Matematikte üstün yetenekli ve üstün yetenekli olmayan öğrencilerin problem çözme süreçleri

This study aimed to investigate the use of problem-solving phases and strategies of seven mathematically gifted, seven successful, and six average students attending fifth-grade in different public and private schools. The participants were selected through purposeful sampling among those who volunteered to participate in the study in a city in Western Turkey. The study was designed as a qualitative case study. Data were collected through clinical task-based interviews that included six problems, researchers' field notes, and students' solution sheets. All sessions were audio-recorded. Participants' observation forms, solution sheets, and voice recordings were analyzed to determine the problem-solving phases suggested by Polya (2004) and strategies used as they attempted to solve each problem. The results showed that three groups of participants varied concerning the use and style of problem-solving phases and problem-solving strategies. Mathematically gifted students presented a higher number of attempts in applying problem-solving phases. They applied the phases sequentially while successful and average students applied them as not sequentially. Mathematically gifted students were also observed as using problem-solving strategies most and most efficiently. Adopting a different point of view and acting it out or simulation strategies were the most preferred and effectively used strategies by them while logical reasoning was the most used strategy by successful and average participants. However, logical reasoning was not utilized most effectively by the successful students. Mathematically gifted students were the most successful group in generalization and considering all conditions in a problem when using a problem-solving strategy.