mathematics education in singapore: how can mathematics ...€¦ · teacher education and...
TRANSCRIPT
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 1
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
Mathematics Education in Singapore: How can Mathematics
Education in Singapore inform Mathematics Education in US
Brian R. Evans
Pace University, New York, United States
The purpose of this article is to examine how the mathematics education system of the
Republic of Singapore can benefit the United States. U.S. students had consistently
ranked poorly as compared with their peers in many other nations on international
studies, while Singapore has consistently scored very well. The intention of the article is
to inform and improve mathematics education in the United States by analyzing the
literature on Singapore’s educational system and exploring aspects that may be helpful to
U.S. education.
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 2
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
Introduction
There had been an ongoing crisis in mathematics education in the United States in
recent years (Carson & Rowland, 2007; Gott, 2007; Klein et al., 2005; Starkman, 2007;
Thomas B. Fordham Foundation, 1998). U.S. students had consistently ranked poorly as
compared with their peers in many other nations, as apparent in the Program for
International Student Assessment (PISA, 2013) and Trends in International Mathematics
and Science Study (TIMSS, 2013a). PISA is an assessment of 15-year-old achievement
in mathematics, science, and reading, which has been conducted every three years
beginning in 2000 and continuing in 2003, 2006, 2009, and 2012. On average, PISA
results had indicated that U.S. students scored below the average among Organization for
Economic Cooperation and Development (OECD) countries. Results from the 2012
assessment indicated that U.S. students had scored below average compared to
participant nations, while the Republic of Singapore consistently ranks at the top of the
participating nations (PISA, 2013).
The TIMSS is an international assessment of fourth and eighth grade students’
achievement in mathematics and science content knowledge that has been conducted
every four years beginning in 1995 and continuing in 1999, 2003, 2007, and 2011. While
the United States has been improving its rankings over the TIMSS studies, it had
continued to rank lower than other participating nations (Garelick, 2006; Ginsburg,
Leinwand, Anstrom, & Pollock, 2005) and can be considered a “second tier” nation in
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 3
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
mathematics (TIMSS, 2013b; TIMSS, 2013c; TIMSS, 20013d; TIMSS, 2013e). In the
first implementation of the study in 1995 it was found that U.S. eighth grade students
ranked 28th
in mathematics out of 41 participating countries and regions (Beaton et al.,
1996). U.S. eighth grade students ranked 19th
in mathematics out of 38 participating
countries and regions in the 1999 study (TIMSS, 2013b), and ranked 15th
out of 45
participants in the 2003 study (TIMSS, 2013c). Singapore, however, has consistently
ranked first in mathematics in the first three implementations (1995, 1999, and 2003) of
the TIMSS (Beaton et al., 1996; TIMSS, 2013b; TIMSS, 2013c). Gonzales et al. (2004)
indicated that in the 2003 TIMSS study it was found that 45% of eighth grade students in
Singapore scored at the advanced level in mathematics. In the United States, only 7% of
eighth grade students scored at the advanced level in mathematics. Other countries and
administrative regions to consistently score very well in mathematics include Hong
Kong, Japan, South Korea, and Taiwan.
The 2007 results of the TIMSS revealed that Singapore, while no longer ranking
first in mathematics for eighth grade students, still ranked very highly with only Taiwan
and South Korea ranking slightly higher. However, there was no statistically significant
difference between the top five scoring nations in 2007. U.S. eighth grade students were
found to rank 9th
in mathematics out of 48 participants, with a statistically significant
lower score than only the five highest achieving countries and administrative regions,
Taiwan, South Korea, Singapore, Hong Kong, and Japan (TIMSS, 2013d). In 2011 the
United States continued to rank 9th
, just as in 2007, for 8th
grade mathematics
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 4
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
performance out of 42 participating countries and regions, while Singapore moved up to
2nd
place, just behind South Korea but ahead of Taiwan (TIMSS, 2013e). The same five
countries and regions that had significantly higher scores in 2007 than the United States
continued to score higher than the United States, with the addition of Russia having a
statistically higher score than the United States (TIMSS, 2013e).
The steady improvement of the eighth grade mathematics rankings has continued
in the United States since the initial 1995 TIMSS study. There was a significant
difference between eighth grade mathematics scores in the United States in 1995 (M =
492) and 2011 (M = 508) (TIMSS, 2013f). However, despite a much lauded
improvement, the United States still lags behind more than high-performing East Asian
nations and administrative regions, in addition to Russia. Further, 2011 results indicated
while 48% of eighth grade students in Singapore scored at the advanced level in
mathematics, only 7% of U.S. eighth grade students scored at the advanced level
(TIMSS, 2013g). However, it would be remiss not to acknowledge that U.S. students in
affluent suburban schools scored nearly as well as students in Singapore and the gap
between high and low performing U.S. schools is greater than the gap between the U.S.
and high achieving nations (Brown & LaVine Brown, 2007). China, for example, only
uses data from Shanghai and Hong Kong in the Pisa results, which tends to skew scores
upward.
Teacher preparation in mathematics education has recently been reported as
inadequate compared to other higher achieving countries on the TIMMS, particularly for
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 5
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
middle school teacher preparation (Babcock et al., 2010). Babcock et al. (2010), in the
Teacher Education and Development Study in Mathematics (TEDS-M), found that in
many top achieving countries pre-service middle school teachers had about half of their
preparation in mathematics content and half in pedagogy. In the U.S. this was about 40%
in content and 60% in pedagogy. Further, on average about 90% of the highest
achievement nations had pre-service middle school teachers taking linear algebra and a
full year of calculus while about two-thirds of U.S. middle school pre-service teachers
had linear algebra and slightly more than half of them had a full year of calculus.
