Teaching Mathematics by Comparison: Analog Visibility as a Double-Edged Sword
Teaching Mathematics by Comparison: Analog Visibility as a Double-Edged Sword
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DOI：
10.1037/edu0000056
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发表时间：
2016-02-01
影响因子：
4.9
通讯作者：
Richland, Lindsey Engle
中科院分区：
文献类型：
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作者：
Begolli, Kreshnik Nasi;Richland, Lindsey Engle
比较单个问题的多种解决方案是发展灵活数学思维的重要模式，但指导性地领导这项活动具有挑战性（Stein、Engle、Smith 和 Hughes，2008）。我们测试教师在让学生解决问题后必须做出的一项决定：是仅口头讨论学生的解决方案还是让其他人看到它们。五年级的学生观看了一堂有关比例的数学视频录像，其中学生描述了一个误解和两个正确的策略。最初的课程是通过视频编辑来创建 3 个具有恒定音频的版本，但其中比较的解决方案是 a）仅口头呈现，b）按照描述的顺序顺序可见，或 3）所有解决方案在整个讨论过程中描述后都是可见的。当所有解决方案在整个讨论过程中都可见时，后测试和延迟后测试措施显示出最大的收益，特别是比仅口头陈述概念知识更好。按顺序向学生展示解决方案的视觉表示导致总体收益最低，误解率最高。这些结果表明，类似物的视觉表示可以支持学习和图式形成，但它们也可能是有害的——在我们的例子中，如果按顺序呈现为可见的。
Comparing multiple solutions to a single problem is an important mode for developing flexible mathematical thinking, yet instructionally leading this activity is challenging (Stein, Engle, Smith, & Hughes, 2008). We test 1 decision teachers must make after having students solve a problem: whether to only verbally discuss students' solutions or make them visible to others. Fifth grade students were presented with a videotaped mathematics lesson on ratio in which students described a misconception and 2 correct strategies. The original lesson was manipulated via video editing to create 3 versions with constant audio but in which the compared solutions were a) presented only orally, b) visible sequentially in the order they were described, or 3) all solutions were visible after being described throughout the discussion. Posttest and delayed posttest measures revealed the greatest gains when all solutions were visible throughout the discussion, particularly better than only oral presentation for conceptual knowledge. Sequentially showing students visual representations of solutions led to the lowest gains overall, and the highest rates of misconceptions. These results suggest that visual representations of analogs can support learning and schema formation, but they can also be hurtful-in our case if presented as visible in sequence.