Application and Confidence Inventories for Assessing Curricular Change in Introductory Engineering Mathematics Instruction

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This project is a continuation of efforts to enhance engineering students' abilities to transfer and apply the calculus they learn in their first year of college to the introductory engineering courses they take in their second year. In the course of a 2006 curriculum review, engineering faculty observed that many students who succeed in the first year mathematics courses nonetheless have difficulty using elementary mathematical concepts to represent physical quantities and their relationships in their second year engineering courses. Spurred by Engineering Curriculum Task Force recommendations, in the spring of 2007 a group of engineering and mathematics faculty began to infuse core engineering mathematics courses with engaging and diverse problem solving experiences, incorporating example applications from the physical sciences and engineering. In a pilot effort in Fall 2007 these types of applications were integrated into the first required math course in the engineering math sequence. This was accomplished by transforming one of two weekly recitation sections into a collaborative problem-solving session. This project is evaluating the effect of adding these activities to the curriculum, by developing instruments to assess students' understanding of mathematics as representative of physical phenomena and their skill in applying mathematics to solve problems involving physical quantities and relationships, both before and after their participation in the problem-solving workshops; and also to assess students' confidence about their understanding of mathematics and their ability to use mathematics to succeed in engineering, both before and after their participation in the problem-solving workshops. The project is also assessing whether the inclusion of collaborative applied problem-solving in the first-year calculus courses leads to improvement in students' abilities to apply mathematics in the core second-year engineering courses - mechanics, dynamics, electrical circuits, and thermodynamics. The project's central questions are exploring how curricular changes in both content and method of instruction might enhance student ability to apply mathematics to classical engineering applications and improve student confidence in solving problems. Tools are being developed for assessing the degree of integration of core math, science, and engineering content. The project is being evaluated by an independent evaluator.