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Zack, Vicki; Graves, Barbara Ann

doi:10.1023/a:1014045408753

Cited by 50 publications

(3 citation statements)

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“…The word "argument" has been attached to several distinct kinds of mathematical artefacts and activities. This term may indicate proofs Gasteren (1990), informallypresented proofs (Tanswell, 2015), proof sketches (Lamport, 1995), aspects of reasoning that are not addressed by formal deduction (Aberdein and Dove, 2013) and elements of persuasive discussion (Zack and Graves, 2001). Some theorists have expressly contended that proofs are not arguments: this is because proofs offer certainty, while arguments cannot (Dufour, 2013).…”

Section: Argumentation and Mathematical Argumentsmentioning

confidence: 99%

Argumentation Theory for Mathematical Argument

et al. 2019

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To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the discourse unfolds. We introduce a framework with these properties, which has been used to analyse mathematical dialogues and expository texts. The framework can recover salient elements of discourse at, and within, the sentence level, as well as the way mathematical content connects to form larger argumentative structures. We show how the framework might be used to support computational reasoning, and argue that it provides a more natural way to examine the process of proving theorems than do Lamport's structured proofs.

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Section: Argumentation and Mathematical Argumentsmentioning

confidence: 99%

Argumentation Theory for Mathematical Argument

et al. 2019

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“…Examining these variables provides further context for the proposed inquiry framework. Role influences include attitudes and beliefs (Kedar-Voivodas, 1983;Kinchin, 2004;Lyons, 1990), norms and expectations (Ryu & Sandoval, 2010;Webb, 2009), experience (Eick & Reed, 2002;Kagan, 1992;Knowles, 1992), and social factors (Chandler & Helm, 1984;Kohlberg, 1969;Reiman & Peace, 2002;Selman, 1980;Yackel, Cobb, & Wood, 1991;Zack & Graves, 2001). …”

Section: Role Theorymentioning

confidence: 99%

“…Only some of these studies focused specifically on a socialconstructivist or inquiry-based teaching and learning context (notably, Eick & Reed, 2002;Kinchin, 2004;Kohlberg, 1969;Reiman & Peace, 2002;Webb, 2009;Zack & Graves, 2001); however, all pointed to the importance of these variables in classrooms, and therefore, they should be considered when developing a framework for student-teacher role diversification.…”

Section: Role Theorymentioning

confidence: 99%

Understanding Classroom Roles in Inquiry Education

Walker

Shore

2015

Sage Open

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Inquiry-based teaching and learning are rooted in social constructivism and are central to curricular reform. Role theory and social constructivism provided insight into a commonly observed but insufficiently understood phenomenon in inquiry. Within inquiry, role shifts have been described as the switching of roles between students and teachers; however, the process may be better conceptualized as role diversification because students and teachers may undertake multiple roles simultaneously in inquiry. This article expands on existing research and proposes a framework potentially applicable to both learners and teachers, but here focused on learners. Beyond exploration, engagement, and stabilization of roles, diversification was added and described. This framework expanded on current education theory, adding new insight to a minimally explored topic, with implications for students, teachers, consultants, and researchers.

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Discourse, Mathematics and Mathematics Education

Barwell

Encyclopedia of Language and Education

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Cited by 50 publications

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Argumentation Theory for Mathematical Argument

Argumentation Theory for Mathematical Argument

Understanding Classroom Roles in Inquiry Education

Discourse, Mathematics and Mathematics Education

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