When Can Making a Drawing Hinder Problem Solving? Effect of the Drawing Strategy on Linear Overgeneralizations and Problem Solving

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.

Model method drawing acts as a double-edged sword for solving inconsistent word problems

“…The results of our study show that there is a positive impact of drawing bar diagrams on both consistent and inconsistent word problems, with effects of drawing being the most pronounced on inconsistent word problems. It is important to consider that, as hypothesized, this positive impact strongly depends on the accuracy of the drawn bar diagram, which is in line with earlier research showing that the accuracy (or quality) of drawing influences word problem-solving performance (e.g., Krawitz & Schukajlow, 2020;Ott, 2020;Rellensmann et al, 2019Rellensmann et al, , 2020. That is, bar diagram drawing is mostly supportive to problem solving on inconsistent word problems if an accurate bar diagram is drawn.…”

“…Fig. 2 Bar model drawing accurately representing the relations of the inconsistent word problem presented in Table 1 the present study contributes to better understanding of the use and effectiveness of the model method and extends previous research on (accuracy of) drawing in word problem solving (e.g., Krawitz & Schukajlow, 2020).…”

“…Comparable beneficial effects of drawing have been reported outside the mathematical domain such as in the comprehension of science topics from text (e.g., Schwamborn et al, 2010). Recent lines of research on the role of drawing in word problem-solving have focused on various aspects related to drawing such as the effects of strategic knowledge about drawing (i.e., students' views on the characteristics of a drawing that fit a given problem), the type of drawing (e.g., situational vs. mathematical; number lines, diagrams), and the accuracy of drawing (i.e., the correctness of representation of the relevant objects and relations, including the correct labeling of the drawing with numbers) on word problem solving performance (e.g., Chu et al, 2017;Csíkos et al, 2012;Gvozdic & Sander, 2020;Krawitz & Schukajlow, 2020;Munez et al, 2013;Ott, 2020;Rellensmann et al, 2019Rellensmann et al, , 2020. For the present study, particularly, the research on the accuracy of drawing is relevant as this work shows that benefits of drawing for word problem solving are strongly related to the accuracy of the drawing with more accurate drawings correlating with better word problem solving performance (e.g., De Bock et al, 1998).…”

Impact of the Mass Media on Adherence to the Mediterranean Diet, Psychological Well-Being and Physical Activity. Structural Equation Analysis

“…In terms of gender differences, it should be noted that the results for men showed that mass media pressure has a negative impact on psychological well-being, leading to a decrease in physical activity and a worsening diet. According to the results obtained in the study by Izydorczyk et al [ 50 ], the mass media pressure for men to conform to an ideal standard is evident, leading them to suffer great emotional dissatisfaction if their body size does not coincide with society’s ideal. Similarly, Tylka [ 51 ] notes that mass media pressure acts as a promoter of physical activity among men, who use it to improve their muscle tone, causing an imbalance in their eating behaviour.…”

Desain Aktivitas Siswa Pada Pembelajaran Pemecahan Masalah

“…Ini dikarenakan yang tertanam dalam diri siswa adalah matematika selalu berkaitan dengan rumus dan tidak boleh dikerjakan menggunakan tebakan ataupun menggambar. Padahal dengan menggunakan strategi membuat gambar dapat membantu siswa menyelesaikan masalah (Krawitz & Schukajlow, 2020).…”