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Spiral Approach to Teaching Mathematics The presentation slides are available at  www.mathz4kidz.com   Dr Yeap Ban Har Nat...
Singapore Education System
About Singapore Education System <ul><li>The vision of Ministry of Education is  Moulding the Future of Our Nation  . </li...
About Singapore Education Singapore <ul><li>It focuses on developing  high-quality workforce  as human resource is the onl...
About Singapore Education Singapore <ul><li>Teacher training  to coach teachers to bring textbooks to life are conducted b...
Education System in Singapore <ul><li>Primary School  </li></ul><ul><li>6 Years </li></ul><ul><li>National Test: PSLE </li...
Mathematics Curriculum  in Singapore
 
The Singapore mathematics curriculum states that “an emphasis on mathematics education will ensure that we have an increas...
The rationale of teaching mathematics is that it is “a  good vehicle  for the development and improvement of a person’s  i...
Mathematics Curriculum in Singapore New Syllabus Mathematics is used for Secondary 1 to Secondary 4. New Syllabus Addition...
Problem-Solving Curriculum
TEACHING THROUGH PROBLEM SOLVING <ul><li>Example from NSM Textbooks </li></ul>
Activity Draw a 4-sided polygon. Cut it into triangles. How many triangles can you get?
 
WHAT IS PROBLEM SOLVING? <ul><li>Example from National Test in Singapore </li></ul>
<ul><li>  National Test Grade 10 </li></ul><ul><li>A fly, F, starts at a point with position vector  ( i  + 12 j ) cm and ...
(1, 12) (4, 14) (7, 16) (1+3t, 12+2t) At time t, the fly is at (1+3t, 12+2t)  And the spider is at (85-5t, k+5t)  Given th...
Spiral Curriculum
 
 
 
 
TEACHING AS EXTENDING STUDENTS’ KNOWLEDGE (PIAGET) <ul><li>Example from NSM Textbooks </li></ul>
 
Spiral Curriculum
Spiral Approach <ul><li>Primary 6 </li></ul><ul><ul><li>Writing expressions in one variable </li></ul></ul><ul><li>Seconda...
Spiral Approach <ul><li>Secondary 2 </li></ul><ul><ul><li>Factorisation  </li></ul></ul><ul><ul><ul><li>a 2 x 2  – b 2 y 2...
Meaningful Learning
Grade 8 Lesson on Volume of Pyramid <ul><li>A class in  Semarang, Indonesia doing a lesson from NSM 2 </li></ul>
TEACHING AS DEVELOPING CONCEPTUAL UNDERSTANDING (SKEMP) <ul><li>Example from NSM Textbooks </li></ul>
21st Century Curriculum
WHY STUDENTS LEARN MATHEMATICS? <ul><li>Example from NSM Textbooks </li></ul>
Visualization
Modelling
Connection
 
Communication
Outcomes
Learning Outcomes:  Achievement & Attitude
HOW WELL HAVE THE STUDENTS LEARN? <ul><li>Findings from TIMSS </li></ul>
International Benchmarks
Advanced Intermediate Low High 2 40 31 15 70 64 46 88 85 75 97 94 Grade 8 Telok Kurau Primary School TIMSS Trends in Inter...
Advanced Intermediate Low High 2 3 0 15 12 4 46 44 14 75 66 48 Grade 8 Effective Methods in Teaching Mathematics TIMSS Tre...
 
 
Advanced Intermediate Low High 41 74 92 98 Singapore Catholic High School (Primary) TIMSS Trends in International Maths an...
Advanced Intermediate Low High 10 40 77 95 U S A Catholic High School (Primary) TIMSS Trends in International Maths and Sc...
Advanced Intermediate Low High 16 48 79 94 England Catholic High School (Primary) TIMSS Trends in International Maths and ...
Advanced Intermediate Low High 5 26 67 90 International Catholic High School (Primary) TIMSS Trends in International Maths...
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Spiral Approach For Mathematics Teaching Manila Jan2010

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Spiral Approach for Mathematics Teaching (High School)

