How students connect mathematical models to descriptions of real-world situations

Research has shown that problem posing, in some sense the “inverse activity” of problem solving, can positively affect students’ problem-solving skills. We report the design and results of an empirical study in which the potential positive effect of a specific problem-posing variant, namely “inverse modelling”, that is the selection of a real-world situation given a mathematical model, on modelling was investigated. Eighty 11th-grade students were randomly divided in two equal-sized subgroups, one first receiving a modelling task and then an inverse-modelling task. The other subgroup received both tasks in the reversed order. Results indicated that inverse modelling did not have an overall positive effect on modelling: Only for affine functions with negative slope, accuracy scores for modelling significantly improved after inverse modelling.status: publishe