Babcock et al. (2010) referred to these courses as gateway courses to higher level
mathematics. Further, they found that middle school mathematics teachers in the United
States were much less adequately prepared than were secondary school teachers.
Moreover, they found that quality in teacher preparation varied greatly throughout the
United States.
The U.S. Commission on National Security in the Twenty-First Century (2001)
reported that inadequacies of U.S. education pose one of the biggest threats to the
national security of the United States. There is a need to improve U.S. education, and
given the high mathematics achievement found in Singapore schools, learning more
about the education model in Singapore could inform and improve U.S. education. The
TIMSS 1999 Video Study compared teacher practice in seven countries: Australia, Czech
Republic, Hong Kong, Japan, Netherlands, Switzerland, and the United States (Heibert et
al., 2003; Leung, 2005), but did not include observations in the highest achieving nation,
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 6
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
Singapore. VanTassel-Baska et al. (2008) examined teacher practices in both Singapore
and the United States in secondary classrooms with gifted students. More observational
research is necessary to understand what typical teachers in Singapore are doing in their
classrooms and how this could inform instruction in the United States. Cathy Seeley,
former president of the National Council of Teachers of Mathematics (NCTM) said:
But we have to look beyond their [Singapore’s] textbooks to determine
what these lessons are. The more we learn about what is being done in the
Asian Rim countries, the more it appears that mathematics is not taught in
the same way in which we have traditionally taught mathematics in this
country (Seeley, 2005).
Observing how mathematics is taught in actual Singapore classrooms goes well beyond
simply comparing mathematics textbooks used in the United States with those used in
Singapore.
A Brief History of Singapore: Republic and Education
Sir Thomas Raffles established Singapore as a trading post for the British East
India Company in 1819. It served as a major trading and military center of the British
Empire during the 19th
and early 20th
Centuries. During World War II the Japanese
occupied the city before it was returned back to the British after the end of the war. In
1963 Singapore declared independence from the United Kingdom to join 13 other states
in the region to create Malaysia. On August 9, 1965 Singapore left Malaysia to become
the Republic of Singapore.
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 7
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
Singapore is a city-state nation and one of the smallest countries in the world by
area, and about the size of New York City by land. It has a population over five million
people, making it considerably larger than Los Angles, but smaller than New York, in
terms of population. About 75% of the population is ethnic Chinese, with the remaining
population consisting primarily of ethnic Malaysians and Indians.
Since Singapore’s independence in 1965, it has gone from being a poor nation to
being among the richest nations in the world, based on per capita income. It is
considered an astonishing success, due to its lack of natural resources, attributed to its
education system that produced a highly educated population. The research division of
Citigroup, a major financial service corporation, places Singapore at the top of list of
countries for per capita GDP (PPP) every decade until 2050, the extent of Citigroup
predictions (Buiter &, Rahbari, 2011). Interestingly, by 2030 Citigroup predicts the top
four countries or administrative regions will be Singapore, Hong Kong, Taiwan, the
United States, and South Korea. By 2040 South Korea is predicted to switch places with
the United States (Buiter & Rahbari, 2011).
Instruction in Singapore’s elementary schools is primarily conducted in English,
which continues to be the primary language of instruction in later grades in mathematics
and science. The Ministry of Education is the governmental department charged with the
responsibility of overseeing the centralized school system and creating the curriculum.
High stakes standardized testing is used at the end of primary and secondary education
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 8
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
(Ginsburg et al, 2005). Teacher preparation is solely conducted by the National Institute
of Education (NIE), an autonomous part of Nanyang Technological University (NTU).
Singapore Mathematics Textbooks and Method
After the 1999 TIMSS had been conducted, it was very clear that Singapore was
excelling in mathematics among the international community after ranking first in
mathematics for two consecutive studies (Beaton et al., 1996, TIMSS, 2013a). At the
turn of the 21st Century, a publishing company, Singapore Math Inc., published
mathematics books based upon the Singapore method of mathematics instruction in the
United States. These books were based upon the mathematics textbooks used in
Singapore, but adapted for a U.S. audience. For example, in Singapore, like most of the
world, the metric system is used exclusively. The U.S. version of the series focuses on
both metric and the U.S. customary system of measurement. Problems involving money
use U.S. dollars in the U.S. version. Since school instruction in Singapore is conducted
in English, this makes the transition from Singapore to the United States even easier.
Singapore Math books are usually thinner than their traditional, and sometimes
reform-based, U.S. counterparts, and they cover fewer topics, but in greater depth
(Ginsburg et al., 2005; Schmidt, Houang, & Cogan, 2002). The U.S curriculum has been
often been described as “a mile wide and an inch deep” (Schmidt & Houang, 2007).
Purportedly, fewer topics in greater depth may lead to better understanding and better
adaptability when confronted with unfamiliar concepts. A major problem is that U.S.
textbook publishers must accommodate 50 states and their standards, whereas Singapore
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 9
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
has a centralized system that enables the books to have more focus. The U.S. has moved
toward a common national curriculum with the Common Core Standards, but more
differences persist between individual U.S. states as compared to small-sized Singapore.
