Date of Award

12-2016

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Dr. Jon Davis

Second Advisor

Dr. Laura Van Zoest

Third Advisor

Dr. Jane-Jane Lo

Fourth Advisor

Dr. David Coffey

Keywords

Instrumental orchestration, student-centered instruction, case study, instrumental genesis, pedagogy, instructional techniques

Abstract

Those supporting contemporary reform efforts for mathematics education in the United States have called for increased use of technologies to support student-centered learning of mathematical concepts and skills. There is a need for more research and professional development to support teachers in transitioning their instruction to better meet the goals of such reform efforts.

Instrumental approaches to conceptualizing technology use in mathematics education, arising out of the theoretical and empirical work in France and other European nations, show promise for use to frame studies on school mathematics in the United States. Instrumental genesis is used to describe the bidirectional and influential relationship that develops between a mathematical user and the mathematical and technological tool—the tool shapes the user and the user shapes the tool. Instrumental orchestration is used to describe the teacher’s role in guiding and shaping students’ use of technology and their opportunities to engage in instrumental genesis. Although recent work has revealed different types of instrumental orchestrations, researchers have not yet unpacked the finer-grained characteristics of the performance phase of teachers’ instrumental orchestrations; doing so would help educators build their repertoires of teaching techniques from which they can draw when supporting technology-enhanced mathematical activities. Attending to teachers’ use of pedagogical moves during their instrumental orchestrations is one way to investigate and reveal such finer-grained characteristics.

The case study presented here is used to discuss data collected from two sections of one college instructor’s class for preservice elementary teachers (PSETs). Instrumental approaches are elaborated by way of pedagogical moves related to the PSETs’ opportunities to engage in instrumental genesis with Tinkerplots and the TI-73 Explorer. The instructor’s use of different pedagogical moves is cross-referenced with her use of different types of instrumental orchestrations.

Results show two different categories of pedagogical moves related to the PSETs’ instrumental geneses—student-centered instrument moves and teacher-centered instrument moves. These pedagogical moves are viewed as technological variants of more general pedagogical moves that teachers might use during their instruction— including the notions of wait time, requesting students to participate in an aspect of the lesson, and think-pair-share. The participating instructor favored the use of both student-centered types of instrumental orchestrations and student-centered instrument moves.

One implication for teacher training and development programs is that teachers can be informed about different types of pedagogical moves they might choose to use during their instrumental orchestrations and that teachers should engage in the discussion of how and when to use different instrumental orchestrations and pedagogical moves.

Access Setting

Dissertation-Open Access

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