Mathematically talented students' approaches to mathematics problems with apparatus

In this research, mathematically talented students' approaches to mathematics problems with apparatus are examined. Besides "math problems with apparatus" being a new concept, this research will be one of the former studies about this topic. The purpose of the study is to identify mathematically talented middle school and high school students' understanding, solving and posing approaches about math problems with apparatus which they have not encountered with before. Since our research is the first thesis study related to math problems with apparatus, for the problems which the students will solve and pose to be diverse and to have different qualities in the process of research, it is planned that participants to consist of mathematically talented students. Hence, it is decided that participants will be chosen from middle school and high school students who take education in Science and Arts Centers. The study is applied in the four Science and Arts center in İzmir. Study group consisted of six seventh grade students, five eight grade students and seven ninth grade students, totally eighteen students who are in the general mental talented group and take math classes. Students are chosen according to their voluntariness and views of math teachers who work and give lectures in Science and Arts centers. The reseach is designed as qualitative case study. Case study research is a qualitative approach in which the investigator explores a bounded system (a case) or multiple bounded systems (cases) over time, through detailed, in-depth data collection involving multiple sources of information (e.g., observations, interviews, audiovisual material, and documents and reports), and reports a case description and case-based themes (Cresswell, 2007, s.73). In this study, mathematically talented students' approaches to math problems with apparatus; Their solving styles of mathematics problems with apparatus, the charactesristics of mathematical thinking they show (generalising, looking for patterns and relations, economicity etc.) during the solving processes and the qualities and the features (originality, having awareness of solution) of mathematics problems with apparatus which they posed are examined in detail. Data collection is carried through "semi-structured interviews". Participants were asked to solve ten math problems which are developed based on four different apparatus and to pose two math problems based on two apparatus which were assigned by the researcher from the four apparatus students used in solving processes. During the interviews, the researcher directed the researcher questions she prepared separately for solving and posing processes to the participants. In addition, participants were asked to think aloud during the solving processes. During semi-structured interviews video records were taken. Data analysis is conducted through case study content (transcriptions, documents) analysis. It is seen that students solved the problems mostly with planned applications and strategical trials, they reached correct results and alternative results highly and they had not encounterd with similar problems to math problems with apparatus before In addition, the students showed particular characteristics of mathematically gifted students' mathematical thinking (generalizing, looking for patterns and relations, economicity, mathematical memory etc…) in particular problems. Lastly, it is seen that students can pose qualified math problems with apparatus but the rate of original ones and the ones they had awareness of solutions were limited.