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Make a drawing. Effects of strategic knowledge, drawing accuracy, and type of drawing on students’ mathematical modelling performance

Abstract

Drawing strategies are widely used as a powerful tool for promoting students’ learning and problem solving. In this article, we report the results of an inferential mediation analysis that was applied to investigate the roles that strategic knowledge about drawing and the accuracy of different types of drawings play in mathematical modelling performance. Sixty-one students were asked to create a drawing of the situation described in a task (situational drawing) and a drawing of the mathematical model described in the task (mathematical drawing) before solving modelling problems. A path analysis showed that strategic knowledge about drawing was positively related to students’ modelling performance. This relation was mediated by the type and accuracy of the drawings that were generated. The accuracy of situational drawing was related only indirectly to performance. The accuracy of mathematical drawings, however, was strongly related to students’ performance. We complemented the quantitative approach with a qualitative in-depth analysis of students’ drawings in order to explain the relations found in our study. Implications for teaching practices and future research are discussed.

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Correspondence to Johanna Rellensmann.

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Author note

The present study was conducted within the framework of the project Visualization while solving modelling problems (ViMo), which is directed by Stanislaw Schukajlow and Claudia Leopold and funded by the German Research Foundation [Deutsche Forschungsgemeinschaft].

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Appendices

Appendix A

1.1 Explanation of a situational drawing and a mathematical drawing for the sugarloaf task (Blum & Leiss, 2007)

Sugarloaf

From a newspaper article:

The Sugarloaf cableway takes approximately 3 min for its ride from the valley station to the peak of the Sugarloaf mountain in Rio de Janeiro. It runs with a speed of 30 \( \frac{\mathrm{km}}{\mathrm{h}} \) and covers a height difference of approximately 180 m. The chief engineer, Giuseppe Pelligrini, would very much prefer to walk—as he did previously when he was a mountaineer and first ran from the valley station across the vast plain to the mountain and then climbed it in 12 min.

What is the approximate distance that Giuseppe had to run from the valley station to the foot of the mountain?

This task is given as an explanation. You do not have to solve the task!

When working on a word problem, you can make a situational drawing or a mathematical drawing . These drawings show you what exactly the problem is about.

figure a

Appendix B

2.1 Modelling problem “Maypole” used in this study (Schukajlow & Leiss, 2011)

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Rellensmann, J., Schukajlow, S. & Leopold, C. Make a drawing. Effects of strategic knowledge, drawing accuracy, and type of drawing on students’ mathematical modelling performance. Educ Stud Math 95, 53–78 (2017). https://doi.org/10.1007/s10649-016-9736-1

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Keywords

  • Visualization
  • Drawing
  • Strategy
  • Representation
  • Mathematical modelling
  • Real-world problems