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![Singapore National Examination
Find the value of 12.2 ÷ 4 .
Answer : 3.05 [B1]
Example 1](https://image.slidesharecdn.com/highlinesession5-130312210603-phpapp02/75/Highline-Session-5-39-2048.jpg)
![A show started at 10.55 a.m. and
ended at 1.30 p.m. How long was
the show in hours and minutes?
2 h 30 min
11 a.m. 1.30
p.m.
Answer : 2 h 35 min [B1]
Example 2](https://image.slidesharecdn.com/highlinesession5-130312210603-phpapp02/75/Highline-Session-5-41-2048.jpg)
Uploaded byJimmy Keng
Highline Session 5
This document summarizes a presentation on Singapore Math given at Highline Public Schools in March 2013. It discusses key aspects of Singapore Math including the concrete-pictorial-abstract approach, the spiral curriculum, and an emphasis on relational understanding. It also references several educational theorists and compares international test results that show Singapore students performing well. The document contains examples of how Singapore Math concepts and methods are taught.
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Highline Session 5
- 1. Singapore Math atHighline Public Schools March 2013 Session 5 Yeap Ban Har www.banhar.blogspot.com The Merlion by Yeap Ken Min
- 2. John had 1.5m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm. How much of the copper wire was left?
- 6. 19 cm x5 = 95 cm 150 cm – 95 cm = 55 cm 55 cm was left.
- 7. Lesson 6 12th March 2013
- 8. Lesson 6 12th March 2013
- 9. Lesson 6 12th March 2013
- 10. “… over-emphasising proceduralskills without understanding the underlying mathematical principles should be avoided.” Ministry of Education 2006
- 13. Student Achievement Average Learners Performing Well Pathlight School, Singapore
- 14. Singapore Math allows average learners perform at a high level. The following are some data from some international research on math achievement and attitude. East Coast Primary School, Singapore
- 15. All major internationaltests (literacy, science and mathematics) between 1964 and 2003 were placed on a common scale. Selected countries shown in the table. Score 1960-1970s 1980s 1990s 2000s 500 Japan Hong Kong Hong Kong Hong Kong Japan Japan Japan Korea Korea Korea Singapore Singapore 400 Thailand The Philippines Malaysia Malaysia Singapore Thailand Thailand Thailand 300 Indonesia Indonesia The Philippines The Philippines Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
- 16.
- 17. intermediate advanced high low average Singapore 606 43 78 94 99 South Korea 605 39 80 97 100 grade four mathematics Hong Kong 602 37 80 96 99 Taiwan 591 34 74 93 99 Japan 585 30 70 93 99 Northern Ireland 562 24 59 86 96 Belgium 549 10 50 89 99 Finland 545 12 49 85 98 England 542 18 49 78 93 Russia 542 13 47 82 97 International 500 4 28 69 90
- 18. intermediate advanced high low average South Korea 613 47 77 93 99 Singapore 611 48 78 92 99 grade eight mathematics Taiwan 609 49 73 88 96 Hong Kong 586 34 71 89 97 Japan 570 27 61 87 97 Russia 539 14 47 78 95 Israel 516 12 40 68 87 Finland 514 4 30 73 96 United States 509 7 30 68 92 England 507 8 32 65 88 International 500 3 17 46 75
- 19. intermediate grade eight mathematics advanced average high low Singapore 611 48 78 92 99 Malaysia 440 2 12 36 65 Thailand 427 2 8 26 55 Indonesia 386 0 2 15 43 International 500 3 17 46 75
- 20. Singapore Math The CPA Approach, The Spiral Approach and Emphasis on Relational Understanding Globe Academy, London
- 21. J Bruner Enactive, Iconic, Symbolic Representations Edgewood Elementary School, New York
- 22. Greenville Elementary School,New York
- 23. Escuela de Guetamala,Chile 6 6 6 6
- 26. J Bruner Spiral Curriculum Greenville Elementary School, New York
- 27. Z Dienes Play Structured Learning Practice Bina Bangsa School, Indonesia
- 28. x x x x x Jenaplanschool Cleoplas, The Netherlands
- 29. L Vygotsky Interaction Pathlight School, Singapore Bina Bangsa School, Indonesia
- 30. R Skemp Relational and Instrumental Understanding Globe Academy, London
- 31. Using bar modelto introduce solving algebraic equations Solve 7 – 3y = 1 . 7 3y 1
- 32. Using bar modelto introduce solving algebraic equations Solve 7 – 3y = 1 . 7 3y 1
- 33. J Piager Assimilation, Accommodation Keys Grade School, Manila
- 34. H Gardner Multiple Intelligences Keys Grade School, Manila
- 35. Observing patterns and makinggeneralizations involves reflection. Seely Place Elementary School, New York
- 39. Singapore National Examination Findthe value of 12.2 ÷ 4 . Answer : 3.05 [B1] Example 1
- 40. 3 .05 12.20 4 12.20 12 12 20 hundredths 0.20 0.20 Number Bond Method 0 Long Division Method
- 41. A show startedat 10.55 a.m. and ended at 1.30 p.m. How long was the show in hours and minutes? 2 h 30 min 11 a.m. 1.30 p.m. Answer : 2 h 35 min [B1] Example 2
- 42. Find <y inthe figure below. 70 o 70 o y 70 o 360o – 210o = 150o Example 3
- 43. Cup cakes aresold at 40 cents each. What is the greatest number of cup cakes that can be bought with $95? $95 ÷ 40 cents = 237.5 Answer: 237 cupcakes Example 4
- 44. Mr Tan renteda car for 3 days. He was charged $155 per day and 60 cents for every km that he travelled. He paid $767.40. What was the total distance that he travelled for the 3 days? $767.40 – 3 x $155 = $302.40 $302.40 ÷ 60 cents per km = 504 km Example 5
- 45. “Mathematical problem solving is central to mathematics learning.” Ministry of Education 2006
- 46. “… including non-routine, open-endedand real-world problems.” Ministry of Education 2006
