# Investigation of Pre-Service Teachers’ Pedagogical Content Knowledge Related to Division by Zero

### Abstract

Although the topic of division by zero has been widely discussed in the literature, this subject is still confusing for students, pre-service teachers and teachers. Because of this, teachers at various grade levels may encounter difficulties in conveying the concept to their students. Therefore, in order to provide students with a strong conceptual understanding of division by zero, it is important to examine the ways that teachers and pre-service teachers structure their instructional explanations about division by zero. The aim of this study was to explore the instructional explanations given by pre-service teachers concerning division by zero, as well as the effects of teacher training programs on these explanations. The study consisted of a cross-sectional design and was carried out with 197 pre-service teachers of elementary mathematics. To determine the pre-service teachers’ instructional explanations given at different grade levels, a written questionnaire was used. Analysis of the results revealed that although most of the pre-service teachers gave correct answers related to division by zero, few of them provided conceptual-based explanations. Rather, those who gave correct explanations mainly responded with rule-based statements.

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