Philosophiae Doctor - PhDThis study in an extension of a Master's study, entitled Realistic Mathematics Education and the strategies grade 8 learners develop for the solution of two simultaneous linear equations. the current study investigates how new content could be introduced into a school mathematical curriculum. The new topic under discussion for this study is the topis of Cryptology. Two research cycles were carried out. For the first design research cycle there were three teaching experiments with teachers, grade 10 learners and students as participants. Seven activities weere developed from the second design research cycle which was worked through with gade 10 learners. All sessions for the second design research cycle were video taped. Important to the development of instrutional materials was the development of a hypothetical learning trajetory about the learning and teaching of each activity. the results of the study indicated that the way learners understood the content and the different ways in which they presented solutions augers well for the introduction of a specific new content strand, cryptology, into a new school mathematical curriculum. It is also important for developers of instructional material to have a strong mathematical content knowledge for the design of instructional materialsSouth Afric
