Profiles in understanding operations with rational numbers

IF 1.5 4区教育学 Q2 EDUCATION & EDUCATIONAL RESEARCH Mathematical Thinking and Learning Pub Date : 2021-02-04 DOI:10.1080/10986065.2021.1882287

Juan Manuel González-forte, C. Fernández, Joris J. van Hoof, W. Van Dooren

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引用次数: 3

Abstract

ABSTRACT Students often show difficulties in understanding rational numbers. Often, these are related to the natural number bias, that is, the tendency to apply the properties of natural numbers to rational number tasks. Although this phenomenon has received a lot of research interest over the last two decades, research on the existence of qualitatively different profiles regarding students’ understanding is scarce. The current study investigated the different ways students reasoned in arithmetic operation items with fractions and decimals. A cross-sectional study with 1,262 participants from 5th to 10th grade was performed. A TwoStep Cluster Analysis revealed eight different student reasoning profiles. We found that the natural number bias is first overcome in addition and subtraction, and later in multiplication and division. Moreover, differences regarding representation were only found in addition and subtraction items, indicating that natural numbers interfered more strongly in fractions than in decimal numbers. Finally, results showed that some students’ difficulties with rational number multiplications and divisions had other explanations than the natural number bias.

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了解有理数运算的概况

学生在理解有理数方面经常表现出困难。通常，这些都与自然数偏差有关，即倾向于将自然数的性质应用于有理数任务。尽管这一现象在过去二十年中引起了很多研究兴趣，但关于学生理解存在质的不同概况的研究很少。本研究调查了学生在分数和小数算术运算项目中的不同推理方式。对1,262名五年级至十年级的参与者进行了横断面研究。两步聚类分析揭示了八种不同的学生推理特征。我们发现自然数偏差首先在加法和减法中被克服，然后在乘法和除法中被克服。此外，仅在加法和减法项目中发现了表征方面的差异，这表明自然数在分数中的干扰比在十进制数中的干扰更强。最后，结果表明，部分学生在有理数乘法和除法方面的困难有其他原因，而不是自然数偏差。

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来源期刊

Mathematical Thinking and Learning EDUCATION & EDUCATIONAL RESEARCH-

CiteScore

4.40

自引率

6.20%

发文量