Abstract:

Mathematics not only consists of procedures, symbols or operations, but also involves connections, representations, problem solving, reasoning and proof, communication, and conceptual understanding. Learners should make necessary connections among mathematical concepts and representations in order to develop deep mathematical understandings. For this reason, this study aims to explore prospective middle school mathematics teachers’ views about mathematical connections and their knowledge of connections among external representations in the context of proportionality. Multiple case study was used as a research design and the participants were three prospective middle school teachers enrolled in a teacher education program at a public university in the inner region of Turkey. Data were collected through semi-structured interviews, note taking, and written tasks. The findings of the study suggested that prospective teachers viewed connections mainly as a link between different mathematical topics or concepts, as a link between mathematics and daily life, and as a tool for improving students’ understanding of mathematics. Moreover, prospective teachers were able to translate easily among different representations. However, the translations were carried out without conceptual understanding. Besides, participants had limited understanding of proportionality in the case of graphical representations. 

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