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Ellis, Amy B.; Lockwood, Elise; Tillema, Erik; Moore, Kevin – Cognition and Instruction, 2022
Generalization is a critical component of mathematical reasoning, with researchers recommending that it be central to education at all grade levels. However, research on students' generalizing reveals pervasive difficulties in creating and expressing general statements, which underscores the need to better understand the processes that can support…
Descriptors: Generalization, Mathematics Instruction, Algebra, Advanced Courses
Levin, Mariana – Cognition and Instruction, 2018
This article elaborates a new direction for studying the construction of novel strategies that enables researchers to model the conceptual underpinnings of students' observable strategic actions during episodes of mathematical problem solving. The nature of the relationship between conceptual and procedural knowledge has been persistently debated…
Descriptors: Mathematics Instruction, Problem Solving, Algebra, Word Problems (Mathematics)
Ma, Jasmine Y. – Cognition and Instruction, 2017
This study interrogates the contributions of multi-party, whole-body interactions to students' collaboration and negotiation of mathematics ideas in a task setting called walking scale geometry, where bodies in interaction became complex resources for students' emerging goals in problem solving. Whole bodies took up overlapping roles representing…
Descriptors: Human Body, Interaction, Cooperative Learning, Mathematics Instruction
Richland, Lindsey Engle – Cognition and Instruction, 2015
Deictic linking gestures, hand and arm motions that physically embody links being communicated between two or more objects in the shared communicative environment, are explored in a cross-cultural sample of mathematics instruction. Linking gestures are specifically examined here when they occur in the context of communicative analogies designed to…
Descriptors: Foreign Countries, Nonverbal Communication, Role, Mathematics Instruction
Earnest, Darrell – Cognition and Instruction, 2015
This article reports on students' problem-solving approaches across three representations--number lines, coordinate planes, and function graphs--the axes of which conventional mathematics treats in terms of consistent geometric and numeric coordinations. I consider these representations to be a part of a "hierarchical representational…
Descriptors: Problem Solving, Mathematics Instruction, Graphs, Numbers