An analysis of elementary school children’s fractional knowledge depicted with circle, rectangle, and number line representations
An analysis of elementary school children’s fractional knowledge depicted with circle, rectangle, and number line representations
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小学生用圆形、矩形和数轴表示的分数知识分析
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发表时间：
2015
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通讯作者：
Zelha Tunç
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作者：
Zelha Tunç
现在大家都知道，分数是一个既难教又难学的概念。在分数教学中，教师通常使用纸上的圆饼、矩形和数轴作为教学工具。本文通过研究广泛使用的三种外部图形表示（即圆、矩形、数轴）与学生分数知识的关系，以及反之亦然，对该领域做出了贡献。为了理解这种情况，在分数方案理论框架内开发了一个使用具有相同分数知识框架的三种表示的测试。656名4年级和5年级的美国学生参加了测试。对六种分数问题类型进行了统计分析，每种类型都有三种外部图形表示（共18个问题）。研究结果表明，学生在要求使用部分-整体分数推理的圆形和矩形题中表现出相似的表现，但在所有问题类型中，学生在使用数轴图形表示的题中的表现明显较低。此外，不管表现如何，与部分-整体推理相比，他们在需要更高级的分数思维的项目上的表现更低。讨论了可能的原因，并提出了用图形表示教学分数的建议。
It is now well known that fractions are difficult concepts to learn as well as to teach. Teachers usually use circular pies, rectangular shapes and number lines on the paper as teaching tools for fraction instruction. This article contributes to the field by investigating how the widely used three external graphical representations (i.e., circle, rectangle, number line) relate to students’ fractional knowledge and vice versa. For understanding this situation, a test using three representations with the same fractional knowledge framed within Fractional Scheme Theory was developed. Six-hundred and fifty-six 4th and 5th grade US students took the test. A statistical analysis of six fractional Problem Types, each with three external graphical representations (a total of 18 problems) was conducted. The findings indicate that students showed similar performance in circle and rectangle items that required using part-whole fractional reasoning, but students’ performance was significantly lower on the items with number line graphical representation across the Problem Types. In addition, regardless of the representation, their performance was lower on items requiring more advanced fractional thinking compared to part-whole reasoning. Possible reasons are discussed and suggestions for teaching fractions with graphical representations are presented.