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Problem-solving experience through light dose computational mathematical modules for undergraduate engineering students Abstract

In this paper, the authors discuss the development of a framework for creating computational mathematics modules for engineering students. The purpose of the modules is to introduce mathematical concepts through modeling real-world applications and is intended to develop the students’ ability to generalize a concept and to work with models of varying abstraction. The authors represent an interdisciplinary team contributing expertise from the fields of mathematics, computational science, and teacher education.

Introduction

Postmodern technology is characterized by great complexity and demands tremendous modeling and abstraction capabilities. For students to be successful in most engineering program, they should be able to apply the mathematics to model this complexity1,2. Problem-solving experiences have been advocated for decades in numerous textbooks, reference articles, and teaching modules3,4,5,6,7,8,9,10,11. The authors observed that many students enrolled in entry-level engineering and computer science courses tend to plug in data without considering the purpose of the analysis and demonstrate little ability to extend mathematical concepts beyond an algorithmic level. These observations motivated the authors to form an interdisciplinary team of university faculty to discuss the development of instructional mathematics and computer science modules that would enhance students’ ability to apply complex mathematical reasoning when presented with novel real world problems. The authors met once a week for six months in roundtable discussions. In these discussions the authors identified the following challenges teachers face when teaching mathematics : 1) motivating students in the applications of the mathematical concepts that reflect realistic problems in their prospective engineering careers, 2) integrating these complicated applications into the tight schedule of engineering courses, 3) leveraging the overwhelming complexity so that the students are not intimidated, and 4) compensating for the lack of physical models required in most engineering applications The authors considered these challenges in the development of modules and agreed that a framework for module development was required. The authors began preliminary research to develop such a framework centered on the concept of abstraction.

The authors began by exploring resources developed by other colleagues, reviewing the existing digital library and organizations that provide free course materials relevant to engineering courses offered at the authors' home institutions. Researches also examined a past module developed by one of the authors that implemented light doses of mathematical modeling that accommodated the tight schedule of various mathematics courses taught by those authors. Based on polarized feedback from students who participated in these past modules, the authors began exploring ways to address the diverse learning needs of entry level computer science, and engineering students.

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Raghavan, J., & Sena, L., & Liu, H., & Bethelmy, D. (2008, June), Problem Solving Experience Through Light Dose Computational Mathematical Modules For Engineering Students Paper presented at 2008 Annual Conference & Exposition, Pittsburgh, Pennsylvania. 10.18260/1-2--4408