Cross-context look at upper-division student difficulties with integration

Bethany R Wilcox,Giaco Corsiglia

doi:10.1103/physrevphyseducres.15.020136

Bethany R Wilcox, Giaco Corsiglia

Open Access

https://doi.org/10.1103/physrevphyseducres.15.020136

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Abstract

We investigate upper-division student difficulties with direct integration in multiple contexts involving the calculation of a potential from a continuous distribution (e.g., mass, charge, or current). Integration is a tool that has been historically studied at several different points in the curriculum including introductory and upper-division levels. We build off of these prior studies and contribute additional data around student difficulties with multi-variable integration at two new points in the curriculum: middle-division classical mechanics, and upper-division magnetostatics. To facilitate comparisons across prior studies as well as the current work, we utilize an analytical framework that focuses on how students activate, construct, execute, and reflect on mathematical tools during physics problem solving (i.e., the ACER framework). Using a mixed-methods approach involving coded exam solutions and student problem-solving interviews, we identify and compare students' difficulties in these two different context and relate them to what has been found previously in other levels and contexts. We find that some of the observed student difficulties were persistent accross all three contexts (e.g., identifying integration as the appropriate tool, and expressing the difference vector), while other difficulties seemed to fade as students advanced through the curriculum (e.g., expressing differential line, area, and volume elements). We also identified new difficulties that appear in different contexts (e.g., interpreting and expressing the current density).

Highlights

Physics education research (PER) as a field has a long history of conducting student difficulties research focused on identifying the challenges and problems that students face when dealing with specific physics concepts or mathematical tools [1,2]
It is important to note that these studies were not designed or conducted using the ACER framework, and often had goals that went beyond pure investigations of students’ difficulties; for the purposes of this summary, we focus on the aspects of these findings that directly relate to student difficulties with integration as a mathematical tool in physics problem solving
We build on prior work investigating students’ use of direct integration as a mathematical tool in physics problem solving. We extend this prior work, which focused on students’ difficulties in the context of junior-level electrostatics, by investigating students’ use of integration in two additional points in the undergraduate curriculum: in the context of gravitation at the sophomore level, and magnetostatics at the junior level

Summary

Introduction

Physics education research (PER) as a field has a long history of conducting student difficulties research focused on identifying the challenges and problems that students face when dealing with specific physics concepts or mathematical tools [1,2]. We begin with a summary of our own prior work using the ACER framework to investigate students use of direct integration in the context of upper-division electrostatics and continue to discuss comparisons with work in other contexts and at other levels. The framework considers four main components present in this type of mathematically involved problem solving: activation of the mathematical tool, construction of the mathematical model, execution of the mathematics, and reflection on the results These components were identified by studying the general structure of expert problem solving using modified task analysis [8]. For the purposes of cross-study comparisons, we will focus categorizing students’ difficulties within the general components of the framework (i.e., activation, construction, execution, and reflection)

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