The Many Faces of the Mathematical Modeling Cycle

In literature about mathematical modeling a diversity can be seen in ways of presenting the modeling
cycle. Every year, students in the Bachelor’s program Applied Mathematics of the Eindhoven
University of Technology, after having completed a series of mathematical modeling projects, have
been prompted with a simple three-step representation of the modeling cycle. This representation
consisted out of 1) problem translation into a mathematical model, 2) the solution to mathematical
problem, and 3) interpretation of the solution in the context of the original problem. The students’ task
was to detail and complete this representation. Their representations also showed a great diversity.
This diversity is investigated and compared with the representations of the students’ teachers. The
representations with written explanations of 77 students and 20 teachers are analyzed with respect to
the presence of content aspects such as problem analysis, worlds/models/knowledge other than
mathematical, verification, validation, communication and reflection at the end of the modeling
process. Also form aspects such as iteration and complexity are analyzed. The results show much
diversity within both groups concerning the presence or absence of aspects. Validation is present most,
reflection least. Only iteration (one is passing the modeling cycle) more than once is significantly
more present in the teachers’ group than in the students’ group. While accepting diversity as a natural
phenomenon, the authors plea for incorporating all aspects mentioned into mathematical modeling
education.