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

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 .