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Thinking With
Numbers
Teacher Actions in a Student-Centered Approach
to Teach Basic Facts and Mental Computation
Edward C. Rathmell
Larry P. Leutzinger

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A 5-minute Problem Solving Lesson

Pose a problem.

  • Repeat the problem as needed.
  • Encourage students to invent their own solutions to the problem.

Allow time for students to think.

  • Expect every student to think about the problem for about 20-30 seconds.
  • Encourage students to invent their own solutions to the problem.
  • Provide support and encouragement to individuals.

Encourage students to share solutions.

  • Ask two or three students to explain different ways to solve the problem or verify the answer.
  • Expect students to listen carefully to the explanations.
  • Ask students to clarify or repeat their explanations.
  • Illustrate with a model as students repeat their explanations.
  • Summarize/restate the thinking strategy and name the strategy.
  • Ensure that different thinking strategies are explained.

Highlight an efficient thinking strategy.

  • Repeat the thinking or have another student repeat the thinking.
  • Sometimes model concretely to illustrate the thinking.
  • Model appropriate language, especially parts and wholes.

Ask all students to try that same thinking with a second problem.

  • Expect every student to try using the highlighted strategy for about 15 seconds.
  • Provide support and encouragement.

Ecourage one student to share their solution with the highlighted strategy.

  • Ask one student to use that thinking to explain the second problem.
  • Ask another student if the explanation used the same thinking.
  • Discuss when the strategy is efficient.

Encourage students to use this new thinking.

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