tandfonline.com har udgivet en rapport under søgningen “Teacher Education Mathematics”:
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.