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Clayton M. Edwards and Brian E. Townsend

Changes to classroom rules of engagement, such as assessment, the curriculum, instruction, and the environment, can produce real results.

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Clayton M. Edwards, Rebecca R. Robichaux-Davis and Brian E. Townsend

Three inquiry-based tasks highlight the planning, classroom discourse, positive results, and growth in one class's journey.

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Brian E. Townsend, John K. Lannin and David D. Barker

Helping students determine different strategies to explore algebraic reasoning tasks can help them draw accurate conclusions.

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John K. Lannin, Fran Arbaugh, David D. Barker and Brian E. Townsend

Give me a productive error over a boring, mundane, and unproductive fact any day.

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John K. Lannin, Brian E. Townsend, Nathan Armer, Savanna Green and Jessica Schneider

An important goal of school mathematics involves helping students use the powerful forms of representation that have been developed over the centuries through the work of mathematicians throughout the world. However, challenges exist in encouraging students to develop meaning for the mathematical symbols used in formal algebra. Research has demonstrated that students often fail to develop a deep understanding of the meaning of symbolic representations of variables (e.g., Booth 1984; Clement 1982), so much so that Thompson (1994) found that a limited understanding of the meaning of variables negatively impacts students who later take college calculus. The question arises as to how we can develop meaning for formal algebraic symbols in the middle grades so that instruction can build on this meaning throughout students' high school and college experiences.