Cognitive and metacognitive skills performed by math teachers in the proving process of number theory

Evaluating the proving process of mathematics teachers is important for the development of their proof skills. Developing the proof skills of teachers can contribute to their students’ meaningful learning of mathematics. For example, teachers showing simple proofs about number theory can make it easier for students to understand the concepts of multipliers and factors and the concepts of the greatest common divisor and the least common multiple. Within this context, this study was conducted in order to examine the cognitive and metacognitive skills performed by math teachers in the proving process. The study was conducted as a case study using qualitative research design. A total of 14 teachers participated in the study, six of which were elementary math teachers and eight were secondary math teachers. The data were collected through task-based interviews (think-aloud protocol), documents and observation forms. The collected data were analysed using the content analysis method. The results of the study showed that, based on the operational definition of cognition and metacognitive skills made in this study, elementary math teachers generally used cognitive skills, while secondary mathematics teachers performed metacognitive skills.