Fraction images: the case of six and a half
Fraction images: the case of six and a half
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分数图像：六分半的情况
DOI：
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发表时间：
2020
影响因子：
1.3
通讯作者：
Rina Zazkis
中科院分区：
文献类型：
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作者：
Ofer Marmur;Xiaoheng Yan;Rina Zazkis
摘要本研究探讨未来国小教师在以非整数为分子或分母的情形下，尝试提供具有数学意义的符号。这些数据包括对一项任务的33个响应，该任务询问1/6和1/7之间的数字是否存在，其中参与者被要求编写一个假设的课堂对话来解决这个问题，并对所涉及的数学进行解释。分析运用了“符号表征”和“概念意象”的理论框架。研究结果表明，强烈依赖于流行的分数图像和困难分配的意义“6½”时，它出现在分子或分母的分数表示。这些困难是通过三种方法证明了脚本中，有关分数的符号表示，分数的视觉表示，和允许的操作分数。我们建议教师教育课程可以进一步强调分数和非典型符号表征的集合模型。
ABSTRACT We explore prospective elementary-school teachers’ attempts to provide signs and symbols with mathematical meaning in a case involving non-integers as numerator or denominator. The data comprises 33 responses to a task inquiring about the existence of numbers between 1/6 and 1/7, in which the participants were asked to compose a hypothetical classroom dialogue addressing this issue, and provide explanations on the mathematics involved. The analysis utilised the theoretical frameworks of “semiotic representation” and “concept image”. The findings indicate a strong reliance on prevalent fraction images and difficulties in assigning meaning to “6½” when it appears in the numerator or denominator of a fraction representation. These difficulties are examined via three approaches demonstrated in the scripts, relating to the symbolic representation of fractions, visual representation of fractions, and permissible operations on fractions. We suggest teacher-education courses may put further emphasis on the set model of fractions and atypical semiotic representations.