Mathematical Mediation from Zoltan Dienes to Spreadsheets via Data Tables


Technology creates new mathematical objects requiring new modes of student interaction - for example, the National Library of Virtual Manipulatives. These virtual manipulatives draw much of their efficacy from prior embodiment as hands-on materials currently in elementary mathematics classrooms. In preparing teacher candidates to make use of these new manipulative-based virtual resources Zoltan Dienes writings and views on manipulatives in instruction were explicitly referenced throughout my elementary mathematics methods courses. Dienes is best known for multi-base blocks created for teaching place value – particularly base10 - and seminal algebraic materials and logic blocks. To many mathematics educators, he was seminal in establishing manipulatives in teaching and learning mathematics. The samples of Dienes work used in this paper centered on mathematics in the early grades including manipulatives, games, stories and dance. Following discussion of Dienes and his ideas, students explored a surface area problem where a base10 physical manipulative was used to create a data table of results. This data table then served as a mediational tool for spreadsheet exploration at a level of mathematics much higher than would be otherwise possible. Student comment, work samples, and professor observation showed these teacher candidates demonstrating greater insight into both traditional and technology-enabled virtual manipulatives than past groups lacking this exposure. The discussion of base10 blocks had powerful and personally meaningful connections with their own experiences as learners. By reminding the students of these experiences, it empowered their use of both traditional and technology enabled manipulatives.


Mathematics Education, Curriculum, Learning Theory, Teacher Preparation, Technology, Activity Theory


Pedagogy and Curriculum


Paper Presentation in a Themed Session


  • Michael Connell
    • Professor of Mathematics Education, Urban Education, University of Houston-Downtown, United States United States
    • Michael L. Connell, Ph.D., is Professor of Mathematics Education at University of Houston-Downtown. Dr. Connell has over 30 years of mathematics education experience at both graduate and undergraduate levels working with students in field-based teacher preparation programs. His research interests lie at the intersection of educational technology, learning theory, and mathematics education. He has written, presented and published extensively in these areas.