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- 1. MahasarakhamRajabhat University<br />Transforming The Mathematics Classroom<br />Dr Yeap Ban Har<br />Principal<br />Marshall Cavendish Institute<br />Singapore<br />Director for Curriculum & Professional Development<br />Pathlight School<br />Singapore<br />12 – 13 August 2010<br />Princess Elizabeth Primary School<br />CHIJ Our Lady of Good Counsel<br />Day 2<br />Catholic High School (Primary)<br />Keys Grade School, Manila<br />
- 2. effective<br />mathematics<br />teaching<br />learning theories<br />BinaBangsa School, Indonesia<br />
- 3. Bruner<br />
- 4. 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, Singapore<br />
- 5.
- 6.
- 7. Division<br />Princess Elizabeth Primary School, Singapore<br />
- 8. mathz4kidz Learning Centre, Penang, Malaysia<br />bruner’s theory<br />concrete<br />A lesson from Earlybird Kindergarten Mathematics<br />
- 9. mathz4kidz Learning Centre, Penang, Malaysia<br />concrete<br />experiences<br />
- 10. mathz4kidz Learning Centre, Penang, Malaysia<br />from<br />concrete<br />to<br />pictorial<br />
- 11. from<br />pictorial<br />to<br />abstract<br />All Kids Are Intelligent Series<br />
- 12. mathz4kidz Learning Centre, Penang, Malaysia<br />symbols<br />
- 13. 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 />
- 14. Multiplication<br />Catholic High School (Primary), Singapore<br />
- 15. Primary Mathematics (Standards Edition) 2A<br />Pictorial Before Abstract<br />
- 16. bruner<br />Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile<br />
- 17. skemp’s<br />theory<br />conceptual<br />understanding<br />BinaBangsa School, Semarang, Indonesia<br />
- 18. Keys Grade School, Manila, The Philippines<br />
- 19. Keys Grade School, Manila, The Philippines<br />
- 20. 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 />
- 21. skemp<br />Scarsdale Middle School, New York<br />
- 22. Spiral Approach<br />
- 23. Spiral<br />Spiral Within Grade<br />Grade 2<br />Lesson 1 347 + 129<br />Lesson 2 182 + 93<br />Lesson 3 278 + 86<br />Spiral Between Grade<br />Grade 1 Adding up to 100<br />Grade 2 Adding up to 1000<br />Grade 3 Adding up to 10000<br />
- 24. Spiral<br />Spiral Between Grade<br />Grade 2 Add 1/5 and 2/5<br />Grade 3 Add 1/5 and 1/10<br />Is adding 1/5 and 1/10 the same as adding 1/5 and 3/10?<br />Grade 4 Add 3/5 and 4/5<br />Add 5/6 and 1/3<br />Grade 5 Add 2/5 and 1/4<br />Add 4/5 and 3/4 <br />Add 1 ¾ and 2 ½ <br />
- 25. Spiral Within and Between Grades<br />
- 26.
- 27.
- 28. focus on<br />visualization<br />bar model method<br />Wellington Primary School, Singapore<br />
- 29. 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 />
- 30. mathematics<br />education<br />“<br />an excellent vehicle for the development and improvement of a person’s intellectual competence<br />”<br />Wellington Primary School, Singapore<br />Ministry of Education Singapore 2006<br />
- 31. Move 3 sticks to get two squares.<br />
- 32. Move 3 sticks to get two squares.<br />
- 33. Wellington Primary School, Singapore<br />
- 34. Wellington Primary School, Singapore<br />
- 35. Wellington Primary School, Singapore<br />
- 36. Wellington Primary School, Singapore<br />
- 37. Wellington Primary School, Singapore<br />
- 38. Wellington Primary School, Singapore<br />
- 39. “…development and improvement of a person’s intellectual competencies...” such as visualization <br />Singapore Ministry of Education 2006<br /> <br />
- 40. Primary Mathematics Standards Edition <br />
- 41. model method <br />in kindergarten <br />and early grades<br />
- 42. Ali has 3 sweets. <br />Billy has 5 sweets.<br />How many sweets do they have altogether?<br />
- 43.
- 44.
