative results for the third
focus question were gained from the reflective journal kept by me, and an interview with the
principal. These results were coded for themes aligned with whether Singapore math methods
positively affected student performance on the Math CRCT from the student’s math CRCT
results to the student’s fifth grade Math CRCT results in the domain of measurement.
Through the coding of the daily journal sheet, there was a recurring theme of student
behavior and discipline interfering with instructional delivery. Additionally from the journal,
when possible, small group instruction was the most valuable form of Singapore math delivery.
The small groups’ ratio consisted of no more than four students per teacher. A positive student
comment documented in the journal in regards to the Singapore Math methods was that the
Singapore Math 29
students enjoyed using manipulatives. Additionally, the students liked that greater and longer
use of time was spent on mastering the concepts of measurement.
The following are responses from my principal when I interviewed her. In response to
the question about the observation of the implementation of the Singapore math methods in
regards to instruction and student learning, the principal stated, “I saw numerous use of
manipulatives and the implementation of writing in mathematics. Even though there was not a
significant difference in the students’ measurement scores, I was very happy to see the
improvement in the overall math CRCT scores.” In response to the question about would these
methods be beneficial in other grade levels, the principal stated, “I think the methods of using
manipulatives, writing, spiraling and reviewing would be very beneficial in other grade levels.”
In response to the question were there any negatives during the implementation of the Singapore
math methods, the principal stated, “I saw no negatives. However, I wish our curriculum was
designed to allow more time to be spent on a topic, especially those topics of recurring difficulty
through the grade levels.” In response to the question about the change process, the principal
stated, “If we were to integrate some of these methods into other grade levels, I think others
would feel positive about this change process as long as these methods were delivered in a
beneficial, understanding lesson.”
The results of all quantitative data were determined through a dependent t-test and a chi
square test. The results of these two tests were shown in table format for the ease of the reader
and to display the findings of significance. The results from the quantitative data were coded for
themes. In Chapter 5, the results of these findings will be analyzed and discussed in detail.
There will also be implications and recommendations for future research in the Singapore Math
Method.
Singapore Math 30
CHAPTER 5: ANALYSIS AND DISCUSSION OF RESULTS
Analysis
Within this chapter, the results of the research project are further analyzed to give an indepth look at the outcomes attained. The data will then be disaggregated in a discussion of the
meaning as related to answering the three focus questions, and a discussion of the implications of
the results. The impact on school improvement will follow as well as recommendations for
further research.
For the first focus question, “did the International Singapore Math approach positively
affect fifth grade math achievement?”, quantitative data were used. The results for the first focus
question were gained through the use of a dependent t-test using students’ math CRCT scores
from fourth grade and students’ math CRCT scores from fifth grade in the measurement domain.
The purpose for this focus question was to see if there would be a significant difference between
the students’ fourth grade math CRCT scores from the students’ fifth grade math CRCT scores in
the measurement domain after the implementation of the Singapore Math methods. As stated by
Ginsburg et al. (2005) in a previous chapter, Singaporean students are “more successful in math
than their U.S. counterparts because Singapore has a world-class mathematics system with
quality components aligned to produce students who learn mathematics to mastery” (p. 13).
The data, as measured by a dependent t-test, looked for a significant difference between
the students’ fourth grade math CRCT scores from the students’ fifth grade math CRCT scores in
the measurement domain and showed no significance. From the dependent t-test the obtained
value of 0.60 did not exceed the critical value of 2.20, and, therefore, the null was accepted.
Additionally, with an Effect Size r value of 0.165141 indicated a small effect size in the
difference. Even though no significance was shown in the measurement domain between the
Singapore Math 31
fourth grade math CRCT scores and the fifth grade math CRCT scores, there was a gain in
overall achievement from the students’ fifth grade math CRCT scores compared to the fourth
grade math CRCT scores. Within my experimental group, I had 83% of those twelve students
(ten out of twelve) coming to me from fourth grade with a Level 1 math CRCT score which
shows they did not meet. After their fifth grade overall math CRCT were obtained, I had 25% of
those same twelve students score Level 1. Therefore, my experimental group at the beginning of
year came to me with a 17% success rate as determined by their fourth grade math CRCT scores,
with only two of those twelve students scoring a Level 2 (meets) on their fourth grade math
CRCT scores. At the end of their fifth grade school year, the same group of students had a 75%
success rate determined by their fifth grade math CRCT scores, with nine of those twelve
students scoring a Level 2 (meets) on their fifth math CRCT scores.
