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Teaching Mathematics Effectively for the 21 st Century Yeap Ban-Har, Ph.D. National Institute of Education Nanyang Technological University Singapore

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Presentasi berjudul: "Teaching Mathematics Effectively for the 21 st Century Yeap Ban-Har, Ph.D. National Institute of Education Nanyang Technological University Singapore"— Transcript presentasi:

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

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

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 • 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? A Problem from Singapore Classroom 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 • 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? A Problem from Singapore Classroom Fairfield Methodist Primary School

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. How many girls wore swimming goggles on that day? 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?

13 • 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? 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?

14 34 54 – 34 = – 20 = 14 54

15 3 x 7 = girls wear goggles. A Curriculum That Helps Average Students Reach High Achievement 21 anak perempuan memakai kacamata renang Kurikulum yang membantu murid-murid dengan kemampuan biasa / rata-rata mencapai prestasi yang tinggi.

16

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

18 Advanced Intermediate Low High Grade 4 Catholic High School (Primary) TIMSS Trends in International Maths and Science Studies

19 Advanced Intermediate Low High Sweden Median U S A Grade 4 Elementary School in Japan TIMSS Trends in International Maths and Science Studies Japan Singapore

20 Advanced Intermediate Low High Average Hong Kong Singapore Grade 8 Telok Kurau Primary School TIMSS Trends in International Maths and Science Studies Korea Taiwan

21 Advanced Intermediate Low High Average Indonesia Thailand Grade 8 Effective Methods in Teaching Mathematics TIMSS Trends in International Maths and Science Studies Malaysia Singapore

22 mathematics teaching effective Bina Bangsa School, Indonesia

23 Pedagogical Principle: Bruner Prinsip Pedagogi: Bruner Primary Mathematics 1A

24 Number Bonds PCF Kindergarten Telok Blangah

25 Number Bonds PCF Kindergarten Telok Blangah

26 Bruner 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. Division Pembagian

27 My Pals Are Here! Mathematics 1B Division Pembagian

28 Photo: Princess Elizabeth Primary School Division Pembagian

29 My Pals Are Here! Mathematics 1B Division Pembagian

30 summary Elementary School in Chile

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

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

33 Fraction Division Pembagian Pecahan Primary Mathematics Standards Edition Grade 6

34 3 kue dibagi secara rata kepada beberapa anak. Setiap anak mendapatkan ¾ bagian kue. Berapa anak yang mendapatkan ¾ bagian kue? Jika Anda memotong 1 bagian penuh menjadi ¾ bagian, Anda mendapatkan 1 dan 1/3 tiga seperempat. Jadi, di dalam 3 bagian penuh ada 3 x 1 1/3 atau 3 x 4/3.

35 summary Scarsdale Middle School New York

36 How to make sure the butterfly cannot fly How 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 Guan Head, Civil Service

37 Primary Mathematics Standards Edition Pedagogical Principle: Dienes Prinsip Pedagogi: Dienes 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.

38 Pedagogical Principle: Dienes Prinsip Pedagogi: Dienes

39 Pedagogical Principle: Dienes Prinsip Pedagogi: Dienes

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

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 Mathematical Variation Variasi dari segi Matematika

42 Nicole membeli 30 butir telur. Dia memakai 2/3 telur yang dibeli untuk memanggang kue. Berapa telur yang tersisa? 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? Mathematical Variation Variasi dari segi Matematika

43 effective Keys Grade School, Manila teaching

44 Pictorial Before Abstract Gambar sebelum abstrak

45 Primary Mathematics Standards Edition Perceptual Variation Variasi dari segi persepsi

46 Mathematical Variation Variasi dari segi matematika

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

48 Advanced Intermediate Low High Grade Singapore Catholic High School (Primary) TIMSS Trends in International Maths and Science Studies Grade

49 Advanced Intermediate Low High Grade U S A Catholic High School (Primary) TIMSS Trends in International Maths and Science Studies Grade

50 Advanced Intermediate Low High Grade England Catholic High School (Primary) TIMSS Trends in International Maths and Science Studies Grade

51 Advanced Intermediate Low High Grade International Catholic High School (Primary) TIMSS Trends in International Maths and Science Studies Grade

52 conclusion PCF Kindergarten Pasir Ris

53 Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competence.. Ministry of Education 2006 Fuchun Primary School Matematika adalah kendaraan / alat yang hebat untuk membangun dan memperbaiki kompetensi dan intelektual seseorang …

54 Bina Bangsa School Bandung Patterns

55 Bina Bangsa School Bandung

56 SD Negeri in Palembang Visualization

57 Teacher Training for LEAP Programme for Public School Teachers in Manila Visualization

58 mathz4kidz Learning Centre in Malaysia Communication

59 Pathlight School Communication

60 Primary 2 Wellington Primary School Primary Mathematics Syllabus 2007

61 Balestier Hill Primary School Fuchun Primary School Primary Mathematics Syllabus 2007

62 Princess Elizabeth Primary School

63 “Children are truly the future of our nation. “ Irving Harris


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