Examining the Relationship Between Rectangles and Parallelograms Through an Erroneous Example

The aim of this study is to investigate how pre-service mathematics teachers make sense of the relationship between rectangle and parallelogram through an erroneous example. The study was conducted with 90 pre-service mathematics teachers studying in the second and third grades in the Department of Elementary Mathematics Teaching at a state university in Turkey. The data collection tools of the case study consisted of a task involving an erroneous example and the task suggestions of the pre-service teachers. The data obtained were analyzed by content analysis. The findings show that only 13% of the pre-service teachers had sufficient conceptual knowledge to analyze the erroneous example and propose an acceptable task. It was found that the majority of the participants (64%) were unsuccessful in analyzing the erroneous example and 59% of these pre-service teachers proposed tasks that included erroneous examples. The results of the study support that erroneous examples can be used as a pedagogical tool in teacher education as well as an effective tool for determining pre-service teachers' level of understanding of concepts. In particular, the results of this study revealed that the knowledge of "Rectangle is a special case of parallelogram" held by pre-service teachers through erroneous examples was based on visual perception rather than conceptual foundations for most of them.