利用同构问题对学习入门物理：从两步问题到三步问题的转换
Using an Isomorphic Problem Pair to Learn Introductory Physics: Transferring from a Two-step Problem to a Three-step Problem
摘要：
在这项研究中，我们研究了入门物理学生的能力，执行类比推理之间的两个同构的问题，采用相同的基本物理原理，但有不同的表面特征。382名学生从微积分为基础的和代数为基础的入门物理课程被要求学习从一个解决的问题，并利用他们从它学到的解决另一个同构的问题（我们称之为测验问题）。所提供的解决问题有两个子问题，而测验问题有三个子问题，这是已知的具有挑战性的入门学生从以前的研究。除了已解决的问题，学生还获得了额外的脚手架支持，旨在帮助他们辨别和利用同构解决和测验问题的潜在相似性。结果表明，学生有很大的困难，他们所学到的从一个2步的问题，以3步的问题。虽然大部分学生都能够从所解决的问题在一定程度上与脚手架提供的学习，并调用测试问题中的相关原则，他们不一定能够正确地应用这些原则。我们还与6名入门学生进行了有声思维访谈，以深入了解他们遇到的困难，并探索提供更好支架的策略。访谈表明，学生往往肤浅地映射的原则，在解决问题的测验问题，没有必要了解每个原则背后的管理条件，并检查在新的情况下，在深入的方式原则的适用性。研究结果表明，需要更多的脚手架，以帮助学生从一个两步的问题转移到一个三步的问题，并适当地应用物理原理。
英文摘要：
In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred and eighty two students from a calculus-based and an algebra-based introductory physics course were asked to learn from a solved problem provided and take advantage of what they learned from it to solve another isomorphic problem (which we call the quiz problem). The solved problem provided has two sub-problems while the quiz problem has three sub-problems, which is known to be challenging for introductory students from previous research. In addition to the solved problem, students also received extra scaffolding supports that were intended to help them discern and exploit the underlying similarities of the isomorphic solved and quiz problems. The results suggest that students had great difficulty in transferring what they learned from a 2-step problem to a 3-step problem. Although most students were able to learn from the solved problem to some extent with the scaffolding provided and invoke the relevant principles in the quiz problem, they were not necessarily able to apply the principles correctly. We also conducted think-aloud interviews with 6 introductory students in order to understand in-depth the difficulties they had and explore strategies to provide better scaffolding. The interviews suggest that students often superficially mapped the principles employed in the solved problem to the quiz problem without necessarily understanding the governing conditions underlying each principle and examining the applicability of the principle in the new situation in an in-depth manner. Findings suggest that more scaffolding is needed to help students in transferring from a two-step problem to a three step problem and applying the physics principles appropriately.
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