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

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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 Presentation Transcript

  • 1. Dr Yeap Ban Har
    Marshall Cavendish Institute
    Singapore
    banhar@sg.marshallcavendish.com
    Seminar on Singapore Math in Chile
    SANTIAGO  CONCEPTION
    This seminar is about how textbooks can help average students learn mathematics well.
    Presentation is available at www.banhar.com
  • 2. 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
    In Singapore, a curriculum that focuses on mathematical problem solving was introduced in 1992.
  • 3. thinking schools
    learning nation
    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.
  • 4. Textbooks that place an emphasis on problem solving and thinking naturally will be able to help many students becoming good in problem solving.
    Singapore textbooks do not focus on tedious computations or learning procedures without the corresponding conceptual understanding.
  • 5. Textbooks place an emphasis on problem solving and thinking.
  • 6. first day
    first day
    first day
  • 7. It focuses on the development of visualization.
     
    The bar model is used extensively to help students represent problems well as well as to develop visualization.
  • 8.
  • 9. Visuals are used extensively to develop conceptual understanding.
     
    In learning how to write mixed numbers as improper fractions in Grade 4, the visual approach is a common approach in the textbooks.
  • 10. This visual shows why
    It is clear that there are 5 halves in
  • 11. It focuses on the development of number sense.
  • 12. There is an emphasis on mental strategies.
    Mental strategies help students become flexible thinkers as they need to make decisions on the best strategy to use for a particular computation.
  • 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.
  • 14. bruner’s theory
    concrete
    Singapore Math in Malaysia
  • 15. concrete
    experiences
    Singapore Math in Malaysia
  • 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.
  • 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.
  • 18.
  • 19.
  • 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.
     
    Singapore Math in the Netherlands
  • 21.  
    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.
    Singapore Math in USA
  • 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.
    Singapore Math
    in
    The Philippines
  • 23. Systematic Variation – students are presented with a variety of tasks in a systematic way. This is based on the idea of ZoltanDienes.
  • 24. Students in Singapore have demonstrated high achievement and positive attitude towards mathematics.
    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).
    1995
    2003
    2007
    International
    5
    Advanced
    38
    41
    38
    Grade 4
    26
    High
    70
    74
    73
    67
    Intermediate
    89
    92
    91
    90
    Low
    96
    98
    97
  • 25. Average
    Hong Kong
    Singapore
    S. Korea
    Taiwan
    Grade 8
    Advanced
    2
    40
    31
    45
    40
    High
    15
    70
    64
    71
    71
    Intermediate
    46
    88
    85
    86
    90
    Low
    75
    97
    94
    95
    98
    Singapore Math in Indonesia
  • 26. TIMSS
    Trends in International Mathematics and Science Studies
    Grade 4 2003
    Grade 8 2007
    Grade 4 1995
    Grade 8 1999
    38
    40
    Advanced
    38
    42
    73
    70
    High
    70
    77
    91
    88
    Intermediate
    89
    94
    97
    97
    Low
    96
    99
  • 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.
    How many cookies did Mrs Hoon sell?
  • 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.
    How many cookies did Mrs Hoon sell?
    210
  • 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.
    How many cookies did Mrs Hoon sell?
    210
    MrsHoon sold 960 cookies.
  • 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%.
  • 31. Schools make problem solving a priority in their mathematics programme because of the demands of the PSLE.
     
    Grade 3 Examination Item (Raffles Girls’ Primary School 2009)
    Devi had some $2 notes and $5 notes.
    She had a total of $76.
    She had 4 more $5 notes than $2 notes.
    How many $2 notes did she have?
  • 32. Schools make problem solving a priority in their mathematics programme because of the demands of the PSLE.
     
    Grade 3 Examination Item (Raffles Girls’ Primary School 2009)
    Devi had some $2 notes and $5 notes.
    She had a total of $76.
    She had 4 more $5 notes than $2 notes.
    How many $2 notes did she have?
    $78
    Number of $5 notes
    4
    $20
    $58
    8
    Number of $2 notes
    $58 ÷ 7 = 8
    8
    She had eight $2 notes.
  • 33. The attitude index for Singapore students in TIMSS is also relatively high compared to other high-performing countries.
    Also, the majority of students in Singapore opt to study mathematics in Grades 11 and 12 when they are no longer required to.
  • 34. Attitude
    Achievement
    Singapore
    71
    41
    Grade 4
    Hong Kong
    67
    40
    Taiwan
    50
    24
    Japan
    62
    23
    Kazakhstan
    89
    19
    England
    62
    16
    Russia
    80
    16
    International
    72
    5
  • 35. Attitude
    Achievement
    Taiwan
    37
    45
    Grade 8
    S Korea
    33
    40
    Singapore
    60
    40
    Hong Kong
    47
    31
    Japan
    30
    26
    Hungary
    30
    10
    England
    40
    8
    International
    54
    2
  • 36. Other than the curriculum, assessment and textbooks, another important factor is the teachers.
  • 37. Teachers received about 100 hours of courses in mathematics teaching and learning during pre-service training.
     
  • 38.  
    Teachers are expected to engage in professional development throughout their career.
     
  • 39.  
    Some study for certification while others just for improvement. It is also an expectation.
  • 40.   
    Textbooks are designed for teachers to learn the mathematics that they teach.
  • 41. Dr Yeap Ban Har
    Marshall Cavendish Institute
    Singapore
    banhar@sg.marshallcavendish.com
    Seminar on Singapore Math in Chile
    SANTIAGO  CONCEPTION
    Singapore Math in Chile
    Presentation is available at www.banhar.com