Principles for a new mathematics curriculum buildup

Abstract

Accreditation rules for many curricula include mathematical knowledge, proficiency in mathematics and ability to apply (advanced) mathematics. They specify which broad mathematical subjects should be covered, but never state precise contents, or how this should be achieved, and they avoid discussion on the relevance of mathematical thinking and mathematical proof. An overview of curricula in European countries confirms this. Everybody agrees that use of technology enhances teaching at all levels. Published guidelines state that institutes should provide processes to prepare students for achieving education goals without specific recommendations. Moreover content implementation has to be updated regularly following the rapid changes in the technology, and this is expensive in printed formats. Symbolic platforms are doing all technical computing and modeling. They also allow better insight in concepts and proofs. It is necessary to study how these capabilities can be transferred to the learners. The presentation will concentrate on what learner attitudes should be cultivated for maximal profit. The question of organisation of exams in a technology environment will also be addressed. Finally, a vertical approach in the curriculum by project work is made possible by efficient use of technology. This will be illustrated by a case study around one topic (the spirograph) which reaches from elementary geometry into advanced analysis and its applications. The principles outlined in the presentation apply to undergraduate tertiary education and to the final years of the secondary curriculum as well.