Üstün Yetenekli Öğrencilerin Matematiksel Yaratıcılıklarının Matematiksel Modelleme Sürecinde İncelenmesi

Abstract

The purpose of this study was to investigate gifted middle school students’ individual and collective creativity regarding mathematics as they engage in model eliciting activities. The study also aimed at describing characteristics of model eliciting activities that were better at revealing students’ mathematical creativity. Multiple case study design was adopted. The participants were six students identified as mathematically gifted, who were at 7 th and 8 th grades and attending to Science and Art Center in Ankara. Purposive sampling method was used to select the participants. Participants worked as a group of three and engaged in five model- eliciting activities. This process and the models they produced as a group at the end were examined in terms of mathematical creativity. In addition, each participant was engaged in one, and the same model eliciting activity individually. This process and the model each participant produced individually at the end of the activity were also examined. Participants’ work and solutions as a group and as an individual constituted the main source of data. Both group work and individual work were video recorded. The written products (models, posters, diaries, etc.) that students produced were also included in the data set. Individual creativity and collective creativity regarding mathematics as students engage in model eliciting activities were described and assessed in terms of the following components: Producing ideas/solutions (fluency), producing different ideas (flexibility), making connections among ideas, concepts, representations (making connections), and solutions’ progressivity (progressivity). On the other hand, students’ models were described and assessed in terms of the following components: Mathematical quality, generalizability, correctness of solutions (quality), and originality of solutions (originality). The findings of the study showed that groups exhibited different levels of mathematical creativity as they engaged in different modeling activities. Besides, it was observed that students discovered different mathematical structures, ximathematical rules, and new information as they construct unknown mathematical information in an interactive process. In addition, it was observed that students produced products (i.e., models) that were considered as high quality and original when they produced more and different type of ideas (i.e., thinking fluently and flexible), produced solutions more progressively, and made more connections among concepts and representations. Moreover, students’ individual work revealed differences in terms of individual creativity. In particular, each student demonstrated strengths on different aspects of creativity, which was revealed through group and individual work. Furthermore, two groups’ mathematical creativity assessed as a process and a product were compared for each modelling activity. In this way, characteristics of model eliciting activities that reveal creativity better were determined. Therefore, results showed that model-eliciting activities that revealed mathematical creativity better were the ones that were less structured, that were included implicit data and a few variables in the problem statement, and that were perceived as challenging by the students.