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ERIC Number: ED534157
Record Type: Non-Journal
Publication Date: 2011
Pages: 302
Abstractor: As Provided
Reference Count: 0
ISBN: ISBN-978-1-1248-3562-4
How to Do Math with Words: Learning Algebra through Peer Discussions
Zahner, William C.
ProQuest LLC, Ph.D. Dissertation, University of California, Santa Cruz
This study investigates how two groups of bilingual algebra students reasoned about rate, slope, and linear functions during peer discussions. This investigation brings together and advances research that investigates issues at the intersection of collaborative learning, algebraic reasoning, and the use of mathematical discourse practices. A sociocultural approach to thinking (Wertsch, 1998) frames this investigation, and the analysis follows a naturalistic approach to the study of mathematical cognition (Moschkovich and Brenner, 2000) to investigate three broad research questions: 1) How did students use semiotic tools to reason about rate, slope, and linear functions in peer discussions? 2) What patterns of interaction emerged during the students' discussions; in particular, how did the groups co-construct authority in their discussions? 3) How did the students and their teacher use mathematical discourse to reason about rate, slope, and linear functions? The participating students were two groups of four students each enrolled in a ninth grade bilingual remedial algebra class. One group of students spoke primarily English and the other spoke primarily Spanish. Three separate analyses were used for each research question, drawing on methods from microgenetic, interactionist, and discourse analytic perspectives. The primary findings of this investigation are as follows. 1) The two groups focused on different semiotic resources while discussing a linear generalization problem, and the different foci had implications for each group's success generalizing. 2) The groups co-constructed relations of authority differently, and each group's construction of authority mediated their problem-solving success. 3) The teacher and her students both showed a tendency to start mathematical discussions focused on conceptual relationships, but then transitioned to a focus on computations and procedures over time. The results of this study reveal the affordance of various types of semiotic connections, the importance of attending to the co-construction of authority in group discussions, and the challenge faced by teachers who attempt to maintain a conceptual focus in their teaching of the relationship between rate and slope in linear functions. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page:]
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Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: Grade 9
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A