Date of Award

Spring 1-1-2017

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Victoria Hand

Second Advisor

Rogers Hall

Third Advisor

Kris Gutiérrez

Fourth Advisor

Eve Manz

Fifth Advisor

Michael Eisenberg

Abstract

Abstract

This dissertation describes a mathematics curriculum and instruction design experiment involving a series of embodied mathematical activities conducted in two Colorado elementary schools Activities designed for this experiment include multi-scalar number line models focused on supporting students’ understanding of elementary mathematics. Realistic Mathematics Education (RME) served as a roadmap for the development of models and problem contexts during the design process, and maintained the focus on mathematics as human activity. Key ideas and insights from scholars who have employed embodied, enactive, ecological, multimodal, and inclusive materialist theories of mathematical activity/cognition on spatiality, human vision, and perception also informed the work. Departing from the sedentary approach to U.S. elementary school mathematics learning and instruction, the designed activities intentionally required students to use their bodies and tools in space to coordinate solutions to mathematical problems. As a design experiment, the research took place in two phases over the course of a year. Phase 1 occurred over 17 days in a suburban 2nd grade public school classroom, and phase 2 consisted of six 55-minute clinical interviews with six student pairs from two 3rd grade classrooms in an urban public school. Findings from this research included students using the designed models to support mathematical arguments and to increase levels of precision in their mathematical activity. Themes also emerged around the ways that students responded to affordances and constraints of the models, by shifting orientations, authority, and re-purposing

and creating new tools. Multi-scalar mathematical models, activities, and activity spaces afforded novel and intentionally embodied ways for students to participate in model-centric mathematical activity.

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