The hypothesis investigated is that understanding of the long division algorithm requires a higher cognitive level than understanding of fundamental division concepts. Sixth-grade children were tested on performance and understanding of a given algorithm and concepts of division. (MP)

This paper presents a theoretical framework for investigating the role of algorithms in mathematical thinking using a combined ontological-psychological outlook. The intent is to demonstrate that the processes of learning and of problem solving incorporate an elaborate interplay between operational and structural conceptualizations of the same…