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Teaching about thermal expansion: investigating the effectiveness of a cognitive bridging approach

机译：关于热膨胀的教学：研究认知桥接方法的有效性

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Background: It is widely known that for many students it is very difficult to correctly predict how thermal expansion affects the appearance of a metal plate with a circular hole. Interviews with school teachers show that the source of this difficulty could stem from the fact that students' internal visualizations of an arbitrary object's thermal expansion often boil down to visualizing changes along one dimension only. Purpose: In this study, we investigated how students' mental models about one-dimensional expansion can be extended for purposes of running mental simulations about expansion along two dimensions. Sample: To that end a pretest-posttest quasi-experiment has been conducted, with 100 students in the control group and 95 students in the experimental group. Design and methods: Whereas control group students received traditional instruction with a focus on formal representations, in the experimental group the students were led to draw an analogy between heating of a straight rod and a circular rod of same length, whereby the internal structure of the rods was represented by springs. Results: Eventually, it has been found that students from the experimental group were significantly more successful at predicting the effects of thermal expansion, especially within contexts of objects with holes. Conclusion: Analogies and extreme case reasoning can be effectively used for helping the students to correctly transfer their mental models about one-dimensional expansion to situations that require reasoning about expansion along two dimensions.
机译：背景：众所周知，对于许多学生来说，很难正确预测热膨胀如何影响具有圆孔的金属板的外观。与学校教师的访谈显示，造成这种困难的根源可能是因为学生对任意物体热膨胀的内部可视化通常归结为仅沿一个维度进行可视化。目的：在这项研究中，我们研究了如何扩展学生关于一维扩展的心理模型，以进行关于二维扩展的心理模拟。样本：为此，进行了前测后测准实验，对照组100名学生，实验组95名学生。设计和方法：对照组的学生接受的是注重形式表示的传统教学，而实验组的学生则被引导在加热相同长度的直杆和圆杆之间进行类比，从而使内部结构保持一致。杆以弹簧为代表。结果：最终，发现实验组的学生在预测热膨胀的影响上更为成功，特别是在有孔物体的环境下。结论：类推和极端案例推理可以有效地帮助学生正确地将他们关于一维扩展的思维模型转移到需要沿二维扩展进行推理的情况。

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