Physical and Virtual Manipulative Framework Conceptions of Undergraduate Pre-service Teachers


  • Enrique Ortiz University of Central Florida
  • Heidi Eisenreich Georgia Southern University
  • Laura Tapp Alvin Community College


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.

Author Biographies

Enrique Ortiz, University of Central Florida

Associate Professor

School of Teaching, Learning and Leadership

College of Education and Human Performance

Associate Professor

Heidi Eisenreich, Georgia Southern University

Assistant Professor

Department of Mathematical Sciences

College of Science and Mathematics

Laura Tapp, Alvin Community College