- 45. model method <br />in <br />upper grades<br />
- 46. Cheryl has $20 less than David.<br />Cheryl and David have $148 altogether,<br />Find the amount of money Cheryl has.<br />Cheryl<br />$148<br />20<br />David<br />
- 47. Cheryl has $20 less than David.<br />Cheryl and David have $148 altogether,<br />Find the amount of money Cheryl has.<br />Cheryl<br />$148 - $20<br />= $128<br />20<br />David<br />$128 ÷ 2 = $64<br />Cheryl has $64.<br />How about David? $84<br />
- 48. Cheryl has $20 less than David.<br />Cheryl and David have $148 altogether,<br />Find the amount of money Cheryl has.<br />Cheryl<br />$148<br />20<br />David<br />
- 49. Cheryl has $20 less than David.<br />Cheryl and David have $148 altogether,<br />Find the amount of money Cheryl has.<br />20<br />Cheryl<br />$148 + $20 = $168<br />20<br />David<br />$168 ÷ 2 = $84<br />David has $84.<br />Cheryl has $64.<br />
- 50.
- 51.
- 52.
- 53. At first Shop A had 156 kg of rice and Shop B had 72 kg of rice. After each shop sold the same quantity of rice, the amount of rice that Shop A had was 4 times that of Shop B. How many kilograms of rice did Shop A sell? <br />156 kg<br />A<br />B<br />72 kg<br />
- 54. At first Shop A had 156 kg of rice and Shop B had 72 kg of rice. After each shop sold the same quantity of rice, the amount of rice that Shop A had was 4 times that of Shop B. How many kilograms of rice did Shop A sell? <br />3 units = 156 kg – 72 kg = 84 kg<br />1 unit = 28 kg<br />Each shop sold 64 kg of rice.<br />156 kg<br />A<br />28<br />B<br />72 kg<br />
- 55. Siti packs her clothes into a suitcase and it weighs 29 kg. Rahim packs his clothes into an identical suitcase and it weighs 11 kg. Siti’s clothes are three times as heavy as Rahim’s clothes. <br />What is the mass of Rahim’s clothes?<br />What is the mass of the suitcase?<br />29 kg<br />Siti<br />Rahim<br />11 kg<br />
- 56. Siti packs her clothes into a suitcase and it weighs 29 kg. Rahim packs his clothes into an identical suitcase and it weighs 11 kg. Siti’s clothes are three times as heavy as Rahim’s clothes. <br />What is the mass of Rahim’s clothes?<br />What is the mass of the suitcase?<br />29 kg<br />11 kg<br />18 kg<br />Siti<br />2 units = 18 kg<br />1 unit = 9 kg<br />Rahim<br />Rahim’s clothes is 9 kg.<br />The suitcase is 2 kg.<br />11 kg<br />We can also find the mass of Siti’s clothes (27 kg) if required.<br />
- 57. Siti packs her clothes into a suitcase and it weighs 29 kg. Rahim packs his clothes into an identical suitcase and it weighs 11 kg. Siti’s clothes are three times as heavy as Rahim’s clothes. <br />What is the mass of Rahim’s clothes?<br />What is the mass of the suitcase?<br />x + y = 11<br />x + 3y = 29<br />x<br />y<br />y<br />y<br />Siti<br />2y = 29 – 11 = 18<br />x<br />y<br />Rahim<br />y = 18 ÷ 2 = 9<br />
- 58.
- 59.
- 60. engaging<br />pedagogies<br />bar model method<br />RajabhatMahasarakham University, Thailand<br />
- 61. Start with any number of beans.<br />Take turns to remove beans from the table.<br />Either take one or two beans.<br />The one who take the last one or two beans wins the game!<br />
- 62. How many npn-congruent quadrilaterals of area 5 square units can be drawn on the geo-paper? The vertices must be on the dots.<br />RajabhatMahasarakham University, Thailand<br />
- 63. RajabhatMahasarakham University, Thailand<br />
- 64. RajabhatMahasarakham University, Thailand<br />
- 65. RajabhatMahasarakham University, Thailand<br />
- 66. RajabhatMahasarakham University, Thailand<br />
- 67. RajabhatMahasarakham University, Thailand<br />
- 68. RajabhatMahasarakham University, Thailand<br />
- 69. RajabhatMahasarakham University, Thailand<br />
- 70. RajabhatMahasarakham University, Thailand<br />
- 71. RajabhatMahasarakham University, Thailand<br />
- 72. RajabhatMahasarakham University, Thailand<br />
- 73. RajabhatMahasarakham University, Thailand<br />
- 74.
- 75. RajabhatMahasarakham University, Thailand<br />

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