Singapore textbooks are well aligned with their national framework, which is not always
true in the United States. U.S. students comparatively learn too many topics with not
enough understanding or depth for each topic covered. In Singapore, fewer topics are
covered, but mastery is emphasized. For example, in early grades the highest
achievement countries on the TIMSS cover about four to six topics per year, compared to
20 topics in the United States (Schmidt, 2008). In later grades, some U.S. states cover
about twice as many topics as does Singapore (Ginsburg et al., 2005). Schmidt and
Houang (2007) suggested more coherence for the U.S. curriculum. A coherent
curriculum would mean that there is a logical flow of topics in sequence that are well
articulated and organized (Schmidt, Houang, & Cogan, 2002). Video analysis
demonstrated that in “East Asian classrooms more advanced content was covered and the
lessons were more coherent” (VanTassel-Baska, 2008, p. 342). Specially, this was
conducted in Hong Kong (Leung, 2005). Ginsburg et al. (2005) said that U.S. education
“lacks a centrally identified core of mathematical content that provides a focus for the
rest of the system” (p. ix). Schmidt (2008) said, “The single most important result of the
Third International Mathematics and Science Study (TIMSS) is that we now know that
student performance is directly related to the nature of the curricular expectations.”
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 10
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
The Singapore mathematics books do not “spiral” in the same way U.S. books do
(Ginsburg et al., 2005). The idea is that the concepts are taught well enough not to revisit
in the same manner. Instead, if a concept is spiraled in Singapore mathematics, it is
explored in a deeper manner, not taught over again as it is in the United States (Schmidt,
Houang, & Cogan, 2002). Singapore mathematics books typically do not have colored
graphics, but instead ground basic mathematical ideas through pictures such as the
comparisons of bars method (Hoven & Garelick, 2007). This method involves using bars
to help understand mathematical concepts. Garelick (2006) provides an example: Mary
and Bill have $10 between them. Mary has $2 more than Bill. How much money does
each person have? Given this situation, students will set up two bars, one drawn directly
above the other, representing Bill and Mary’s money separately. Mary’s bar extends for
$2 more than Bill’s bar. This means that other than the $2 extension, their bars are the
same length. Students then can see that Bill has $4 and Mary has $4 + $2 = $6.
According to Ginsburg et al. (2005), “Singapore’s textbooks build deep understanding of
mathematical concepts through multistep problems and concrete illustrations that
demonstrate how abstract mathematical concepts are used to solve problems from
different perspectives” (p. xii).
The interesting aspect is that in the United States the Singapore mathematics
books are considered to be an alterative to reform-based mathematics textbooks currently
used in the United States. Singapore mathematics books are championed by the “back to
the basics” proponents, and are seen as promoting traditional mathematics education.
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 11
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
Interestingly, the Singapore mathematics books teach mathematics from a conceptual, in
addition to procedural, perspective while teaching for understanding. They engage
students in the problem solving process (Hoven & Garelick, 2007). Ginsburg et al.
(2005) said, “The Singapore texts are rich with problem-based development in contrast to
traditional U.S. texts that rarely get much beyond exposing students to the mechanics of
mathematics and emphasizing the application of definitions and formulas to routine
problems” (p. xii). According to Singapore’s Ministry of Education (2001), “The
primary aim of the mathematics curriculum is to enable pupils to develop their ability in
mathematical problem solving” (p. 5). It would appear that Singapore mathematics
books conform to the spirit of reform-based constructivist perspectives with their
emphasis on student derived knowledge and understanding through constructivism.
However, certain areas such as data analysis, statistics, and probability are left out of the
Singapore mathematics books (Garelick, 2006). This means that state, Common Core,
and NCTM standards will not be accomplished using the Singapore mathematics books
exclusively, and thus supplemental materials are needed. Further, real-life applications
and problems that require trial and error are not found in Singapore mathematics books as
they are found in their U.S. counterparts (Garelick, 2006). Thus, more supplemental
materials are needed.
Singapore Mathematics Pilot in the United States
Pilot programs using mathematics textbooks based upon the Singapore system
have been conducted in over 80 school systems in the United States (Ginsburg et al.,
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 12
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
2005). One of the best known pilots of the Singapore mathematics program occurred in
four schools in Montgomery County, Maryland (Garelick, 2006). According to Garelick
(2006), there were mixed results from the use of the Singapore mathematics program
with some schools performing the same or worse as before the Singapore mathematics
program was piloted. Two Maryland schools had their students outperform control
groups in achievement (Ginsburg et al., 2005). However, only one school, College
Gardens, continued to use the Singapore mathematics program into the second year.
After the second year Montgomery County ended the program. A major reason given for
the failure of this program was the lack of support for teachers using it. The Singapore
mathematics program requires teachers to have a deeper understanding of mathematics
than U.S. teachers typically do. In order to succeed, more preparation for U.S. teachers
would be necessary. Furthermore, as mentioned previously, the Singapore mathematics
books lack some topics that are part of state, Common Core, and NCTM standards such
as data analysis, statistics, and probability. These areas had to be supplemented with
additional materials that were a further cost to the schools.
More recently the South River Primary School and South River Elementary
School in South River, New Jersey, has employed the Singapore mathematics program
(Hoven & Garelick, 2007). According to Hoven and Garelick (2007), teachers in this
district first had difficulty with the transition given the slower and more in-depth method
of teaching. The assistant superintendent in South River claimed that an advantage of the
Singapore mathematics program was that it teaches for mastery so there is no need to re-
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 13
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
teach the same material year after year. Another advantage is that the Singapore
mathematics method focuses on essential mathematics skills as recommended in the
NCTM Focal Points (2006).
