Does strategic knowledge matter? Effects of strategic knowledge about drawing on students’ modeling competencies in the domain of geometry

ABSTRACT

We investigated how students’ strategic knowledge about situational (pictorial) drawings and mathematical (schematic) drawings affects drawing accuracy and modeling competencies in the domain of geometry. We conducted a pre-posttest experimental study with 473 students in grade 9. Students were randomly assigned to one of three treatment conditions in which we used a 90-minute intervention to promote strategic knowledge about situational drawing (EG1), strategic knowledge about mathematical drawing (EG2), or strategic knowledge about situational and mathematical drawing (EG3). We also used a control group in which we did not promote any knowledge about drawing (CG). Results of a multilevel path analysis did not show a total effect of the strategic knowledge treatments on students’ modeling competencies. However, the results indicated an indirect effect: Students who participated in the treatments demonstrated higher modeling competencies than students in the control condition, and strategic knowledge and drawing accuracy were mediating variables. Moreover, students who constructed a more accurate situational or mathematical drawing for a modeling problem were more likely to solve this problem adequately. Our findings indicate that strategic knowledge is a necessary but not sufficient precondition for the construction of high-quality drawings and high modeling competencies in geometry.

KEYWORDS:

• Mathematical modeling
• strategic knowledge
• self-generated drawing
• geometry

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

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Additional information

Funding

The present study was conducted as part of the project Visualization while solving modelling problems, which has been funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, grant number SCHU 2629/3-1) and by the Swiss National Science Foundation (Schweizer Nationalfond, grant number 100019E-164816/1).

Notes on contributors

Johanna Rellensmann

Johanna Rellensmann is a post-doctoral fellow at the University of Münster, Germany, since her graduation in 2018. Her current research interests are mathematical modelling and visualization strategies. She studied Secondary School Education at the University of Münster and majored in Mathematics and Social Sciences. In 2021, she finished her teacher training at a German secondary school.

Stanislaw Schukajlow

Stanislaw Schukajlow is Professor of Mathematics Education at the University of Münster, Germany. His research interests are mathematical modelling, visualization strategies, emotions, and motivation in the context of mathematics learning. Stanislaw Schukajlow was a leader of the Affect and Mathematical Teaching and Learning Group of the 11th Congress of European Research in Mathematics Education. From 2014-2018 he served as an elected member of International Committee of PME (International Group for the Psychology in Mathematics Education).

Judith Blomberg

Judith Blomberg is a trained teacher and teacher trainer with many years of experience in mathematics teaching. She worked as a doctoral fellow at the University of Münster, Germany until 2019. Her research interests are mathematical modelling, visualization strategies, attitudes, and beliefs.

Claudia Leopold

Claudia Leopold is Professor of Educational Psychology at the University of Fribourg, Switzerland. Her research interests include learning strategies, mental visualizations, learning with multiple representations. Stanislaw Schukajlow and Claudia Leopold are responsible for the project: Visualizations in solving modelling problems, within the framework of which the present study was conducted.