Examining teacher trainees' belief of mathematics and mathematics problem solving
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Background: Problem solving has been considered as a student's mental development from kindergarten to high school, as a skill to be taught, and a method of teaching in mathematics education. Problem solving is emphasized as an integral part of the mathematics curriculum, and as a skill that students need to demonstrate in all subject matters. There is much concern regarding the learning of problem solving and the improvement of the current status of mathematics education at all levels of schools. Beliefs have great impact on the individual's decisions, choices and his behaviors (Pajares, 1992). Several research studies have been done on elementary students and pre-service teachers' beliefs about mathematics, as well as, problem solving. These studies found that pre-service teachers' beliefs about mathematical problem solving have an impact on their organization of the learning environment and student achievement. There is a need to examine the pre-service teachers' beliefs about general problem solving and mathematical problem solving. In the present study, we only considered some aspects of the main issues-- to find out the factors affecting mathematical problem solving beliefs. Aims: To examine beliefs of pre-service class teachers and pre-service mathematics teachers' beliefs as predictors of beliefs about nature of mathematics, and mathematical problem solving. General characteristics of the problems, problem solving activity, and teaching problem solving, in particular, were examined. Sample: The beliefs study about problem solving scale was conducted with pre-service elementary classroom teachers (Nimö=71, (imö=the number of pre-service classroom teacher)) and pre-service elementary mathematics teachers (Nsö=62, (sö=the number of pre-service mathematics teachers)) at School of Necatibey Education, Balikesir University, Turkey. Method: Surveys were conducted and all written responses received from the respondents were considered. Data was collected using The Mathematical Problem Solving Scale. Collected data was analyzed using SPSS 11.0. In order to determine the degree of the relationship between pre-service class teachers' and pre-service mathematics teachers' mathematics beliefs and mathematical problem solving beliefs, the Pearson correlation co-efficient was used. Results: The participant beliefs about teaching mathematics and problem solving reflected the characteristics of the traditional approach to mathematics teaching and the inefficiencies of that system. The results indicated that participants showed positive beliefs about mathematical problem solving. Conclusion: The non-significant difference between the beliefs of pre-service elementary class teachers and pre-service elementary mathematics teachers points out the issues in mathematics teacher training, since it is expected that pre-service mathematics teachers are more familiar with mathematics and problem solving. Such finding could be due to the courses they all took pertaining to general education and mathematics education, in particular. In this study, some recommendations are given to the pre-service teachers.