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The Use of Mathematical Thinking to Deal with Uncertainty in a Capstone Design Course mathematics, engineering design, uncertainty, situated cognition, naturalistic inquiry

Abstract

In order to understand how engineering students deal with uncertainty in a normal design task, we studied a team of five industrial engineering students in a capstone class over the course of five months as they worked with professional engineers from a local company. The framework of mathematical thinking that guided this study as we investigated how these students engaged in mathematical thinking while they designed. We found that two aspects of mathematical thinking were most often used when the students were dealing with uncertainty in their design: problem solving strategies and the use of social resources. These findings have the potential to influence how engineering educators integrate engineering science and real-world design tasks.

Introduction

There have been debates among the engineering education community on how and how much mathematics should be taught to engineering students. The debates arise because studies like the one done by Underwood show that mathematics used in people’s jobs are different from what is taught in school1. Also, studies such as the one by Jonassen et al. show that engineering workplace problems are ill-structured2. So the question of how teaching well-structured problems in engineering science courses would transfer to ill-structured design tasks is another motivation for rethinking the engineering curriculum. Dym pointed out that design problems have the quality of “divergent inquiry”, that “there exist multiple alternative known answers, regardless of being true or false, as well as multiple unknown possible answers for any given question” 3. That quality seems to conflict with the principles and values of “convergent thinking” that are at the core of engineering science approaches, which always lead to a specific set of answers.

Design is a complex cognitive process, and a good designer has to tolerate ambiguity and handle uncertainty3 that can occur or reemerge at any stage of design. This paper will address the question of how engineering students deal with the ambiguity and uncertainty that emerges throughout the process of design (in this paper, we will only use the term “uncertainty”). The uncertainty students might encounter in design could be in a number of forms: information that needs to be gathered, precise information that does not exist, and multiple alternatives that students must chose between. Individuals may take multiple approaches to deal with the

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Hsu, M., & Cardella, M. (2009, June), The Use Of Mathematical Thinking To Deal With Uncertainty In A Capstone Design Course Paper presented at 2009 Annual Conference & Exposition, Austin, Texas. 10.18260/1-2--4889