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Teaching Freshman Engineering Students to Solve Hard Problems Robert Leland1, James Richardson2, Tan-Yu Lee3, John Dantzler4 1 Electrical and Computer Engineering Dept. /2Civil and Environmental Engineering Dept./3Mathematics Department, University of Alabama/4Censeo Research, Inc.

1. Introduction

The typical freshman engineering student encounters subject matter that is more complex and delivered at a faster rate than what they experienced in high school. Combined with weak problem solving skills and inadequate study habits, this can be a recipe for disaster. “Judgment day” for many students occurs when the first round of midterms are handed back. Some students give up and make plans to switch majors. Others continue to struggle in spite of increased study effort. A common complaint is, “I understand the material, but I can’t seem to work the problems on the exam correctly.”

We are developing a course to make freshman engineering students better problem solvers. We focus on how to set up problems that are unfamiliar to the students, but can be solved with the math concepts the students are already familiar with.

We emphasize the use of hard problems and explanation. In hard problems the solution method and concepts needed for solution are not immediate. Exercises are designed to train students to expend effort to obtain a mathematical understanding of a problem sufficient to allow its solution, recognize when such understanding has been achieved, and rely on a wide spectrum of prior knowledge.

The emphasis on explanation appears to be a unique feature of our course. We emphasize explanation as a learning skill by fostering self-explanation, in which students’ process worked examples by explaining the concepts and purposes behind each step. Students also explain their solutions to others in the context of cooperative learning exercises and short class presentations. Explaining helps students clarify the concepts in their solutions, which facilitates transfer of those concepts to new situations, and builds self- efficacy, or domain specific self-confidence, in both the explainer and listener.

The authors are teaching the course to one of 8 sections of GES 131 Foundations of Engineering I, an existing introduction to engineering course. The impact of our course was assessed through a pre and post test and a pre and post math/problem solving self-efficacy questionnaire given to both our section and a control section, matched for ACT scores. Students were selected for the experimental and control sections to avoid the volunteer effect. A key goal of our course is the transfer of problem solving skills to future coursework. To assess transfer, we will compare performance of the experimental and control groups on certain exam problems in follow-on math and physics courses.

2. Rationale for the Course

The goal of our course is to teach mathematical problem solving in a way that leads to transfer of knowledge and skills to future coursework. We felt several factors were essential:

Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright © 2005, American Society for Engineering Education

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Lee, T., & Dantzler, J., & Leland, R., & Richardson, J. (2005, June), Teaching Freshman Engineering Students To Solve Hard Problems Paper presented at 2005 Annual Conference, Portland, Oregon. 10.18260/1-2--14804