As stated previously in this paper, Ginsburg et al. (2005) stated Singapore math “…
covers a relatively small number of topics in-depth and carefully sequenced grade-by-grade,
following a spiral organization in which topics presented at one grade are covered in later grades,
but only at a more advanced level” (p. 15). The success of the students’ overall fifth grade math
CRCT scores was because of the sequencing and spiraling of the math standards throughout the
school year, however, this did not show success within the measurement domain. Additionally,
the statement by Ginsberg et al. (2005) stated Singaporean students are “more successful in math
than their U.S. counterparts because Singapore has a world-class mathematics system with
quality Components aligned to produce students who learn mathematics to mastery” (p. 13)
substantiated the results of the study.
For the analysis of the second focus question, “how do learners feel about the
International Singapore Math approach?”, quantitative results were gained from student surveys.
Singapore Math 32
These quantitative results were analyzed using a Chi-square test and Cronbach’s alpha. The Chisquare test was used to determine if the observed distribution of frequencies was what was
expected to occur by chance. The rationale was to determine which questions were significant
and which questions were not significant. The significance level was reported at the p < .05, p <
.01 and the p < .001 levels. To determine reliability a Cronbach’s alpha was also computed.
The student survey consisted of five questions pertaining to the Singapore math methods and
measurement. Item 1 had a Chi-square result of χ²(2) = 10.5, p. < .05. This means the student
responses were significant. The raw data revealed that most students agreed with the belief that
they liked math when using the Singapore math methods. Item 2 had a Chi-square result of χ²(2)
= 10.5, p. < .05. This means the student responses were significant. The raw data revealed that
most students agreed with the belief that they felt better about math after using the Singapore
math methods. Item 3 had a Chi-square result of χ²(2) = 13.5, p. < .05. This means the student
responses were significant. The raw data revealed that the majority of the students agreed with
the belief that they would like to use the Singapore math methods again when learning math.
Item 4 had a Chi-square result of χ²(2) = 24, p. < .05. This means the student responses were
highly significant. The raw data revealed that all the students agreed with the belief that they
liked the hands-on activities that were used to teach measurement. Item 5 had a Chi-square
result of χ²(2) = 3.5, p. > .05. This means the student responses were not significant. The raw
data revealed that student responses were mixed between all possible categories as far as the
belief that they still feel like they need more help with measurement.
To determine the internal consistency reliability of the items on the survey given to the
students, a Cronbach’s alpha test was conducted using the survey responses. The purpose of this
test was to correlate the score for each item with the total score for each student in order to make
Singapore Math 33
sure the survey items measured only what they were intended to measure. The Cronbach’s alpha
of a = 0.28 showed a moderate level of internal consistency reliability using the results of the
Cronbach’s alpha test which may indicate that the trends were different among the questions.
Through the review of the raw data, there was significance in that the students liked the
Singapore math methods and would like to use them again. However, the one item that showed
no significance was the in regards to students still not feeling confident about their understanding
of measurement. This correlated with previous literature in regards to Singapore math in that if
more time could have been given to the teaching of measurement, there could have been a higher
level of success. However, in the United States our curriculum is very broad and not very deep.
We are held accountable to teach many math standards in a short amount of time whereas,
supporters of Singapore math, like that ideally students do not move on to a new topic until they
have thoroughly learned a topic. As previously discussed, educators express that slowing down
the learning process gives students a solid math foundation on which they can build increasingly
complex skills, and it makes it less likely that they will forget and have to be re-taught the same
thing in later years (Ginsburg et al., 2005). Additionally, this cycles back to Singapore in 1998,
when the amount of content covered by the national Singapore syllabi was cut by 10 to 30% to
allow for more time (Tsuneyoshi, (2005).
For focus question three, “how well did the International Singapore Math change process
work in relation to fifth grade math achievement?”, qualitative data were used. Results for the
third focus question were gained from a reflective journal kept by the teacher and an interview
with the principal. These results were coded for themes aligned with whether Singapore math
methods positively affected student performance on the Math CRCT from his or her fourth grade
math CRCT results to his or her fifth grade Math CRCT results in the domain of measurement.
