This study is 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 mathematics curriculum. The new content under discussion for this study is the topic of cryptology. Two design 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 were developed for the second design research cycles which were worked through with grade 10 learners. All sessions for the second design research cycle were video taped. Important to the development of instructional materials was the development of a hypothetical learning trajectory about the learning and teaching of each activity. A study of the literature, a historical and didactical phenomenological analysis of cryptology and the following of a course in number theory were done before instructional materials were developed for the research design cycles. The theoretical frameworks of realistic mathematics education, didactical transposition and workbench activity were used as analysis frameworks for the study. 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 mathematics curriculum. Furthermore, developed instruction materials should have links with current school mathematical topics in order to facilitate an easier passage for introducing new content. It is also important for developers of instructional materials to have a strong mathematical content knowledge for the design of instructional materials. A starting point for this content knowledge should be within mathematics. By way of a didactical transposition content of a specific mathematics topic could undergo changes before ending up as content for school mathematics.
- design research,
- reflective analysis,
- didactical transposition,
- realistic mathematics education
Available at: http://works.bepress.com/kalvin_whittles/4/