Exploring the Mathematical Knowledge Needed to Teach Fraction Division

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Exploring the Mathematical Knowledge Needed to
Teach Fraction Division

• Theresa Grant Jane-Jane Lo
• Western Michigan University
• AMS Special Session 2008WMU, Kalamazoo, MI

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NCTM Curriculum Focal Points

• Developing an understanding of, and fluency with,
  multiplication and division of fractions and
  decimals.Students use the meanings of fractions,
  multiplication and division, and the inverse
  relationship between multiplication and division
  to make sense of procedures for multiplying and
  dividing fractions and explain why they work.
  Students use common procedures to multiply and
  divide fractions and decimals efficiently and
  accurately. They multiply and divide fractions
  and decimals to solve problems, including
  multistep problems and problems involving
  measurement.

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Mathematical knowledge needed for teaching
fractions

• Common Content Knowledge
• Computational fluency and conceptual
  understanding expected of 6th graders.
• Specialized Content Knowledge
• e.g. how to choose, make, and use diagrams
  effectively to represent fraction division how
  to reason about and justify properties and
  procedures related to fraction division.

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Pictures generated to solve

• How was the student thinking about the problem?
• How could they have used the diagram to solve
  this problem?

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Tasks for prospective teachers

• Create story problems
• Generate multiple solution strategies
• Compare and contrast strategies and the use of
  diagrams to solve problems
• Compare and contrast partitive and measurement
  division
• Making connections between meanings of division,
  diagrams and number sentences