### S10-AS4-4 - Assessing and Justifying the Reasonableness of Answers to Open-Ended Problems

3. Research Full PaperAaron Johnson

^{2}, Mary Rola

^{1}, Shigemitsu Suzuki

^{3}

^{1}University at Buffalo

^{2}University of Colorado - Boulder

^{3}University of Michigan

**Introduction**

This full paper examines how students determine if there answer is reasonable when solving an open-ended homework problem. Creating mathematical models to model and analyze real world scenarios is an essential part of engineering. Students learn how to create these models in their undergraduate courses such as thermodynamics, fluid mechanics, and statics, typically taught during their second and third years. The goal of these courses is to learn scientific laws and their corresponding mathematical representations, subject to a number of simplifying assumptions. Students often learn these mathematical models by watching the instructor go through examples during lecture and by practicing applying them during assigned homework problems. Typical homework problems are well-defined in nature and have a single numerical answer. Studies in engineering have argued these well-defined problems do not prepare engineering students for their work as a professional engineer where they will have to solve ill-defined problems where success is defined by financial, regulatory, ethical, or environmental standards.

To address this limitation of typical homework problems, our research team has created (BLINDED NAME OF PROBLEMS) as a way for students to practice engineering judgement and discipline-based mathematical modeling as applied to a real-world problem. Our framework of engineering judgement is based off of the work of Gainsburg, who identifies eight ways professional structural engineers use engineering judgement. The first of these is “determining what is a good or precise enough calculation or estimation,” which we refer to as considering the

*reasonableness*of a calculation. This study of homework problems examines how students consider if their answer is reasonable or not after solving an open-ended homework problem. Students enrolled in two sophomore-level statics courses at different universities were given open-ended homework problems in which they were required to analyze different real-world objects by making assumptions to create a mathematical model. In both problems, students were asked to determine the diameter and material of one or two circular support bars of the object. After solving the problem, students were asked if their answer was reasonable and to justify their answer.

This study first examines how students went about calculating the diameter of the support bar(s) and choosing the bars’ material. We then ask two research questions:

- Is there a consistent relationship between the diameters that students calculated and their assessments of reasonableness?
- What evidence do students use to justify their assessment of reasonableness?