Theoretical Underpinnings of Singapore Math<br />Seminar at Harvard Graduate School of Education<br />Yeap Ban-Har, Ph.D.<...
Catholic High School (Primary)<br />
introduction<br />Wellington Primary School<br />
Task<br />Lesson Study Problem <br />Wellington Primary School<br />Move 3 sticks to make 3 squares.<br />
Task<br />Move 3 sticks to make 3 squares.<br />
Task<br />Move 3 sticks to make 3 squares.<br />
Task<br />Move 3 sticks to make 2 squares.<br />
Task<br />Move 3 sticks to make 2 squares.<br />
Task<br />Move 3 sticks to make 2 squares.<br />
A Problem from Singapore Grade 6 National Test<br />Jim bought some chocolates and gave half of them to Ken. Ken bought so...
Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 s...
88 children took part in a swimming competition.  1/3 of the boys and 3/7  of the girls wore swimming goggles. Altogether ...
<ul><li>88 children took part in a swimming competition.  1/3 of the boys and 3/7  of the girls wore swimming goggles. Alt...
88<br />34<br />54<br /><ul><li>88 children took part in a swimming competition.  1/3 of the boys and 3/7  of the girls wo...
34 – 20 = 14<br />54 – 34 = 20<br />34<br />54<br />
3 x 7 = 21<br />21 girls wear goggles.<br />A Curriculum That Helps Average Students Reach High Achievement<br />
TIMSS 2007<br />Trends in International Mathematics and Science Studies<br />1995<br />2003<br />2007<br />Grade 4<br />Ad...
TIMSS 2007<br />Trends in International Mathematics and Science Studies<br />Average<br />Indonesia<br />Thailand<br />Mal...
Beliefs<br />Interest<br />Appreciation<br />Confidence<br />Perseverance<br />Monitoring of one’s own thinking<br />Self-...
Every Child Counts<br />
effective<br />mathematics<br />teaching<br />BinaBangsa School, Indonesia<br />
Primary Mathematics 1A<br />Pedagogical Principle:<br />Bruner<br />
Number Bonds<br />PCF Kindergarten TelokBlangah<br />
Number Bonds<br />PCF Kindergarten TelokBlangah<br />
Bruner<br />The concrete  pictorial  abstract approach is used to help the majority of learners to develop strong founda...
Division<br />Princess Elizabeth Primary School<br />
My Pals Are Here! Mathematics 1B<br />
Catholic High School (Primary)<br />
mathz4kidz Learning Centre, Penang, Malaysia<br />bruner’s theory<br />concrete<br />A lesson from Earlybird Kindergarten ...
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 />Professional Development in AteneoGrade School, Manila, The Philippines<br />Lesso...
Primary Mathematics (Standards Edition) 2A<br />Pictorial Before Abstract<br />
     bruner<br />Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile<br />
skemp’s<br />theory<br />conceptual<br />understanding<br />BinaBangsa School, Semarang, Indonesia<br />
Keys Grade School, Manila, The Philippines<br />
Keys Grade School, Manila, The Philippines<br />
Skemp<br />Understanding in mathematics  <br /> relational<br />  (conceptual) <br /> instrumental  <br />  (procedural)<b...
Fraction Division<br />Primary Mathematics Standards Edition Grade 6<br />
  skemp<br />Scarsdale Middle School New York<br />
Dienes<br />Dienes encouraged the use of variation in mathematics education – perceptual variability and mathematical vari...
Pedagogical Principle:<br />Dienes<br />Primary Mathematics Standards Edition Grade 1<br />
Pedagogical Principle:<br />Dienes<br />Primary Mathematics Standards Edition Grade 2<br />
1 h = 60 min<br />60 ÷ 4 = 15<br />15 x 3 = 45<br />¾  x 60 = 45<br />Primary Mathematics Standards Edition Grade 5<br />
Mathematical Variation<br />16<br />Primary Mathematics Standards Edition Grade 5<br />
16<br />Mathematical Variation<br />30<br />Primary Mathematics<br />
Mathematical Variation<br />Primary Mathematics Standards Edition Grade 2<br />
Earlybird Kindergarten  Mathematics <br />Standards Edition <br />diene’s<br />theory<br />of<br />variation<br />
diene’s<br />theory<br />of<br />variation<br />
  dienes<br />Princess Elizabeth Primary School, Singapore<br />
Emphasis on pictorial representation and systematic variation to enhance conceptual understanding<br />
Fuchun Primary School, Singapore<br />interaction<br />Vygotsky’s Theory<br />Children Learn in Social Situations<br />
conclusion<br />PCF Kindergarten PasirRis<br />
Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competence ..<br />Mini...
