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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The present study explores pupils' constructed definitions of the concept of function in relation to their abilities in dealing with tasks of functions involving different forms of representations and problem solving tasks. A major concern is also to examine the interrelations between these three ways of thinking about or dealing with the concept of function. The sample of the study consisted of secondary school pupils in Cyprus. A test was developed which involved seven items: one item requested pupils to provide a definition of what function is and the other six items were developed in order to investigate pupils' ability to transfer information from one representation to another and to solve problems on function. Findings revealed pupils' difficulties in giving a proper definition for the concept of function and resolving problems on functions involving conversions between diverse modes of representation. Several inconsistencies among pupils' constructed definitions, their competence to use different representations of functions and their problem solving ability, were also uncovered, indicating lack of flexibility between different ways of approaching functions.

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