An examination of preservice primary school mathematics teachers' content and pedagogical content knowledge related to numbers and operations learning domain

It can be said that students related to numbers and operations learning domain, which is one of the most important learning domain of mathematics, have a lot of learning difficulties. Many studies reveal that the source of these learning difficulties is not only the students but also the difficulties stemming from the teacher. Researchers have developed many models to explain the characteristics that a good teacher should have. These models, in general, classified the competencies that a teacher should have as content knowledge and pedagogical content knowledge. Content knowledge includes mastery of key concepts, principles, and rules in mathematics, problem-solving techniques, and strategies. It can be said that a teacher should know the field in depth in order to engage students in mathematical discussions when necessary and to help students make sense of the relationships between concepts. For this reason, it can be stated that teachers should have in-depth content knowledge about the concepts and topics they teach. It is not enough for a teacher to have content knowledge. In addition to having good content knowledge, how he teaches the field and how he reflects his content knowledge to teaching is also important. This reveals the importance of pedagogical content knowledge level. In this study, it is aimed to examine primary school mathematics teacher candidates' content and pedagogical content knowledge related to numbers and operations learning domain. To examine pre-service teachers' content knowledge, the theoretical framework of "level of understandings" organized by Kinach (2002a) was used. Pre-service teachers' content knowledge in the components of the content, concept, problem-solving, and epistemic knowledge levels; pedagogical content knowledge was examined in the components of student knowledge, instructional strategies knowledge, and curriculum knowledge. Tests consisting of open-ended questions were developed for each of the seven components examined within the scope of the research. These tests were applied to 160 pre-service teachers studying at Dokuz Eylul University, primary school mathematics teaching, constituting the study group of the research. In addition, semi-structured interviews were conducted with two students from each grade level within the scope of written data. All the data obtained were subjected to content analysis in the light of various theoretical frameworks and the analysis results were presented in tables with frequencies and percentages. It has been observed that teacher candidates have deficiencies in their content knowledge about teaching. The most difficult component was the level of concept knowledge. Pre-service teachers had difficulties in defining the basic concepts of the learning domain mathematically. It has been observed that the concepts such as places-periods, factor-divisor-multiple, rational number-irrational number, and ratio-rate have difficulty in revealing their relations with each other and they have similar misconceptions to the students. At the level of epistemic knowledge, another component of content knowledge, pre-service teachers' proving, and justification skills were examined. It was seen that they could not reveal the mathematical reasons underlying the rules in the teaching process such as exponential numbers, divisibility, and converting repeating decimal numbers to fractions. It has been observed that deficiencies in content knowledge also influence pedagogical content knowledge. It was understood that pre-service teachers had difficulties in diagnosing students' possible misconceptions, understanding the source of student errors, and giving effective feedback to students. In addition, the examinations of curriculum knowledge revealed some deficiencies. It has been determined that some pre-service teachers do not have sufficient knowledge about the concepts in the introduction part, where the purpose and philosophy of the curriculum are revealed, the goals in the curriculum, the order of instruction of the subjects and the materials. The results of the study show that the teaching of numbers and operations learning domain should be given importance in the teacher education process. It can be said that studies on student difficulties and misconceptions, teaching methods and strategies, curriculum, and materials will be beneficial for the development of pre-service teachers' pedagogical content knowledge. In addition, it can be suggested that studies that improve content knowledge should be given more place in teacher education. Thus, pre-service teachers can make mathematical definitions of the concepts in the subjects they will teach, learn the relations of concepts with each other, explain the mathematical structure underlying the rules, perform procedural operations correctly, and solve non-routine problems.