It was found that in Patterson, New Jersey, an urban school district, that students
were transitory in moving around school to school. Thus, many moved in and out of the
Singapore system and this proved to be problematic (Ginsburg et al., 2005). Similar to
the case in Maryland, additional topics not covered in the Singapore books had to be
supplemented by additional materials to address state standards.
The Singapore mathematics program was specifically successful in the North
Middle Regional School District in Massachusetts (Ginsburg et al, 2005). A much higher
proportion of students using the Singapore mathematics method placed into the advanced
mathematics level as compared with a control group who did not use the Singapore
mathematics method. The state superintendent in Massachusetts has called on other
school districts in the state to consider the Singapore system.
Mathematics Achievement and Teaching in Singapore and East Asia
As previously mentioned, Singapore has consistently placed first in mathematics
achievement in the first three TIMSS studies (Beaton et al., 1996, TIMSS, 2013a). In the
most recent TIMSS, Singapore ranks third, but only slightly behind the Taiwan and South
Korea. Students in several East Asian countries and administrative regions also
consistently rank highly on the TIMSS. Further, as stated earlier, a much higher
percentage of students scored in the advanced level in mathematics than did students in
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 14
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
the United States in recent studies such as the 2003 (Gonzales et al., 2004) and 2007
studies. One variable to consider is teaching practice in the classroom.
VanTassel-Baska et al. (2008) examined teacher practices in secondary
classrooms with gifted students in both Singapore and the United States. It was found
that Singapore teachers were more effective than their U.S. counterparts. They found a
statistically significant difference between teachers in Singapore and the United States in
the areas of curriculum delivery and planning, accommodation for individual differences,
and critical and creative thinking strategies, with Singapore teachers outperforming U.S.
teachers. Despite U.S. teachers generally having more experience and higher academic
degrees than Singapore teachers in the VanTassle-Baska et al. (2008) study, teachers in
Singapore had higher content knowledge (Ginsburg et al., 2005), as found in Ma’s (1999)
comparative study of Chinese and U.S. teachers. This is supported by Leung (2005), who
studied teachers in Hong Kong and Japan, two other places with students achieving
highly on international examinations.
Ingersoll (2007) claimed that U.S. teacher quality is a major problem in the
United States. Interestingly, it was found that many primary school teachers in Singapore
do not have four-year college degrees, but yet have a solid foundation in basic
mathematics. However, Ginsburg et al. (2005) found that teachers in the United States
have mathematical content knowledge that is much below that of teachers in Singapore.
This is alarming considering the need for highly qualified teachers called for by No Child
Left Behind (NCLB) in the United States. Elementary school teachers in Singapore take
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 15
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
about twice as many mathematics courses as do elementary school teachers in the United
States during teacher preparation. Furthermore, teaching in Singapore is more highly
regarded as a profession than it is in the United States (Ginsburg et al., 2005; Ingersoll,
2007). Lai, McCallum, and Soto-Johnson (2011) found that a teacher preparation gap
could be a variable responsible for the student achievement gap between East Asia and
the United States.
Leung (2005) cited video analysis from the TIMSS 1999 Video Study that found
students from Hong Kong and Japan studied mathematics problems that were longer than
in western nations including the United States. More time was dedicated to new material
in Hong Kong and Japan as compared to the new instruction time in the United States.
Students in Hong Kong were exposed to more advanced mathematical instructional
content, were more engaged, and lessons were more coherent, fully developed, and of
better overall quality than in the United States. More proofs were done in Japan and
problems were of more complexity than in the United States. Leung (2005) speculated
that high content knowledge of teachers and use of proof and mathematical language are
contributing factors to success rates in Hong Kong and Japan. Further, Leung (2005)
addressed the cultural issue of respect for a knowledgeable teacher found throughout East
Asia. A strong content knowledge is paramount to receiving respect from students,
which could lead to motivation for teachers to be competent in their area. Leung (2005)
cautioned that each country’s culture influences learning and one cannot simply
transplant practices from one culture to another without considering these differences.
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 16
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
Considerations and Conclusions
Cultural issues may have a big impact on learning in Singapore as compared to
the United States that will not be addressed in this study (Leung, 2005). Tsui (2007)
argued that differences could be due to social and environmental factors. Singapore
generally has a more homogonous student population than does the United States, which
makes transferability between Singapore and the United States complicated. Singapore
students are considered to be highly motivated academically, and families in Singapore
place a great emphasis on education (Ginsburg et al., 2005). Another variable to consider
is teacher preparation. Teachers in Singapore have higher content knowledge than do
teachers in the United States (Ginsburg et al., 2005; VanTassel-Baska et al., 2008).
Further, Singapore is a very small country with a centralized education system, as
compared with the large population and decentralized system in the United States.
However, given the growing influence of the NCTM Standards (2000) at the state level
over the last several decades, and the adoption of more states of the Common Core State
Standards for Mathematics in the United States, the trend is that U.S. education is
becoming more centralized than it has been in the past. Variables such as culture and
teacher preparation should be investigated in subsequent studies.
While there are major differences between the two countries, it’s likely that
understanding the educational system in Singapore could help inform U.S. education,
particularly in mathematics. Culture undoubtedly plays an important role, but individual
strategies used in Singapore, and other high achieving nations, may be helpful for U.S.
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 17
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
education. More studies should be conducted on the Singapore system with effectual
aspects integrated into the U.S. system where relevant and possible.
