Synthesizing the legacy of Varga and Dienes

Tamás Varga worked closely with Zoltán P. Dienes to provide learners with internally related experiences of creating and discovering abstract concepts, a procedure that Dienes described as “internalized action”. In instructing the way Dienes and Varga have promoted, “multiple embodiment” and the cognitive process of the learner in unaccustomed learning situations may be different for teachers and their pupils. Addressing this difference, we outline a lesson for pre-service teachers on comparing divisibility rules in various bases with the use of Dienes’s Multibase Arithmetic Blocks as an illustration of how to interface multi-level experiences. In order to answer the didactic problem of how embodied tools augment the learning process by structuring and organizing the learners’ experiences at different levels, we point to the principles that make the synthesis of the two innovators’ methods possible. Classification: A60, B59, C30, F60, Q69, U60 Keywords: Tamás Varga, multiple embodiment, Zoltán P. Dienes’s principles, multibase arithmetic blocks, divisibility rules, manipulatives, philosophy of mathematics