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Abstract
The aim of this study is to examine the problem-solving processes and problem-posing skills of pre-service mathematics teachers, which consists of four stages (understanding the problem, preparing a plan for the solution, applying the plan, evaluating) defined by Polya (1997) with the progressive scoring scale based on the alternative assessment approach. Qualitative research approach has been adopted in the study. Participants of the study consist of 71 pre-service teachers studying at the department of primary education mathematics teaching at the education faculty of a state university in the Southeastern Anatolia region of Turkey. Since the problem solving and problem posing behaviors of the participants were examined separately in the study, the gradual scoring scale developed by Baki (2008) was used. As a result of the analysis, 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. It was determined that participants who failed in the problem posing phase either wrote the same problem or could not write a problem. Another result reached in the study is that the participants had difficulties in expressing the operations in mathematical language.
Highlights
Mathematics is one of the few school subjects that to its content does not differ that much across the world
Since mathematics students spend a lot of time doing tasks it is important to study these tasks from a learning perspective
Since creative reasoning seems to be more effective than algorithmic reasoning, it would be good for students to encounter more of this type of task in textbooks as well as in teacher presentations
Summary
Mathematics is one of the few school subjects that to its content does not differ that much across the world. Teachers are more or less directed by syllabuses, textbooks are used to differing extent, and more or less responsibility is left to the student. In this thesis the starting point will be the tasks and relating to them both design, learning outcome, and influence on student work and brain activity will be studied. Brousseau (1997) suggested that students have to consider such important aspects while constructing solutions by themselves and that teachers have to develop situations where this is possible for the students. Students’ cognitive abilities are important to consider when constructing tasks or didactical situations. The aim of this thesis is to examine how task design and students’ cognitive abilities will influence students’ mathematical reasoning, student outcome and students’ brain activity
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