raising<br />critical thinkers<br />through<br />singapore math<br />Dr Yeap Ban Har<br />National Institute of Education<...
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Edgewood Elementary School, New York<br />
Edgewood Elementary School, New York, USA<br />
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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 ...
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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 Albu...
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TIMSS<br />Trends in International Maths and Science Studies<br />1995<br />2003<br />2007<br />Grade 4<br />Advanced<br /...
TIMSS<br />Trends in International Maths and Science Studies<br />Sweden<br />Median<br />U S A<br />Japan<br />Singapore<...
TIMSS<br />Trends in International Maths and Science Studies<br />Average<br />Hong Kong<br />Singapore<br />Korea<br />Ta...
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TIMSS<br />Trends in International Maths and Science Studies<br />Grade 4<br />Grade  8<br />Singapore<br />Advanced<br />...
TIMSS<br />Trends in International Maths and Science Studies<br />Grade 4<br />Grade  8<br />U S A<br />Advanced<br />10<b...
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x<br />Keys Grade School, Manila, The Philippines<br />
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Photos: Keys Grade School, Manila, The Philippines<br />singapore<br />math<br />Bruner’s<br />theory<br />We use concrete...
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singapore<br />math<br />especially on<br />the model method<br />Photo: mathz4kidz Learning Center, Malaysia<br />
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 ele...
mathz4kidz Learning Centre, Penang, Malaysia<br />bruner’s theory<br />concrete<br />
mathz4kidz Learning Centre, Penang, Malaysia<br />concrete<br />experiences<br />
from<br />concrete<br />to<br />pictorial<br />mathz4kidz Learning Centre, Penang, Malaysia<br />
from<br />pictorial<br />to<br />abstract<br />All Kids Are Intelligent Series<br />
mathz4kidz Learning Centre, Penang, Malaysia<br />symbols<br />
using<br />concrete<br />materials<br />Ateneo Grade School, Manila, The Philippines<br />A Public School in Chile<br />
Fuchun Primary School, Singapore<br />interaction<br />Vygotsky’s Theory<br />Children Learn in Social Situations<br />
skemp’s<br />theory<br />conceptual<br />understanding<br />Bina Bangsa School, Semarang, Indonesia<br />
Keys Grade School, Manila, The Philippines<br />
Keys Grade School, Manila, The Philippines<br />
A  Singapore Textbook for Kindergarten <br />diene’s<br />theory<br />of<br />variation<br />
diene’s<br />theory<br />of<br />variation<br />
diene’s<br />theory<br />of<br />variation<br />
mathematical<br />big ideas<br />number sense<br />visualization<br />connections<br />Princess Elizabeth Primary School, ...
Princess Elizabeth Primary School, Singapore<br />
Princess Elizabeth Primary School, Singapore<br />
singapore<br />math<br />banhar.yeap@nie.edu.sg<br />www.askyeapbanhar.blogspot.com<br />www.math.nie.edu.sg<br />thank yo...
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Raising Critical Thinkers Through Singapore Math Keys Grade School Manila January 2010

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Keys Grade School, Manila, January 2010

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Raising Critical Thinkers Through Singapore Math Keys Grade School Manila January 2010

  1. 1. raising<br />critical thinkers<br />through<br />singapore math<br />Dr Yeap Ban Har<br />National Institute of Education<br />Nanyang Technological University<br />Singapore<br />
  2. 2. TanjongPagar PCF Kindergarten Singapore<br />international<br />perspectives<br />mathematics<br />on<br />teaching<br />
  3. 3. What counts as mathematical proficiency?<br />
  4. 4. procedural fluency<br />conceptual reasoning<br />Keys Grade School, Manila, The Philippines<br />
  5. 5. strategic competence<br />K E Y S<br />1 2 3 4<br />5 6 7 8<br />9 10 11 12<br />3948 ?<br />Keys Grade School, Manila, The Philippines<br />
  6. 6. 17<br />7<br />10<br />17 – 3 <br />adaptive reasoning<br />Keys Grade School, Manila, The Philippines<br />
  7. 7. productive disposition<br />Keys Grade School, Manila, The Philippines<br />
  8. 8. What counts as mathematical proficiency?<br />
  9. 9. mathz4kidz Learning Centre, Penang, Malaysia<br />Trends in<br />Mathematics<br />This whole shape stands for 1.<br />& Science Studies<br />What does this stand for?<br />apply<br />their understanding<br />and knowledge<br />in a variety of<br />complex situations<br />
