Dr Yeap Ban Har<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />Seminar on Sing...
Beliefs<br />Interest<br />Appreciation<br />Confidence<br />Perseverance<br />Monitoring of one’s own thinking<br />Self-...
thinking schools<br />learning nation<br />The emphasis on thinking continues in the late 1990s with the introduction of T...
Textbooks that place an emphasis on problem solving and thinking naturally will be able to help many students becoming goo...
Textbooks place an emphasis on problem solving and thinking.<br />
first day<br />first day<br />first day<br />
It focuses on the development of visualization.<br /> <br />The bar model is used extensively to help students represent p...
Visuals are used extensively to develop conceptual understanding.<br /> <br />In learning how to write mixed numbers as im...
This visual shows why             <br />It is clear that there are 5 halves in   <br />
It focuses on the development of number sense.<br />
There is an emphasis on mental strategies.<br />Mental strategies help students become flexible thinkers as they need to m...
A strong foundation is necessary for the students to do well in mathematics. In the Singapore textbooks, such a strong fou...
bruner’s theory<br />concrete<br />Singapore Math in Malaysia<br />
concrete<br />experiences<br />Singapore Math in Malaysia<br />
The CPA Approach – the progression from concrete to pictures to abstract symbols is recommended for concept development. T...
For example, students learn the idea of division by sharing 12 cookies among 4 persons as well as by putting 12 eggs in gr...
The Spiral Approach – students get to revisit core ideas as they deepen their understanding of those ideas. This is also o...
 <br />For example, students learn to do division of discrete quantities without the need to write division sentence in Gr...
In Grade 4, 4-digit numbers are used. In Grade 5, division of continuous quantities are dealt with where 13 ÷ 4 = 3.25 rat...
Systematic Variation – students are presented with a variety of tasks in a systematic way. This is based on the idea of Zo...
Students in Singapore have demonstrated high achievement and positive attitude towards mathematics. <br />In Trends in Mat...
Average<br />Hong Kong<br />Singapore<br />S. Korea<br />Taiwan<br />Grade  8<br />Advanced<br />2<br />40<br />31<br />45...
TIMSS<br />Trends in International Mathematics and Science Studies<br />Grade  4   2003<br />Grade  8   2007<br />Grade  4...
Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210...
Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210...
Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210...
In the PSLE, the national average for students who are capable of completing the most challenging items in the examination...
Schools make problem solving a priority in their mathematics programme because of the demands of the PSLE.<br /> <br />Gra...
Schools make problem solving a priority in their mathematics programme because of the demands of the PSLE.<br /> <br />Gra...
The attitude index for Singapore students in TIMSS is also relatively high compared to other high-performing countries. <b...
Attitude<br />Achievement<br />Singapore<br />71<br />41<br />Grade 4<br />Hong Kong<br />67<br />40<br />Taiwan<br />50<b...
Attitude<br />Achievement<br />Taiwan<br />37<br />45<br />Grade 8<br />S Korea<br />33<br />40<br />Singapore<br />60<br ...
Other than the curriculum, assessment and textbooks, another important factor is the teachers.<br />
Teachers received about 100 hours of courses in mathematics teaching and learning during pre-service training.<br /> <br />
 <br />Teachers are expected to engage in professional development throughout their career.<br /> <br />
 <br />Some study for certification while others just for improvement. It is also an expectation.<br />
  <br />Textbooks are designed for teachers to learn the mathematics that they teach.<br />
Dr Yeap Ban Har<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />Seminar on Sing...
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Seminar at Colegio Inmaculada Conception, Universidad Andres Bello &San Benito School Santiago

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Pensar sin Limites Seminars
This seminar was held at various places including Colegio Inmaculada in Conception, Universidad Andres Bello in Santiago & San Benito School in Santiago. The seminar explains the pedagogy behind the Spanish edition of My Pals Are Here! Mathematics.