Singapore Math 34
Additionally, focus question three relates to school improvement and the change process. As
previously discussed, the most effective school improvement plans are not unyielding
prescriptions for day-to-day action, but rather are guides for ongoing improvement in critical
areas. A successful plan implements action steps, establishes timelines, and identifies outcome
measures to monitor and evaluate success. This is supported by Schmoker (1999) who stated,
“we have to acknowledge that people work more effectively, efficiently, and persistently when
they work collectively, while gauging their efforts against results” (pp. 1-2).
Common themes discovered from the interview with the principal were mental math
techniques, manipulatives, and the connection of pictures, words, and numbers through “Writing
to Win.” The following are responses from my principal when I interviewed her. In response to
the question about the observation of the implementation of the Singapore math methods in
regards to instruction and student learning, the principal stated, “I saw numerous use of
manipulatives and the implementation of writing in mathematics. Even though there was not a
significant difference in the students’ measurement scores, I was very happy to see the
improvement in the overall math CRCT scores.” In response to the question about would these
methods be beneficial in other grade levels, the principal stated, “I think the methods of using,
manipulatives, writing, spiraling and reviewing would be very beneficial in other grade levels.”
In response to the question were there any negatives during the implementation of the Singapore
math methods, the principal stated, “I saw no negatives. However, I wish our curriculum was
designed to allow more time to be spent on a topic, especially those topics of recurring difficulty
through the grade levels.” In response to the question about the change process, the principal
stated, “If we were to integrate some of these methods into other grade levels, I think others
would feel positive about this change process as long as these methods were delivered in a
Singapore Math 35
beneficial, understanding lesson.” This statement did not correlate with Elbousty and Bratt
(2010), in that with the change process teachers express a sense of frustration about fairness and
equity which pose significant threats to the development of the learning community.
Through the coding of the daily journal sheet, there was a recurring theme of student
behavior and discipline interfering with instructional delivery. Additionally from the journal,
when possible, small group instruction was the most valuable form of Singapore math delivery.
The small groups’ ratio consisted of no more than four students per teacher. A positive student
comment documented in the journal in regards to the Singapore Math methods was that the
students enjoyed using manipulatives. Additionally, the students liked that greater and longer
use of time was spent on mastering the concepts of measurement. However, another recurring
theme was the students’ resistance to writing about math.
Discussion
The results of this study showed that the implementation of the Singapore math methods
in the teaching of measurement made no significant differences in the students’ fourth grade
CRCT results in the domain of measurement to the students’ fifth grade CRCT results in the
domain of measurement. However, as I stated previously in this chapter, there was a gain in
overall achievement from the students’ fifth grade math CRCT scores compared to the fourth
grade math CRCT scores. There are several reasons why I think there was not a significant
difference in the students’ fourth grade CRCT results in the domain of measurement to the
students’ fifth grade CRCT results in the domain of measurement. First, in Singapore math, the
curriculum covers fewer standards but goes deeper into each standard. Whereas, here in the
United States, our curriculum covers many standards within a year and therefore the depth of
knowledge of each standard is difficult to achieve. Second, knowing how low mathematically
Singapore Math 36
the students in the experimental group entered fifth grade, a large amount of instructional time
was spent on re-teaching previous years’ standards. Additionally, the confidence level was low
for these students and I think that contributed to their concentration level. Many times I
observed the students shutting down because the measurement problems required higher order
thinking skills and were multiple step problems. I observed them becoming overwhelmed with
this and because they were not confident, would easily give up.
The results of the student surveys showed there was significance in that the students liked
the Singapore math methods and would like to use them again. Additionally, the students like
using manipulatives. However, the one item that showed no significance was the in regards to
students still not feeling confident about their understanding of measurement. This item showed
that 50% of the students felt confident about their understanding of measurement, 42% did not
feel confident about their understanding of measurement, and 8% reported I don’t know.
