An investigation of algebra performance and conceptual knowledge of arithmetic in adults.

IF 1.1 4区心理学 Q4 PSYCHOLOGY, EXPERIMENTAL

Canadian Journal of Experimental Psychology-Revue Canadienne De Psychologie Experimentale Pub Date : 2025-06-01 Epub Date: 2024-12-30 DOI:10.1037/cep0000340

Katherine M Robinson, Bethany J Sander

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引用次数: 0

Abstract

Conceptual understanding of arithmetic is considered a key component for success in advanced mathematics topics such as algebra, but the link between them has rarely been investigated, particularly in adults. Participants solved conducive (3 × 26 ÷ 26) and nonconducive (26 × 3 ÷ 26) inversion problems, conducive (3 × 26 ÷ 13) and nonconducive (26 × 3 ÷ 13) associativity problems, and multiplication (3 × 6 × 12 = 3 × ?) and division (36 ÷ 8 ÷ 4 = 36 ÷ ?) equivalence problems and completed an algebra task. Conceptually based shortcut use on the nonconducive inversion problems was the strongest predictor of algebra scores. Participants who used conceptually based shortcuts on more problem types had higher algebra scores than participants who had low use of conceptually based shortcuts on most problem types. The results support the relationship between algebra and conceptual understanding of arithmetic and demonstrate that even in adulthood there are pronounced individual differences in conceptual understanding of arithmetic, which may impact success in advanced mathematics. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

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成人代数表现和算术概念知识的调查。

对算术的概念理解被认为是在代数等高等数学课题中取得成功的关键组成部分，但它们之间的联系很少被研究，特别是在成人中。参与者解决有利（3 × 26 ÷ 26）和不利（26 × 3 ÷ 26）逆问题，有利（3 × 26 ÷ 13）和不利（26 × 3 ÷ 13）结合律问题，乘法（3 × 6 × 12 = 3 × 12）和除法（36 ÷ 8 ÷ 4 = 36 ÷ ？）等价问题，并完成代数任务。以概念为基础的捷径在无益的反转问题上的使用是代数分数的最强预测因子。在更多问题类型上使用基于概念的快捷方式的参与者比在大多数问题类型上很少使用基于概念的快捷方式的参与者在代数方面的得分更高。研究结果支持代数与算术概念理解之间的关系，并表明即使在成年期，算术概念理解也存在明显的个体差异，这可能会影响高等数学的成功。（PsycInfo Database Record (c) 2025 APA，版权所有）。

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来源期刊

Canadian Journal of Experimental Psychology-Revue Canadienne De Psychologie Experimentale PSYCHOLOGY, EXPERIMENTAL-

CiteScore

2.30

自引率

7.70%

发文量

期刊介绍： The Canadian Journal of Experimental Psychology publishes original research papers that advance understanding of the field of experimental psychology, broadly considered. This includes, but is not restricted to, cognition, perception, motor performance, attention, memory, learning, language, decision making, development, comparative psychology, and neuroscience. The journal publishes - papers reporting empirical results that advance knowledge in a particular research area; - papers describing theoretical, methodological, or conceptual advances that are relevant to the interpretation of empirical evidence in the field; - brief reports (less than 2,500 words for the main text) that describe new results or analyses with clear theoretical or methodological import.