Investigating students’ modelling styles in the process of scientific-mathematical modelling

Abstract

Modelling plays an important role for inquiry in science and mathematics education; therefore, a lot of research has been done in this field from both perspectives. However, an integrated view combining previous findings is rather limited. For the specific case of line graphs as a common representation that models relations between different variables in science, an integrated model of scientific-mathematical modelling was developed. The model integrates a scientific and mathematical perspective that describes line graphs as graphical representations of functional relationships. This model is used as a theoretical framework a) to describe cognitive processes that are necessary for modelling scientific phenomena with mathematical functions represented as line graphs and b) to analyse these processes empirically. In the presented study two modelling tasks were developed in which 10th grade students (N = 15) are asked to model biological phenomena graphically as line graphs. Modelling processes are recorded using a SmartPen and concurrent think aloud. Results show that participants’ modelling processes can be divided into sub-processes, related to the model of scientific-mathematical modelling. Furthermore, different individual modelling processes are reconstructed and graphically represented as graphical representations of individual modelling processes (GRIMPs). Based on a clustering process using GRIMPs, eight modelling styles are defined.