The purpose of current study was to shed light on what concepts or ideas prospective elementary teachers drew on (and how) when they reasoned about problems related to division of fractions. The participants were 153 senior prospective elementary teachers who registered for a mathematics-methods course either during the 2004-2005 or 20052006 academic year. The participants were from a metropolitan city university located in the central part of Turkey. The study was based on an open-ended written assessment item administered during the very first class of the semester before any teaching. One of the applied open-ended questions was: Write a real-world problem that would be solved or modeled by 4 3 2 1 2 ÷ . A question like this requires a detailed analysis of the concepts of division and fractions as opposed to getting a single numeric result. Such a question, to some extent, provided an opportunity to investigate these teachers reasoning about division and fractions. The results showed that prospective elementary teachers had significant difficulties in thinking about fractions, division, and units.
Key words: Conceptual understanding, reasoning, division of fractions, prospective elementary teachers, assessment.
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