Remembering Zoltan Dienes, a Maverick of Mathematics Teaching and Learning: Applying the Variability Principles to Teach Algebra

  • Serigne M. Gningue City University of New York


This paper is written in honor of Zoltan Paul Dienes, an internationally renowned mathematician and educator, who passed away in January 2014. It is an attempt to describe, analyze and apply Dienes’ theory on how mathematical structures can be taught by applying his four principles of learning upon which he believed a teacher can base concept development around the use of multiple embodiments through manipulatives, how such usage leads to abstraction, and the implications for teaching mathematics in today’s mathematics classroom. It illustrates how abstraction can result from the passage of concrete manipulations of objects to representational mapping of such manipulations and then to formalizing such representations into rule structures through the application of Dienes’ four principles to teach the concepts and processes of simplification of algebraic expressions.