Cryptology: A didactical transposition into a grade 10 school mathematics classroom

Abstract

For an array of activities such as, for example, PIN numbers used in automated transactions, there is vast underlying mathematical machinery that ensures secrecy and security of such activities. Mr. Whittles pursued the issue of making some of this mathematics of coding and decoding cryptology accessible to school pupils. The traditional way of making novel high-level mathematics accessible for the school situation through elementarization is not followed. He argues for and successfully implements a procedure that takes as starting point the historical development of the mathematical topic and the experiences pupils have of this topic. Design principles emanating from the French and Dutch mathematics didactics traditions were used to develop classroom materials. These materials were refined through feed forwarding until the activities were in classroom workable form for meaningful mathematics learning. The major outcome of the study is the representation and description of an avenue to be followed for introducing new content in the school mathematics curriculum. This points in the direction of the need for research-driven curriculum development rather than the current path of curriculum declaration and tinkering. The work is unique in that it is only the second one in the past 25 to 30 years that considers curriculum-making with due respect to the historical development of a domain of mathematics and the experiences pupils have of the domain.