The benefits and boundary conditions of drawing prompts to solve modelling problems
Final Report Abstract
Using mathematics to solve real-world problems is considered a core competency in being mathematically literate. Previous research has shown that solving a real-world problem is demanding, with building an adequate problem representation being the major hurdle. According to the generative drawing principle in the cognitive theory of multimedia learning, making a representational drawing for a real-world geometry problem can help students construct an adequate problem representation. However, extraneous processing associated with drawing (e.g., reasoning about the realistic appearance of the elements) might take up cognitive resources, hindering students from making accurate drawings and benefiting from the drawing strategy. In the present study, we aimed to minimize extraneous processing and thereby maximize the benefits of drawing for real-world problem solving. In a 2x2 betweensubjects design, we examined how two instructional techniques of reducing cognitive load affected students' solution accuracy: (1) mathematical drawing instructions (aimed at fewer situational, irrelevant elements in the drawing) and (2) drawing support in the form of pre-drawn objects that should be copied onto a background template (for higher drawing accuracy). A total of 112 students solved four real-word problems after being randomly assigned to one of four drawing conditions. In line with our expectations, we found that students who were provided with drawing support and mathematical drawing instructions solved the problems better than students of the other conditions. The effect was mediated by higher drawing accuracy and fewer situational elements in their drawings. For student learning, this means that drawing instructions should aim at making mathematical drawings and that students should be provided with drawing support so that they benefit from making a drawing for a realworld problem.
