The influence of reasoning with emergent quantities on students' generalizations
The influence of reasoning with emergent quantities on students' generalizations
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DOI：
10.1080/07370000701632397
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发表时间：
2007-01-01
影响因子：
3.3
通讯作者：
Ellis, Amy B.
中科院分区：
文献类型：
--
作者：
Ellis, Amy B.
本文报告了两组代数学生的数学概括，一组主要关注数量关系，另一组主要关注与数量无关的数字模式。结果表明，鼓励关注数字模式的教学支持对模式、程序和规则的概括，而鼓励关注数量的教学支持关于关系、情景之间的联系和动态现象的概括，如恒定速度的本质。对学生概括的相似性和差异性的考察表明，学生所从事的定量推理的类型最终证明对他们概括的影响比仅仅关注数量与数字更重要。为了开发关于关系的强大的、全局的概括，学生们必须将比率构建为联系两个初始量的突发量。本文讨论了涌现比数量的作用，因为它与支持学生正确概括能力的教学实践有关。
This paper reports the mathematical generalizations of two groups of algebra students, one which focused primarily on quantitative relationships, and one which focused primarily on number patterns disconnected from quantities. Results indicate that instruction encouraging a focus on number patterns supported generalizations about patterns, procedures, and rules, while instruction encouraging a focus on quantities supported generalizations about relationships, connections between situations, and dynamic phenomena, such as the nature of constant speed. An examination of the similarities and differences in students' generalizations revealed that the type of quantitative reasoning in which students engaged ultimately proved more important in influencing their generalizing than a mere focus on quantities versus numbers. In order to develop powerful, global generalizations about relationships, students had to construct ratios as emergent quantities relating two initial quantities. The role of emergent-ratio quantities is discussed as it relates to pedagogical practices that can support students' abilities to correctly generalize.