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Casey Hord and Samantha Marita

Support math conversations and teach students to approach various problem-solving tasks by encouraging the use of tables.

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Debra I. Johanning and James D. Mamer

Developing number and operation sense associated with fraction division is viewed from multiple perspectives: modeling, equivalence, and symbolism.

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Juli K. Dixon and Jennifer M. Tobias

Anticipate and address errors that arise when fractions are placed in context and illustrated with models.

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Kara L. Imm and Meredith D. Lorber

By exploring an open-ended investigation involving proportional reasoning, students were able to walk through both problem solving and modeling.

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Nicole Pitsolantis and Helena P. Osana

Three specific sites, or points in real time, during problem solving gave fifth and sixth graders conceptual understanding, procedural skill, and the ability to justify their mathematical thinking about fractions.

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Jessica S. Cohen

Use strip diagrams to model and solve problems requiring proportional reasoning.

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Jeffrey M. Choppin, Carolyn B. Clancy, and Scott J. Koch

Allowing students to reason and communicate about integer operations, or any idea, before these ideas are formalized can be an important tool for fostering deep understanding.