Investigating preservice teachers' content knowledge on multiplication and division

The aim of the current study was to investigate preservice teachers' content knowledge on multiplication and division. The study was conducted in five universities in Turkey, during the Spring semester of 2021-2022 academic year. A total of 111 senior university students from middle school mathematics, middle school science, secondary school mathematics, chemistry, and physics education programs participated in the study. The instrument including fifteen items developed by the researcher was used as a data collection source. Before the items on the instrument were developed, three indicators of understanding of multiplication and division multiplicatively were determined in light of the literature. Data were analyzed descriptively to examine preservice teachers' performances on each item. Results regarding understanding of a quantity revealed that preservice teachers experienced difficulties in specifying the quantities and determining the referents of the quantities, especially of the intensive quantities in multiplication and division problems. Also, results related figural representation indicated that preservice teachers were not able to multiplicatively explain the pictorial figures they drew in equal groups problem situations especially. Similarly, results regarding understanding of multiplicative problem situations showed that although preservice teachers were able to construct multiplication or division problems, they were not able to provide multiplicative explanations requiring for related problems. Results also suggested that preservice teachers were not successful at explaining multiplicative relationship between the quantities in the problems. It was also concluded that they were inclined to make explanations in a procedural way.