Manila, January 2010

Published in: Education

Spiral Approach For Mathematics Teaching Manila Jan2010

  1. 1. Spiral Approach to Teaching Mathematics The presentation slides are available at www.mathz4kidz.com Dr Yeap Ban Har National Institute of Education Nanyang Technological University Singapore [email_address]
  2. 2. Singapore Education System
  3. 3. About Singapore Education System <ul><li>The vision of Ministry of Education is Moulding the Future of Our Nation . </li></ul><ul><li>It focuses on academic as well as non-academic aspects of the students’ education. </li></ul>
  4. 4. About Singapore Education Singapore <ul><li>It focuses on developing high-quality workforce as human resource is the only resource in Singapore. </li></ul><ul><li>Teaching resources including textbooks are prepared to facilitate school programmes that can achieve this goal. </li></ul>
  5. 5. About Singapore Education Singapore <ul><li>Teacher training to coach teachers to bring textbooks to life are conducted by NIE for pre-service and in-service teachers. </li></ul><ul><li>University graduates in mathematics and engineering undergo one-year training before they become mathematics teachers in schools where they also teach another subject. </li></ul>
  6. 6. Education System in Singapore <ul><li>Primary School </li></ul><ul><li>6 Years </li></ul><ul><li>National Test: PSLE </li></ul><ul><li>Secondary School </li></ul><ul><li>4 or 5 Years </li></ul><ul><li>National Test: GCE O Level </li></ul><ul><li>Junior College </li></ul><ul><li>2 or 3 Years </li></ul><ul><li>National Test: GCE A Level </li></ul><ul><li>We have Independent, Autonomous, Government-Aided and Government Schools. </li></ul>We also have specialized schools like sports school, school for the arts, science and technology school, mathematics and science high school as well as two schools for struggling students. Some students go polytechnics after secondary school.
  7. 7. Mathematics Curriculum in Singapore
  8. 9. The Singapore mathematics curriculum states that “an emphasis on mathematics education will ensure that we have an increasingly competitive workforce to meet the challenges of the 21st century”
  9. 10. The rationale of teaching mathematics is that it is “a good vehicle for the development and improvement of a person’s intellectual competence ”.
  10. 11. Mathematics Curriculum in Singapore New Syllabus Mathematics is used for Secondary 1 to Secondary 4. New Syllabus Additional Mathematics is used by students good in mathematics in Secondary 3 and Secondary 4.
  11. 12. Problem-Solving Curriculum
  12. 13. TEACHING THROUGH PROBLEM SOLVING <ul><li>Example from NSM Textbooks </li></ul>
  13. 14. Activity Draw a 4-sided polygon. Cut it into triangles. How many triangles can you get?
  14. 16. WHAT IS PROBLEM SOLVING? <ul><li>Example from National Test in Singapore </li></ul>
  15. 17. <ul><li>  National Test Grade 10 </li></ul><ul><li>A fly, F, starts at a point with position vector ( i + 12 j ) cm and crawls across the surface with a velocity of (3 i + 2 j ) cm s -1 . At the instant the fly starts crawling, a spider, S, at the point with position vector (85 i + 5 j ) cm, sets off across the surface with a velocity of (-5 i + k j ) cm s -1 , where k is a constant. Given that the spider catches the fly, calculate the value of k. </li></ul><ul><li>  </li></ul>
  16. 18. (1, 12) (4, 14) (7, 16) (1+3t, 12+2t) At time t, the fly is at (1+3t, 12+2t) And the spider is at (85-5t, k+5t) Given that the fly caught the spider: 1 + 3t = 85 – 5t and 12 + 2t = k + 5t 8t = 84 or t = 10.5 k = 12 – 3 (10.5) = …
  17. 19. Spiral Curriculum
  18. 24. TEACHING AS EXTENDING STUDENTS’ KNOWLEDGE (PIAGET) <ul><li>Example from NSM Textbooks </li></ul>
  19. 26. Spiral Curriculum
  20. 27. Spiral Approach <ul><li>Primary 6 </li></ul><ul><ul><li>Writing expressions in one variable </li></ul></ul><ul><li>Secondary 1 </li></ul><ul><ul><li>Writing expressions in more than one variables </li></ul></ul><ul><ul><li>Factorisation </li></ul></ul><ul><ul><ul><li>ax + by </li></ul></ul></ul><ul><ul><ul><li>ax + bx + kay + kby </li></ul></ul></ul>
  21. 28. Spiral Approach <ul><li>Secondary 2 </li></ul><ul><ul><li>Factorisation </li></ul></ul><ul><ul><ul><li>a 2 x 2 – b 2 y 2 </li></ul></ul></ul><ul><ul><ul><li>a 2 + 2ab + b 2 </li></ul></ul></ul><ul><ul><ul><li>ax 2 + bx + c </li></ul></ul></ul><ul><li>Secondary 3 – 4 </li></ul><ul><ul><li>Factorisation </li></ul></ul><ul><ul><ul><li>cubic expressions* </li></ul></ul></ul><ul><ul><ul><li>other expressions* (e.g. trigonometric expressions reducible to quadratic or cubic expressions) </li></ul></ul></ul>
  22. 29. Meaningful Learning
  23. 30. Grade 8 Lesson on Volume of Pyramid <ul><li>A class in Semarang, Indonesia doing a lesson from NSM 2 </li></ul>
  24. 31. TEACHING AS DEVELOPING CONCEPTUAL UNDERSTANDING (SKEMP) <ul><li>Example from NSM Textbooks </li></ul>
  25. 32. 21st Century Curriculum
  26. 33. WHY STUDENTS LEARN MATHEMATICS? <ul><li>Example from NSM Textbooks </li></ul>
  27. 34. Visualization
  28. 35. Modelling
  29. 36. Connection
  30. 38. Communication
  31. 39. Outcomes
  32. 40. Learning Outcomes: Achievement & Attitude
  33. 41. HOW WELL HAVE THE STUDENTS LEARN? <ul><li>Findings from TIMSS </li></ul>
  34. 42. International Benchmarks
  35. 43. Advanced Intermediate Low High 2 40 31 15 70 64 46 88 85 75 97 94 Grade 8 Telok Kurau Primary School TIMSS Trends in International Maths and Science Studies 45 40 71 71 86 90 95 98
  36. 44. Advanced Intermediate Low High 2 3 0 15 12 4 46 44 14 75 66 48 Grade 8 Effective Methods in Teaching Mathematics TIMSS Trends in International Maths and Science Studies 40 2 70 18 88 50 97 82
  37. 47. Advanced Intermediate Low High 41 74 92 98 Singapore Catholic High School (Primary) TIMSS Trends in International Maths and Science Studies 40 70 88 97
  38. 48. Advanced Intermediate Low High 10 40 77 95 U S A Catholic High School (Primary) TIMSS Trends in International Maths and Science Studies 6 31 67 92
  39. 49. Advanced Intermediate Low High 16 48 79 94 England Catholic High School (Primary) TIMSS Trends in International Maths and Science Studies 8 35 69 90
  40. 50. Advanced Intermediate Low High 5 26 67 90 International Catholic High School (Primary) TIMSS Trends in International Maths and Science Studies 2 15 46 75

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