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Teaching Mathematics Effectively for the 21 st Century

Teaching Mathematics Effectively for the 21 st Century. Yeap Ban-Har, Ph.D. National Institute of Education Nanyang Technological University Singapore banhar.yeap@nie.edu.sg. Catholic High School (Primary). The MPK Lecture

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Teaching Mathematics Effectively for the 21 st Century

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  1. Teaching Mathematics Effectively for the 21st Century Yeap Ban-Har, Ph.D. National Institute of Education Nanyang Technological University Singapore banhar.yeap@nie.edu.sg

  2. Catholic High School (Primary) The MPK Lecture Teaching Mathematics Effectively to Engage Students for the 21st Century

  3. introduction Wellington Primary School

  4. Task Move 3 sticks to make 2 squares.

  5. Task Move 3 sticks to make 2 squares.

  6. Task Move 3 sticks to make 2 squares.

  7. Task Move 3 sticks to make 3 squares.

  8. Task Move 3 sticks to make 3 squares.

  9. Task Move 3 sticks to make 3 squares.

  10. A Problem from Singapore Classroom • 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. How many girls wore swimming goggles on that day? Fairfield Methodist Primary School 88 anak mengikuti perlombaan berenang. 1/3 anak laki-laki dan 3/7 anak perempuan memakai kacamata renang. Total ada 34 anak yang memakai kacamata renang. Berapa jumlah anak perempuan yang memakai kacamata renang pada hari itu?

  11. A Problem from Singapore Classroom • 88 anak mengikuti perlombaan berenang. 1/3 anak laki-laki dan 3/7 anak perempuan memakai kacamata renang. Total ada 34 anak yang memakai kacamata renang. Berapa jumlah anak perempuan yang memakai kacamata renang pada hari itu? Fairfield Methodist Primary School

  12. 88 anak mengikuti perlombaan berenang.1/3 anak laki-laki dan 3/7 anak perempuan memakai kacamata renang.Total ada 34 anak yang memakai kacamata renang. Berapa jumlah anak perempuan yang memakai kacamata renang pada hari itu? • 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. How many girls wore swimming goggles on that day?

  13. 88 anakmengikutiperlombaanberenang. 1/3 anaklaki-lakidan 3/7 anakperempuan memakaikacamatarenang.Total ada 34 anak yang memakaikacamatarenang. Berapajumlahanakperempuan yang memakaikacamatarenangpadahariitu? 88 34 54 • 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. How many girls wore swimming goggles on that day?

  14. 34 – 20 = 14 54 – 34 = 20 34 54

  15. 3 x 7 = 21 21 girls wear goggles. Kurikulum yang membantumurid-murid dengankemampuanbiasa / rata-rata mencapaiprestasi yang tinggi. 21 anak perempuan memakai kacamata renang A Curriculum That Helps Average Students Reach High Achievement

  16. Beliefs Interest Appreciation Confidence Perseverance Monitoring of one’s own thinking Self-regulation of learning Attitudes Metacognition Numerical calculation Algebraic manipulation Spatial visualization Data analysis Measurement Use of mathematical tools Estimation Mathematical Problem Solving Reasoning, communication & connections Thinking skills & heuristics Application & modelling Skills Processes Concepts Numerical Algebraic Geometrical Statistical Probabilistic Analytical Mathematics Curriculum Framework

  17. TIMSS Trends in International Maths and Science Studies 1995 2003 2007 Grade 4 Advanced 38 38 41 High 70 73 74 Intermediate 89 91 92 Low 96 97 98 Catholic High School (Primary)

  18. TIMSS Trends in International Maths and Science Studies Sweden Median U S A Japan Singapore Grade 4 Advanced 3 5 10 23 41 High 24 26 40 61 74 Intermediate 69 67 77 89 92 Low 93 90 95 98 98 Elementary School in Japan

  19. TIMSS Trends in International Maths and Science Studies Average Hong Kong Singapore Korea Taiwan Grade 8 Advanced 2 31 40 40 45 High 15 64 70 71 71 Intermediate 46 85 88 90 86 Low 75 94 97 98 95 Telok Kurau Primary School

  20. TIMSS Trends in International Maths and Science Studies Average Indonesia Thailand Malaysia Singapore Grade 8 Advanced 2 0 3 2 40 High 15 4 12 18 70 Intermediate 46 14 44 50 88 Low 75 48 66 82 97 Effective Methods in Teaching Mathematics

  21. effective mathematics teaching Bina Bangsa School, Indonesia

  22. Primary Mathematics 1A Pedagogical Principle: Bruner PrinsipPedagogi: Bruner

  23. Number Bonds PCF Kindergarten Telok Blangah

  24. Number Bonds PCF Kindergarten Telok Blangah

  25. Bruner Division Pembagian The concrete  pictorial  abstract approach is used to help the majority of learners to develop strong foundation in mathematics. National Institute of Education Pendekatan kongkret  gambar  abstrak, dipergunakan untuk menolong sebagian besar pelajar untuk membangun dasar matematika yang kuat.

