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Chile MOE Seminar English
 

Chile MOE Seminar English

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This is the English version of the presentation at Avancemos en las Matematicas: La Mirada de Singapur

This is the English version of the presentation at Avancemos en las Matematicas: La Mirada de Singapur

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    Chile MOE Seminar English Chile MOE Seminar English Presentation Transcript

    • Dr Yeap Ban Har
      Marshall Cavendish Institute
      Singapore
      banhar@sg.marshallcavendish.com
      Seminar on Singapore Math in Chile
      SANTIAGO  CONCEPTION
      This seminar is about mathematics teaching and learning that focuses on helping average and struggling learners do well in mathematics while maintaining a suitable challenge for advanced learners.
      Presentation is available at www.banhar.com
    • 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.
    • 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.
    • The assessment reflects the focus of the curriculum. For example, the Grade 6 national examination (Primary School Leaving Examination or PSLE) includes a significant section that requires problem solving.
    • 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?
    • 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
    • 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.
    • 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?
    • 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.
    • Textbooks place an emphasis on problem solving and thinking.
      2740 + 3560
      = 6300
      Mr Khan
      5 units = 6300
      1 unit = 1260
      Mr Chen
      4 units = 4 x 1260
      4 units = 5040
      In the end, Mr Chen had 5040 sacks and Mr Khan had 1260 sacks.
    • Textbooks place an emphasis on problem solving and thinking.
    • first day
      first day
      first day
    • 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.
      Singapore Math in Chile
    • bruner’s theory
      concrete
      Singapore Math in Malaysia
    • concrete
      experiences
      Singapore Math in Malaysia
    • 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.
    • 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.
    • 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
    •  
      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
    • 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
    • Systematic Variation – students are presented with a variety of tasks in a systematic way. This is based on the idea of ZoltanDienes.
    • 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
    • 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
    • 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
    • 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%. We saw one such challenging items earlier.
      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?
    • 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.
    • 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
    • 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
    • Other than the curriculum, assessment and textbooks, another important factor is the teachers.
    • Teachers received about 100 hours of courses in mathematics teaching and learning during pre-service training.
       
    •  
      Teachers are expected to engage in professional development throughout their career.
       
    •  
      Some study for certification while others just for improvement. It is also an expectation.
    •   
      Textbooks are designed for teachers to learn the mathematics that they teach.
    • 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