## Abstract

Many researchers have investigated flexibility of strategies in various mathematical domains. This study investigates strategy use and strategy flexibility, as well as their relations with performance in non-routine problem solving. In this context, we propose and investigate two types of strategy flexibility, namely inter-task flexibility (changing strategies across problems) and intra-task flexibility (changing strategies within problems). Data were collected on three non-routine problems from 152 Dutch students in grade 4 (age 9–10) with high mathematics scores. Findings showed that students rarely applied heuristic strategies in solving the problems. Among these strategies, the trial-and-error strategy was found to have a general potential to lead to success. The two types of flexibility were not displayed to a large extent in students’ strategic behavior. However, on the one hand, students who showed inter-task strategy flexibility were more successful than students who persevered with the same strategy. On the other hand, contrary to our expectations, intra-task strategy flexibility did not support the students in reaching the correct answer. This stemmed from the construction of an incomplete mental representation of the problems by the students. Findings are discussed and suggestions for further research are made.

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## Notes

CITO (Central Institute for the Development of Tests) provides Dutch schools with standardized tests for different subjects and grade levels. One of the CITO Tests is the Student Monitoring Tests for Mathematics. The DLE Test (Didactic Age Equivalent Test) is a different instrument published by Eduforce that teachers can use to measure their students’ development in a particular subject.

The original versions of these problems have been developed for the World Class Tests. In 2004, Peter Pool and John Trelfall from the Assessment and Evaluation Unit, School of Education, University of Leeds who were involved in the development of these problems asked us to pilot them in the Netherlands.

The coding scheme was developed by two of the authors, Marja van den Heuvel-Panhuizen and Angeliki Kolovou, and our Freudenthal Institute colleague Arthur Bakker.

This control coding was done by Conny Bodin-Baarends who was involved in the data collection, but did not participate in the development of the coding scheme.

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Elia, I., van den Heuvel-Panhuizen, M. & Kolovou, A. Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics.
*ZDM Mathematics Education* **41**, 605–618 (2009). https://doi.org/10.1007/s11858-009-0184-6

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DOI: https://doi.org/10.1007/s11858-009-0184-6

### Keywords

- Inter-task strategy flexibility
- Intra-task strategy flexibility
- Strategy use
- Non-routine problem solving