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Seminar at Colegio Inmaculada Conception, Universidad Andres Bello &San Benito School Santiago

  1. 1. Dr Yeap Ban Har<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />Seminar on Singapore Math in Chile<br />SANTIAGO  CONCEPTION<br />This seminar is about how textbooks can help average students learn mathematics well.<br />Presentation is available at www.banhar.com<br />
  2. 2. 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 />In Singapore, a curriculum that focuses on mathematical problem solving was introduced in 1992. <br />
  3. 3. thinking schools<br />learning nation<br />The emphasis on thinking continues in the late 1990s with the introduction of Thinking School, Learning Nation philosophy to the entire education system in 1997.<br />
  4. 4. Textbooks that place an emphasis on problem solving and thinking naturally will be able to help many students becoming good in problem solving. <br />Singapore textbooks do not focus on tedious computations or learning procedures without the corresponding conceptual understanding. <br />
  5. 5. Textbooks place an emphasis on problem solving and thinking.<br />
  6. 6. first day<br />first day<br />first day<br />
  7. 7. It focuses on the development of visualization.<br /> <br />The bar model is used extensively to help students represent problems well as well as to develop visualization.<br />
  8. 8.
  9. 9. Visuals are used extensively to develop conceptual understanding.<br /> <br />In learning how to write mixed numbers as improper fractions in Grade 4, the visual approach is a common approach in the textbooks. <br />
  10. 10. This visual shows why <br />It is clear that there are 5 halves in <br />
  11. 11. It focuses on the development of number sense.<br />
  12. 12. There is an emphasis on mental strategies.<br />Mental strategies help students become flexible thinkers as they need to make decisions on the best strategy to use for a particular computation.<br />
  13. 13. A strong foundation is necessary for the students to do well in mathematics. In the Singapore textbooks, such a strong foundation is achieved through the application of a few learning principles.<br />
  14. 14. bruner’s theory<br />concrete<br />Singapore Math in Malaysia<br />
  15. 15. concrete<br />experiences<br />Singapore Math in Malaysia<br />
  16. 16. The CPA Approach – the progression from concrete to pictures to abstract symbols is recommended for concept development. This is based on the work of Jerome Bruner.<br />
  17. 17. For example, students learn the idea of division by sharing 12 cookies among 4 persons as well as by putting 12 eggs in groups of 4 before progressing to using drawings to solve division problems. Later they learn to use division sentence 12 ÷ 4 = 3. <br />
  18. 18.
  19. 19.
  20. 20. The Spiral Approach – students get to revisit core ideas as they deepen their understanding of those ideas. This is also one of Jerome Bruner’s ideas.<br /> <br />Singapore Math in the Netherlands<br />
  21. 21.  <br />For example, students learn to do division of discrete quantities without the need to write division sentence in Grade 1. In Grade 2, the revisit this idea and use division sentences to represent the situations. In Grade 3, the idea is extended to include the idea of a remainder. They also learn to regroup before dividing for 2-digit and 3-digit numbers. <br />Singapore Math in USA<br />
  22. 22. In Grade 4, 4-digit numbers are used. In Grade 5, division of continuous quantities are dealt with where 13 ÷ 4 = 3.25 rather than 3 remainder 1. <br />Singapore Math <br />in <br />The Philippines<br />
  23. 23. Systematic Variation – students are presented with a variety of tasks in a systematic way. This is based on the idea of ZoltanDienes.<br />
  24. 24. Students in Singapore have demonstrated high achievement and positive attitude towards mathematics. <br />In Trends in Mathematics and Science Study, more than 40% of Singapore’s 4th and 8th graders are in the Advanced International Benchmark (the international average is 5% and 2% respectively). <br />1995<br />2003<br />2007<br />International<br />5<br />Advanced<br />38<br />41<br />38<br />Grade 4<br />26<br />High<br />70<br />74<br />73<br />67<br />Intermediate<br />89<br />92<br />91<br />90<br />Low<br />96<br />98<br />97<br />
