Innovative perspectives in research in mathematical modelling education

The research forum shares and discusses innovative perspectives in research on mathematical modelling education. Specifically, the proposed research forum intends to give an overview of current perspectives from different research strands (amongst others, psychologically and pedagogically oriented research) and from different social-cultural contexts (including Eastern and Western contexts). Finally, the research forum aims to develop prospects for further developments in modelling education research

Drawing instructions, strategic knowledge, strategy-based motivation, and students’ use of drawings

Although self-generated drawing is a powerful strategy in the domain of geometry, students lack spontaneous use of the drawing strategy. In the current study, we investigated instructional, cognitive, and motivational predictors of students’ drawing use. We first assessed strategic knowledge about drawing and strategy-based motivation in 132 students in Grades 9 and 10. Then, students were randomly assigned to solve geometry modelling problems either with or without drawing instructions. Students with drawing instructions constructed more drawings than students without drawing instructions. Strategic knowledge about drawing, self-efficacy expectations, and perceived costs predicted drawing use while intramathematical abilities were controlled for. Utility value did not predict drawing use in the current study.The present study was funded by the German Research Foundation [Deutsche Forschungsgemeinschaft, grant number SSCHU 2629/3-1] and the Swiss National Science Foundation [Schweitzer Nationalfond, grant number 100019E-164816/1]

Make a drawing. Effects of strategic knowledge, drawing accuracy, and type of drawing on students’ mathematical modelling performance

Drawing strategies are widely used as a powerful tool for promoting students’ learning and problem solving. In this article, we report the results of an inferential mediation analysis that was applied to investigate the roles that strategic knowledge about drawing and the accuracy of different types of drawings play in mathematical modelling performance. Sixty-one students were asked to create a drawing of the situation described in a task (situational drawing) and a drawing of the mathematical model described in the task (mathematical drawing) before solving modelling problems. A path analysis showed that strategic knowledge about drawing was positively related to students’ modelling performance. This relation was mediated by the type and accuracy of the drawings that were generated. The accuracy of situational drawing was related only indirectly to performance. The accuracy of mathematical drawings, however, was strongly related to students’ performance. We complemented the quantitative approach with a qualitative in-depth analysis of students’ drawings in order to explain the relations found in our study. Implications for teaching practices and future research are discussed

The process of modelling-related problem posing – A case study with preservice teachers

In real life, problems emerge from situations and often need to be posed before they can be solved. Despite the ongoing emphasis on the processes involved in solving modelling problems, little is known about the process of problem posing. To help fill this gap, the current study examined (1) what activities are involved in modelling-related problem posing and (2) the sequence in which they occur. For this purpose, we invited seven preservice teachers to pose a problem based on given real-world situations and analyzed their problem-posing activities. We identified the five most frequent activities that occurred in the sequence: understanding–exploring–generating–problem solving–evaluating. These results contribute to the uncovering of important activities and contribute to theories of modelling and problem posing