Same Mathematical Structure, Different Design: How Does Task Format Affect Creative Problem-Posing Performance?

Abstract

Abstract Introduction: The purpose of the study was to investigate the effect of task format on pre-service mathematics teachers’ creative problem-posing performance. Methods: In this quantitative study, a figural and a written pattern related to daily life with the same mathematical structure were presented to participants and they were asked to write as many problems as they could. The problems were analyzed based on whether they were viable and then on the components of fluency, flexibility, and originality of creativity. Results: The results of the study indicated that, although the flexibility and originality scores in the figural pattern were higher, the only statistical difference was observed in the originality component. Moreover, it has been found that some of the participants wrote similar problems in both tasks; however, the problems in the figural pattern were inclined to be more difficult. Discussion: Developing students’ creative-thinking skills is a main purpose of mathematics education research (Mann, 2006). However, the results of the research have indicated that the teachers’ knowledge of how to develop students’ creative-thinking skills is still lacking (Shriki & Lavy, 2012) and, consequently, students are provided with few opportunities to experience creative thinking and learning in class (Silver, 1997; Sriraman, 2005). Problem posing has a close association with creativity as well as with problem solving (Haylock, 1997; Silver, 1997). Therefore, to develop creative-thinking skills, learning environments should be enriched with problem-posing tasks. The results of this research do not assert that only one of the figural or written pattern types must be preferred to stimulate creative-thinking skills in the context of problem posing. Instead, the results emphasize that each of the written and figural patterns has its own strengths. Limitations: The fluency, flexibility, and originality scores are affected by the sample size. Conducting similar studies on larger samples may provide more valid conclusions about possible differences. This study has taken two different task formats into account as follow; being in written form related to daily life or including figural patterns. Figural patterns can also be structured based on whether they explicitly provide the pattern rule (Barbosa & Vale, 2016). The effect of these types of problem-posing tasks on creativity components is another case that can be investigated. Conclusions: Considering these results together, while including problem-posing tasks for both written and figural patterns to improve the flexibility and originality components of creativity is supported, the use of problem-posing tasks for figural patterns may be further recommended.