Patterns<br />BinaBangsa School Bandung, Indonesia<br />
Patterns<br />BinaBangsa School Bandung, Indonesia<br />
Visualization<br />Yangzheng Primary School<br />
Communication<br />PathlightSchool<br />
Primary Mathematics Syllabus 2007<br />Primary 2 <br />Wellington Primary School<br />
Balestier Hill<br />Primary School<br />Fuchun Primary School<br />Primary Mathematics Syllabus 2007<br />
Princess Elizabeth Primary School<br />
“Children are trulythe future of our nation. “<br />Irving Harris<br />
TEDS-M Elementary Teachers<br />Content Knowledge<br />TEDS-M Elementary Teachers<br />Pedagogical Content Knowledge<br />
TEDS-M Middle School Teachers<br />Content Knowledge<br />TEDS-M Middle School Teachers<br />Pedagogical Content Knowledge...
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Seminar at Harvard Graduate School of Education 15 April 2010

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Seminar at Harvard Graduate School of Education 15 April 2010

  1. 1. Theoretical Underpinnings of Singapore Math<br />Seminar at Harvard Graduate School of Education<br />Yeap Ban-Har, Ph.D.<br />National Institute of Education<br />Nanyang Technological University <br />Singapore<br />banhar.yeap@nie.edu.sg<br />
  2. 2. Catholic High School (Primary)<br />
  3. 3. introduction<br />Wellington Primary School<br />
  4. 4. Task<br />Lesson Study Problem <br />Wellington Primary School<br />Move 3 sticks to make 3 squares.<br />
  5. 5. Task<br />Move 3 sticks to make 3 squares.<br />
  6. 6. Task<br />Move 3 sticks to make 3 squares.<br />
  7. 7. Task<br />Move 3 sticks to make 2 squares.<br />
  8. 8. Task<br />Move 3 sticks to make 2 squares.<br />
  9. 9. Task<br />Move 3 sticks to make 2 squares.<br />
  10. 10. A Problem from Singapore Grade 6 National Test<br />Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. <br />Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. <br />How many sweets did Ken buy?<br />
  11. 11. Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. How many sweets did Ken buy?<br />chocolates<br />sweets<br />Assuming that both boys did not have any sweet or chocolate before they bought the chocolates and sweets.<br />12<br />Jim<br />12<br />18<br />12<br />12<br />12<br />12<br />Ken<br />3 parts  12 + 12 + 12 + 12 + 18 = 66<br />1 part  22<br />Half of the sweets Ken bought = 22 + 12 = 34<br />So Ken bought 68 sweets.`<br />
  12. 12. 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. <br /> How many girls wore swimming goggles on that day?<br />A Problem from a Singapore Classroom<br />Fairfield Methodist Primary School<br />
  13. 13. <ul><li>88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. </li></ul> How many girls wore swimming goggles on that day?<br />
  14. 14. 88<br />34<br />54<br /><ul><li>88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. </li></ul>How many girls wore swimming goggles on that day?<br />
  15. 15. 34 – 20 = 14<br />54 – 34 = 20<br />34<br />54<br />
  16. 16. 3 x 7 = 21<br />21 girls wear goggles.<br />A Curriculum That Helps Average Students Reach High Achievement<br />
  17. 17. TIMSS 2007<br />Trends in International Mathematics 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 />North Vista Primary School<br />
  18. 18. TIMSS 2007<br />Trends in International Mathematics and Science Studies<br />Average<br />Indonesia<br />Thailand<br />Malaysia<br />Singapore<br />Grade 8<br />Advanced<br />2<br />3<br />0<br />40<br />2<br />High<br />15<br />12<br />4<br />70<br />18<br />Intermediate<br />46<br />44<br />14<br />88<br />50<br />Low<br />75<br />66<br />48<br />97<br />82<br />Method Used in Singapore Textbooks<br />
  19. 19. Beliefs<br />Interest<br />Appreciation<br />Confidence<br />Perseverance<br />Monitoring of one’s own thinking<br />Self-regulation of learning<br />Attitudes<br />Metacognition<br />Numerical calculation<br />Algebraic manipulation<br />Spatial visualization<br />Data analysis<br />Measurement<br />Use of mathematical tools<br />Estimation<br />Mathematical Problem Solving<br />Reasoning, communication & connections<br />Thinking skills & heuristics<br />Application & modelling<br />Skills<br />Processes<br />Concepts<br />Numerical<br />Algebraic<br />Geometrical<br />Statistical<br />Probabilistic<br />Analytical<br />Mathematics Curriculum Framework<br />
  20. 20. Every Child Counts<br />
  21. 21. effective<br />mathematics<br />teaching<br />BinaBangsa School, Indonesia<br />
  22. 22. Primary Mathematics 1A<br />Pedagogical Principle:<br />Bruner<br />
