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Student Understanding of States of Stress in Mechanics of Materials

Abstract

Students often have far less conceptual understanding in core engineering courses than faculty assume. The first wide-spread application of the Force Concept Inventory in the early 1980’s highlighted students’ lack of understanding in fundamental physics principles. Recently, educators have been reevaluating student understanding of concepts in the standard science and engineering curriculum using concept inventory instruments in topics such as thermodynamics, mechanics, and fluid mechanics. The objective of this study is to develop a methodology to observe specific examples of difficulty in conceptual understanding which could be used to infer specific student misconceptions. To achieve this task a pilot study was undertaken using students in mechanics of materials (alternately known as strength of materials). The general topic of stress states was chosen for more intensive study. Exploratory interviews using three basic loading cases, pure axial tension, pure shear, and a simply supported beam in bending, revealed that the students interviewed were unable to relate internal stresses to loadings. The students had just completed a summer session of mechanics of materials, but most were unable to define stress. They rarely differentiated between internal and external forces when answering conceptual questions or performing calculations. These difficulties suggest student misconceptions within the topics of stress, and stress distributions. Results of this study augment the poor results that university educators find when implementing concept inventory tests, while providing some general guidance in developing new curriculum materials.

I. Introduction

It has been shown that most students do not gain fundamental knowledge in introductory science and engineering courses.1 The high graduation rates and successful completion of standardized tests such as the Fundamentals of Engineering exam show that the majority of students graduating from accredited universities have some form of understanding of the subjects, but concept inventories and student interviews consistently show that a majority of students cannot qualitatively analyze the most basic situations. These difficulties are most often attributed to a lack of deeper conceptual understanding of the topics. Application of validated concept inventories also suggests that standard instruction does not significantly improve student understanding of these basic concepts. In order to address these issues new instructional methods are being developed. These new approaches are based on theoretical and applied studies of why some concepts are more difficult to learn than others.

II. Literature Review

A simple theory that explains many aspects of student learning and suggests plausible solutions is Micheline Chi and Rod Roscoe’s theory of misconceptions.2 Building upon the commonly accepted theoretical backgrounds of constructivism and Piaget’s theory of

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Brown, S., & Montfort, D., & Findley, K. (2007, June), Student Understanding Of States Of Stress In Mechanics Of Materials Paper presented at 2007 Annual Conference & Exposition, Honolulu, Hawaii. 10.18260/1-2--2809