Using isomorphic problems to learn introductory physics

Shih-Yin Lin,Chandralekha Singh

doi:10.1103/physrevstper.7.020104

Shih-Yin Lin, Chandralekha Singh

Open Access

https://doi.org/10.1103/physrevstper.7.020104

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Abstract

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 sixty two students from a calculus-based and an algebra-based introductory physics course were given a quiz in the recitation in which they had to first learn from a solved problem provided and take advantage of what they learned from it to solve another problem (which we call the quiz problem) which was isomorphic. Previous research suggests that the multiple-concept quiz problem is challenging for introductory students. Students in different recitation classes received different interventions in order to help them discern and exploit the underlying similarities of the isomorphic solved and quiz problems. We also conducted think-aloud interviews with four introductory students in order to understand in-depth the difficulties they had and explore strategies to provide better scaffolding. We found that 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. However, they were not necessarily able to apply the principles correctly. Research suggests that more scaffolding is needed to help students in applying these principles appropriately. We outline a few possible strategies for future investigation.

Highlights

IntroductionLearning physics requires unpacking these principles and understanding their applicability in a variety of contexts that share deep features [1,2]
Research has shown that when physics experts and novices are given several introductory physics problems and asked to categorize the problems based upon similarity of solution, experts tend to categorize them based upon the fundamental physics principles while novices tend to group them based upon the surface features such as pulley or inclined plane [1]
We found that students in both the calculusbased and algebra-based courses were able to recognize the similarities between the isomorphic problems in terms of the relevant physics principles involved when they were asked to learn from a solved problem and transfer what they learned from the example problem to solve another isomorphic quiz problem

Summary

Introduction

Learning physics requires unpacking these principles and understanding their applicability in a variety of contexts that share deep features [1,2]. A major goal of most calculus-based and algebra-based introductory physics courses is to help students learn to recognize the applicability of a physics principle in diverse situations and discern the deep similarities between the problems that share the same underlying physics principles but have different surface features. Research has shown that when physics experts and novices are given several introductory physics problems and asked to categorize the problems based upon similarity of solution, experts tend to categorize them based upon the fundamental physics principles (e.g., conservation of mechanical energy, Newton’s 2nd law, etc.) while novices tend to group them based upon the surface features such as pulley or inclined plane [1]. When a group of introductory physics students and physics faculty were asked to rate the similarities

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