Session A4 K-1 Math
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Session A4 K-1 Math

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This session is on early grade mathematics. It focuses on key ideas in early grades mathematics. I have previously done a keynote lecture on this topic at Erikson Institute, Chicago (First ...

This session is on early grade mathematics. It focuses on key ideas in early grades mathematics. I have previously done a keynote lecture on this topic at Erikson Institute, Chicago (First International Symposium on Early Mathematics).

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Session A4 K-1 Math Session A4 K-1 Math Presentation Transcript

  • National Conference on Singapore Math Strategies Las Vegas
    PCF Kindergarten Telok Blangah Singapore
    Session A4
    Teaching Kindergarten
    and First Grade Math
    Yeap Ban Har
    banhar.yeap@pathlight.org.sg
    Slides are available at www.banhar.blogspot.com
    Princess Elizabeth Primary School Singapore
  • PCF Kindergarten Telok Blangah Singapore
    In Singapore, formal education starts at Primary 1 (Grade 1). Compulsory education is for the first six grades.
  • overview
    Theories Behind Singapore Math
    Jerome Bruner
    Zoltan Dienes
    Richard Skemp
    Big Ideas in Early Mathematics
    Number Bonds & Basic Facts
    Visualization
    Connections
    Communication
    PCF Kindergarten Telok Blangah Singapore
    View slide
  • introduction
    PART 2
    PCF Kindergarten Telok Blangah Singapore
    View slide
  • The formal education system in Singapore is uniform with only public schools, a national curriculum, and a single teacher-training institute.
    The gaps among children in the first year of primary school are large depending on the kindergarten education they have received. Some children have not attended kindergartens.
    St Anthony’s Canossian Primary School, Singapore
  • Conscious effort not to put the disadvantage children in a position of greater disadvantage. Textbooks are written for learners of the language, yet challenging for advanced learners.
    My Pals Are Here! Mathematics 1
  • Textbooks are also written simply so that non-specialist teachers can understand the mathematics they are teaching. Hopefully, it is not complicated to put the less educated parents off helping their kids. Children bring their books home every day.
    My Pals Are Here! Mathematics 1
  • Since 2005, Grade 1 and Grade 2 teachers have been asked to adopt the SEED Approach. SEED is the acronym for Strategies for Effective Engagement and Development.
    More holistic assessment approaches are favored over written tests.
    Hands-on learning have been given added emphasis.
    Catholic High School (Primary), Singapore
  • Further efforts to strengthen primary education is evident. A high-profile committee reviewed primary education in Singapore and made suggestions this stage of education can be further improved.
    It recommended, among other things, pedagogies that engage students better.
    • Learning by Doing
    • Learning through Inquiry
    • Learning by Collaborating
    • Learning by Reflecting
    • Learning in and about the Real World
  • big ideas in early mathematicsin kindergarten through grade one
    PART 2
    PCF Kindergarten Telok Blangah Singapore
  • Number Bonds
    Number Bonds is emphasized prior to the learning of addition.
    Children are given, say, 5 unifix cubes and guided to see that 1 and 4 make 5, for example. Others may say that 3 and 2 make 5 or 4 and 1 make 5. Yet others may say that 5 and 0 make 5.
    Earlybird Kindergarten Mathematics
  • PCF Kindergarten Telok Blangah Singapore
  • PCF Kindergarten Telok Blangah Singapore
    One duck is big.
    Six ducklings are small.
  • PCF Kindergarten Telok Blangah Singapore
  • PCF Kindergarten Telok Blangah Singapore
  • PCF Kindergarten Telok Blangah Singapore
  • PCF Kindergarten Telok Blangah Singapore
  • My Pals Are Here! Mathematics 1
    Number Bonds continues to receive attention in Grade 1.
  • concrete  pictorial  abstractBRUNER’S THEORY
    PART 2
    PCF Kindergarten Telok Blangah Singapore
  • Addition Facts
    Addition Facts are given emphasis in the first six months of grade one.
    The children learn it in stages as the textbooks distinguished between Numbers to 10, Numbers to 20, Numbers to 40 and Numbers to 100.
    Count On and Count All are used in Numbers to 10.
    Kindergarten Textbook
  • Addition Facts &Number Sense
    While Count On and Count All are used in Numbers to 10, Make Ten is given emphasis in Numbers to 20.
    Princess Elizabeth Primary School
  • 7 + 8
  • 7 + 8
  • mathematical variationDIENES’ THEORY
    PART 2
    PCF Kindergarten Telok Blangah Singapore
  • perceptual variationDIENES’ THEORY
    PART 2
    PCF Kindergarten Telok Blangah Singapore
  • Example on Place Value
  • Example on Number Bonds
  • Why are the illustrations in three consecutive tasks are as such?
  • spiral approach
    PART 2
    PCF Kindergarten Telok Blangah Singapore
  • An Example
    Study how students get to revisit ideas of number bonds as the deal with number bonds for 6 through 9.
  • spiral approach
    PART 2
    PCF Kindergarten Telok Blangah Singapore
  • Between Grades: Division
    Primary 1
    without symbol
    Primary 2
    with symbol, no remainder
    Primary 3
    with symbol, with remainder
    long division to 3-digit
    Primary 4
    long division to 4-digit
    Primary 5
    include continuous quantities
  • Within Grade: Whole Numbers
    Number to 10
    Numbers to 20
    Numbers to 40
    Numbers to 100
    Within each unit, numbers, place value, comparing, adding and subtracting are dealt with.
    This allows students to review materials as they learn new ideas.
  • spiral approach
    PART 2
    PCF Kindergarten Telok Blangah Singapore
  • Whole Numbers in Grade 1
    Basic Review
    Children count shapes in the unit on Shapes
    Review to Extend Knowledge
    Children learn another use of whole numbers in the unit on Ordinal Numbers
    Pre-requisite
    Children apply counting, comparing, addingand subtracting in the unit on Picture Graphs
  • conceptual understandingSKEMP’S THEORY
    PART 2
    PCF Kindergarten Telok Blangah Singapore
  • 17 + 19
    Number Sense
    16 + 20
  • Connections
    Looking for Patterns is introduced through exploration with Shapes. Subsequently, this is done using numbers – in a more abstract context.
    Princess Elizabeth Primary School
    MakeConnections to Generalize
  • Visualization
    In the learning of Numbers to 10, children use square tiles to form patterns of 3 and patterns of 4, for instance.
    Illustrations in textbooks were also carefully varied to develop this competency.
  • Connections
    Princess Elizabeth Primary School
  • Communication
    Articulating one’s thoughts orally, at first, and in written forms using words, pictures, diagrams and symbols is important.
    Maris Stella High (Primary) School