This study ensured credibility through the use of multiple data sources. These data
sources included CRCT scores, student surveys, a reflective journal, and an interview with my
principal. By using the CRCT scores, I feel my argument was more credible because the CRCT
is a state wide test consisting of only multiple choice questions that were scored by a non-bias
agency. Therefore my outcome was not biased in any way. I was successful in finding opposing
views by presenting alternative perspectives in the literature review as well as selecting
participants in the data collection process who had opposing views. Additionally, the interview
with my principal re-affirmed the reliability, relevance, and unsuccessful/successful attributes of
this study. However, because there was no significance after the implementation of the
Singapore math methods in relation to the students’ achievement in the domain of measurement,
the evidence is not sufficiently strong to assert judgments.
Singapore Math 37
Implications
In reference to the quantitative results, it was proven through the dependent t-test that
there was no significance between the students’ fourth grade math CRCT scores and the
students’ fifth grade math CRCT scores in the measurement domain. Therefore, I do not feel
confident that my results can be generalized to the larger population. However, since there was a
gain in overall achievement from the students’ fifth grade math CRCT scores compared to the
fourth grade math CRCT scores, I think this research could be transferred into other areas of
math. This is further supported by the qualitative results. Through the surveys, interview, and
reflective journal there was a recurring theme of students and educators finding the Singapore
math methods beneficial and enjoyable. As a teacher, I realized through this study and the
research pertaining to the study, how beneficial it is to have a curriculum that covers fewer
standards. Covering fewer standards, allows our students to gain deeper knowledge and create
higher order thinking skills.
Impact on School Improvement
The impact that the research has made on school improvement is just a small part of the
bigger picture. One of the differences mentioned between Singapore and the United States math
curriculum is the larger number of standards to be covered in the United States than that of
Singapore. One of the reasons Singapore is successful is because there curriculum covers less
standards, therefore allowing a standard to be taught deeply and not just skimmed on the surface.
The state of Georgia, where this study took place, is currently rolling out a new math curriculum
which will have fewer standards taught in a given amount of time. This presents a positive
aspect on the future of this study and on school improvement.
Singapore Math 38
Recommendations for Future Research
Though the study did not show significant differences between the students’ fourth grade
math CRCT scores and the students’ fifth grade math CRCT scores in the measurement domain,
there was a gain in overall achievement from the students’ fifth grade math CRCT scores
compared to the fourth grade math CRCT scores. Therefore, I feel that future research could be
expanded over a greater length of time, maybe up to a year, especially with the new curriculum
being introduced. The next step would be to extend the study to include all the standards instead
of just the measurement domain. Additionally, in future research I would perform a pre-test and
post-test in addition to CRCT scores to obtain more statistical data. Furthermore, I would
implement the student surveys before and after each standard taught to see if there would be
significant differences in student responses. In conclusion, through the research, I have learned
the vast differences in our educational system compared to that of Singapore and why Singapore
is successful. As a result, this study has transformed how I view the implementation of math
standards to be taught using effective strategies I have learned from Singapore.
Singapore Math 39
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Singapore Math 42
Appendix A
Student Math Survey
Circle your response for each question.
1. Did you like math when using Singapore math methods?
Yes
No
I don’t know
2. Do you feel better about math after using the Singapore math methods?
Yes
No
I don’t know
3. Would you like to use the Singapore math methods again when learning math?
Yes
No
I don’t know
4. Did you like the hands-on activities that were used to teach measurement?
Yes
No
I don’t know
5. Do you still feel like you need more help with measurement?
Yes
No
I don’t know
Singapore Math 43
Appendix B
Daily Reflective Journal
Three main things I
learned from this
lesson.
1.
2.
3.
Did we finish everything
in the lesson?
If not, why?
Were there any
surprises?
Is there something
I will do differently
next time?
What do I like and
dislike most from this
lesson?
Like:
Dislike:
Singapore Math 44
Appendix C
Interview with Principal about
Singapore Math
1. What did you observe with the implementation of the Singapore math methods in regards
to instruction?
2. What did you observe with the implementation of the Singapore math methods in regards
to student learning?
3. As principal, do you think these methods would be beneficial in other grade levels?
4. Did you observe any negatives during the implementation of the Singapore math methods?
5. If our school decided to integrate some of the Singapore math methods within math
instruction, how do think others would feel about the change process?
6. In conclusion, are there any other questions or comments you would like to share?