Abstract
This chapter introduces a long-term modelling project that has been conducted at Goethe-Gymnasium-Germersheim with 14-/15-year-old students. The main question of this project was if (and how) it is possible to integrate real-world modelling tasks into regular math lessons in a way that demands for the application of knowledge from selected topics of a whole school year. Moreover we wanted to know if the pupils accept the intended frequency of five modelling phases as a convenient diversion or if they consider them not worthwhile (concerning the effort)? Finally, we were curious to learn to which extent we can expect pupils to learn mathematical modelling through frequent repetition. The students had to deal with five realistic modelling tasks and one final comparison task. Solutions developed by the students as well as the concept of the questionnaires used for evaluation are presented.
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Notes
- 1.
ECMI = European Consortium for Mathematics in Industry.
- 2.
Another reason was the fact that mathematical modelling started to appear more often in the math curricula in Germany.
- 3.
This is no general statement of course – it relates to our experience with schools in our region, but studies indicate that this phenomenon is not only restricted to Germany (see Kaiser and Maaß 2007).
- 4.
- 5.
Specific strategies which have been investigated and trained in preparatory lessons might be helpful during the modelling process.
- 6.
–4 pages, as a homework.
- 7.
How large is the moon? or Will there ever be a man running 100 m below 9 s?
- 8.
The comparison task was presented to the pupils at the end of the project (cf. Sect. 7).
- 9.
cf. (Fries et al. 2004 ).
- 10.
The pupils worked for approximately 5 weeks on this task in the form of a constant homework with an estimated work load of five lessons; this was in addition to two regular lessons spent on modelling this task.
- 11.
Idea taken from Gablonsky and Lang ( 2005 ).
- 12.
Besides the final comparison task.
- 13.
Note that the solid and dashed lines shall not indicate a development over time but are there to show the common bonds of the different data sets.
- 14.
Again they were supposed to work in teams of three to four pupils and we had an equal number of teams working on each task.
- 15.
Note, that only 95 pupils participated in the comparison project – hence there is no simple generalisation of these findings.
- 16.
The reports were assessed by members of TU Kaiserslautern who did not know any of the pupils.
- 17.
Here it was just 4.5 h for the comparison event – this is definitely too short!
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Bracke, M., Geiger, A. (2011). Real-World Modelling in Regular Lessons: A Long-Term Experiment. In: Kaiser, G., Blum, W., Borromeo Ferri, R., Stillman, G. (eds) Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0910-2_52
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