Mathematics Education Seminar Series, Boston College 14 April 2010.

1. mathematics teaching & learning in singapore schools Yeap Ban Har National Institute of Education Nanyang Technological University Mathematics Education Seminar Series Boston College 14 April 2010 Slides can be downloaded from www.mathz4kidz.com

2. The lecture focuses on selected aspects of mathematics education in Singapore that have significant impact on high achievement of its students. It provides selected insights on the role of curriculum development, structures in the education system that support curriculum implementation, textbooks, teacher training, assessment and testing, and societal expectations on student outcomes. DaQiao Primary School

3. Overview ofEducation System Grades 1 – 6 (compulsory education) Primary School Leaving Examination Grade 6 Grade 7 – 10 General Certificate of Education Ordinary Level Grade 10 Grade 11 – 12 or Polytechnic General Certificate of Education Advanced Level Grade 12 or Diploma There are variations for advanced and struggling students.

4. curriculum Fuchun Primary School Pre-service Practicum

5. emphasis on problem solving Reference: Singapore Ministry of Education 2006

6. Wellington Primary School rationale The rationale of teaching mathematics is that it is “a good vehicle for the development and improvement of a person’s intellectual competence”.

7. Thinking Schools Learning Nations This initiative was introduced in 1997. Since then Ministry of Education in Singapore has been injecting various initiatives into the system. These initiatives are intended to give schools the impetus to refine their programs to include the development of generic competencies.

8. national test North Vista Primary School

9. in the national test emphasis on problem solving

10. A B F E D C Reference: Singapore Examinations & Assessment Board 2004-2008

11. Reference: Singapore Examinations & Assessment Board

13. 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? almond cookies 5/8 3/8 210 chocolate cookies 1/5 3/8 – 1/5 = 7/40  210 1/40  30 32/40  960 She sold 960 cookies.

15. Parents Up In Arms Over PSLE Mathematics Paper TODAY’S 10 OCT 2009 SINGAPORE: The first thing her son did when he came out from the Primary School Leaving Examination (PSLE) maths paper on Thursday this week was to gesture as if he was "slitting his throat". "One look at his face and I thought 'oh no'. I could see that he felt he was condemned," said Mrs Karen Sng. "When he was telling me about how he couldn't answer some of the questions, he got very emotional and started crying. He said his hopes of getting (an) A* are dashed." Not for the first time, parents are up in arms over the PSLE Mathematics paper, which some have described as "unbelievably tough" this year. As recently as two years ago, the PSLE Mathematics paper had also caused a similar uproar. The reason for Thursday's tough paper, opined the seven parents whom MediaCorp spoke to, was because Primary 6 students were allowed to use calculators while solving Paper 2 for the first time. … Said Mrs Vivian Weng: "I think the setters feel it'll be faster for them to compute with a calculator. So the problems they set are much more complex; there are more values, more steps. But it's unfair because this is the first time they can do so and they do not know what to expect!" … "The introduction of the use of calculators does not have any bearing on the difficulty of paper. The use of calculators has been introduced into the primary maths curriculum so as to enhance the teaching and learning of maths by expanding the repertoire of learning activities, to achieve a better balance between the time and effort spent developing problem solving skills and computation skills. Calculators can also help to reduce computational errors." … Another common gripe: There was not enough time for them to complete the paper. A private tutor, who declined to be named, told MediaCorp she concurred with parents' opinions. "This year's paper demanded more from students. It required them to read and understand more complex questions, and go through more steps, so time constraints would have been a concern," the 28-year-old said.

17. chocolates sweets 12 Jim 12 18 12 12 12 12 18 Ken 3 parts  12 + 12 + 12 + 12 + 18 = 66 1 part  22 Half of the sweets Ken bought = 22 + 12 = 34 So Ken bought 68 sweets.