A Brief History of Singapore: Republic and Education
Sir Thomas Raffles established Singapore as a trading post for the British East
India Company in 1819. It served as a major trading and military center of the British
Empire during the 19th
and early 20th
Centuries. During World War II the Japanese
occupied the city before it was returned back to the British after the end of the war. In
1963 Singapore declared independence from the United Kingdom to join 13 other states
in the region to create Malaysia. On August 9, 1965 Singapore left Malaysia to become
the Republic of Singapore.
Singapore is a city-state nation and one of the smallest countries in the world by
area, and about the size of New York City by land. It has a population over five million
people, making it considerably larger than Los Angles, but smaller than New York, in
terms of population. About 75% of the population is ethnic Chinese, with the remaining
population consisting primarily of ethnic Malaysians and Indians.
Since Singapore’s independence in 1965, it has gone from being a poor nation to
being among the richest nations in the world, based on per capita income. It is
considered an astonishing success, due to its lack of natural resources, attributed to its
education system that produced a highly educated population. The research division of
Citigroup, a major financial service corporation, places Singapore at the top of list of
countries for per capita GDP (PPP) every decade until 2050, the extent of Citigroup
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 18
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
predictions (Buiter &, Rahbari, 2011). Interestingly, by 2030 Citigroup predicts the top
four countries or administrative regions will be Singapore, Hong Kong, Taiwan, the
United States, and South Korea. By 2040 South Korea is predicted to switch places with
the United States (Buiter & Rahbari, 2011).
Instruction in Singapore’s elementary schools is primarily conducted in English,
which continues to be the primary language of instruction in later grades in mathematics
and science. The Ministry of Education is the governmental department charged with the
responsibility of overseeing the centralized school system and creating the curriculum.
High stakes standardized testing is used at the end of primary and secondary education
(Ginsburg et al, 2005). Teacher preparation is solely conducted by the National Institute
of Education (NIE), an autonomous part of Nanyang Technological University (NTU).
Singapore Mathematics Textbooks and Method
After the 1999 TIMSS had been conducted, it was very clear that Singapore was
excelling in mathematics among the international community after ranking first in
mathematics for two consecutive studies (Beaton et al., 1996, TIMSS, 2013a). At the
turn of the 21st Century, a publishing company, Singapore Math Inc., published
mathematics books based upon the Singapore method of mathematics instruction in the
United States. These books were based upon the mathematics textbooks used in
Singapore, but adapted for a U.S. audience. For example, in Singapore, like most of the
world, the metric system is used exclusively. The U.S. version of the series focuses on
both metric and the U.S. customary system of measurement. Problems involving money
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 19
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
use U.S. dollars in the U.S. version. Since school instruction in Singapore is conducted
in English, this makes the transition from Singapore to the United States even easier.
Singapore Math books are usually thinner than their traditional, and sometimes
reform-based, U.S. counterparts, and they cover fewer topics, but in greater depth
(Ginsburg et al., 2005; Schmidt, Houang, & Cogan, 2002). The U.S curriculum has been
often been described as “a mile wide and an inch deep” (Schmidt & Houang, 2007).
Purportedly, fewer topics in greater depth may lead to better understanding and better
adaptability when confronted with unfamiliar concepts. A major problem is that U.S.
textbook publishers must accommodate 50 states and their standards, whereas Singapore
has a centralized system that enables the books to have more focus. The U.S. has moved
toward a common national curriculum with the Common Core Standards, but more
differences persist between individual U.S. states as compared to small-sized Singapore.
Singapore textbooks are well aligned with their national framework, which is not always
true in the United States. U.S. students comparatively learn too many topics with not
enough understanding or depth for each topic covered. In Singapore, fewer topics are
covered, but mastery is emphasized. For example, in early grades the highest
achievement countries on the TIMSS cover about four to six topics per year, compared to
20 topics in the United States (Schmidt, 2008). In later grades, some U.S. states cover
about twice as many topics as does Singapore (Ginsburg et al., 2005). Schmidt and
Houang (2007) suggested more coherence for the U.S. curriculum. A coherent
curriculum would mean that there is a logical flow of topics in sequence that are well
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 20
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
articulated and organized (Schmidt, Houang, & Cogan, 2002). Video analysis
demonstrated that in “East Asian classrooms more advanced content was covered and the
lessons were more coherent” (VanTassel-Baska, 2008, p. 342). Specially, this was
conducted in Hong Kong (Leung, 2005). Ginsburg et al. (2005) said that U.S. education
“lacks a centrally identified core of mathematical content that provides a focus for the
rest of the system” (p. ix). Schmidt (2008) said, “The single most important result of the
Third International Mathematics and Science Study (TIMSS) is that we now know that
student performance is directly related to the nature of the curricular expectations.”
The Singapore mathematics books do not “spiral” in the same way U.S. books do
(Ginsburg et al., 2005). The idea is that the concepts are taught well enough not to revisit
in the same manner. Instead, if a concept is spiraled in Singapore mathematics, it is
explored in a deeper manner, not taught over again as it is in the United States (Schmidt,
Houang, & Cogan, 2002). Singapore mathematics books typically do not have colored
graphics, but instead ground basic mathematical ideas through pictures such as the
comparisons of bars method (Hoven & Garelick, 2007). This method involves using bars
to help understand mathematical concepts. Garelick (2006) provides an example: Mary
and Bill have $10 between them. Mary has $2 more than Bill. How much money does
each person have? Given this situation, students will set up two bars, one drawn directly
above the other, representing Bill and Mary’s money separately. Mary’s bar extends for
$2 more than Bill’s bar. This means that other than the $2 extension, their bars are the
same length. Students then can see that Bill has $4 and Mary has $4 + $2 = $6.
