Abstract
The strategy of making a drawing has been claimed to facilitate mathematical problem solving. However, De Bock et al. (2003) surprisingly found that drawing negatively affected performance in solving non-linear geometry problems, in which the area or volume of similar figures or solids had to be determined by a given scaling factor. The authors suggested that making a drawing increased the number of overgeneralizations and negatively affected students’ performance. Our study involves a partial replication and also an important validation and extension of this study by addressing two factors: low-quality drawing strategy and poor visual monitoring, both of which might explain the negative effect of drawing. First, we expected that improving the quality of the drawing strategy by prompting students to highlight important information in their drawings would diminish the negative effect of the drawing strategy. Second, we expected that fostering visual monitoring while drawing, by offering problems with small scaling factors, would diminish the negative effect of the drawing strategy. We conducted a randomized controlled trial with 180 students (ninth- to eleventh-graders) to investigate the effects of drawing and visual monitoring on solving non-linear geometry problems. Our results replicated the previous finding that drawing negatively affects performance. We confirmed that linear overgeneralizations are a prevalent reason for this finding. Elaborating on previous findings revealed that the quality of the drawing strategy but not visual monitoring was responsible for the effect of the drawing strategy on linear overgeneralizations. Furthermore, an exploratory analysis of students’ awareness of linear overgeneralizations indicated that improving the quality of drawing strategy and enhancing visual monitoring did not lead to a greater awareness of the mistakes learners made because of linear overgeneralizations. We conclude that the way the drawing strategy is used determines whether it is useful or damaging, and more efforts are essential to enable students to apply it appropriately.
Highlights
Making a drawing is considered a powerful strategy in mathematical problem solving (Pólya, 1945)
On the basis of prior research, we suggest that the insufficient quality of the drawing strategy and a lack of opportunity to use the drawing strategy for monitoring purposes are crucial factors that have contributed to the negative effects of drawing
We aimed to elaborate on the potential reasons for this finding by addressing two factors: the quality of the drawing strategy and visual monitoring
Summary
Making a drawing is considered a powerful strategy in mathematical problem solving (Pólya, 1945). According to the theory of external representations (Cox, 1999), it can support problem solving by helping problem solvers organize the information, and it can make missing and implicit information (e.g., relations between objects) explicit. It deepens understanding and facilitates self-explanatory activities. On the basis of these considerations, the goals of the present study are twofold: (a) to replicate De Bock et al (2003) surprising finding that drawing hinders students’ ability to solve non-linear geometry problems and (b) to find explanations for this unexpected phenomenon. Our aim is to clarify whether these factors come into play while students solve non-linear geometry problems and, whether it is possible to diminish the negative effect of drawing by addressing these factors
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