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.
Based on this definition, the first important characteristic of flexibility is to have information about multiple strategies.
Flexible problem solvers know more than one way to complete tasks.
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.These records, pupils’ scripts, and notes taken by the researchers were used in data analysis.Four criteria (selection and use of the most appropriate strategy, changing strategies when it does not work for the solution of a problem, using multiple strategies for the solution of a problem and changing strategies between problems) were established to determine students’ flexibility levels.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.A longitudinal study including more students at different achievement levels and different kind of non-routine problems will give in-depth information about this subject.One of the important issues in the psychology of (mathematics) education is how students can be taught curricular subjects so that they develop “adaptive expertise”, namely “the ability to apply meaningfully learned procedures flexibly and creatively” .In connection with all aforementioned studies, “strategy use” and “strategy flexibility” terms can be exemplified with the following non-routine problem: “A male bee is born from an unfertilized egg, a female bee from a fertilized one.So, in other words, a male bee only has a mother, while a female bee has a mother and a father.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.