Mathematical modelling in mathematics education and instruction

This paper aims at giving a concise survey of the present state-of-the-art of mathematical modelling in mathematics education and instruction. It will consist of four parts. In part 1, some basic concepts relevant to the topic will be clarified and, in particular, mathematical modelling will be defined in a broad, comprehensive sense. Part 2 will review arguments for the inclusion of modelling in mathematics teaching at schools and universities, and identify certain schools of thought within mathematics education. Part 3 will describe the role of modelling in present mathematics curricula and in everyday teaching practice. Some obstacles for mathematical modelling in the classroom will be analysed, as well as the opportunities and risks of computer usage. In part 4, selected materials and resources for teaching mathematical modelling, developed in the last few years in America, Australia and Europe, will be presented. The examples will demonstrate many promising directions of development.

An introduction to ordinary differential equations by computer algebra-systems

We report on an elementary course in ordinary differential equations (odes) for students in engineering sciences. The course is also intended to become a self-study package for odes and is is based on several interactive computer lessons using REDUCE and MATHEMATICA . The aim of the course is not to do Computer Algebra (CA) by example or to use it for doing classroom examples. The aim ist to teach and to learn mathematics by using CA-systems.

Gone with the internet - How the old education was lost

Despite its young history, Computer Science Education has seen a number of "revolutions". Being a veteran in the field, the author reflects on the many changes he has seen in computing and its teaching. The intent of this personal collection is to point out that most revolutions came unforeseen and that many of the new learning initiatives, despite high financial input, ultimately failed. The author then considers the current revolution (MOOC, inverted lectures, peer instruction, game design) and, based on the lessons learned earlier, argues why video recording is so successful. Given the fact that this is the decade we lost print (papers, printed books, book shops, libraries), the author then conjectures that the impact of the Internet will make this revolution different from previous ones in that most of the changes are irreversible. As a consequence he warns against storming ahead blindly and suggests to conserve - while it is still possible - valuable components of what might soon be called the antebellum age of education.