Physical and Virtual Manipulation Framework Conceptions of Undergraduate Pre-Service Teachers

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International Journal for Mathematics Teaching and Learning


SSN: ISSN-1473-0111


The goal of this study is to analyze undergraduate elementary school pre-service teachers’ conceptions and misconceptions of physical and virtual manipulative materials using an interpretive framework. The framework involved the use of the Concrete, Pictorial and Abstract cognitive levels combined with the Virtual-level, or CPVA-framework. The CPVA instrument was used to answer two research questions related to participants’ understanding of CPVA-levels using the framework during a mathematics methods course. Pre-, post and follow-up test scores were analyzed. The participants demonstrated improvement from pre-test to post- and follow-up-tests. However, this improvement was limited by their understanding of the Virtual-level.