Extending Modelling Activity Diagrams as a tool to characterise mathematical modelling processes

In this paper, we present a qualitative study in which we analyse the videorecordings of four groups of students solving Fermi Problems. Previous studies show that Secondary School students solve this type of problems using complex problem solving processes and developing mathematical models. In order to analyse the students’ problem solving processes, so-called Modelling Activity Diagrams were used. The results of the present study demonstrate that solving Fermi problems is a complex matter, and that some of the theoretical tools used in the field of Mathematical Education fail to adequately reflect this level of complexity. In addition, Modelling Activity Diagrams are presented as a more detailed analysis tool to characterise student choices and actions, as well as to make the structure of the Fermi problem addressed more visible

Reflections on progress in mathematical modelling research

The terms, models and modelling, have been used variously in the literature, including in reference to solving word problems, conducting mathematical simulations, generating representations of problem situations (including constructing explanations of natural phenomena), creating cognitive representations while solving a particular problem, and engaging in a bidirectional process of translating between a real-world situation and mathematics (e.g., Cai, Cirillo, Pelesko, Borromeo Ferri, Borba, Geiger, Stillman, English, Wake, Kaiser, & Kwon, 2014; Doerr & Tripp, 1999; English & Halford, 1995; Gravemeijer, 1999; Greer, 1997; Lesh & Doerr, 2003; Romberg, Carpenter, & Dremock, 2005)..