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

IF 2.3 1区心理学 Q2 PSYCHOLOGY, EDUCATIONAL

Cognition and Instruction Pub Date : 2021-11-22 DOI:10.1080/07370008.2021.2000989

Amy B. Ellis, E. Lockwood, E. Tillema, Kevin Moore

引用次数: 7

Abstract

Abstract 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 more productive generalizations. In response, we report on results from 146 interviews with 93 participants in middle school through college in the domains of algebra, advanced algebra, trigonometry/pre-calculus, and combinatorics while solving complex problems. Our findings yielded the Relating-Forming-Extending (RFE) Framework, which distinguishes multiple related forms and types of generalizing. We also present two aspects of mental activity that promote generative generalizations: operative activity, and building and refining activity.

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跨多个数学领域的泛化:关联、形成和扩展

摘要概括是数学推理的重要组成部分，研究人员建议将其作为各级教育的核心。然而，对学生概括的研究表明，在创建和表达一般性陈述方面普遍存在困难，这突出表明需要更好地理解能够支持更有效概括的过程。作为回应，我们报告了在解决复杂问题时，对93名中学至大学期间的参与者进行的146次访谈的结果，这些参与者涉及代数、高级代数、三角学/微积分前和组合数学领域。我们的发现产生了关联形成扩展（RFE）框架，该框架区分了多种相关的泛化形式和类型。我们还介绍了促进生成概括的心理活动的两个方面：操作活动，以及构建和提炼活动。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Cognition and Instruction Multiple-

CiteScore

7.90

自引率

12.10%

发文量

期刊介绍： Among education journals, Cognition and Instruction"s distinctive niche is rigorous study of foundational issues concerning the mental, socio-cultural, and mediational processes and conditions of learning and intellectual competence. For these purposes, both “cognition” and “instruction” must be interpreted broadly. The journal preferentially attends to the “how” of learning and intellectual practices. A balance of well-reasoned theory and careful and reflective empirical technique is typical.