A Seminar on SingaporeMath @ SALT LAKE CITY, UTAH

1. A Seminar on SingaporeMath@ SALT LAKE CITY, UTAH Yeap Ban Har, Ph.D. National Institute of Education Nanyang Technological University Singapore banhar.yeap@nie.edu.sg

2. Singapore A multi-racial, multi-cultural, multi-religious and multi-lingual society. Gained independence in 1965. Population of 4 million with ½ million students in about 350 schools, all public.

6. Presentation Outline • Singapore Education in a Nutshell • Singapore Mathematics Curriculum • National Tests in Singapore • Mathematics Teaching in Singapore • Mathematics Teachers & Professional Development • Achievements of Singapore Students • Questions & Discussion

7. Mathematics Curriculum Development & Focus

8. Vision of Ministry of Education Moulding the Future of the Nation

9. Columbus was searching for hardware – precious metals, silk, and spices – the sources of wealth in his days. Thomas L. Friedman 2006 The World Is Flat

10. I was searching for software – brain power and knowledge workers – the sources of wealth in our day. Thomas L. Friedman 2006 The World Is Flat

11. Future of the Nation Nurturing Knowledge Workers through Ability-Driven Education

12. As the 21st century approaches … countries will need citizens prepared to participate in ‘brain-power’ industries Beaton, Mullis, Martin, Gonzalez, Kelly & Smith 1996

13. The Singapore mathematics curriculum states that “an emphasis on mathematics education will ensure that we have an increasingly competitive workforce to meet the challenges of the 21st century”

14. Impact of Globalization Schools around the world are forced to move forward if they want to make a difference to the future of their students.

15. Problem-Solving Curriculum Agenda for Action (USA) and Cockcroft Report (UK) led to the introduction of a problem-solving curriculum in 1992.

16. Beliefs Interest Appreciation Confidence Perseverance Monitoring of one’s own thinking Self-regulation of learning Attitudes Metacognition Numerical calculation Algebraic manipulation Spatial visualization Data analysis Measurement Use of mathematical tools Estimation Mathematical Problem Solving Reasoning, communication & connections Thinking skills & heuristics Application & modelling Skills Processes Concepts Numerical Algebraic Geometrical Statistical Probabilistic Analytical Singapore Mathematics Curriculum Framework

17. Thinking SchoolsLearning Nation This initiative was introduced in 1997. It focuses on explicit teaching of thinking through school subjects.

18. Problem-Solving Curriculum It was revised in 2001 to give more emphasis on a range of heuristics.

19. Innovation & Enterprise This initiative was introduced in 2003. It focuses on inculcating good habits of minds amongst students.

20. Teach LessLearn More This call was made in 2004 to encourage the development of strong foundation knowledge.

21. Sample Test Item 3 cm 5 cm 3 cm 7 cm Find the area of the figure shown.

22. 3 cm 5 cm 3 cm 7 cm Find the area of the figure shown.

23. 3 cm 5 cm 3 cm 7 cm Find the area of the figure shown.

24. 3 cm 5 cm 3 cm 7 cm Find the area of the figure shown.

26. Nurturing Every Child This call has been made since 2005. Every child should be developed to maximize their potential using different approaches.

27. Impact of Technology Technological advances have compelled educators to re-consider what is considered significant in school curriculum.

28. Otherwise, schools will be teaching students “19th-century school mathematics concentrating on isolated skills” Kaput, Noss & Hoyles 2002

29. Problem-Solving Curriculum It was revised in 2007 for this reason. It places greater emphasis on visualization and number sense. With the introduction of calculator, mental strategies are also emphasized.

30. PSLE: Emphasis on Visualization The figure below is made up of 2 identical squares, 4 identical rectangles and 3 identical semi-circles. What is the area of the figure? 70 cm

31. PSLE: Emphasis on Number Sense Each of the three cards shown is printed with a different whole number. The smallest number is 23. When these numbers are added two at a time, the sums are 61, 71 and 86. What is the largest number on the cards? 23

32. It is recognized that mathematics is “an excellent vehicle for the development and improvement of a person’s intellectual competence in logical reasoning, spatial visualization, analysis and abstract thought” Ministry of Education Singapore 2006

33. National Test Emphasis on Basics & Problem Solving

34. National Tests in Singapore • Grade 6 Primary School Leaving Examination PSLE • Has always been under the control of Singapore Ministry of Education • Singapore Examinations and Assessment Board (SEAB) was set up recently to handle national tests in Singapore • Grade 10 GCE Ordinary Level • Has always been offered by Cambridge Examination Syndicate until 2008. • Grade 12 GCE Advanced Level • Has always been offered by Cambridge Examination Syndicate until 2007.

35. PSLE Paper 1 50 minutes

36. PSLE Paper 2 1 hour 40 minutes 

37. Knowledge 25% • Recall specific • mathematical facts, • concepts, • rules, and • formulae. • Perform straight-forward computations

38. Comprehension 35% • Interpret data • Use mathematical concepts, rules, and formulae • Solve routine or familiar problems

39. Application & Analysis 40% • Analyse data • Apply mathematical concepts, rules and formulae in a complex situation • Solve unfamiliar problems

40. Basic & Routine Skills • Example 1 • Find the value of 12.2 ÷ 4 . • Example 2 • A show started at 10.55 a.m. and ended at 1.30 p.m. • How long was the show in hours and minutes?

41. Basic & Routine Skills • Example 3 • Find <y in the figure below. 70o 70o y 70o

42. Basic & Routine Skills • Example 4  • Cup cakes are sold at 40 cents each. • What is the greatest number of cup cakes that can be bought with $95? • Example 5 • From January to August last year, Mr Tang sold an average of 4.5 cars per month, He did not sell any car in the next 4 months. On average, how many cars did he sell per month last year?

43. Novelty Students are expected to handle novel situations i.e. those not in the textbooks or previous examinations.

44. Problem Solving 1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97 The first 97 whole numbers are added up. What is the ones digit in the total?

45. Problem Solving Rena used stickers of four different shapes to make a pattern. The first 12 stickers are shown below. What was the shape of the 47th sticker?  ………? 1st 12th 47th

46. Complexity Students are expected to handle multi-step problems with some degree of complexity.

47. Problem Solving In Figure 1, Tank A is completely filled with water and Tank B is empty. Water is poured from Tank A into Tank B without spilling. The heights of the water level in the two tanks are now equal as shown in Figure 2. What is the height of the water level in Tank A in Figure 2?

48. Problem Solving Siti started saving some money on Monday. On each day from Tuesday to Friday, she saved 20 cents more than the amount she saved the day before. She saved a total of $6 from Monday to Friday. How much money did she save on Monday?

49. Problem Solving Siti started saving some money on Monday. On each day from Tuesday to Friday, she saved 20 cents more than the amount she saved the day before. She saved a total of $6 from Monday to Friday. How much money did she save on Monday? $6

50. Problem Solving Siti started saving some money on Monday. On each day from Tuesday to Friday, she saved 20 cents more than the amount she saved the day before. She saved a total of $6 from Monday to Friday. How much money did she save on Monday? $4