Does representation matter? Teacher-provided tables and drawings as cognitive tools for solving non-routine word problems in primary school

Timo Reuter 1 * , Wolfgang Schnotz 2, Renate Rasch 3
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1 Graduate School “Teaching and Learning Processes”, University of Koblenz-Landau, Landau, Germany
2 Department of General and Educational Psychology, University of Koblenz-Landau, Landau, Germany
3 Institute for Mathematics, University of Koblenz-Landau, Landau, Germany
* Corresponding Author
EUROPEAN J SCI MATH ED, Volume 2, Issue 2A, pp. 34-43.
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According to the German educational standards, students should be familiar with problem-solving as a general mathematical competency by the end of grade 4. Non-routine word problems are suitable tasks for mathematical problem-solving in elementary mathematics classes. They are characterized by the fact that the problem-solver cannot simply use well-trained algorithmic calculating procedures (Rasch, 2001). As a result, many students struggle with word problems in mathematics, especially with non-routine word problems (Hohn, 2012). Representation plays a central role in the process of problem-solving. It involves representing a problem situation adequately, constructing a mental model and comparing it in a dynamic and iterative process with the information externalized in the representation (Schnotz et al, 2011). This study aims to shed light on teacher-provided representations as cognitive tools for students when working on non-routine word problems. In an experimental study, we examined a sample of 67 primary school students who worked on six non-routine word problems with provided representations. The tasks were accompanied by a table or a drawing. Furthermore, the tables and drawings differed with regard to the amount of information provided. Statistical data analysis generated, among other findings, two results: Overall solution rates were low (10 to 24%). Tables and drawings facilitated the solution process differently depending on the type of word problem. Consequences for subsequent future research are discussed.


Reuter, T., Schnotz, W., & Rasch, R. (2014). Does representation matter? Teacher-provided tables and drawings as cognitive tools for solving non-routine word problems in primary school. European Journal of Science and Mathematics Education, 2(2A), 34-43.


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