Mathematics education in Singapore gained international recognition with successive good results in the Trends in International Mathematics and Science Study (TIMMS).1 Singapore-based mathematics textbooks are used in countries as diverse as the United States and Indonesia. Two key features of the Singapore Mathematics curriculum are the Model method and the Mathematics framework.2
Teaching of Mathematics in Singapore Schools
Mathematics is compulsory in primary and secondary schools, taking up around 1600 hours of total curriculum time. Curriculum time for Mathematics increases as students move up from lower primary to upper primary. Weaker students are given more curriculum time. Scientific calculators are allowed from 2008, restricted to Primary 5 and 6 students only. Full syllabuses are available on the Ministry of Education (MOE) and Singapore Examination and Assessment Boards (SEAB) websites.3
Model Method
The Model Method uses visuals to represent mathematical quantities and their relationships, and concrete manipulations to represent abstract algebraic functions. By using pictorial representations instead of words, the structure of a word problem will be more evident. It was developed in the 1980s.
The model has been successful for around 30 years. Inevitably, some problems have surfaced over the years in curriculum, assessment and instructional areas. One was whether algebra should be taught at upper primary where some problems can be more easily solved by algebra than the Model Method, yet doing so would require more curriculum time that could otherwise be spent on using IT and incorporating higher order thinking. Another was that some teachers forbade algebraic methods in school-based assessment even though any mathematically valid method will be accepted at the PSLE.4
Mathematical Framework
The Mathematical Framework (or Pentagon framework as it is sometimes known) was introduced in the 1990s to stress both the process and product in learning mathematics. It articulates the underlying principles for an effective mathematics programme. Within the framework, mathematical problem solving is at the heart of mathematics learning, and it involves the application of mathematical concepts and skills, the development of process skills such as reasoning and communicating, raising meta-cognition in problem solving, and nurturing a positive attitude towards learning mathematics (summarised by the five inter-related components of concepts, skills, processes, attitudes and metacognition).5
Results of TIMSS
The Trends in International Mathematics and Science Study (TIMSS) is a well-known international study on Mathematics and Science educational achievements. It is part of the series of the International Association for the Evaluation of Educational Achievement (IEA) studies. In each study, there are usually around 40–50 countries participants, such as the United States and Japan.6
Since 1995, Singapore has ranked within the top 3 positions with the exception of Primary 4 Science (ranked 7th) in 1995.7 (MOE, 2008).
The study shows that not only do both top and average Singapore students perform very well against international benchmarks, they also show a positive attitude to learning mathematics.
The TIMSS data suggests that qualification of teachers is related to good student performance. A study by the American Institutes for Research observed that rigorous selection and good professional development help to raise the overall quality of Singapore primary mathematics teachers above American ones.8
Use of the Singapore Mathematics in the United States
Of all the elements of Singapore’s successful mathematics system, its textbooks are the easiest to transfer to U.S. schools, as observed by the American Institutes for Research.
Based on an exploratory study conducted by the American Institutes for Research, on implementing the teaching of Singapore mathematics, the researchers found that teachers appreciated the deeper treatment of mathematic topics in Singapore textbooks, and that the text returns to a topic only to teach it in more depth. The teachers also liked the pictorial explanations in the textbooks that explained abstract concepts in a concrete way (i.e. Model Method) and the numerous multi-step problems. However, they would prefer Singapore books to emphasise applied mathematics as much as U.S. textbooks. The researchers noted that teachers needed adequate preparation to use Singapore mathematics textbooks effectively.9
Historical Development
Prior to Singapore’s self-independence in 1959, Singapore did not have an unified system of education. Each type of school will teach their own type of mathematics, using textbooks from different countries. A common curriculum was developed only after self-government, and increasing emphasis was given to ensure that Singapore could develop an industrialised economy. However, various studies conducted in 1975 and 1981 suggested that many students did not meet basic numeracy standards.
With the setting up of the Curriculum Development Institute of Singapore (CDIS) in 1980, there was an opportunity to delve deeper into developing teaching approaches and producing instructional materials. The Primary Mathematics Project team, led by Dr Kho Tek Hong (an MOE subject specialist until his retirement), developed the Model Method (a pictorial way to represent mathematical quantities and relations in a concrete way) that proved very successful over the next few decades.
A Mathematical Framework was developed in the 1990s, following a review of the mathematics curriculum, to articulate the principles of mathematical teaching. It has remained largely the same over the years, retaining mathematical problem solving as its core, and the five inter-related components of concepts, skills, processes, attitudes and metacognition. Minor revisions were made to stress new initiatives such as thinking skills, information technology and National Education.10
Author
Tan Wen Sze
References
1. Ministry of Education. (2012, December 11). International Studies Affirm Singapore Students’ Strengths In Reading, Mathematics & Science [Press release]. Retrieved 2016, May 26 from Ministry of Education website: https://www.moe.gov.sg/news/press-releases/international-studies-affirm-singapore-students--strengths-in-reading--mathematics-and-science
2. IE Singapore. (2009, April 22). Singapore shares insights on its math education model. Retrieved 2016, May 26 from IE Singapore website: http://www.iesingapore.gov.sg/Partner-Singapore/Singapore-Industry-Capabilities/Lifestyle-Business/Education/News/mc/Media-Releases/2009/4/Singapore-shares-insights-on-its-math-education-model
3. Kho, T.H., et al. (2009). The Singapore model method for learning mathematics. Singapore: EPB Pan Pacific, pp. 1–3. (Call no.: RSING 510.71095957 KHO)
4. Kho, T.H., et al. (2009). The Singapore model method for learning mathematics. Singapore: EPB Pan Pacific, pp. 1–3. (Call no.: RSING 510.71095957 KHO)
5. Kho, T.H., et al. (2009). The Singapore model method for learning mathematics. Singapore: EPB Pan Pacific, pp. 4–10. (Call no.: RSING 510.71095957 KHO)
6. TIMMS & PIRLS. (2016). About TIMMS & PIRLS International Study Centre. Retrieved on 2016, May 26 from website: http://timss.bc.edu/about.html
7. Wong, K.Y. & Lee, N.H. (2009). Singapore Education and Mathematics Curriculum. In K.Y. Wong, et als. (Eds), Mathematics education: The Singapore journey. Singapore: World Scientific, pp. 446–448. (Call no.: RSING 510.7105957 MAT)
8. Wong, K.Y. & Lee, N.H. (2009). Singapore Education and Mathematics Curriculum. In K.Y. Wong, et al. (Eds), Mathematics education: The Singapore journey. Singapore: World Scientific, pp. 439–446. (Call no.: RSING 510.7105957 MAT)
9. Ginsburg, A., Leinward S, et.al. (2005, January 28). What the United States can learn from Singapore’s world-class Mathematics system: An exploratory study. Retrieved on 2016, May 26 from American Institute for Research website: http://www.air.org/resource/what-united-states-can-learn-singapore%E2%80%99s-world-class-mathematics-system-exploratory-study
10. Wong, K.Y. & Lee, N.H. (2009). Singapore Education and Mathematics Curriculum. In K.Y. Wong et al. (Eds.). Mathematics education: The Singapore journey. Singapore: World Scientific, pp. 13–47. (Call no.: RSING 510.7105957 MAT)
The information in this article is valid as at 2016 and correct as far as we are able to ascertain from our sources. It is not intended to be an exhaustive or complete history of the subject. Please contact the Library for further reading materials on the topic.
The information in this article is valid as at 2016 and correct as far as we are able to ascertain from our sources. It is not intended to be an exhaustive or complete history of the subject. Please contact the Library for further reading materials on the topic.
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