Date of Award

Spring 1-1-2017

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

David C. Webb

Second Advisor

Ben Shapiro

Third Advisor

Edd V. Taylor

Fourth Advisor

Daniel Liston

Fifth Advisor

Joseph Polman

Abstract

This study investigates instructional moves by teachers in mathematics classrooms in which technology-based activities (i.e., student-oriented simulations) and features of those simulations influence classroom practices. Four teachers were studied over the course of a year as an exploratory study to build interpretive cases that described instructional practices in technology-based lessons. Teachers developed lessons using PhET simulations designed to support algebraic reasoning. Data sources included teachers’ process of selecting and designing lessons, observations of teachers’ non-technology and technology-based mathematical activities, and teacher interviews and reflections.

This work was based on a conceptual framework blending the ideas of Mathematical Tasks (Stein, Smith, Henningsen, & Silver, 1998), Mathematical Pedagogical Content Knowledge (Ball, Thames, & Phelps, 2008), and Technological Pedagogical Content Knowledge (Mishra & Koehler, 2006), in which teachers’ instructional practices are determined by teachers’ mathematical pedagogical content knowledge, task selection and design, and use of technology.

Results indicated that teachers see simulations as having significant benefits in the classroom. Teachers leveraged these opportunities by increasing class discussions, engaging in higher levels of thinking and reasoning, and focusing on mathematical representations. When teachers used simulations, the teachers spent less time in direct instruction, focused more on the mathematics, and focused more on investigations rather than drill-oriented tasks.

Technology in the classroom, however, was problematic for some teachers. The very nature of students working independently with their own devices meant that student-student interactions decreased in some lessons. Furthermore, teachers’ discomfort in managing technology seems to limit ongoing use.

Specific features of the simulations that prompted instructional moves included the ability to support conceptual understanding and build student engagement. Simulations also provided a ‘low floor, high ceiling,’ supporting differentiation, and a dynamic responsiveness, facilitating connections between representations. On the other hand, teachers raised concerns that some features of the simulation could do the math for the students. Furthermore, the perception of simulations as being a game may impact how and when simulations are used.

The emergent use of technology in math classrooms is under-supported. For simulations to be used in a more extensive fashion in mathematics classes, professional development and curricular materials are needed to support implementation.

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