  23. 23. Number Bonds<br />PCF Kindergarten TelokBlangah<br />
  24. 24. Number Bonds<br />PCF Kindergarten TelokBlangah<br />
  25. 25. Bruner<br />The concrete  pictorial  abstract approach is used to help the majority of learners to develop strong foundation in mathematics. <br />Division<br />National Institute of Education<br />
  26. 26. Division<br />Princess Elizabeth Primary School<br />
  27. 27. My Pals Are Here! Mathematics 1B<br />
  28. 28. Catholic High School (Primary)<br />
  29. 29. mathz4kidz Learning Centre, Penang, Malaysia<br />bruner’s theory<br />concrete<br />A lesson from Earlybird Kindergarten Mathematics<br />
  30. 30. mathz4kidz Learning Centre, Penang, Malaysia<br />concrete<br />experiences<br />
  31. 31. from<br />concrete<br />to<br />pictorial<br />mathz4kidz Learning Centre, Penang, Malaysia<br />
  32. 32. from<br />pictorial<br />to<br />abstract<br />All Kids Are Intelligent Series<br />
  33. 33. mathz4kidz Learning Centre, Penang, Malaysia<br />symbols<br />
  34. 34. using<br />concrete<br />materials<br />Professional Development in AteneoGrade School, Manila, The Philippines<br />Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile<br />
  35. 35. Primary Mathematics (Standards Edition) 2A<br />Pictorial Before Abstract<br />
  36. 36. bruner<br />Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile<br />
  37. 37. skemp’s<br />theory<br />conceptual<br />understanding<br />BinaBangsa School, Semarang, Indonesia<br />
  38. 38. Keys Grade School, Manila, The Philippines<br />
  39. 39. Keys Grade School, Manila, The Philippines<br />
  40. 40. Skemp<br />Understanding in mathematics <br /> relational<br /> (conceptual) <br /> instrumental <br /> (procedural)<br /> conventional <br />Teaching for conceptual understanding is given emphasis in Singapore Math.<br />Pedagogical Principle:<br />Skemp<br />Primary Mathematics Standards Edition Grade 6<br />
  41. 41. Fraction Division<br />Primary Mathematics Standards Edition Grade 6<br />
  42. 42. skemp<br />Scarsdale Middle School New York<br />
  43. 43. Dienes<br />Dienes encouraged the use of variation in mathematics education – perceptual variability and mathematical variability. <br />Pedagogical Principle:<br />Dienes<br />Primary Mathematics Standards Edition <br />Primary Mathematics Standards Edition Grade 1<br />
  44. 44. Pedagogical Principle:<br />Dienes<br />Primary Mathematics Standards Edition Grade 1<br />
  45. 45. Pedagogical Principle:<br />Dienes<br />Primary Mathematics Standards Edition Grade 2<br />
  46. 46. 1 h = 60 min<br />60 ÷ 4 = 15<br />15 x 3 = 45<br />¾ x 60 = 45<br />Primary Mathematics Standards Edition Grade 5<br />
  47. 47. Mathematical Variation<br />16<br />Primary Mathematics Standards Edition Grade 5<br />
  48. 48. 16<br />Mathematical Variation<br />30<br />Primary Mathematics<br />
  49. 49. Mathematical Variation<br />Primary Mathematics Standards Edition Grade 2<br />
  50. 50. Earlybird Kindergarten Mathematics <br />Standards Edition <br />diene’s<br />theory<br />of<br />variation<br />
  51. 51. diene’s<br />theory<br />of<br />variation<br />
  52. 52. dienes<br />Princess Elizabeth Primary School, Singapore<br />
  53. 53. Emphasis on pictorial representation and systematic variation to enhance conceptual understanding<br />
  54. 54. Fuchun Primary School, Singapore<br />interaction<br />Vygotsky’s Theory<br />Children Learn in Social Situations<br />
  55. 55. conclusion<br />PCF Kindergarten PasirRis<br />
  56. 56. Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competence ..<br />Ministry of Education 2006<br />DaQiao Primary School<br />
  57. 57. Patterns<br />BinaBangsa School Bandung, Indonesia<br />
  58. 58. Patterns<br />BinaBangsa School Bandung, Indonesia<br />
  59. 59. Visualization<br />Yangzheng Primary School<br />
  60. 60. Communication<br />PathlightSchool<br />
  61. 61. Primary Mathematics Syllabus 2007<br />Primary 2 <br />Wellington Primary School<br />
  62. 62. Balestier Hill<br />Primary School<br />Fuchun Primary School<br />Primary Mathematics Syllabus 2007<br />
  63. 63. Princess Elizabeth Primary School<br />
  64. 64. “Children are trulythe future of our nation. “<br />Irving Harris<br />
  65. 65. TEDS-M Elementary Teachers<br />Content Knowledge<br />TEDS-M Elementary Teachers<br />Pedagogical Content Knowledge<br />
  66. 66. TEDS-M Middle School Teachers<br />Content Knowledge<br />TEDS-M Middle School Teachers<br />Pedagogical Content Knowledge<br />

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