Singapore Mathematics Curriculum: Some Insight and Reflections

1. Singapore Mathematics Curriculum: Some Insight and Reflections Lee Ngan Hoe School of Education, College of Health and Human Services, St. Ambrose University, USA LeeNganH@sau.edu Mathematics & Mathematics Education, National Institute of Education, Nanyang Technological University, Singapore nganhoe.lee@nie.edu.sg

2. OVERVIEW • Singapore – A Brief Introduction • The Singapore Mathematics Curriculum • Reflections • Concluding Comments • Questions and Discussion

3. Singapore: A brief introduction - Island, City, State, Country

6. Source: Singapore Department of Statistics - http://www.singstat.gov.sg/

8. Founded in : 1819 Gained independence in : 1965 People : Mainly migrants National Language : Malay Official /Working Language : English

9. A Summary • A small country – island, city, state, country • Warm and humid • Generally safe from natural disasters and crime • Known for shopping and eating • Common use of English

10. International Benchmarking Studies That Places Singapore In The Limelight: • TIMSS – the Trends in International Mathematics and Science Study or as previously known Third International Mathematics and Science Study • PISA – Programme for International Student Assessment • TEDS-M – Teacher Education and Development Study in Mathematics

11. Singapore Mathematics Curriculum

12. Context The Singapore Mathematics Curriculum – Basically a national curriculum: Textbooks must be approved before being adopted in schools.

13. The Curriculum • The Ministry of Education Primary Mathematics Syllabus Document (Year of implementation – 2007) (http://www.moe.edu.sg/education/syllabuses/sciences/files/maths-primary-2007.pdf) • The Ministry of Education Primary Mathematics Syllabus Document (Year of implementation – 2013) (http://www.moe.edu.sg/education/syllabuses/sciences/files/maths-primary-2013.pdf)

14. Other than content … • Framework – What to address? • Approaches – How to address?

15. Singapore mathematics Curriculum Framework

16. Singapore mathematics Curriculum Framework ... A History 2007 2013 1992 2001

17. The Framework for the Singapore Mathematics Curriculum, developed in 1990, for example, survived, with minor modification, the major curriculum review for the 2000 syllabuses which took into account the three new Initiatives. One of the key reasons for the Framework’s survival is its rigour and robustness in presenting the philosophy and principles underlying decisions made about what mathematics education should equip our students with. Lee, N.H. (2008). Nation Building Initiative: Impact on Singapore Mathematics Curriculum. In Niss, M. (Ed.) 10th International Congress on Mathematical Education Proceedings (CD). Copenhagen: Roskilde University.

18. The Content – Multi-faceted:

19. The Pedagogy – Multi-faceted

20. The Performance – Multi-faceted

22. Using Calculator / Computer Effective?

23. Using Paper Cutting Unit Square Unit Length Unit Length + + + + + . . . = 1 + Efficient?

24. Using Generalizable Pattern – An Algebraic Approach Recognized that it is a Geometric Progression (GP), with first term a = and common ratio r = , and the required answer is the sum to infinity, which exists since r < 1. This approach is generalizable to any GP with r < 1. Elegance? Lead to problem posing – rather than consumers of mathematics, students are encouraged to be creators of mathematics.

25. The KEY ApproachES: • The spiral curriculum (Curriculum Approach) • The concrete-pictorial-abstract (C-P-A) development of concepts (Pedagogical approach) • Learning experiences (2013) (Learning approach)

26. The Spiral Curriculum Each topic is revisited and introduced in increasing depth from one level to the next to enable students to consolidate the concepts and skills learned and to develop these concept and skills further.

27. The C-P-A Development of concepts It is not just about representing an idea in different forms, it is about connecting the various representation to make sense of the mathematics to be learnt

28. Learning Experiences

29. http://www.flashlightcreative.net/swf/mindreader/

30. The KEY Approaches through the curriculum, teaching, and learning – Learning is about making connections : • The spiral curriculum (Curriculum Approach) – Connecting to extend existing knowledge and skills • The concrete-pictorial-abstract (C-P-A) development of concepts (Pedagogical approach) – Connecting to make sense of learning • Learning experiences (2013) (Learning approach) – connections to realise the curriculum

31. Reflections…

32. Curriculum • Eclectic approach towards teaching and learning of mathematics in a centralised system • Consistency-based and integrated approach towards curriculum changes An ironical curriculum?

33. Sociocultural • Value on education and mathematics • Exposure to eclecticism, striking for balance, strive for unity An “rojak” culture?

34. Geographical • Size • East or West? A blessed nation?

35. Advantages In International Benchmarking Studies • Every school is a good school concept: Raising the average • National examinations • Emphasise on strategic use of Information and Communication Technology

36. Are International Benchmarking Studies Useful?

37. What have we gained? • Economically • Educationally

38. CONCLUDING COMMENTS

39. One way to help Americans excel at math is to copy the approach of the Japanese, Chinese, and Koreans.  In Intelligence and How to Get It,Nisbett describes how the educational systems of East Asian countries focus more on hard work than on inborn talent: • “Children in Japan go to school about 240 days a year, whereas children in the United States go to school about 180 days a year.” • “Japanese high school students of the 1980s studied 3 ½ hours a day, and that number is likely to be, if anything, higher today.” • “[The inhabitants of Japan and Korea] do not need to read this book to find out that intelligence and intellectual accomplishment are highly malleable. Confucius set that matter straight twenty-five hundred years ago.” • “When they do badly at something, [Japanese, Koreans, etc.] respond by working harder at it.” • “Persistence in the face of failure is very much part of the Asian tradition of self-improvement. And [people in those countries] are accustomed to criticism in the service of self-improvement in situations where Westerners avoid it or resent it.” • We certainly don’t want America’s education system to copy everything Japan does (and we remain agnostic regarding the wisdom of Confucius). But it seems to us that an emphasis on hard work is a hallmark not just of modern East Asia, but of America’s past as well. In returning to an emphasis on effort, America would be returning to its roots, not just copying from successful foreigners. • Source: The Atlantic – The Myth of ‘I’m Bad at Math (2013) http://www.theatlantic.com/education/print/2013/10/the-myth-of-im-bad-at-math/280914/

40. Some Thoughts … Education is embedded in a sociocultural context. Curriculum development should be approached from a integrative rather than additive manner, reflecting and refining the aspiration of the people. International benchmark studies is but just one way to better understand the gaps that exist in curriculum, teaching and learning. A balanced and holistic approach is needed for curriculum development.

41. Questions & discussion

42. Thank You & All the Best! It has been great being part of this community. You may continue to contact me at: leenganhoe@gmail.com

43. Recognized that it is a Geometric Progression (GP), with first term a = and common ratio r = , and the required answer is the sum to infinity, which exists since r < 1. This approach is generalizable to any GP with r < 1.

44. Let AB be the 2-digit number. So, A = 1, 2, 3, 4, ..., 7, 8, 9 and B = 0, 1, 2, 3, 4, ..., 7, 8, 9 The value of AB is: 10 × A + B. The value of sum of the two digits is: A + B. So, your answer is: 10 × A + B – (A + B) = 9 × A In other words, your answer is 9, 18, 27, 36, 45, 54, 63, 72, 81.