This article presents the results of a small-scale teaching experiment with three middle school s... more This article presents the results of a small-scale teaching experiment with three middle school students who explored exponential growth by reasoning with the co-varying quantities height and time. Three major conceptual shifts occurred during the course of the teaching experiment: a) From repeated multiplication to a coordination of growth in height and time values; b) From coordinating height and time to coordinating constant ratios; and c) Generalizing to non-natural exponents. The details of each of the three shifts is explored, ...
Supporting students’ mathematical reasoning is an important goal of mathematics instruction, but ... more Supporting students’ mathematical reasoning is an important goal of mathematics instruction, but can be challenging for many teachers. We report the results of a study aimed at better understanding and identifying the ways in which teachers support student reasoning when provided with conceptually rich tasks. This study resulted in the Teacher Moves for Supporting Student Reasoning (TMSSR) framework, which organizes moves vis-à-vis their function and their potential for fostering student thinking. We describe the TMSSR framework, illustrate its affordances for studying teacher practices, and highlight its utility for teachers, teacher educators, and researchers.
This article presents the results of a small-scale teaching experiment with three middle school s... more This article presents the results of a small-scale teaching experiment with three middle school students who explored exponential growth by reasoning with the co-varying quantities height and time. Three major conceptual shifts occurred during the course of the teaching experiment: a) From repeated multiplication to a coordination of growth in height and time values; b) From coordinating height and time to coordinating constant ratios; and c) Generalizing to non-natural exponents. The details of each of the three shifts is explored, ...
Supporting students’ mathematical reasoning is an important goal of mathematics instruction, but ... more Supporting students’ mathematical reasoning is an important goal of mathematics instruction, but can be challenging for many teachers. We report the results of a study aimed at better understanding and identifying the ways in which teachers support student reasoning when provided with conceptually rich tasks. This study resulted in the Teacher Moves for Supporting Student Reasoning (TMSSR) framework, which organizes moves vis-à-vis their function and their potential for fostering student thinking. We describe the TMSSR framework, illustrate its affordances for studying teacher practices, and highlight its utility for teachers, teacher educators, and researchers.
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