Özet:

Teaching mathematics gives students the opportunity to explore a wide range of problems and problem situations, from exercises to open-ended problems and exploration situations. Problem solving simply refers to the entire process of dealing with a problem while trying to solve it. Problem posing is the generation of new problems and mathematical questions, the reformulation of problems to make them more accessible for solution in the process of solving a particular problem. The aim of the study is to examine the problem-solving processes and problem-posing skills of expat teacher candidates with the gradual scoring scale, which consists of four stages (understanding the problem, preparing a plan for the solution, applying the plan, evaluating) based on the alternative assessment approach, as stated by Polya (1997). Qualitative research approach was adopted in the study. The participants of the study are 8 foreign teacher candidates studying at the Department of Mathematics Education at the Siirt University Faculty of Education. Purposive sampling method was used to determine the participants. In this study, three problems prepared by the researchers using the MEB textbooks were used as data collection tools. Since the problem-solving and problem-posing behaviors of the participants were examined separately in the study, the progressive scoring scale developed by Baki (2008) was used. Descriptive analysis technique was used in the analysis of the obtained data. As a result of the study, it was determined that the participants showed the highest performance in the category of understanding the problem, and the lowest performance in the category of evaluation and problem posing. While it was determined that foreign teacher candidates were successful above the medium level in the categories of understanding the problem, preparing a plan and implementing the plan, it was concluded that they were unsuccessful in the evaluation and problem posing categories.

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