The use of problem solving steps of preservice primary teachers in the process of mathematics and science teaching

In this research, case study design which is a qualitative research design has been adopted to investigate the use of problem-solving steps in mathematics and science teaching process of preservice primary teachers. Data were collected through in-class observations, field notes and individual interviews of two selected participants' lectures that they delivered during teaching practice. Problem-solving beliefs scale was applied to preservice 4th grade primary school teachers who are enrolled in Mehmet Akif Ersoy University and the study was conducted with two preservice primary teachers who rated highly on the scale and volunteered to participate in the study. The observation form developed by the researcher is used in class observations and semi-structured interviewing protocols were used in the interviews. The data obtained from observations and interviews were transformed into written documents and analyzes were subjected to content analysis using qualitative analysis program through these written documents. For the content analysis, a data analysis framework was created mainly using Polya's problem-solving model, together with codes from other problem-solving process models mentioned in the literary review and codes obtained from course observations. In the data analysis framework, the problem-solving process is divided into four themes and these themes were divided into 12 categories, each of which was organized according to their similarities and differences of the codes. "Understanding the problem" consists of reading, explaining the problem, making the problem concrete and checking the preliminary information categories. "Devising the plan" consists of deciding operations, asserting the hypothesis and determining the strategy. Applying the plan consists of 'strategy use', 'determining the time for solving the problem' and doing mathematical operations. Evaluating the solution consists of 'control' and 'interpretation'. After the findings of mathematics and science teaching process of preservice teachers presented one by one, findings from cross-case analyzes were presented. In the step of understanding the problem, preservice teachers explain the problem situation by explaining the unknown words, expressing the problems in different ways and explaining the keywords to the students. However, they are unable to express clearly what is given and asked in the problems. In order to understand the problem in a better way, problems are divided into sub-problems and also concrete materials, technology, figure-schema drawings and examples encountered in everyday life were used. It has been determined that in most of the problems, preservice teachers have gone directly to the applying the planning stage without showing any plan making behavior in the problem. This situation has been observed in a very clear way for science lessons. The preservice teachers specify the operations to be carried out in the problems, but they do not consider the conceptual reasons for the selection of these operations. It has been determined that the preservice teachers make plans using the strategy of going back in mathematics and by asserting the hypothesis and making the plan for the experiment strategies in science courses. Preservice teachers have made it possible for students to acquire scientific process skills by establishing experiments and planning experiments in science courses. For the devising a plan step preservice teachers have not used any figures, diagrams, and tables and never determine a formula and have not shown the behavior of predicting the solution of the problem at all. The fact that the preservice teachers frequently use the rule-principle and concept teaching during the implementation of the plan step in both lessons contributes to their conceptual learning. One of the preservice teachers made closed-ended hypothesis testing experiments in the labs. Also, preservice teachers' attempts' to question hypotheses through reasoning and efforts to bring scientific process skills to students contribute to the student's implementation of the plan steps. While the students work on the problems, preservice teachers provide them with hints to complete their solution and they check the solutions of the students by going around the class. Preservice teachers solved first problems of the subject on the board and in other problems the teachers asked the students to participate actively in the solution process. In both lessons, it was determined that the preservice teachers did not exhibit a formula application and equation solving behavior. Preservice teachers' behaviors on evaluating the solution were seen limited. Preservice teachers have controlled their solutions in mathematics classes by redoing their solution using a different way or by repeating their operation and crosschecking the operations. In the science courses, they have never used the different ways of solving and controlling mathematical operations, but instead, they have controlled their results logically. Preservice teachers have demonstrated high-level behaviors such as trying to interpret the results they found and producing and generalizing formulas in mathematics and science lessons. In addition to these behaviors, they tried to relate the result to the hypothesis established in the science courses. It has been determined that the preservice teachers do not give the necessary importance to the planning and evaluation of the solution, however, they generally refer to the problem-solving process more on the understanding the problem and applying the plan steps. In the step of understanding the problem, devising a plan and evaluating the solutions the students were not made as active as the preservice teachers. It has not been observed that the preservice teachers managed all the steps of the problem-solving process with proper behavior. Key Words: Preservice Primary Teachers, Problem Solving, Mathematics Teaching, Science Teaching, Cross-case Analysis