☆ 3.8 Article

First Graders' Definitions, Generalizations, and Justifications of Even and Odd Numbers

CANADIAN JOURNAL OF SCIENCE MATHEMATICS AND TECHNOLOGY EDUCATION (2023)

Generalization Across Multiple Mathematical Domains: Relating, Forming, and Extending

Amy B. Ellis et al.

Summary: Generalization is crucial in mathematical reasoning, but students often struggle to create and express general statements, highlighting the need to better understand processes that can support more productive generalizations. Through interviews with middle school to college students in algebra and related domains, the Relating-Forming-Extending (RFE) Framework was developed to distinguish different forms of generalizing. Two mental activities, operative activity and building/refining activity, were identified as promoting generative generalizations.

COGNITION AND INSTRUCTION (2022)

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Article Education & Educational Research

Progressions in young learners' understandings of parity arguments

Maria Blanton et al.

Summary: This study investigates the development of mathematical argumentation in young learners, specifically in relation to the concept of parity and sums of evens and odds. The findings suggest that students can develop viable arguments about mathematical generalizations and that an early algebra instructional sequence can promote their practice of argumentation.

MATHEMATICAL THINKING AND LEARNING (2022)

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Article Education & Educational Research