  10. 10. Trends in<br />Mathematics<br />& ScienceStudy<br />explain<br />their reasoning<br />mathz4kidz Learning Centre, Penang, Malaysia<br />
  11. 11. What is Singapore Math?<br />
  12. 12. “an excellent vehicle to develop and improve a person’s intellectual competence”<br />Princess Elizabeth Primary School, Singapore<br />
  13. 13. mathematics<br />education<br />“<br />an excellent vehicle for the development and improvement of a person’s intellectual competence<br />”<br />Bina Bangsa School, Bandung, Indonesia<br />Ministry of Education Singapore 2006<br />
  14. 14. mathematics<br />using to develop<br />children’s<br />intelligence<br />
  15. 15. 4<br />7<br />47<br />11<br />Edgewood Elementary School, New York, USA<br />47 – 11 <br />
  16. 16. Edgewood Elementary School, New York<br />
  17. 17. Edgewood Elementary School, New York, USA<br />
  18. 18. What is Singapore Math?<br />Challenging Materials<br />
  19. 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.<br />(a) At what time did the trip start?<br />(b) What was Meiling’s average speed for the remaining 24 km of the trip in m/min?<br />(PSLE Grade 6)<br />Meiling’s average speed was 480 m/min for the last part of the trip.<br />Meiling<br />Raja<br />Raja: 1o min  4 km<br />Raja: First 12 km  30 min <br />Raja: 1o min  4 km<br />Raja: Last 24 km  60 min<br />??? min  36 km<br />Meiling: Last 24 km  50 min<br />Raja: 90 min  36 km<br />Meiling: 24000 m  50 min<br />11 10 hrs 10 10 hours  09 40 hrs<br />Raja, and hence Meiling, started the trip at 09 40.<br />Meiling: 2400 m  5 min<br />Meiling: 480 m  1 min<br />
  20. 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?<br />(TeckWhye Primary School, Grade 6)<br />Album A<br />Album B<br />Album C<br />
  21. 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?<br />(TeckWhye Primary School, Grade 6)<br />7 units  ?<br />7 units  36 x 7 = 210 + 42 = 252<br />There were 252 more stamps in Album C than Album A in the end.<br />Album A<br />Album B<br />Album C<br />468<br />13 units  444 + 24 = 468<br />1 unit  468 ÷ 13 = 36 <br />390<br />78<br />
  22. 22. What is Singapore Math?<br />Challenging Materials for Every Child<br />
  23. 23. TIMSS<br />Trends in International Maths and Science Studies<br />1995<br />2003<br />2007<br />Grade 4<br />Advanced<br />38<br />41<br />38<br />High<br />70<br />74<br />73<br />Intermediate<br />89<br />92<br />91<br />Low<br />96<br />98<br />97<br />Catholic High School (Primary)<br />
  24. 24. TIMSS<br />Trends in International Maths and Science Studies<br />Sweden<br />Median<br />U S A<br />Japan<br />Singapore<br />Grade 4<br />Advanced<br />3<br />10<br />5<br />41<br />23<br />High<br />24<br />40<br />26<br />74<br />61<br />Intermediate<br />69<br />77<br />67<br />92<br />89<br />Low<br />93<br />95<br />90<br />98<br />98<br />Elementary School in Japan<br />
  25. 25. TIMSS<br />Trends in International Maths and Science Studies<br />Average<br />Hong Kong<br />Singapore<br />Korea<br />Taiwan<br />Grade 8<br />Advanced<br />2<br />40<br />31<br />45<br />40<br />High<br />15<br />70<br />64<br />71<br />71<br />Intermediate<br />46<br />88<br />85<br />86<br />90<br />Low<br />75<br />97<br />94<br />95<br />98<br />Telok Kurau Primary School<br />
  26. 26. TIMSS 2007<br />AVERAGE<br />MALAYSIA<br />SINGAPORE<br />Grade 8<br />Advanced<br />2<br />40<br />2<br />High<br />15<br />70<br />18<br />Intermediate<br />46<br />88<br />50<br />Low<br />75<br />97<br />82<br />Northlight School, Singapore<br />
  27. 27. TIMSS<br />Trends in International Maths and Science Studies<br />Grade 4<br />Grade 8<br />Singapore<br />Advanced<br />41<br />40<br />High<br />74<br />70<br />Intermediate<br />92<br />88<br />Low<br />98<br />97<br />Catholic High School (Primary)<br />
  28. 28. TIMSS<br />Trends in International Maths and Science Studies<br />Grade 4<br />Grade 8<br />U S A<br />Advanced<br />10<br />6<br />High<br />40<br />31<br />Intermediate<br />77<br />67<br />Low<br />95<br />92<br />Catholic High School (Primary)<br />
  29. 29. TIMSS<br />Trends in International Maths and Science Studies<br />Grade 4<br />Grade 8<br />England<br />Advanced<br />16<br />8<br />High<br />48<br />35<br />Intermediate<br />79<br />69<br />Low<br />94<br />90<br />Catholic High School (Primary)<br />
