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Singapore Math at Highline Public SchoolsMarch 2013  Session 5Yeap Ban Harwww.banhar.blogspot.com                        ...
John had 1.5 m ofcopper wire. He cutsome of the wire tobend into the shapeshown in the figurebelow. In the figure,there ar...
19 cm x 5 = 95 cm150 cm – 95 cm = 55 cm55 cm was left.
Lesson 6   12th March 2013
Lesson 6   12th March 2013
Lesson 6   12th March 2013
“… over-emphasising procedural skillswithout understanding the underlying mathematical principles should be             av...
Student Achievement                              Average Learners Performing                              WellPathlight Sc...
Singapore      Math   allows                               average learners perform at                               a hig...
All major international tests (literacy, science and mathematics) between 1964 and2003 were placed on a common scale. Sele...
mathematics
intermediate                                                      advanced                                                ...
intermediate                                                    advanced                                                  ...
intermediategrade eight mathematics                                                    advanced                           ...
Singapore Math                        The CPA Approach, The Spiral                        Approach and Emphasis on Relatio...
J Bruner                               Enactive, Iconic, Symbolic                               RepresentationsEdgewood El...
Greenville Elementary School, New York
Escuela de Guetamala, Chile                              6                              6                              6  ...
J Bruner                                         Spiral CurriculumGreenville Elementary School, New York
Z Dienes                                Play  Structured Learning                                 PracticeBina Bangsa Sc...
xx   x   x    x            Jenaplanschool Cleoplas, The Netherlands
L Vygotsky                              InteractionPathlight School, Singapore                              Bina Bangsa Sc...
R Skemp                        Relational and Instrumental                        UnderstandingGlobe Academy, London
Using bar model to introduce solvingalgebraic equationsSolve 7 – 3y = 1 .             7     3y              1
Using bar model to introduce solvingalgebraic equationsSolve 7 – 3y = 1 .             7           3y              1
J Piager                            Assimilation, AccommodationKeys Grade School, Manila
H Gardner                            Multiple IntelligencesKeys Grade School, Manila
Observing patterns andmaking generalizationsinvolves reflection.Seely Place Elementary School, New York
Singapore National ExaminationFind the value of 12.2 ÷ 4 .                               Answer : 3.05 [B1]               ...
3 .05       12.20            4 12.20                          12     12 20 hundredths                              0.20   ...
A show started at 10.55 a.m. andended at 1.30 p.m. How long wasthe show in hours and minutes?                     2 h 30 m...
Find <y in the figure below.                     70 o                 70 o       y                   70 o360o – 210o = 150...
Cup cakes are sold at 40 cents each.What is the greatest number of cupcakes that can be bought with $95?   $95 ÷ 40 cents...
Mr Tan rented a car for 3 days. Hewas charged $155 per day and 60cents for every km that he travelled.He paid $767.40. Wha...
“Mathematical problem  solving is central tomathematics learning.”              Ministry of Education 2006
“… including non-routine,open-ended and real-world        problems.”               Ministry of Education 2006
Parents Up In Arms                                                      Said Mrs Vivian Weng: "I think the setters        ...
Trends in InternationalMathematics and Science      Study TIMSS Students in the highest international benchmark are able t...
“Skill proficiencies include the    ability to use technologyconfidently, where appropriate,  for exploration and problem ...
1    2    3    4    5    6    7     89    10   11   12   13   14   15    1617   18   19   20   21   22   23    2425   26  ...
Table 1 consists of numbers from 1 to 56. Kay and Lin are given aplastic frame that covers exactly 9 squares of Table 1 wi...
Table 1 consists of numbers from 1 to 56. Kay and Lin are given aplastic frame that covers exactly 9 squares of Table 1 wi...
Table 1 consists of numbers from 1 to 56. Kay and Lin are given aplastic frame that covers exactly 9 squares of Table 1 wi...
(b) Lin puts the frame on some other 9 squares.    The sum of the 8 numbers that can be seen in the frame is 272.    What ...
Weiyang started a savings plan byputting 2 coins in a money box everyday. Each coin was either a 20-cent or50-cent coin. H...
three      keysto successful implementation
Reference: Department of Education State of New Yorkassessment
assessment    Reference: Department of Education State of Hawaii
 Teacher as a learner (professor as a  model) Teacher as an observer of learning  (lesson study) Teacher as reflective ...
teacher preparation    National Institute of Education                         SingaporeSingapore teachers learn what they...
teacher preparationNational Institute of Education                     SingaporeThe practice component is given emphasis –...
teacher preparation               There is an               emphasis on               teachers               solving the  ...
teacher developmentTeachers learn from thetextbooks and teachersguide.
teacher developmentWe learn from the Japanese method to help teachersdevelop better skills in observing students. This is ...