  26. Division Pembagian My Pals Are Here! Mathematics 1B

  27. Division Pembagian Photo: Princess Elizabeth Primary School

  28. Division Pembagian My Pals Are Here! Mathematics 1B

  29. summary Elementary School in Chile

  30. Skemp Understanding in mathematics relational (conceptual) instrumental (procedural) conventional Teaching for conceptual understanding is given emphasis in Singapore Math. Pedagogical Principle: Skemp PrinsipPedagogi: Skemp Primary Mathematics Standards Edition Grade 6

  31. Skemp Matematika Singapura menitik-beratkan pengajaran pada pemahaman konsep. Pedagogical Principle: Skemp PrinsipPedagogi: Skemp Primary Mathematics Standards Edition Grade 6

  32. Fraction Division PembagianPecahan Primary Mathematics Standards Edition Grade 6

  33. 3 kue dibagi secara rata kepada beberapa anak. Setiap anak mendapatkan ¾ bagian kue. Berapa anak yang mendapatkan ¾ bagian kue? JikaAndamemotong 1 bagianpenuhmenjadi ¾ bagian, Andamendapatkan 1 dan 1/3 tigaseperempat. Jadi, didalam 3 bagianpenuhada 3 x 1 1/3 atau 3 x 4/3. Primary Mathematics Standards Edition Grade 6

  34. summary Scarsdale Middle School New York

  35. 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 "help" the butterfly by cutting the cocoon, the butterfly will come out easily but it will never fly. Your "help" 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

  36. Dienes Dienes encouraged the use of variation in mathematics education – perceptual variation and mathematical variation. Dienes menganjurkan penggunaan variasi dalam pengajaran matematika - variasi persepsi dan variasi matematika. Pedagogical Principle: Dienes PrinsipPedagogi: Dienes Primary Mathematics Standards Edition

  37. Pedagogical Principle: Dienes PrinsipPedagogi: Dienes

  38. Pedagogical Principle: Dienes PrinsipPedagogi: Dienes

  39. Jane berlatih piano selama ¾ jam per hari. Berapa menit dia berlatih setiap harinya? 1 jam = 60 menit 60 ÷ 4 = 15 15 x 3 = 45 ¾ x 60 = 45

  40. Mathematical Variation VariasidarisegiMatematika Di sebuah kelas, 2/5 muridnya memakai kacamata. a) Berapa bagiankah murid yang tidak memakai kacamata? b) Jika 16 murid memakai kacamata, berapa jumlah murid seluruhnya? 16

  41. Di sebuah kelas, 2/5 muridnya memakai kacamata. a) Berapa bagiankah murid yang tidak memakai kacamata? b) Jika 16 murid memakai kacamata, berapa jumlah murid seluruhnya? 16 Nicole membeli 30 butir telur. Dia memakai 2/3 telur yang dibeli untuk memanggang kue. Berapa telur yang tersisa? Mathematical Variation VariasidarisegiMatematika 30

  42. effective teaching Keys Grade School , Manila

  43. Pictorial Before Abstract Gambar sebelum abstrak

  44. Perceptual Variation Variasi dari segi persepsi Primary Mathematics Standards Edition

  45. Mathematical Variation Variasi dari segi matematika

  46. Penekanan pada pemaparan visual dan variasi sistematis memperkuat pemahaman konsep Emphasis on pictorial representation and systematic variation to enhance conceptual understanding

  47. TIMSS Trends in International Maths and Science Studies Grade 4 Grade 8 Singapore Advanced 41 40 High 74 70 Intermediate 92 88 Low 98 97 Catholic High School (Primary)

  48. TIMSS Trends in International Maths and Science Studies Grade 4 Grade 8 U S A Advanced 10 6 High 40 31 Intermediate 77 67 Low 95 92 Catholic High School (Primary)

  49. TIMSS Trends in International Maths and Science Studies Grade 4 Grade 8 England Advanced 16 8 High 48 35 Intermediate 79 69 Low 94 90 Catholic High School (Primary)

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