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The document summarizes key aspects of Singapore's mathematics curriculum that has achieved high student performance and positive attitudes towards mathematics. It focuses on developing mathematical problem solving and thinking skills. The curriculum emphasizes concrete, pictorial, and abstract representations of concepts. Assessment is aligned with the curriculum and emphasizes higher-order thinking. As a result, over 40% of Singapore students demonstrate advanced understanding of mathematics compared to an international average of 5%. Students also have relatively high attitudes towards mathematics compared to other high-performing countries.
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- 1. The Average Student on Top The High School Renewal Committee 27 October 2010 Yeap Ban Har Marshall Cavendish Institute Singapore banhar@sg.marshallcavendish.com Slides are available at www.banhar.com
- 3. Singapore mathematics curriculum has its focus mathematical problem solving and it is set within an education system that emphasizes thinking.
- 5. In Singapore, a curriculum that focuses on mathematical problem solving was introduced in 1992. Mathematical Problem Solving Concepts Numerical Algebraic Geometrical Statistical Probabilistic Analytical Reasoning, communication & connections Thinking skills & heuristics Application & modelling Numerical calculation Algebraic manipulation Spatial visualization Data analysis Measurement Use of mathematical tools Estimation Monitoring of one’s own thinking Self-regulation of learning Beliefs Interest Appreciation Confidence Perseverance
- 6. thinking
- 7. The emphasis on thinking continues in the late 1990s with the introduction of Thinking School, Learning Nation philosophy to the entire education system in 1997. thinking schools learning nation
- 9. Princess Elizabeth Primary School, Singapore 2 4 6 3 5
- 10. Princess Elizabeth Primary School, Singapore
- 11. pedagogy
- 12. Pedagogy that focuses on visuals, patterning and number sense.
- 14. The CPA Approach – the progression from concrete to pictures to abstract symbols is recommended for concept development. This is based on the work of Jerome Bruner. Fuchun Primary School, Singapore
- 15. For example, students learn the idea of division by sharing 12 cookies among 4 persons as well as by putting 12 eggs in groups of 4 before progressing to using drawings to solve division problems. Later they learn to use division sentence 12 ÷ 4 = 3. Princess Elizabeth Primary School, Singapore
- 16. For example, students learn to do division of discrete quantities without the need to write division sentence in Grade 1.
- 18. The Spiral Approach – students get to revisit core ideas as they deepen their understanding of those ideas. This is also one of Jerome Bruner’s ideas. Singapore Math in the Netherlands
- 19. In Grade 2, the revisit this idea and use division sentences to represent the situations. In Grade 3, the idea is extended to include the idea of a remainder. They also learn to regroup before dividing for 2-digit and 3-digit numbers. Singapore Math in USA
- 20. In Grade 4, 4-digit numbers are used. In Grade 5, division of continuous quantities are dealt with where 13 ÷ 4 = 3.25 rather than 3 remainder 1. Singapore Math in The Philippines
- 21. assessment
- 22. Source PSLE Mathematics Singapore Examination and Assessment Board
- 23. Source Primary Three Examination Item from Henry Park Primary School, Singapore Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?
- 24. Source Primary Three Examination Item from Henry Park Primary School, Singapore Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have? Angela Bala Cheng Hao 50 872
- 25. Source Primary Three Examination Item from Henry Park Primary School, Singapore Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have? Angela Bala Cheng Hao 822 1 unit = 822 ÷ 6 1 unit = 137 Bala has 137 marbles. 600 180 42
- 26. Source Primary Three Examination Item from Henry Park Primary School, Singapore Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have? Angela Bala Cheng Hao 50 872y y y y y y 4y + y + (y + 50) = 872 6y + 50 = 872 6y = 872 – 50 y = 822 ÷ 6 y = 137
- 27. outcomes
- 28. Students in Singapore have demonstrated high achievement and positive attitude towards mathematics. In Trends in Mathematics and Science Study, more than 40% of Singapore’s 4th and 8th graders are in the Advanced International Benchmark (the international average is 5% and 2% respectively). Advanced Intermediate Low High 1995 2003 2007 38 4138 70 7473 89 9291 96 9897 Grade4 International 5 26 67 90
- 29. Advanced Intermediate Low High Indonesia Thailand 2 30 15 124 46 4414 75 6648 Grade 8 Method Used in Singapore Textbooks TIMSS 2007 Trends in International Mathematics and Science Studies Malaysia Singapore 402 7018 8850 9782 International
- 30. Advanced Intermediate Low High Average HongKong Singapore 2 4031 15 7064 46 8885 75 9794 S.Korea Taiwan 4540 7171 8690 9598 Grade8 Singapore Math in Indonesia TIMSS 2007 Trends in International Mathematics and Science Studies
- 31. Advanced Intermediate Low High Grade41995 38 70 89 96 TIMSS Trends in International Mathematics and Science Studies Grade81999 42 77 94 99 Grade42003 Grade82007 38 73 91 97 40 70 88 97
- 32. In the PSLE, the national average for students who are capable of completing the most challenging items in the examination is between 40% and 45%. We saw one such challenging items earlier. Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210 almond cookies and 5/6 of the chocolate cookies, she had 1/5 of the cookies left. How many cookies did Mrs Hoon sell?
- 33. The attitude index for Singapore students in TIMSS is also relatively high compared to other high-performing countries. Also, the majority of students in Singapore opt to study mathematics in Grades 11 and 12 when they are no longer required to.
- 34. Taiwan Singapore Hong Kong S Korea Attitude Achievement 37 45 33 40 60 40 47 31 Grade8 Japan England International Hungary 30 26 30 10 40 8 54 2
- 35. Making the Average Student on Top • Thinking-oriented Curriculum • Theoretically-sound Pedagogy • Assessment that is coherent with the curriculum • Teacher professional development • Changing mindset about what mathematics is • Constructing knowledge • Enhancing capacity to learn