TEDS-M FindingsTEDS-M Elementary Teachers   TEDS-M Elementary TeachersContent Knowledge            Pedagogical Content Kno...
National Institute of Education, Singapore                                             Edgewood Elementary School, New Yor...
Bina Bangsa School, Indonesia                                Keys Grade School, The Philippines                           ...
leadership   Mayor of Newark gave an inspirational message to               teachers attending professional development on...
•   What can I do as a teacher?•   What can my school do?•   What can the education schools do?•   What government support...
Singapore Math at Highline Public SchoolsMarch 2013 Yeap Ban Haryeapbanhar@gmail.com                                     ...
Highline Session 5
Highline Session 5
Highline Session 5
Highline Session 5
Highline Session 5
Highline Session 5
Highline Session 5
Highline Session 5
Highline Session 5
Highline Session 5
Highline Session 5
Highline Session 5
Highline Session 5
Highline Session 5
Highline Session 5
Highline Session 5
Highline Session 5
Highline Session 5
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  1. 1. Singapore Math at Highline Public SchoolsMarch 2013  Session 5Yeap Ban Harwww.banhar.blogspot.com The Merlion by Yeap Ken Min
  2. 2. John had 1.5 m ofcopper wire. He cutsome of the wire tobend into the shapeshown in the figurebelow. In the figure,there are 6 equilateraltriangles and thelength of XY is 19 cm.How much of thecopper wire was left?
  3. 3. 19 cm x 5 = 95 cm150 cm – 95 cm = 55 cm55 cm was left.
  4. 4. Lesson 6 12th March 2013
  5. 5. Lesson 6 12th March 2013
  6. 6. Lesson 6 12th March 2013
  7. 7. “… over-emphasising procedural skillswithout understanding the underlying mathematical principles should be avoided.” Ministry of Education 2006
  8. 8. Student Achievement Average Learners Performing WellPathlight School, Singapore
  9. 9. 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
  10. 10. All major international tests (literacy, science and mathematics) between 1964 and2003 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 PhilippinesReference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
  11. 11. mathematics
  12. 12. intermediate advanced high low average Singapore 606 43 78 94 99 South Korea 605 39 80 97 100grade 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
  13. 13. intermediate advanced high low average South Korea 613 47 77 93 99 Singapore 611 48 78 92 99grade 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
  14. 14. intermediategrade 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
  15. 15. Singapore Math The CPA Approach, The Spiral Approach and Emphasis on Relational UnderstandingGlobe Academy, London
  16. 16. J Bruner Enactive, Iconic, Symbolic RepresentationsEdgewood Elementary School, New York
  17. 17. Greenville Elementary School, New York
  18. 18. Escuela de Guetamala, Chile 6 6 6 6
  19. 19. J Bruner Spiral CurriculumGreenville Elementary School, New York
  20. 20. Z Dienes Play  Structured Learning  PracticeBina Bangsa School, Indonesia
  21. 21. xx x x x Jenaplanschool Cleoplas, The Netherlands
  22. 22. L Vygotsky InteractionPathlight School, Singapore Bina Bangsa School, Indonesia
  23. 23. R Skemp Relational and Instrumental UnderstandingGlobe Academy, London
  24. 24. Using bar model to introduce solvingalgebraic equationsSolve 7 – 3y = 1 . 7 3y 1
  25. 25. Using bar model to introduce solvingalgebraic equationsSolve 7 – 3y = 1 . 7 3y 1
  26. 26. J Piager Assimilation, AccommodationKeys Grade School, Manila
  27. 27. H Gardner Multiple IntelligencesKeys Grade School, Manila
  28. 28. Observing patterns andmaking generalizationsinvolves reflection.Seely Place Elementary School, New York
  29. 29. Singapore National ExaminationFind the value of 12.2 ÷ 4 . Answer : 3.05 [B1] Example 1
  30. 30. 3 .05 12.20 4 12.20 12 12 20 hundredths 0.20 0.20Number Bond Method 0 Long Division Method
  31. 31. A show started at 10.55 a.m. andended at 1.30 p.m. How long wasthe show in hours and minutes? 2 h 30 min 11 a.m. 1.30 p.m. Answer : 2 h 35 min [B1] Example 2
  32. 32. Find <y in the figure below. 70 o 70 o y 70 o360o – 210o = 150o Example 3
  33. 33. Cup cakes are sold at 40 cents each.What is the greatest number of cupcakes that can be bought with $95? $95 ÷ 40 cents = 237.5 Answer: 237 cupcakes Example 4
  34. 34. Mr Tan rented a car for 3 days. Hewas charged $155 per day and 60cents for every km that he travelled.He paid $767.40. What was the totaldistance that he travelled for the 3days? $767.40 – 3 x $155 = $302.40$302.40 ÷ 60 cents per km = 504 km Example 5
