Investigation of pre-service class and primary mathematics teacher's field and pedagogical content knowledge through multi-solved mathematics problems

Purpose: In this study, it was aimed to determine the field and pedagogical content knowledge level of primary school classroom and mathematics pre-service teachers by examining their answers for the multi- solution mathematics problems. Method: In this study, the case study pattern, one of the qualitative research methods, was adopted. The study group of the research consisted of 20 pre-service teachers, ten from each group, who took the "Teaching Practice" course in Eskişehir Osmangazi University Education Faculty Classroom Teaching and Elementary Mathematics Teaching Undergraduate Program in the fall semester of the 2022-2023 academic year. For data collection tools, interview forms and problem forms consisting of five multi-solution problems were used. Pre-service teachers were asked to solve the given five problems with different strategies as if they were explaining them to the students. This study, which was conducted with both classroom and mathematics pre-service teachers, lasted for seven weeks. The data obtained were analyzed with content analysis. Results: When we look at the before the application views of the classroom and primary school mathematics pre-service teachers on the concepts of "problem, problem solving, problem types and problem solving strategies" in the interview form, it was seen that they included keywords that were not suitable for the literature. After the application, it was determined that almost all of the pre-service teachers made explanations in accordance with the literature by differentiating the keywords related to the aforementioned concepts. When the strategies used by the pre-service teachers in multi-solution problems were examined in the context of Mathematics Content Knowledge, it was determined that almost all of them preferred strategies and solutions that were not suitable for the level before the application, and that the majority of them used strategies suitable for the level after the application. Since more than half of the pre-service teachers did not use all of the existing strategies in solving the problems in the research, they included only a few of them in their solutions, it was evaluated that they had partially sufficient solutions. In response to the request to solve five multi-solution problems as if explaining them to the students, it can be interpreted that only one of the classroom pre-service teacher and only four of the mathematics pre-service teachers were able to solve the problem with detailed explanations in accordance with this demand, so it can be evaluated that their teaching knowledge in the context of Pedagogical Content Knowledge is at an epistemic level. Conclusion and Suggestions: It was determined that almost all of the pre-service teachers did not have knowledge about the problem and problem-solving strategies before the application, and that most of the pre-service teachers were able to define the concept of problem in accordance with the literature after the application. At the end of the application, it was concluded that among the strategies included in the research, they could determine the ones suitable for the level and use them in problem solutions. It was determined that the majority of both classroom and pre-service mathematics teachers had solutions suitable for the grade level in the context of Mathematics Content Knowledge after the application. When the problem solutions were evaluated in the context of Pedagogical Content Knowledge, it was concluded that most of the pre-service teachers were able to solve the problems as if they were explaining them to the students after the application, but they could not explain these solutions by basing them on logical expressions, so their teaching knowledge was at the level of problem solving. In order to advance this research, multi-solution problems can be given to senior teacher candidates in the teaching practice courses, and studies in which the students in the schools where they have done their internship are asked to solve these problems and the different solutions obtained are experienced by the teacher candidates in the classroom environment can be included. With a quantitative research, researches involving a wider audience can be carried out to examine the strategy use, field and pedagogical content knowledge of teacher candidates.