A fit model for model fitting – an a-didactical situation for model
building
Petersson Jöran
Mathematical modelling in school mathematics encompasses a wide range of questions such as curricular aspects, mathematical concepts involved, orchestrating lesson activities, and many more. When building models, one approach is to use epistemological arguments and another approach is to base the model on empirical data. In the latter case, we can either focus on applying the resulting model to real life problems or we can focus on the mathematical methods needed to find the resulting model.
In this empirical study, students in school year 10 in Sweden were asked “How do you think a digital tool calculates the fitted curve?” Doing so, the students were given an open-response task where they themselves are expected to develop mathematical knowledge that is new to them. One outcome of the students’ work was the following: They suggested mathematical methods corresponding to those analytical and geometrical methods that have been developed and used through the history of mathematics. Moreover, they suggested both discrete and continuous metric spaces as a means for measuring the distance between data and model. They also suggested modern methods from exploratory data analysis such as trimming the empirical data before fitting the model to them. Another outcome was that the tasks for the students were formulated so that they promoted and enthused the students’ mathematical creativity and reasoning in a way that in this mathematical area reached far beyond the curriculum for secondary school mathematics.
Source for this document
Petersson, J. (2019). A fit model for model fitting –an a-didactical situation for model building. NOFA7 Abstracts, Stockholm University, 13-15 May, 2019 (p. 169). <
https://www.su.se/polopoly_fs/1.437496.1557495063!/menu/standard/file/NOFA7 abstracts 190510.pdf>