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 21
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
According to Ginsburg et al. (2005), “Singapore’s textbooks build deep understanding of
mathematical concepts through multistep problems and concrete illustrations that
demonstrate how abstract mathematical concepts are used to solve problems from
different perspectives” (p. xii).
The interesting aspect is that in the United States the Singapore mathematics
books are considered to be an alterative to reform-based mathematics textbooks currently
used in the United States. Singapore mathematics books are championed by the “back to
the basics” proponents, and are seen as promoting traditional mathematics education.
Interestingly, the Singapore mathematics books teach mathematics from a conceptual, in
addition to procedural, perspective while teaching for understanding. They engage
students in the problem solving process (Hoven & Garelick, 2007). Ginsburg et al.
(2005) said, “The Singapore texts are rich with problem-based development in contrast to
traditional U.S. texts that rarely get much beyond exposing students to the mechanics of
mathematics and emphasizing the application of definitions and formulas to routine
problems” (p. xii). According to Singapore’s Ministry of Education (2001), “The
primary aim of the mathematics curriculum is to enable pupils to develop their ability in
mathematical problem solving” (p. 5). It would appear that Singapore mathematics
books conform to the spirit of reform-based constructivist perspectives with their
emphasis on student derived knowledge and understanding through constructivism.
However, certain areas such as data analysis, statistics, and probability are left out of the
Singapore mathematics books (Garelick, 2006). This means that state, Common Core,
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 22
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
and NCTM standards will not be accomplished using the Singapore mathematics books
exclusively, and thus supplemental materials are needed. Further, real-life applications
and problems that require trial and error are not found in Singapore mathematics books as
they are found in their U.S. counterparts (Garelick, 2006). Thus, more supplemental
materials are needed.
Singapore Mathematics Pilot in the United States
Pilot programs using mathematics textbooks based upon the Singapore system
have been conducted in over 80 school systems in the United States (Ginsburg et al.,
2005). One of the best known pilots of the Singapore mathematics program occurred in
four schools in Montgomery County, Maryland (Garelick, 2006). According to Garelick
(2006), there were mixed results from the use of the Singapore mathematics program
with some schools performing the same or worse as before the Singapore mathematics
program was piloted. Two Maryland schools had their students outperform control
groups in achievement (Ginsburg et al., 2005). However, only one school, College
Gardens, continued to use the Singapore mathematics program into the second year.
After the second year Montgomery County ended the program. A major reason given for
the failure of this program was the lack of support for teachers using it. The Singapore
mathematics program requires teachers to have a deeper understanding of mathematics
than U.S. teachers typically do. In order to succeed, more preparation for U.S. teachers
would be necessary. Furthermore, as mentioned previously, the Singapore mathematics
books lack some topics that are part of state, Common Core, and NCTM standards such
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 23
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
as data analysis, statistics, and probability. These areas had to be supplemented with
additional materials that were a further cost to the schools.
More recently the South River Primary School and South River Elementary
School in South River, New Jersey, has employed the Singapore mathematics program
(Hoven & Garelick, 2007). According to Hoven and Garelick (2007), teachers in this
district first had difficulty with the transition given the slower and more in-depth method
of teaching. The assistant superintendent in South River claimed that an advantage of the
Singapore mathematics program was that it teaches for mastery so there is no need to re-
teach the same material year after year. Another advantage is that the Singapore
mathematics method focuses on essential mathematics skills as recommended in the
NCTM Focal Points (2006).
It was found that in Patterson, New Jersey, an urban school district, that students
were transitory in moving around school to school. Thus, many moved in and out of the
Singapore system and this proved to be problematic (Ginsburg et al., 2005). Similar to
the case in Maryland, additional topics not covered in the Singapore books had to be
supplemented by additional materials to address state standards.
The Singapore mathematics program was specifically successful in the North
Middle Regional School District in Massachusetts (Ginsburg et al, 2005). A much higher
proportion of students using the Singapore mathematics method placed into the advanced
mathematics level as compared with a control group who did not use the Singapore
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 24
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
mathematics method. The state superintendent in Massachusetts has called on other
school districts in the state to consider the Singapore system.
Mathematics Achievement and Teaching in Singapore and East Asia
As previously mentioned, Singapore has consistently placed first in mathematics
achievement in the first three TIMSS studies (Beaton et al., 1996, TIMSS, 2013a). In the
most recent TIMSS, Singapore ranks third, but only slightly behind the Taiwan and South
Korea. Students in several East Asian countries and administrative regions also
consistently rank highly on the TIMSS. Further, as stated earlier, a much higher
percentage of students scored in the advanced level in mathematics than did students in
the United States in recent studies such as the 2003 (Gonzales et al., 2004) and 2007
studies. One variable to consider is teaching practice in the classroom.
VanTassel-Baska et al. (2008) examined teacher practices in secondary
classrooms with gifted students in both Singapore and the United States. It was found
that Singapore teachers were more effective than their U.S. counterparts. They found a
statistically significant difference between teachers in Singapore and the United States in
the areas of curriculum delivery and planning, accommodation for individual differences,
and critical and creative thinking strategies, with Singapore teachers outperforming U.S.
teachers. Despite U.S. teachers generally having more experience and higher academic
degrees than Singapore teachers in the VanTassle-Baska et al. (2008) study, teachers in
Singapore had higher content knowledge (Ginsburg et al., 2005), as found in Ma’s (1999)
comparative study of Chinese and U.S. teachers. This is supported by Leung (2005), who
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 25
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
studied teachers in Hong Kong and Japan, two other places with students achieving
highly on international examinations.
