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Burkhard Alpers
Department of Mechanical Engineering, Hochschule Aalen, Germany
In the SEFI Mathematics Working Group's Curriculum Document (Alpers et al. 2013) the mathematical modelling competency is listed as one of eight competencies making up the overall mathematical competence. One might assume that this competency is mainly acquired in application subjects like statics where mathematical concepts are used to create models and to solve problems of application interest in such models. Yet, the investigation in (Alpers 2015) has shown that only a few steps of the mathematical modelling cycle described in (Blum & Leiß 2007) are really addressed in statics tasks presented in two widespread textbooks. A typical task in (Hauger et al. 2012) is the "tumbler task" where the tumbler is already idealized as an object consisting of a hemisphere and a cone on top and the question of whether it will work is also already clearly stated by asking when the center of gravity is below the separating plane. In this contribution this task is used as an example for showing how a standard statics task can be reformulated as a project task that offers many learning opportunities regarding the different steps in the modelling cycle. One particular reformulation was given to a group of students as a mathematical project. They had to create a design environment in Maple
(R) where the user can specify the cross section of the upper part and the worksheet gives information on the suitability. For some examples, the design had to be exported to a CAD programme in order to create a body which then should be produced using a turning lathe such that the design could be validated. We will report on the results.
Alpers, B. et al. (2013). A Framework for Mathematics Curricula in Engineering Education. A Report of the Mathematics Working Group, SEFI, Brussels.
Alpers, B. (2015). The Mathematical Modelling Competencies Required for Solving Engineering Statics Assignments, ICTMA 17 (Nottingham), preprint
Blum, W., Leiß, D. (2007). How do students and teachers deal with modelling problems? In: Haines, C. et al. (Eds.): Mathematical Modelling, ICTMA 12, Horwood Publishing, Chichester, 222-231
Hauger, W. et al. (2012). Aufgaben zu Technische Mechanik 1-3. Statik, Elastostatik, Kinetik, 7th edition, Berlin-Heidelberg: Springer
Professor for Mathematics and Computer Science