  35. 35. “Mathematical problem solving is central tomathematics learning.” Ministry of Education 2006
  36. 36. “… including non-routine,open-ended and real-world problems.” Ministry of Education 2006
  37. 37. Parents Up In Arms Said Mrs Vivian Weng: "I think the setters feel itll be faster for them to compute with aOver PSLE calculator. So the problems they set are much more complex; there are more values, more steps. But its unfair because this is the firstMathematics 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 ofSINGAPORE: The first thing her son did when he came out from paper. The use of calculators has beenthe Primary School Leaving Examination (PSLE) maths paper on introduced into the primary maths curriculumThursday this week was to gesture as if he was "slitting his so as to enhance the teaching and learning ofthroat". 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 betweenhe was condemned," said Mrs Karen Sng. "When he was telling the time and effort spent developing problemme about how he couldnt 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 notMathematics 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 parentsThe reason for Thursdays tough paper, opined the seven parents opinions. "This years paper demanded morewhom MediaCorp spoke to, was because Primary 6 students were from students. It required them to read andallowed 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.
  38. 38. Trends in InternationalMathematics and 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.
  39. 39. “Skill proficiencies include the ability to use technologyconfidently, where appropriate, for exploration and problem solving.” Ministry of Education 2006
  40. 40. 1 2 3 4 5 6 7 89 10 11 12 13 14 15 1617 18 19 20 21 22 23 2425 26 27 28 29 30 31 3233 34 35 36 37 38 39 4041 42 43 44 45 46 47 4849 50 51 52 53 54 55 56 Example 6
  41. 41. Table 1 consists of numbers from 1 to 56. Kay and Lin are given aplastic frame that covers exactly 9 squares of Table 1 with the centresquare darkened.
  42. 42. Table 1 consists of numbers from 1 to 56. Kay and Lin are given aplastic frame that covers exactly 9 squares of Table 1 with the centresquare 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?
  43. 43. Table 1 consists of numbers from 1 to 56. Kay and Lin are given aplastic frame that covers exactly 9 squares of Table 1 with the centresquare 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?
  44. 44. (b) Lin puts the 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
  45. 45. Weiyang started a savings plan byputting 2 coins in a money box everyday. Each coin was either a 20-cent or50-cent coin. His mother also puts in a$1 coin in the box every 7 days. Thetotal value of the coins after 182 dayswas $133.90.(a) How many coins were there altogether?(b) How many of the coins were 50-cent coins? Example 7
  46. 46. three keysto successful implementation
  47. 47. Reference: Department of Education State of New Yorkassessment
  48. 48. assessment Reference: Department of Education State of Hawaii
  49. 49.  Teacher as a learner (professor as a model) Teacher as an observer of learning (lesson study) Teacher as reflective practitioner (professional learning community)teacher preparation
  50. 50. teacher preparation National Institute of Education SingaporeSingapore teachers learn what they need to learn through anapproach that balances content and pedagogy.
  51. 51. teacher preparationNational Institute of Education SingaporeThe practice component is given emphasis – micro teaching,practicum and lesson study.
  52. 52. teacher preparation There is an emphasis on teachers solving the problems themselves during the course.
  53. 53. teacher developmentTeachers learn from thetextbooks and teachersguide.
  54. 54. teacher developmentWe learn from the Japanese method to help teachersdevelop better skills in observing students. This is lessonstudy. Princess Elizabeth Primary School Singapore
  55. 55. TEDS-M FindingsTEDS-M Elementary Teachers TEDS-M Elementary TeachersContent Knowledge Pedagogical Content Knowledge
  56. 56. National Institute of Education, Singapore Edgewood Elementary School, New York Fuchun Primary School, Singapore
  57. 57. Bina Bangsa School, Indonesia Keys Grade School, The Philippines Kranji Secondary School, Singapore
  58. 58. leadership Mayor of Newark gave an inspirational message to teachers attending professional development on Singapore Math.
  59. 59. • 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
  60. 60. Singapore Math at Highline Public SchoolsMarch 2013 Yeap Ban Haryeapbanhar@gmail.com The Merlion by Yeap Ken Min
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