Seeing number relations when solving a three-digit subtraction task

IF 3.4 2区教育学 Q1 EDUCATION & EDUCATIONAL RESEARCH Educational Studies in Mathematics Pub Date : 2024-01-17 DOI:10.1007/s10649-023-10287-0

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Abstract

The decomposition of numbers when solving subtraction tasks is regarded as more powerful than counting-based strategies. Still, many students fail to solve subtraction tasks despite using decomposition. To shed light upon this issue, we take a variation theoretical perspective (Marton, 2015) seeing learning as a function of discerning critical aspects and their relations of the object of learning. In this paper, we focus on what number relations students see in a three-digit subtraction task, and how they see them. We analyzed interview data from 55 second-grade students who used decomposition strategies to solve 204 − 193 = . The variation theory of learning was used to analyze what number relations the students experienced and how they experienced them, aiming to explain why they made errors even though they used presumably powerful strategies in their problem-solving. The findings show that students who simultaneously experienced within-number relations and between-number relations when solving the task succeeded in solving it, whereas those who did not do this failed. These findings have importance for understanding what students need to discern in order to be able to solve subtraction tasks in a proficient way.

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在解决三位数减法任务时看到数字关系

摘要在解决减法问题时，对数字进行分解被认为比以计数为基础的策略更有效。然而，许多学生尽管使用了分解策略，却仍然无法解决减法任务。为了揭示这一问题，我们从变式理论的角度（Marton，2015）将学习视为辨别学习对象的关键方面及其关系的一种功能。在本文中，我们关注学生在三位数减法任务中看到了哪些数字关系，以及他们是如何看待这些关系的。我们分析了 55 名二年级学生的访谈数据，他们使用分解策略解决了 204 - 193 = 。我们采用了学习变异理论来分析学生经历了哪些数字关系，以及他们是如何经历这些数字关系的，旨在解释为什么他们在解决问题时使用了可能很强大的策略，但还是会出错。研究结果表明，在解决任务时同时体验数内关系和数间关系的学生成功地解决了任务，而没有这样做的学生则失败了。这些发现对于理解学生需要辨别什么才能熟练地解决减法任务具有重要意义。

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来源期刊

Educational Studies in Mathematics EDUCATION & EDUCATIONAL RESEARCH-

CiteScore

5.60

自引率

9.40%

发文量

期刊介绍： Educational Studies in Mathematics presents new ideas and developments of major importance to those working in the field of mathematics education. It seeks to reflect both the variety of research concerns within this field and the range of methods used to study them. It deals with methodological, pedagogical/didactical, political and socio-cultural aspects of teaching and learning of mathematics, rather than with specific programmes for teaching mathematics. Within this range, Educational Studies in Mathematics is open to all research approaches. The emphasis is on high-level articles which are of more than local or national interest.? All contributions to this journal are peer reviewed.