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NCTM 2010 Regional Conferences & Expositions Denver 1
 

NCTM 2010 Regional Conferences & Expositions Denver 1

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This is Session 106 on mathematical problem solving.

This is Session 106 on mathematical problem solving.

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    NCTM 2010 Regional Conferences & Expositions Denver 1 NCTM 2010 Regional Conferences & Expositions Denver 1 Presentation Transcript

    • NCTM Regional Conference & Exposition Denver Colorado
      8 – 9 October 2010
      Session 106
      This session includes a selection of problems used in grades K – 3 classrooms in Singapore. Look at how these problems are used to achieve different instructional goals. See how these problems play a role in helping children develop a strong foundation for subsequent learning.     
      Colorado Convention Center, Korbel 3B
    • Problem Solving in the Singapore Classrooms
      Session 106
      DrYeap Ban Har
      Marshall Cavendish Institute
      Singapore
      banhar@sg.marshallcavendish.com
      www.banhar.blogspot.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
      The mathematical problem-solving curriculum framework was introduced in Singapore in 1992 in response to recommendations made in An Agenda for Action (in the US) and the Cockcroft Report (in the UK).
    • The Singapore mathematics curriculum states that mathematics is an “excellent vehicle for the development and improvement of a person’s intellectual competence” (Ministry of Education 2006). The next few examples show how problem solving can be used to develop visualization, number sense and ability to see patterns as well as to facilitate language development.
      intellectual competence
    • example one
      Source
      Earlybird Kindergarten Mathematics – Kindergarten Textbook in Singapore
    • PCF Kindergarten TelokBlangah, Singapore
    • Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?
      example two
      Source
      Primary Three Examination Item from Henry Park Primary School, Singapore
    • Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?
      example two
      Angela
      Bala
      872
      Cheng Hao
      50
      Source
      Primary Three Examination Item from Henry Park Primary School, Singapore
    • Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?
      1 unit = 822 ÷ 6
      1 unit = 137
      Bala has 137 marbles.
      example two
      Angela
      Bala
      822
      Cheng Hao
      600
      42
      180
      Source
      Primary Three Examination Item from Henry Park Primary School, Singapore
    • Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?
      4y + y + (y + 50) = 872
      6y + 50 = 872
      6y = 872 – 50
      y = 822 ÷ 6
      example two
      y = 137
      Angela
      y
      y
      y
      y
      Bala
      y
      872
      Cheng Hao
      50
      y
      Source
      Primary Three Examination Item from Henry Park Primary School, Singapore
    • Using a box to represent known quantities.
      Using a box to represent unknown quantities.
      Angela
      Using a letter to represent unknown quantities.
      4y + y + (y + 50) = 872
    • example three
      Source
      Grade 4 Lesson on Long Division in Keys Grade School, Manila
    • Source
      Grade 4 Lesson on Long Division in Keys Grade School, Manila
    • 1
      2
      0
      4
      4816
      4
      4816
      4
      81
      4000
      16
      8
      800
      16
      16
      0
    • Hugo has ? toy cars.
      His friend has ? toy cars.
      They have ? toy cars altogether.
      example four
      Source
      2oBasico Lesson on Model Drawing in EscuelaRepublica de Guatemala, Chile
    • Hugo has 10 toy cars.
      His friend has 12 toy cars.
      They have ? toy cars altogether.
      Source
      2oBasico Lesson on Model Drawing in EscuelaRepublica de Guatemala, Chile
    • Hugo has 10 toy cars.
      His friend has 12 toy cars.
      They have ? toy cars altogether.
      Source
      2oBasico Lesson on Model Drawing in EscuelaRepublica de Guatemala, Chile
    • Hugo has 121 toy cars.
      His friend has 74 toy cars.
      They have ? toy cars altogether.
      ?
      121
      74
      Source
      2oBasico Lesson on Model Drawing in EscuelaRepublica de Guatemala, Chile
    • Hugo has 20 toy cars.
      His friend has 74 toy cars.
      They have ? toy cars altogether.
      Source
      2oBasico Lesson on Model Drawing in EscuelaRepublica de Guatemala, Chile
    • Hugo has 100 toy cars.
      His friend has 74 toy cars.
      They have ? toy cars altogether.
      Source
      2oBasico Lesson on Model Drawing in EscuelaRepublica de Guatemala, Chile
    • Hugo has ? toy cars.
      His friend has 74 toy cars.
      They have 100 toy cars altogether.
      Source
      2oBasico Lesson on Model Drawing in EscuelaRepublica de Guatemala, Chile
    • example five
      Source
      My Pals Are Here! Maths – Grade 1 Textbook in Singapore
    • Use five consecutive whole numbers so that the vertical sum is equal to the horizontal sum. Start with 1 to 5.
      example six
      Source
      Research Lesson at a Professional Development Course in Singapore
    • Use five consecutive whole numbers so that the vertical sum is equal to the horizontal sum. Start with 1 to 5.
      1
      3
      2
      5
      3
      2
      5
      3
      1
      5
      2
      1
      4
      4
      4
      3
      2
      3
      2
      4
      5
      5
      6
      2
      5
      3
      4
      6
      6
      4
    • 2
      4
      3
      5
      6
      Princess Elizabeth Primary School, Singapore
    • Princess Elizabeth Primary School, Singapore
    • Use the digits 0 to 9 not more than once to make a correct multiplication sentence.
      x
      example seven
      Source
      Teacher Professional Development Course in Singapore
    • 1 2
      x 5
      6 0
      4 3
      x 2
      8 6
      2 9
      x 3
      87
      15
      x 4
      60
      1 2
      x 7
      8 4
      1 5
      x 2
      3 0
      18
      x 2
      3 6
      1 8
      x 3
      5 4
      1 8
      x 4
      7 2
      1 2
      x 8
      9 6
      responses
      1 4
      x 7
      9 8
    • problem solving for various instructional goals
      We have seen the use of problem solving to teach a basic concept or skill, to consolidate learning as well as to provide opportunities for students to apply what they know.
    • PK – K
      G 1
      problem solving to teach a new concept or skill
      G 2
      G 3
      G 4
    • PK – K
      visualization
      metacognition
      G 1
      G 2
      visualization
      G 3
      G 4
      number sense
    • generalization
      problem solving to consolidate a skill or concept
      x
      reasoning
    • problem solving for students to apply their knowledge
      Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?
    • Problem Solving in the Singapore Classrooms
      Slides are available at
      www.banhar.blogspot.com
      Da Qiao Primary School, Singapore