马红斐, 杨伊生. 小学生关于分数数量的迷思概念:一项基于访谈的质性研究J. 内江师范学院学报, 2026, 41(2): 1-9. DOI: 10.13603/j.cnki.51-1621/z.2026.02.001
    引用本文: 马红斐, 杨伊生. 小学生关于分数数量的迷思概念:一项基于访谈的质性研究J. 内江师范学院学报, 2026, 41(2): 1-9. DOI: 10.13603/j.cnki.51-1621/z.2026.02.001
    MA Hongfei, YANG Yisheng. Elementary students’ misconceptions about fraction magnitude: a qualitative study based on interviewsJ. Journal of Neijiang Normal University, 2026, 41(2): 1-9. DOI: 10.13603/j.cnki.51-1621/z.2026.02.001
    Citation: MA Hongfei, YANG Yisheng. Elementary students’ misconceptions about fraction magnitude: a qualitative study based on interviewsJ. Journal of Neijiang Normal University, 2026, 41(2): 1-9. DOI: 10.13603/j.cnki.51-1621/z.2026.02.001

    小学生关于分数数量的迷思概念:一项基于访谈的质性研究

    Elementary students’ misconceptions about fraction magnitude: a qualitative study based on interviews

    • 摘要: 分数概念是小学数学学习的重要难点,迷思概念能够有效反映学生对该概念的掌握情况.为探究小学生在分数数量概念上的认知特点,研究采用认知访谈法对呼和浩特市区公立小学40名六年级学生的迷思概念进行分析.结果显示,学生对分数数量概念的整体理解水平较低,主要存在三方面迷思:分数数量意识薄弱、数字敏感性不足,以及算子概念和除法偏向较为明显.进一步分析表明,分数数量概念的形成遵循特定的认知发展路径,即从涉及两个量的关系概念出发,经过抽象转化为涉及一个量的数量概念,最终发展为表征一个数的数字概念.

       

      Abstract: The concept of fractions is a major challenge in elementary mathematics learning, and misconceptions can effectively reflect students’ grasp of this concept. To explore the cognitive characteristics of elementary students regarding fractional quantities, the study employed cognitive interviews to analyze misconceptions among 40 sixth-grade students from public schools in Hohhot. The results indicate that students generally exhibit a low level of understanding of fractional quantities, with three main types of misconceptions: weak awareness of fractions as quantities, insufficient numerical sensitivity, and a pronounced tendency toward operator concepts and division bias. Further analysis reveals that the formation of fractional quantity concepts follows a specific cognitive developmental pathway-progressing from relational concepts (involving two quantities) to abstract quantity concepts (involving one quantity), and finally evolving into numerical concepts (representing a single number).

       

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