Özet:

Multiplication, fraction and operations with fractions are concepts that elementary students have difficulties to understand and that teachers have difficulties to teach. It is important for students to develop conceptual understanding about these concepts. Therefore, teachers need to relate conceptual and procedural knowledge while teaching. This study aims to investigate pre-service primary teachers' pedagogical content knowledge (PCK) related to multiplication and subtraction of fractions, as well as their beliefs about teaching and learning mathematics. In this qualitative study, a data collection tool consisting of two scenarios was used. The tool was applied to 120, 3rd and 4th grade students studying at the Department of Primary Education at a public university in Ankara, during the 2016-2017 academic year. The data collected by pre-service elementary teachers' written responses were analyzed and coded using descriptive analysis method. The findings obtained from this research revealed that pre-service teachers cared about learning conceptual and procedural knowledge together in order to provide meaningful learning, they were familiar with the different types of solutions of four operations, and they found mental strategies more meaningful than traditional algorithm. Also findings suggest that pre-service teachers consider practicality and speed as important in problem solving. This may indicate that pre-service teachers' pedagogical content knowledge about the use of models in problem solving is not sufficient yet and the pre-service teachers may have traditional beliefs about mathematics teaching and learning at some level.

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