18. program implementation North Vista Primary School

19. school programs include enrichment for all students Wellington Primary School

20. A lion weighs 135 kg. A cow weigh 87 kg more than the lion. An elephant weighs 139 more than the cow. How heavy is the elephant? (Primary 2) TelokKurau Primary School

21. A shop sells bicycles for adults and children. The adult bicycles come in 2 color choices: black and white. The children bicycles come in 3 color choices: red, blue and green. Mr Tan wants to buy a bicycle for himself and another one for his son. How many different color choices does he have to buy both bicycles? A shop sells bicycles for adults and children. The adult bicycles come in 2 color choices: black and white. The children bicycles come in 4 color choices: red, blue, green and purples. Mr Tan wants to buy a bicycle for himself and another one for his son. How many different color choices does he have to buy both bicycles? A shop sells bicycles for adults and children. The adult and children choose from any of these colors: red, blue, green, yellow and purple. bicycles come in 2 color choices: black and white. The children bicycles come in 3 color choices: red, blue and green. Mr Tan wants to buy a bicycle for himself and another one for his son. How many different color choices does he have to buy both bicycles? Materials that delve deeper into a basic topic are used as part of the regular program. For example, this school uses a textbook plus teacher-produced worksheets such as this to enrich students’ ideas about multiplication. Lesson Study at Maris Stella High School (Primary)

22. Maris Stella High School (Primary)

23. Maris Stella High (Primary) School

24. Source: Maris Stella High (Primary) School, Singapore

25. complex problem solving is expected of every student In twice-a-year tests designed by the schools, problems such as this one are given to challenge students. However, there is an expectation that every student makes significant effort to acquire the ability to solve such problems. Raffles Girls’ Primary School

26. parental expectations TanjongPagar PCF Kindergarten

27. parental expectations Seminar for Parents on Problem Solving

28. system-wide intervention Fuchun Primary School Northlight School

29. presence of ‘safety nets’

30. Princess Elizabeth Primary School learning support program at entry point

31. Variation in kindergartens Kindergarten is not part of formal schooling. Pre-school education varies in types and quality. Teachers’ qualification ranges from O-Levels to masters degrees in early childhood. Monthly fees range from $65 to more than $1000. PCF Kindergarten TelokBlangah

32. Kindergartens that the majority of Singapore children attend are run by grass-root organizations and they struggle to provide a high-quality program due to lack of resources and qualified teachers. One such provider of kindergarten education is the PCF Kindergartens which has 255 kindergartens out of 485 kindergartens in Singapore. Variation in kindergartens Also, 50% of first-graders in Singapore come from non-English speaking environment. PCF Kindergarten TanjongPagar,

33. foundation mathematics at halfway point Princess Elizabeth Primary School

34. teacher-initiated intervention DaQiao Primary School Princess Elizabeth Primary School

35. teacher-initiated intervention TelokKurau Primary School

36. pedagogy Kuo Chuan Presbyterian Primary School

37. Catholic High School (Primary) emphasis on concrete to pictorial to abstract representations

39. mathz4kidz Learning Center, Malaysia especially on the model method

41. teacher education National Institute of Education

42. teacher training pre-service National Institute of Education

43. Princess Elizabeth Primary School, Singapore professional development in-service HougangPrimary School, Singapore

44. teacher learning from textbooks

48. achievement Catholic High School (Primary)

49. TIMSS 1995 to 2007 1995 2003 2007 Grade 4 Advanced 38 41 38 High 70 74 73 Intermediate 89 92 91 Low 96 98 97 Catholic High School (Primary), Singapore

50. TIMSS 2007 TAIWAN HONGKONG SINGAPORE Grade 4 Advanced 24 41 40 High 66 74 81 Intermediate 92 92 97 Low 99 98 100 Catholic High School (Primary), Singapore

51. TIMSS 2007 AVERAGE MALAYSIA SINGAPORE Grade 8 Advanced 2 40 2 High 15 70 18 Intermediate 46 88 50 Low 75 97 82 Northlight School, Singapore