Raising Critical Thinkers through Singapore Math (another email) Keys Grade School, Manila, January 2010

1. raising critical thinkers through singapore math Dr Yeap Ban Har National Institute of Education Nanyang Technological University Singapore

2. TanjongPagar PCF Kindergarten Singapore international perspectives mathematics on teaching

3. What counts as mathematical proficiency?

4. procedural fluency conceptual reasoning Keys Grade School, Manila, The Philippines

5. strategic competence K E Y S 1 2 3 4 5 6 7 8 9 10 11 12 3948 ? Keys Grade School, Manila, The Philippines

6. 17 7 10 17 – 3 adaptive reasoning Keys Grade School, Manila, The Philippines

7. productive disposition Keys Grade School, Manila, The Philippines

8. What counts as mathematical proficiency?

9. mathz4kidz Learning Centre, Penang, Malaysia Trends in Mathematics This whole shape stands for 1. & Science Studies What does this stand for? apply their understanding and knowledge in a variety of complex situations

10. Trends in Mathematics & ScienceStudy explain their reasoning mathz4kidz Learning Centre, Penang, Malaysia

11. What is Singapore Math?

12. “an excellent vehicle to develop and improve a person’s intellectual competence” Princess Elizabeth Primary School, Singapore

13. mathematics education “ an excellent vehicle for the development and improvement of a person’s intellectual competence ” Bina Bangsa School, Bandung, Indonesia Ministry of Education Singapore 2006

14. mathematics using to develop children’s intelligence

15. 4 7 47 11 Edgewood Elementary School, New York, USA 47 – 11

16. Edgewood Elementary School, New York

17. Edgewood Elementary School, New York, USA

18. What is Singapore Math? Challenging Materials

19. Meiling and Raja started on a 36-km cycling trip at the same time. They cycled at the same speed for the first 12 km. For the remaining 24 km, Meiling cycled at a faster speed. She arrived at the finishing point 10 minutes before Raja who was 4 km behind her. Raja did not change his speed throughout the trip and he completed the trip at 11 10. (a) At what time did the trip start? (b) What was Meiling’s average speed for the remaining 24 km of the trip in m/min? (PSLE Grade 6) Meiling’s average speed was 480 m/min for the last part of the trip. Meiling Raja Raja: 1o min  4 km Raja: First 12 km  30 min Raja: 1o min  4 km Raja: Last 24 km  60 min ??? min  36 km Meiling: Last 24 km  50 min Raja: 90 min  36 km Meiling: 24000 m  50 min 11 10 hrs 10 10 hours  09 40 hrs Raja, and hence Meiling, started the trip at 09 40. Meiling: 2400 m  5 min Meiling: 480 m  1 min

20. The total number of stamps in Album A, Album B and Album C was 444 at first. Dennis gave away 3/5 of the stamps from Album A, put 24 more new stamps into Album B and added some stamps into Album C until the number of stamps in Album C became three times its original number. The ratio of the number of stamps in Album A to that in Album B to that in Album C became 2 : 5 : 9. How many more stamps were there in Album C than Album A in the end? (TeckWhye Primary School, Grade 6) Album A Album B Album C

21. The total number of stamps in Album A, Album B and Album C was 444 at first. Dennis gave away 3/5 of the stamps from Album A, put 24 more new stamps into Album B and added some stamps into Album C until the number of stamps in Album C became three times its original number. The ratio of the number of stamps in Album A to that in Album B to that in Album C became 2 : 5 : 9. How many more stamps were there in Album C than Album A in the end? (TeckWhye Primary School, Grade 6) 7 units  ? 7 units  36 x 7 = 210 + 42 = 252 There were 252 more stamps in Album C than Album A in the end. Album A Album B Album C 468 13 units  444 + 24 = 468 1 unit  468 ÷ 13 = 36 390 78

22. What is Singapore Math? Challenging Materials for Every Child

23. TIMSS Trends in International Maths and Science Studies 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)

24. TIMSS Trends in International Maths and Science Studies Sweden Median U S A Japan Singapore Grade 4 Advanced 3 10 5 41 23 High 24 40 26 74 61 Intermediate 69 77 67 92 89 Low 93 95 90 98 98 Elementary School in Japan

25. TIMSS Trends in International Maths and Science Studies Average Hong Kong Singapore Korea Taiwan Grade 8 Advanced 2 40 31 45 40 High 15 70 64 71 71 Intermediate 46 88 85 86 90 Low 75 97 94 95 98 Telok Kurau Primary School

26. 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

27. TIMSS Trends in International Maths and Science Studies Grade 4 Grade 8 Singapore Advanced 41 40 High 74 70 Intermediate 92 88 Low 98 97 Catholic High School (Primary)

28. TIMSS Trends in International Maths and Science Studies Grade 4 Grade 8 U S A Advanced 10 6 High 40 31 Intermediate 77 67 Low 95 92 Catholic High School (Primary)

29. TIMSS Trends in International Maths and Science Studies Grade 4 Grade 8 England Advanced 16 8 High 48 35 Intermediate 79 69 Low 94 90 Catholic High School (Primary)

30. TIMSS Trends in International Maths and Science Studies Grade 4 Grade 8 International Advanced 5 2 High 26 15 Intermediate 67 46 Low 90 75 Catholic High School (Primary)

31. Using Mathematics to Develop Intelligent Behaviors

32. what are intelligent behaviors?