Ingersoll (2007) claimed that U.S. teacher quality is a major problem in the
United States. Interestingly, it was found that many primary school teachers in Singapore
do not have four-year college degrees, but yet have a solid foundation in basic
mathematics. However, Ginsburg et al. (2005) found that teachers in the United States
have mathematical content knowledge that is much below that of teachers in Singapore.
This is alarming considering the need for highly qualified teachers called for by No Child
Left Behind (NCLB) in the United States. Elementary school teachers in Singapore take
about twice as many mathematics courses as do elementary school teachers in the United
States during teacher preparation. Furthermore, teaching in Singapore is more highly
regarded as a profession than it is in the United States (Ginsburg et al., 2005; Ingersoll,
2007). Lai, McCallum, and Soto-Johnson (2011) found that a teacher preparation gap
could be a variable responsible for the student achievement gap between East Asia and
the United States.
Leung (2005) cited video analysis from the TIMSS 1999 Video Study that found
students from Hong Kong and Japan studied mathematics problems that were longer than
in western nations including the United States. More time was dedicated to new material
in Hong Kong and Japan as compared to the new instruction time in the United States.
Students in Hong Kong were exposed to more advanced mathematical instructional
content, were more engaged, and lessons were more coherent, fully developed, and of
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 26
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
better overall quality than in the United States. More proofs were done in Japan and
problems were of more complexity than in the United States. Leung (2005) speculated
that high content knowledge of teachers and use of proof and mathematical language are
contributing factors to success rates in Hong Kong and Japan. Further, Leung (2005)
addressed the cultural issue of respect for a knowledgeable teacher found throughout East
Asia. A strong content knowledge is paramount to receiving respect from students,
which could lead to motivation for teachers to be competent in their area. Leung (2005)
cautioned that each country’s culture influences learning and one cannot simply
transplant practices from one culture to another without considering these differences.
Considerations and Conclusions
Cultural issues may have a big impact on learning in Singapore as compared to
the United States that will not be addressed in this study (Leung, 2005). Tsui (2007)
argued that differences could be due to social and environmental factors. Singapore
generally has a more homogonous student population than does the United States, which
makes transferability between Singapore and the United States complicated. Singapore
students are considered to be highly motivated academically, and families in Singapore
place a great emphasis on education (Ginsburg et al., 2005). Another variable to consider
is teacher preparation. Teachers in Singapore have higher content knowledge than do
teachers in the United States (Ginsburg et al., 2005; VanTassel-Baska et al., 2008).
Further, Singapore is a very small country with a centralized education system, as
compared with the large population and decentralized system in the United States.
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 27
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
However, given the growing influence of the NCTM Standards (2000) at the state level
over the last several decades, and the adoption of more states of the Common Core State
Standards for Mathematics in the United States, the trend is that U.S. education is
becoming more centralized than it has been in the past. Variables such as culture and
teacher preparation should be investigated in subsequent studies.
While there are major differences between the two countries, it’s likely that
understanding the educational system in Singapore could help inform U.S. education,
particularly in mathematics. Culture undoubtedly plays an important role, but individual
strategies used in Singapore, and other high achieving nations, may be helpful for U.S.
education. More studies should be conducted on the Singapore system with effectual
aspects integrated into the U.S. system where relevant and possible.
References
Babcock, J., Babcock, P., Buhler, J., Cady, J., Cogan, L., Houang, R., … Wight, K.
(2010). Breaking the cycle: An international comparison of U.S. mathematics
teacher preparation. Initial findings from the Teacher Education and Development
Study in Mathematics (TEDS-M) in the United States, Michigan State University.
Beaton, A. E., Mullis, I. V. S., Martin, M. O., Gonzolas, E. J., Kelly, D. L., & Smith, T.
A.
(1996). Mathematics achievement in the middle school years: IEA’s Third
International Mathematics and Science Study (TIMSS). Chestnut Hill, MA:
International Association for the Evaluation of Educational Achievement.
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 28
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
Brown, A. S., & LaVine Brown, L. (2007). What are science & math tests scores really
telling U.S.? The Bent of Tau Beta Pi (winter), 13-17.
Buiter, W., & Rahbari, E. (2011). Global growth generators: Moving beyond ‘emerging
markets’ and ‘BRIC.” Retrieved from
http://www.investphilippines.info/arangkada/wp-content/uploads/2011/07/Citi-
Global-Growth-Generators.pdf
Carson, R. N., & Rowlands, S. (2007). Strategies for affecting the necessary course of
cognitive growth as an integral part of curricular and instructional planning.
Interchange: A Quarterly Review of Education, 54(26), 137-165.
Garelick, B. (2006). Miracle math: A successful program from Singapore tests the limits
of school reform in the suburbs. Education Next, 6(4), 38-45.
Ginsburg, A., Leinwand, S., Anstrom, T., & Pollock, E. (2005). What the United States
can learn from Singapore’s world-class mathematics system (And what Singapore
can learn from the United States): An exploratory study. Washington, DC:
American Institutes for Research.
Gonzales, P., Guzman, J. C., Partelow, L., Pahlke, E., Jocelyn, L., & Kastberg, D. (2004).