  25. 25. Average<br />Hong Kong<br />Singapore<br />S. Korea<br />Taiwan<br />Grade 8<br />Advanced<br />2<br />40<br />31<br />45<br />40<br />High<br />15<br />70<br />64<br />71<br />71<br />Intermediate<br />46<br />88<br />85<br />86<br />90<br />Low<br />75<br />97<br />94<br />95<br />98<br />Singapore Math in Indonesia<br />
  26. 26. TIMSS<br />Trends in International Mathematics and Science Studies<br />Grade 4 2003<br />Grade 8 2007<br />Grade 4 1995<br />Grade 8 1999<br />38<br />40<br />Advanced<br />38<br />42<br />73<br />70<br />High<br />70<br />77<br />91<br />88<br />Intermediate<br />89<br />94<br />97<br />97<br />Low<br />96<br />99<br />
  27. 27. Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210 almond cookies and 5/6 of the chocolate cookies, she had 1/5 of the cookies left.<br />How many cookies did Mrs Hoon sell?<br />
  28. 28. Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210 almond cookies and 5/6 of the chocolate cookies, she had 1/5 of the cookies left.<br />How many cookies did Mrs Hoon sell?<br />210<br />
  29. 29. Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210 almond cookies and 5/6 of the chocolate cookies, she had 1/5 of the cookies left.<br />How many cookies did Mrs Hoon sell?<br />210<br />MrsHoon sold 960 cookies.<br />
  30. 30. In the PSLE, the national average for students who are capable of completing the most challenging items in the examination is between 40% and 45%. <br />
  31. 31. Schools make problem solving a priority in their mathematics programme because of the demands of the PSLE.<br /> <br />Grade 3 Examination Item (Raffles Girls’ Primary School 2009)<br />Devi had some $2 notes and $5 notes.<br />She had a total of $76.<br />She had 4 more $5 notes than $2 notes.<br />How many $2 notes did she have?<br />
  32. 32. Schools make problem solving a priority in their mathematics programme because of the demands of the PSLE.<br /> <br />Grade 3 Examination Item (Raffles Girls’ Primary School 2009)<br />Devi had some $2 notes and $5 notes.<br />She had a total of $76.<br />She had 4 more $5 notes than $2 notes.<br />How many $2 notes did she have?<br />$78<br />Number of $5 notes<br />4<br />$20<br />$58<br />8<br />Number of $2 notes<br />$58 ÷ 7 = 8<br />8<br />She had eight $2 notes.<br />
  33. 33. The attitude index for Singapore students in TIMSS is also relatively high compared to other high-performing countries. <br />Also, the majority of students in Singapore opt to study mathematics in Grades 11 and 12 when they are no longer required to.<br />
  34. 34. Attitude<br />Achievement<br />Singapore<br />71<br />41<br />Grade 4<br />Hong Kong<br />67<br />40<br />Taiwan<br />50<br />24<br />Japan<br />62<br />23<br />Kazakhstan<br />89<br />19<br />England<br />62<br />16<br />Russia<br />80<br />16<br />International<br />72<br />5<br />
  35. 35. Attitude<br />Achievement<br />Taiwan<br />37<br />45<br />Grade 8<br />S Korea<br />33<br />40<br />Singapore<br />60<br />40<br />Hong Kong<br />47<br />31<br />Japan<br />30<br />26<br />Hungary<br />30<br />10<br />England<br />40<br />8<br />International<br />54<br />2<br />
  36. 36. Other than the curriculum, assessment and textbooks, another important factor is the teachers.<br />
  37. 37. Teachers received about 100 hours of courses in mathematics teaching and learning during pre-service training.<br /> <br />
  38. 38.  <br />Teachers are expected to engage in professional development throughout their career.<br /> <br />
  39. 39.  <br />Some study for certification while others just for improvement. It is also an expectation.<br />
  40. 40.   <br />Textbooks are designed for teachers to learn the mathematics that they teach.<br />
  41. 41. Dr Yeap Ban Har<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />Seminar on Singapore Math in Chile<br />SANTIAGO  CONCEPTION<br />Singapore Math in Chile<br />Presentation is available at www.banhar.com<br />
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