Towards curricular coherence in integers and fractions: a study of the efficacy of a lesson sequence that uses the number line as the principal representational context
Towards curricular coherence in integers and fractions: a study of the efficacy of a lesson sequence that uses the number line as the principal representational context
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实现整数和分数的课程连贯性：对使用数轴作为主要表征背景的课程序列的有效性的研究
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发表时间：
2013
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通讯作者：
M. Gearhart
中科院分区：
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作者：
G. Saxe;Ronli Diakow;M. Gearhart
本文报告了一项关于通过表征学习数学（LMR）的有效性的研究，LMR是一个创新的课程单元，旨在支持小学高年级学生对整数和分数的理解。该单元支持整数和分数的综合处理，通过(a)使用数轴作为跨领域的代表性背景，以及(b)在课堂社区中建立数学定义，成为支持学生论证，概括和解决问题的资源。在有效性研究中，采用相同地区课程（日常数学）的四年级和五年级教师在背景指标上进行匹配，然后分配到LMR实验班（n = 11）或对照组（n = 8, 10个教室）。在秋季学期，LMR教师在19天的数学教学中实施LMR单元，在其他时间实施地区课程。HLM分析表明，在整数和分数知识的期末和年终评估中，LMR学生比比较学生取得了更大的成就；无论入学能力水平如何，LMR学生的增长率是相似的，并且LMR学生的增长发生在包括数轴表示和不包括数轴表示的项目类型上。研究结果指出LMR序列在支持整数和分数领域的教学和学习方面的有效性。
This paper reports a study of the efficacy of Learning Mathematics through Representations (LMR), an innovative curriculum unit designed to support upper elementary students’ understandings of integers and fractions. The unit supports an integrated treatment of integers and fractions through (a) the use of the number line as a cross-domain representational context, and (b) the building of mathematical definitions in classroom communities that become resources to support student argumentation, generalization, and problem solving. In the efficacy study, fourth and fifth grade teachers employing the same district curriculum (Everyday Mathematics) were matched on background indicators and then assigned to either the LMR experimental classrooms (n = 11) or the comparison group (n = 8 with 10 classrooms). During the fall semester, LMR teachers implemented the LMR unit on 19 days and district curriculum on other days of mathematics instruction. HLM analyses documented greater achievement for LMR students than Comparison students on both the end-of-unit and the end-of year assessments of integers and fractions knowledge; the growth rates of LMR students were similar regardless of entering ability level, and gains for LMR students occurred on item types that included number line representations and those that did not. The findings point to the efficacy of the LMR sequence in supporting teaching and learning in the domains of integers and fractions.