Analysis of the pedagocical knowledge of secondary school math teachers concerning prime numbers and relatively prime numbers

This study aimed to analyze the pedagocical content knowledge of secondary school math teachers concerning prime numbers and relatively prime numbers. In the study, the subcomponents of pedagogical content knowledge, subject matter knowledge, knowledge of understanding student and instructional strategies were examined. The content knowledge refers to differentiate between prime numbers and relatively prime numbers correctly, to explain the concepts, to answer the questions correctly and to explain goals and objectives. The content of the knowledge of understanding students is being able to identify students learning difficulties, mistakes and misconceptions and explain their reasons, and to determine students readiness. The knowledge of teaching strategies means to have appropriate strategy, method and technical knowledge that is suitable for teaching process, to identify the most proper strategies for the lesson and overcome misconceptions of students, help them make sense of the correct version of the concepts. Holistic case study desing has been used as a qualitative research method to determine the level of pedagogical content knowledge of math teachers on the subjects of prime numbers and relatively prime numbers. Participants consist of 12 math teachers work in a state school affliated with the Ministry of National Education in southeastern region of Anatolia. Data collection tools are the Prime Numbers Knowledge Test, interview and lesson observation form developed by the researcher. Content analysis has been conducted as a method of data analysis. The result of the study shows that math teachers are identified as insufficient in their subject knowledge regarding the subcomponents of pedagogical content knowledge. It has been observed that the teachers do not tend to include the negative integers teaching the subject of prime numbers and relatively prime numbers, solely giving definition of the concept and answering the questions. It has been determined that the knowledge of the participants in the component of knowledge of understanding students characteristics are at the desired level and that they are more successful than the components of subject matter knowledge and instructional strategy knowledge. The research has indicated that the teachers are in sufficient in the knowledge of teaching strategies. It has been observed that the teachers confuse the terms of strategy, method and technical concepts in spite of using all of them during their lessons. It has been determined that the teachers use expository teaching approach, discovery learning technique and question and answer technique the most.