Measuring and investigating strategic knowledge about drawing to solve geometry modelling problems

Rellensmann, Johanna; Schukajlow, Stanislaw; Leopold, Claudia

doi:10.1007/s11858-019-01085-1

Cited by 23 publications

(18 citation statements)

References 30 publications

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“…The quality of strategy use seems to be an important factor that should be addressed more often in research on strategies. In addition, research on cognitive factors such as strategic knowledge about drawing (Lingel et al, 2014;Rellensmann et al, 2019) or on emotional and motivational factors such as enjoyment of drawing and the costs of drawing (Uesaka and Manalo, 2017;Schukajlow et al, 2019b) can contribute to clarifying the conditions under which drawing is helpful and when it has a hindering effect.…”

Section: Visual Monitoringmentioning

confidence: 99%

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

Krawitz

Schukajlow

2020

Front. Psychol.

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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.

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Section: Visual Monitoringmentioning

confidence: 99%

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

Krawitz

Schukajlow

2020

Front. Psychol.

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“…To assess students' strategic knowledge about drawing, we used the strategic knowledge about drawing scale, which was developed and validated in previous studies (Rellensmann et al, 2020). Half of the scale's items concerned situational drawings, whereas the other half of the items were about mathematical drawings because both types of drawings are important for modeling.…”

Section: Methodsmentioning

confidence: 99%

Section: Strategic Knowledge About Drawingmentioning

confidence: 99%

“…Strategic knowledge is part of the static knowledge component of metacognition and is opposed to the dynamic metacognition component, which includes the actual use of strategies (Brown, 1987; Flavell, 1979). Strategic knowledge about drawing includes knowing the characteristics of a drawing that adequately represent the structure of the modeling problem (Rellensmann et al, 2020). A drawing that adequately represents the structure of the modeling problem shows all relevant objects, accurately represents the relationships between the objects, contains all relevant numbers (which are moreover correctly allocated), and indicates the information that is required.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…In line with this idea, previous research has shown that students' strategic knowledge about drawing had a positive effect on students' situational and mathematical drawing accuracy (Rellensmann et al, 2021). In addition, strategic knowledge about drawing predicted students' modeling performance when cognitive abilities and interest in mathematics were controlled for (Rellensmann et al, 2020). Whether strategic knowledge about drawing predicts students' strategy use in terms of the number of drawings produced and how strategic knowledge about drawing interacts with drawing instructions have not yet been investigated.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

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Effects of drawing instructions and strategic knowledge on mathematical modeling performance: Mediated by the use of the drawing strategy

Rellensmann

Schukajlow

Blomberg

et al. 2022

Applied Cognitive Psychology

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Making drawings can help students avoid and overcome difficulties they encounter when solving real‐world (or modeling) problems. However, many students do not make drawings spontaneously. In the present study, 132 students in Grades 9 and 10 were randomly assigned to the experimental conditions “with situational or mathematical drawing instructions” or to the control condition “without drawing instructions.” Multilevel path analyses showed that mathematical drawing instructions had a positive total effect on performance, and the effect was transmitted via the use of drawings. Also, strategic knowledge about drawing had a positive total effect on performance via the use of drawings. Further, strategic knowledge about drawing moderated the effect of mathematical drawing instructions on students' use of drawings. An in‐depth analysis of an exemplary modeling problem provided us with additional hypotheses about how drawing instructions and the use of drawings affect modeling performance on the problem level.

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Methods for Teaching Modelling Problems

Schukajlow

Blum

2023

International Perspectives on the Teaching and Learning of Mathematical Modelling

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Measuring and investigating strategic knowledge about drawing to solve geometry modelling problems

Cited by 23 publications

References 30 publications

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

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

Effects of drawing instructions and strategic knowledge on mathematical modeling performance: Mediated by the use of the drawing strategy

Methods for Teaching Modelling Problems

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