Danish Students’ Understanding of Fractions: A Replication Study

Implementation and replication studies in mathematics education Pub Date : 2023-11-09 DOI:10.1163/26670127-bja10014

Julie Vangsøe Færch, Jeremy Hodgen

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Abstract

Abstract In this paper, we report on a conceptual replication of a fractions test originally administered in the 1970s in England as part of the ‘Concepts in Secondary Mathematics and Science’ ( CSMS ) research programme documenting lower secondary students’ understanding of mathematics. We present data from a recent study conducted in Denmark with 336 students aged between 12 and 14 years, presenting descriptive results as in the original research. In addition, we use Rasch modelling — a technique that was not widely used in the 1970s — to further analyse the students’ understanding of fractions and to validate the test. Our findings indicate that Danish students’ fractional understanding in word or diagrammatic contexts is slightly stronger in comparison to that of the English students in the original study, whereas the case for computations involving fractions is the reverse. We discuss the possible reasons for these differences. Our study provides evidence that fractional knowledge involves a number of components and suggest ways in which the test might be improved. The Impact Sheet to this article can be accessed at 10.6084/m9.figshare.24219673

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丹麦学生对分数的理解:一项重复研究

摘要在本文中，我们报告了一项分数测试的概念复制，该测试最初是在20世纪70年代在英国进行的，作为“中学数学和科学概念”(csm)研究计划的一部分，记录了中学生对数学的理解。我们提供了最近在丹麦进行的一项研究的数据，其中有336名年龄在12至14岁之间的学生，呈现了原始研究中的描述性结果。此外，我们使用了Rasch模型——一种在20世纪70年代没有广泛使用的技术——来进一步分析学生对分数的理解并验证测试。我们的研究结果表明，与原始研究中的英国学生相比，丹麦学生对单词或图表上下文的分数理解略强，而涉及分数计算的情况则相反。我们将讨论造成这些差异的可能原因。我们的研究提供了证据，证明分数知识涉及许多组成部分，并提出了改进测试的方法。本文的影响表可以在10.6084/m9.figshare.24219673访问

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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Implementation and replication studies in mathematics education

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