## Abstract

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.

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.

Original language | English |
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Pages (from-to) | 3-21 |

Number of pages | 18 |

Journal | Journal of Mathematical Modelling and Application |

Volume | 1 |

Issue number | 6 |

Publication status | Published - 2012 |

## Keywords

- mathematical modeling cycle
- higher education
- representations