  30. 30. TIMSS<br />Trends in International Maths and Science Studies<br />Grade 4<br />Grade 8<br />International<br />Advanced<br />5<br />2<br />High<br />26<br />15<br />Intermediate<br />67<br />46<br />Low<br />90<br />75<br />Catholic High School (Primary)<br />
  31. 31. Using Mathematics to Develop Intelligent Behaviors<br />
  32. 32. what are<br /> intelligent<br />behaviors?<br />
  33. 33. 1000<br />- 124<br />mathematics<br />& intelligent <br />behaviors<br />
  34. 34. 9<br />9<br />1<br />1000<br /> 999<br />- 124<br />- 124<br /> 875<br />for<br />1000<br />looking connections<br />- 124<br /> 876<br />Bina Bangsa School, Bandung, Indonesia<br />
  35. 35. to<br />ability explain<br />A Grade 6 US textbook written using the Singapore Pedagogy<br />
  36. 36. mathematics<br />& intelligent <br />behaviours<br />
  37. 37. 3<br />4<br />÷<br />3<br />=<br />3<br />x<br />4<br />3<br />4<br />=<br />
  38. 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 &quot;help&quot; the butterfly by cutting the cocoon, the butterfly will come out easily but it will never fly. Your &quot;help&quot; 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<br />
  39. 39. 11 cm<br />4 cm<br />5 cm<br />5 cm<br />to use<br />5 cm<br />ability knowledge<br />Area = (11 + 5) ÷ 2 x 4<br />
  40. 40. Teaching Every Child<br />
  41. 41. Some of us come from English-speaking homes. Some of us don’t. I speak Malay at home.<br />This is what help me learn mathematics well.…<br />Princess Elizabeth Primary School, Singapore<br />Factors That Contribute to High Achievement Level in Mathematics<br />
  42. 42. These are my friends in Primary 1. <br />We like our teacher.<br />Once, she was absent for two days. We missed her. She told she had to learn new things to teach us better.<br />teacher<br />quality<br />Princess Elizabeth Primary School, Singapore<br />National Institute of Education, Singapore<br />
  43. 43. x<br />Keys Grade School, Manila, The Philippines<br />
  44. 44. singapore<br />math<br />Photo: Keys Grade School. Manila, The Philippines<br />professional development<br />in-service<br />Photo: Hougang Primary School, Singapore<br />
  45. 45. singapore<br />math<br />parental<br />expectations<br />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. <br />In the end I had to teach her.<br />Photos: Seminar for Parents on Problem Solving<br />
  46. 46. Photos: Keys Grade School, Manila, The Philippines<br />singapore<br />math<br />Bruner’s<br />theory<br />We use concrete materials to learn mathematics.<br />Photos: Princess Elizabeth Primary School, Singapore<br />
  47. 47. singapore<br />math<br />emphasis on<br />concrete to<br />pictorial to abstract<br />representations<br />Photo: Catholic High School (Primary) Singapore<br />
  48. 48.
  49. 49. singapore<br />math<br />especially on<br />the model method<br />Photo: mathz4kidz Learning Center, Malaysia<br />
  50. 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)<br />Photo: Telok Kurau Primary School, Singapore<br />
  51. 51.
  52. 52. mathz4kidz Learning Centre, Penang, Malaysia<br />bruner’s theory<br />concrete<br />
  53. 53. mathz4kidz Learning Centre, Penang, Malaysia<br />concrete<br />experiences<br />
  54. 54. from<br />concrete<br />to<br />pictorial<br />mathz4kidz Learning Centre, Penang, Malaysia<br />
  55. 55. from<br />pictorial<br />to<br />abstract<br />All Kids Are Intelligent Series<br />
  56. 56. mathz4kidz Learning Centre, Penang, Malaysia<br />symbols<br />
  57. 57. using<br />concrete<br />materials<br />Ateneo Grade School, Manila, The Philippines<br />A Public School in Chile<br />
  58. 58. Fuchun Primary School, Singapore<br />interaction<br />Vygotsky’s Theory<br />Children Learn in Social Situations<br />
  59. 59. skemp’s<br />theory<br />conceptual<br />understanding<br />Bina Bangsa School, Semarang, Indonesia<br />
  60. 60. Keys Grade School, Manila, The Philippines<br />
  61. 61. Keys Grade School, Manila, The Philippines<br />
  62. 62. A Singapore Textbook for Kindergarten <br />diene’s<br />theory<br />of<br />variation<br />
  63. 63. diene’s<br />theory<br />of<br />variation<br />
  64. 64. diene’s<br />theory<br />of<br />variation<br />
  65. 65. mathematical<br />big ideas<br />number sense<br />visualization<br />connections<br />Princess Elizabeth Primary School, Singapore<br />
  66. 66. Princess Elizabeth Primary School, Singapore<br />
  67. 67. Princess Elizabeth Primary School, Singapore<br />
  68. 68. singapore<br />math<br />banhar.yeap@nie.edu.sg<br />www.askyeapbanhar.blogspot.com<br />www.math.nie.edu.sg<br />thank you<br />

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