Examining the role of drawing construction and use in mathematical modelling – an eye-tracking study

Baumann, Oliver; Gödecke, Pia; Quarder, Jascha; Schukajlow, Stanislaw; Schindler, Maike; Schoenherr, Johanna

Abstract

Learner-generated drawing has been identified as an approach to support mathematical modelling, especially in geometry problems. However, previous findings have been mixed, suggesting a drawing’s effectiveness depends on the quality of the drawing (i.e. drawing accuracy) and the quality of drawing processes. The aim of this research was to investigate students’ drawing processes while solving modelling problems and their relation to drawing accuracy and modelling performance. We employed a sequential mixed-method design using an eye-tracking methodology across two studies. In Study 1, to generate hypotheses about drawing processes and their relation to drawing accuracy and modelling performance, we qualitatively analysed gaze movements and stimulated recall interviews with six students solving a geometry modelling problem. In Study 2, we tested these hypotheses on a sample of 66 ninth- and tenth-grade students, who solved six geometry modelling problems while their gaze movements were recorded. Our findings indicate that drawing processes include two phases—drawing construction and drawing use—characterised by distinct processes: selecting, organising and integrating relevant information from the text into the drawing (drawing construction) and exploring the drawing to identify mathematical relations and link the drawing to equations (drawing use). Effective drawing construction—both directly and indirectly, through better drawing use—promoted modelling performance. These findings imply that mathematics instruction should not only encourage students to produce accurate drawings but also support them in constructing and using drawings productively to enhance modelling performance.