五年级和六年级学生分数表征转化能力的调查研究

Investigation of Fifth and Sixth Students’ Abilities in Translating among Representations of Fractions

分数表征是分数概念学习的一部分,也是概念理解的重要方法.分数表征包括面积表征、集合表征、数轴表征和符号表征等,这4类表征及其转化与分数概念理解紧密相连,对分数教学具有重要意义.通过改编Kurt和Cakiroglu的分数表征转化测试工具,研究者调查了247名5年级学生和264名6年级学生的分数表征转化能力.调查发现小学生在数轴表征和假分数表征相关转化问题上表现较差,不能很好地理解面积（集合）表征与数轴表征的区别.此外六年级学生数轴表征转化能力较五年级有显著提升.建议教师应该重视分数多元表征的教学尤其是数轴表征和假分数表征的教学,通过分数表征转化任务帮助学生建立起全面的分数表征系统和知识结构,促进学生分数概念的发展.

Representation of fraction is an important part of fraction, it also can help student understand the concept better. And the representations include region, discrete objects, number line, symbol and so on, which relate to the concepts of fraction. It＇s significant for teachers to teach fraction. This paper modified the Translations among Representations of Fractions Test（Kurt Cakiroglu） and used it to investigate 247 fifth and 264 sixth students, abilities in translating among representations of fractions. It finds that students have some difficulties in the transforming tasks that associated with number line and improper fraction. They cannot understand the difference between region（discrete objects） and number line. Besides, the sixth grade students perform better than fifth grade students in the tasks related to number line. Based on our finding, we suggest that math teachers should pay more attention to multiple representations of fraction, especially number line and representations of improper fraction. And translating among representation of fraction tasks can help students build a more comprehensive system of representations of fraction and improve students＇ comprehensions of fraction concept.