Making realistic assumptions in mathematical modelling

Abstract

Making realistic assumptions is an important part of solving open modelling problems and also a potential source of errors. But little is known about the difficulties that result from the openness of modelling problems and how they can be addressed in interventions. Here, we focus on two central solution steps that are necessary for making assumptions: noticing the openness and estimating the missing quantities. In a qualitative study with four ninth graders, we asked students to solve a modelling problem after informing them about the openness of the problem. We identified barriers that expand the two-step model (e.g., trouble integrating assumptions into the model). In addition, informing students about the openness of the problem improved their solution to the problem at hand but did not help them solve subsequent problems.