33. 1000 - 124 mathematics & intelligent behaviors

34. 9 9 1 1000 999 - 124 - 124 875 for 1000 looking connections - 124 876 Bina Bangsa School, Bandung, Indonesia

35. to ability explain A Grade 6 US textbook written using the Singapore Pedagogy

36. mathematics & intelligent behaviours

37. 3 4 ÷ 3 = 3 x 4 3 4 =

38. How to make sure the butterfly cannot flyHow do you get a butterfly?First there is the egg which hatches into a caterpillar. The caterpillar eats and grows. At the right time, it makes a cocoon out of its own body. While in the cocoon, the caterpillar changes into a butterfly.When the butterfly is ready, it starts to break through the cocoon. First a hole appears. Then the butterfly struggles to come out through the hole. This can take a few hours.If you try to "help" the butterfly by cutting the cocoon, the butterfly will come out easily but it will never fly. Your "help" has destroyed the butterfly.The butterfly can fly because it has to struggle to come out. The pushing forces lots of enzymes from the body to the wing tips. This strengthens the muscles, and reduces the body weight. In this way, the butterfly will be able to fly the moment it comes out of the cocoon. Otherwise it will simply fall to the ground, crawl around with a swollen body and shrunken wings, and soon die.If the butterfly is not left to struggle to come out of the cocoon, it will never fly.We can learn an important lesson from the butterfly.If we do not have struggles and challenges in our work, we will never grow strong and capable. If life has no difficulties, we will become weak and helpless.Lim Siong GuanHead, Civil Service

39. 11 cm 4 cm 5 cm 5 cm to use 5 cm ability knowledge Area = (11 + 5) ÷ 2 x 4

40. Teaching Every Child

41. Some of us come from English-speaking homes. Some of us don’t. I speak Malay at home. This is what help me learn mathematics well.… Princess Elizabeth Primary School, Singapore Factors That Contribute to High Achievement Level in Mathematics

42. These are my friends in Primary 1. We like our teacher. Once, she was absent for two days. We missed her. She told she had to learn new things to teach us better. teacher quality Princess Elizabeth Primary School, Singapore National Institute of Education, Singapore

43. x Keys Grade School, Manila, The Philippines

44. singapore math Photo: Keys Grade School. Manila, The Philippines professional development in-service Photo: Hougang Primary School, Singapore

45. singapore math parental expectations Last Saturday, Mum and Dad went to school – to learn the model method so they can help me with schoolwork. But Mum said she did not get it. In the end I had to teach her. Photos: Seminar for Parents on Problem Solving

46. Photos: Keys Grade School, Manila, The Philippines singapore math Bruner’s theory We use concrete materials to learn mathematics. Photos: Princess Elizabeth Primary School, Singapore

47. singapore math emphasis on concrete to pictorial to abstract representations Photo: Catholic High School (Primary) Singapore

49. singapore math especially on the model method Photo: mathz4kidz Learning Center, Malaysia

50. 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) Photo: Telok Kurau Primary School, Singapore

52. mathz4kidz Learning Centre, Penang, Malaysia bruner’s theory concrete

53. mathz4kidz Learning Centre, Penang, Malaysia concrete experiences

54. from concrete to pictorial mathz4kidz Learning Centre, Penang, Malaysia

55. from pictorial to abstract All Kids Are Intelligent Series

56. mathz4kidz Learning Centre, Penang, Malaysia symbols

57. using concrete materials Ateneo Grade School, Manila, The Philippines A Public School in Chile

58. Fuchun Primary School, Singapore interaction Vygotsky’s Theory Children Learn in Social Situations

59. skemp’s theory conceptual understanding Bina Bangsa School, Semarang, Indonesia

60. Keys Grade School, Manila, The Philippines

61. Keys Grade School, Manila, The Philippines

62. A Singapore Textbook for Kindergarten diene’s theory of variation

63. diene’s theory of variation

64. diene’s theory of variation

65. mathematical big ideas number sense visualization connections Princess Elizabeth Primary School, Singapore

66. Princess Elizabeth Primary School, Singapore

67. Princess Elizabeth Primary School, Singapore

68. singapore math banhar.yeap@nie.edu.sg www.askyeapbanhar.blogspot.com www.math.nie.edu.sg thank you