- 47. Parents Up InArms Said Mrs Vivian Weng: "I think the setters feel it'll be faster for them to compute with a Over PSLE 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 Mathematics Paper time they can do so and they do not know what to expect!" TODAY’S 10 OCT 2009 … "The introduction of the use of calculators does not have any bearing on the difficulty of SINGAPORE: The first thing her son did when he came out from paper. The use of calculators has been the Primary School Leaving Examination (PSLE) maths paper on introduced into the primary maths curriculum Thursday this week was to gesture as if he was "slitting his so as to enhance the teaching and learning of throat". maths by expanding the repertoire of learning "One look at his face and I thought 'oh no'. I could see that he felt activities, to achieve a better balance between he was condemned," said Mrs Karen Sng. "When he was telling the time and effort spent developing problem me about how he couldn't answer some of the questions, he got solving skills and computation skills. very emotional and started crying. He said his hopes of getting Calculators can also help to reduce (an) A* are dashed." computational errors." … Not for the first time, parents are up in arms over the PSLE Another common gripe: There was not Mathematics paper, which some have described as "unbelievably enough time for them to complete the paper. tough" this year. As recently as two years ago, the PSLE A private tutor, who declined to be named, Mathematics paper had also caused a similar uproar. told MediaCorp she concurred with parents' The reason for Thursday's tough paper, opined the seven parents opinions. "This year's paper demanded more whom MediaCorp spoke to, was because Primary 6 students were from students. It required them to read and allowed to use calculators while solving Paper 2 for the first time. understand more complex questions, and go … through more steps, so time constraints would have been a concern," the 28-year-old said.
- 48. Trends in International Mathematicsand Science Study TIMSS Students in the highest international benchmark are able to apply their knowledge in a variety of situations and able to explain themselves.
- 57. “Skill proficiencies includethe ability to use technology confidently, where appropriate, for exploration and problem solving.” Ministry of Education 2006
- 58. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Example 6
- 59. Table 1 consistsof numbers from 1 to 56. Kay and Lin are given a plastic frame that covers exactly 9 squares of Table 1 with the centre square darkened.
- 60. Table 1 consistsof numbers from 1 to 56. Kay and Lin are given a plastic frame that covers exactly 9 squares of Table 1 with the centre square darkened. (a) Kay puts the frame on 9 squares as shown in the figure below. 3 4 5 11 13 19 20 21 What is the average of the 8 numbers that can be seen in the frame?
- 61. Table 1 consistsof numbers from 1 to 56. Kay and Lin are given a plastic frame that covers exactly 9 squares of Table 1 with the centre square darkened. (a) Kay puts the frame on 9 squares as shown in the figure below. 3+4+5+11+13+19+20 = 96 3 4 5 96 ÷ 8 = 12 11 13 Alternate Method 4 x 24 = 96 19 20 21 96 ÷ 8 = 12 What is the average of the 8 numbers that can be seen in the frame?
- 62. (b) Lin putsthe frame on some other 9 squares. The sum of the 8 numbers that can be seen in the frame is 272. What is the largest number that can be seen in the frame? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
- 63. Weiyang started asavings plan by putting 2 coins in a money box every day. Each coin was either a 20-cent or 50-cent coin. His mother also puts in a $1 coin in the box every 7 days. The total value of the coins after 182 days was $133.90. (a) How many coins were there altogether? (b) How many of the coins were 50-cent coins? Example 7
- 64. three keys to successful implementation
- 65. Reference: Department ofEducation State of New York assessment
- 66. assessment Reference: Department of Education State of Hawaii
- 67. Teacher asa learner (professor as a model) Teacher as an observer of learning (lesson study) Teacher as reflective practitioner (professional learning community) teacher preparation
- 68. teacher preparation National Institute of Education Singapore Singapore teachers learn what they need to learn through an approach that balances content and pedagogy.
- 69. teacher preparation National Instituteof Education Singapore The practice component is given emphasis – micro teaching, practicum and lesson study.
- 70. teacher preparation There is an emphasis on teachers solving the problems themselves during the course.
- 71. teacher development Teachers learnfrom the textbooks and teachers guide.
- 72. teacher development We learnfrom the Japanese method to help teachers develop better skills in observing students. This is lesson study. Princess Elizabeth Primary School Singapore
- 73. TEDS-M Findings TEDS-M ElementaryTeachers TEDS-M Elementary Teachers Content Knowledge Pedagogical Content Knowledge
- 74. National Institute ofEducation, Singapore Edgewood Elementary School, New York Fuchun Primary School, Singapore
- 75. Bina Bangsa School,Indonesia Keys Grade School, The Philippines Kranji Secondary School, Singapore
- 76. leadership Mayor of Newark gave an inspirational message to teachers attending professional development on Singapore Math.
- 77. • What can I do as a teacher? • What can my school do? • What can the education schools do? • What government support should be in place? Slides are available at www.banhar.blogspot.com
- 78. Singapore Math atHighline Public Schools March 2013 Yeap Ban Har [email protected] The Merlion by Yeap Ken Min