Cryptology: A didactical transposition into grade 10 school Mathematics classroom

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

Exploring Learners’ solutions of an exponential equation.

ArticleThis article reports on grade 12 learners’ solutions of an exponential equation. It is a response to comments made in the National Senior Certificate 2014 Diagnostic Report. Learners from two schools in the Drakenstein area were used as participants for the study. An analysis of the learners’ solutions of an exponential equation was conducted, utilising the work of Tall from a Vygotskian perspective. Learners made use of different solution strategies to the problem, but demonstrated a limited understanding of exponential laws and mathematical ways of reasoning. The article opens up a debate on the influence of teacher talk on solutions of exponential equations and learners’ mathematical solution strategies within the context of school mathematics

Cryptology: cryptosystem

The topic of Cryptology, although new in the field of mathematics, has been at the forefront of developments in the mathematics arena. It is important to understand how cryptology is constituted and what the role of the cryptosystem within cryptology is. It is argued that the cryptosystem together with the development of different ciphers help to build a better understanding of cryptology. Important for this is to understand how the cryptosystem is constituted within cryptology. The role and position of the cipher key is explored and is further espoused by way of an example using the rule, , as a cipher key

Introducing new content into a school mathematics curriculum: the case of cryptology

Book chapterDeveloping learning resources forms an important part of a school mathematics curriculum implementation. This chapter argues for a change in the way we do analysis for developing learning resources. An argument is forwarded for an understanding of the main concepts within the topic as well as a historical and didactical analysis thereof in order to make statements with respect to the teaching and learning of the topic. For this analysis, the topic of cryptology is used as an example. The chapter concludes with recommendations to curriculum designers to revisit the accepted practice to adapt already historically and didactically analysed materials, and warns on the consequences of the currently used methods

Learner development initiative

The initiative aims to develop learner's mathematics content knowledge and ICT skills. It was a collaboration between CPUT and Paulus Joubert Secondary school. Denise Ontong, a retired teacher and Alimni of the school started the initial collaboration with the aim of building capacity in the community

South African teacher application process: the interview.

Video LectureAn important aspect of teacher training is the preparation of teachers for the teacher post application process. Besides the formal application process, shortlisting and interviews form an integral part of this process. The video captures only the interview process where five candidates are interviewed in front of the whole class. The candidates for the interviews and panel members were all students in their final year of study towards a teacher education qualification preparing teachers to teach their specialisation subjects to grade 10 - 12 learners in the Further Education and Training (FET) phase. Although the interview was done with FET students, the video could be useful for all students in teacher training

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

Lecture NotesFor 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