Site map

Big ideas

• Same and different
  • Classification
    • Above and below the line
  • Above and below the line
  • Noticing and comparing properties of shapes
    • Comparing properties of quadrilaterals
  • Comparing properties of quadrilaterals
  • Imagining missing elements
    • Covered by H
  • Covered by H
• Classification
  • Above and below the line
• Above and below the line
• Noticing and comparing properties of shapes
  • Comparing properties of quadrilaterals
• Comparing properties of quadrilaterals
• Imagining missing elements
  • Covered by H
• Covered by H
• Visualisation
  • Visualisation of information
    • Bad apples
  • Bad apples
• Visualisation of information
  • Bad apples
• Bad apples
• Mathematical truth
  • Truth of propositions
    • Do quadrilaterals tessellate?
  • Do quadrilaterals tessellate?
• Truth of propositions
  • Do quadrilaterals tessellate?
• Do quadrilaterals tessellate?
• If-then
  • If-then statements
  • Proportional reasoning
• If-then statements
• Proportional reasoning
• Deduction
  • Deductive reasoning
  • Halving a rectangle
• Deductive reasoning
• Halving a rectangle
• Proof
  • Proof: The foundation of mathematics
• Proof: The foundation of mathematics

Good teaching

• Reasoning for all students
  • Challenging all students
• Challenging all students
• Effective questioning
  • The W questions
    • W questions covered by H
    • Surface area and scaling up
  • Surface area and scaling up
  • W questions covered by H
• The W questions
  • W questions covered by H
  • Surface area and scaling up
• Surface area and scaling up
• W questions covered by H
• Deep thinking
  • Promoting deep thinking
    • Exploring nines
  • Exploring nines
• Promoting deep thinking
  • Exploring nines
• Exploring nines
• A routine element of every class
  • Student-to-student dialogue
  • A social activity
• Student-to-student dialogue
• A social activity
• Making mathematical connections
  • What do connectionist teachers do?
• What do connectionist teachers do?

Assessment

• Assessment approaches
  • Using open tasks
  • Observation
    • Rows of squares
  • Rows of squares
  • Students' writing
    • A learning story
  • A learning story
  • Using problem-posing
• Using open tasks
• Observation
  • Rows of squares
• Rows of squares
• Students' writing
  • A learning story
• A learning story
• Using problem-posing
• Designing tasks for assessing reasoning
  • Levels of proof
    • Triangular numbers
  • Triangular numbers
  • Ability to demonstrate reasoning
    • Mungo man poster
    • Writing about similar triangles
  • Mungo man poster
  • Writing about similar triangles
  • Ability to predict
    • Paper folding
    • Symmetry resources
    • Folding shapes online
  • Paper folding
  • Symmetry resources
  • Folding shapes online
  • Ability to make connections
    • The array
  • The array
• Levels of proof
  • Triangular numbers
• Triangular numbers
• Ability to demonstrate reasoning
  • Mungo man poster
  • Writing about similar triangles
• Mungo man poster
• Writing about similar triangles
• Ability to predict
  • Paper folding
  • Symmetry resources
  • Folding shapes online
• Paper folding
• Symmetry resources
• Folding shapes online
• Ability to make connections
  • The array
• The array

Activities

• Above and below the line
• Bad apples
• Challenging all students
• Comparing properties of quadrilaterals
• Covered by H
• Do quadrilaterals tessellate?
• Exploring nines
• Surface area and scaling up
• W questions covered by H

Downloads

• 'Above and below the line' ideas, F–6
• 'Bad apples': Extension ideas for secondary students
• Addition of Odd and Even Numbers video transcript
• Compare and contrast: Content descriptions
• Insects and spiders: An avenue for if-then thinking
• Jan’s train
• Max's statements
• Other covering shapes
• Problem solving versus reasoning
• Reasoning statements
• Sample response to quadrilateral tessellation
• Some milestones in the development of mathematical reasoning
• Some W question starters

Acknowledgements