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This study aims to investigate whether high-achieving sixth, seventh and eighth graders can exhibit strategy flexibility while they are solving non-routine problems.In this context, four students from each grade level participated in the study.Each answer given by pairs was evaluated based on these criteria and scored as 0, 1 or 2.
The most conspicuous theoretical support in this domain was provided by Elia, van den Heuvel-Panhuizen, and Kolovou ’s study.
In this study, the authors explore the strategies used by high-achieving students for non-routine problems, and they distinguish two types of strategy flexibility: inter-task flexibility (changing strategies across problems) and intra task flexibility (changing strategies within problems).
Therefore, there are different definitions about flexibility in different papers.
According to Verschaffel, Luwel, Torbeyns, and Van Dooren a flexible strategy choice includes “the conscious or unconscious selection and use of the most appropriate solution strategy on a given mathematical item or problem, for a given individual, in a given context.” Besides, Star and Rittle-Johnson attribute a broader meaning to flexibility: They define flexibility as knowledge of multiple strategies and the relative efficiency of these strategies.
Additionally, there were enterprises to use “write an equation” strategy.
Besides, it was observed that students did not need to make a significant change in their thinking ways when their first attempts were wrong and they rarely change their strategies between problems.They found that these two types of flexibility are not displayed to a large extent by the students in their sample.Moreover, according to their findings, students who show inter-task strategy flexibility are more successful than students who persevere with the same strategy, while intra-task strategy flexibility does not help the students to arrive at the correct answer.Another researcher, Selter states that a flexible problem solver must have following abilities: The first is multiple interpretations of data.A flexible problem solver is able to consider several alternative interpretations of a given situation.Similarly, Zhang carried out a study in which four non-routine problem were used.The major goal of the researcher was to determine whether the individual’s performances were consistent across different subject areas and problem types that could be solved different heuristics, and to identify possible factors that influenced children’s choices and strategy use in different contexts.Secondly, flexibility is required knowledge of strategy efficiency.This means that flexible problem solvers can recognize which strategies are more efficient than others under particular circumstances.Studies on flexibility are mostly about specific subject matters such as arithmetic and algebra ’s study, the adaptive use of strategies of different groups of third graders is investigated in relation to the instructional approach of their textbooks.Their study is limited with addition and subtraction of three digit numbers.