Mathematical Application Projects for Mechanical Engineers Concept, Guidelines and Examples Burkhard Alpers FH Aalen - University of Applied Sciences
Abstract: In this article, we present the concept of mathematical application projects as a means to enhance the capabilities of engineering students to use mathematics for solving problems in larger projects as well as to communicate and present mathematical content. As opposed to many case studies, we concentrate on stating criteria and project classes from which instructors can build instances (i.e. specific projects). The main goal of this paper is to facilitate the definition of new „good“ projects in a certain curricular setting. 1. INTRODUCTION Learning and training mathematical concepts and algorithms in engineering departments of German Universities of Applied Sciences ("Fachhochschulen") usually consists of a sequence of "small steps" with "small-sized" assignments. This is necessary in order to gain familiarity without overloading students with too much complexity. But in the end, an engineer is required to use mathematics (models, software) for solving problems in larger projects as well as to communicate and present mathematical content. Without also learning this further step in mathematics education for engineers, mathematical knowledge often remains "inert" (Mandl), i.e. small chunks of knowledge are existing, but the capability of how to apply them for solving a problem is missing. As a remedy, we introduced mathematical application projects in the third semester (Mathematics III) after students have learnt basic mathematical concepts and symbolic computation during semesters 1 and 2 in a mathematically coherent setting. The character and success of such projects heavily depends on the curricular embedding (mathematical and application field knowledge and capabilities of students) and on accompanying organizational and tutorial activities which we will describe in the next section. In order to really achieve the objectives stated above and to avoid frustration, projects have to be defined very carefully. As [Ludwig] already observed, whereas articles containing descriptions of special projects or case studies are frequent (cf. for engineering mathematics: [Mustoe], [Westermann], [Challis], [Janetzko]), there is only few systematic work on projects. In order to pursue a more systematic approach, we present and explain several criteria which projects in our curricular setting should fulfill like openness, mathematical richness, interesting and meaningful application context, usability of mathematical software, modularity. In doing this, we take into account criteria stated by [Ludwig], [Reichel], [Ernsberger], and [Wilkinson], and we compare our type of projects with those described in literature. Defining "good" projects according to these criteria is still a time-consuming task. We therefore tried to identify classes of application projects in mechanical engineering making definition of ever new projects easier by building instances of such classes. This way, individual projects can be defined such there is no copying of work of other groups in the same class or in former classes. As a worked example for a project belonging to one of the classes we then present the project "Motion function for the Hockenheim motodrom". Finally, we discuss our experience so far. 1
Proceedings der Int. Conf. on Technology in Math. Teaching (ICTMT 5), Klagenfurt 2001
2. CURRICULAR EMBEDDING AND ACCOMPANYING ACTIVITIES The mathematical part of the mechanical engineering curriculum at the Aalen University of Applied Sciences consists of three courses to be taken in semesters 1, 2, and 3, respectively. Mathematics I and II are lectured traditionally, including a written exam at the end. These courses contain the usual concepts of linear...