Highlights from the Trends in International Mathematics and Science Study
(TIMSS) 2003. U.S. Department of Education, National Center for Education
Statistics. Washington, DC: U.S. Government Printing Office.
Gott, T. (2007). Kentucky’s new contribution to the global community. Clearing House:
A Journal of Educational Strategies, Issues, and Ideas, 80(6), 253-254.
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 29
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
Heibert, J., Gallimore, R., Garnier, H., Givvin, K. B., Holllingsworth, H., Jacobs,
J.,…Stigler, J. (2003). Teaching mathematics in seven countries: Results from the
TIMSS 1999 video study. Washington DC: National Center for Education
Statistics.
Hoven, J., & Garelick, B. (2007). Singapore math: Simple or complex. Making Math
Count, 65(3), 28-31.
Ingersoll, R. M. (2007). A comparative study of teacher preparation and qualifications in
six nations. Philadelphia, PA: Consortium for Policy Research in Education.
Lai, Y., McCallum, W., & Soto-Johnson, H. (2011). The role of universities in preparing
mathematics teachers: Insights from the International Congress on Mathematics
Education. In An International Perceptive on Mathematics Education: Reflections
on ICME-11. Monterrey, Mexico: ICME.
Klein, D., Braams, B. J., Parker, T., Quirk, W., Schmid, W., & Wilson, W. S. (2005). The
state of state MATH standards. Washington, DC: Thomas B. Fordham
Foundation and Institute.
Leung, F. K. S. (2005). Some characteristics of East Asian mathematics classrooms based
on data from the TIMSS 1999 video study. Educational Studies in Mathematics,
60, 199-215.
Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah, NJ: Lawrence
Erlbaum Associates.
Ministry of Education, Singapore. (2001). Primary mathematics syllabus. Retrieved from
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 30
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
http://www.apecneted.org/resources/downloads/Maths_Pri.pdf
National Council of Teachers of Mathematics. (2000). Principles and standards for
school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics. (2006). Curriculum focal points for
prekindergarten through grade 8 mathematics. Reston, VA: Author.
Program for International Student Assessment. (2013). Mathematics literacy performance
of 15-year-olds. Retrieved from http://www.oecd.org/pisa/keyfindings/pisa-2012-
results-overview.pdf
Schmidt, W. H. (2008). What’s missing from math standards? Focus, rigor, and
coherence. Retrieved from http://www.aft.org/pubs-
reports/american_educator/issues/spring2008/schmidt.htm
Schmidt, W. H., & Houang, R. T. (2007). Lack of focus in the mathematics curriculum:
Symptom or cause? In T. Loveless (Ed.), Lessons learned: What international
assessments tell us about math achievement (pp. 65-84). Washington, DC:
Brookings Institution Press.
Schmidt, W., Houang, R., & Cogan, L. (2002). A coherent curriculum. American
Educator (summer), 1-17.
Seeley, C. (2005). ‘Try harder’ is not the answer. Webchat with former NCTM president
C. Seeley on May 24, 2005. Retrieved from
http://www.nctm.org/about/content.aspx?id=906
Starkman, N. (2007). Problem solvers. T.H.E. Journal, 34(10), 34-35.
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 31
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
Thomas B. Fordham Foundation. (1998). A nation still at risk: An education manifesto.
Document resulting from the proceedings of Nation Still At Risk Summit,
Washington, DC.
Trends in International Mathematics and Science Study. (2013a). Trends in International
Mathematics and Science Study. Retrieved from http://nces.ed.gov/timss/index.asp
Trends in International Mathematics and Science Study. (2013b). Mathematics and
science achievement of eighth-graders in 1999. Retrieved from
http://nces.ed.gov/timss/results99_1.asp
Trends in International Mathematics and Science Study. (2013c). Table 5. Average
mathematics scale scores of eighth-grade students, by country: 2003. Retrieved
from http://nces.ed.gov/timss/TIMSS03Tables.asp?Quest=3&Figure=5
Trends in International Mathematics and Science Study. (2013d). Table 1. Average
mathematics scores of fourth- and eighth-grade students, by country: 2007.
Retrieved from http://nces.ed.gov/timss/table07_1.asp
Trends in International Mathematics and Science Study. (2013e). Table 3. Average
mathematics scores of 8th
-grade students, by education system: 2011. Retrieved
from http://nces.ed.gov/timss/table11_3.asp
Trends in International Mathematics and Science Study. (2013f). Mathematics
achievement of fourth- and eighth-graders in 2011. Retrieved
http://nces.ed.gov/timss/results11_math11.asp
MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE VOL 6, N 4 Winter 2013/2014 32
Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.
www.hostos.cuny.edu/departments/math/mtrj
Trends in International Mathematics and Science Study. (2013g). Figure 4. Percentage of
8th
-grade students reaching the TIMSS international benchmarks in mathematics,
by education system: 2011. Retrieved http://nces.ed.gov/timss/results11_math11.asp
Tsui, M. (2007). Gender and mathematics achievement in China and the United States.
Springer Science and Business Media, 24, 1-11.
VanTassel-Baska, J., Feng, A., MacFarlane, B., Heng, M. A., Teo, C. T., Wong, M. L.,…
Khong, B. C. (2008). A cross cultural study of teachers’ instructional practices in
Singapore and the United States. Journal for the Education of the Gifted, 31(3),
214-239.
U.S. Commission on National Security in the Twenty-First Century. (2001). The phase
III report of the U.S. Commission on National Security in the Twenty-First
Century road map for national security: Imperative for change. Washington,
DC: U.S. Commission on National Security.