The mathematics curriculum differs from continent to continent, from country to country, from region to region. Since ICME exists we are learning from each other.
In its most primitive form a mathematics curriculum is a list of topics. An obvious question is: are there any `absolute topics'? I mean topics that have been taught ever since there are schools and that have figured in mathematics education in almost every culture.
The theorem of Pythagoras seems a serious candidate to be an absolute topic. Even in the period of the "new math", when formalism and structuralism were so dominant, Pythagoras was upright, but... sometimes in a surprising way. Two years ago, a journalist from a Western-European country told me that he had three traumatic experiences in his childhood with the new math. One of them was the proof of Pythagoras' theorem by means of the inner product, as a triumph of linear algebra. Really, sometimes the spirit of the age exaggerates a little...
I surely believe that, except for Pythagoras' theorem, there are more topics in mathematics that will be taught 100 years from now. But we have to be cautious: A period of 100 years ahead will show more changes than a period of 1000 years in the past. Society will change its mathematical requirements permanently, technology will improve at a supersonic rate, the pedagogical climate will oscillate with an increasing frequency. So, a mathematics curriculum satisfying the demands of the age, must have an educational philosophy that is up to date.
In my own country, after a short revival of "no-nonsense-education", nowadays there is a stormy interest for a system of self-employed learning, where the teacher will be a guide rather than a master. The ministry of education has promoted the term "studiehuis", which is hard to translate. Let me say "home of learning". What will be the influence of this climate on the mathematics curriculum? Will there be more room for math-oriented investigations and explorations; will there be room for teaching and learning by means of projects?
A mathematics curriculum also needs a didactical philosophy. In The Netherlands we know the so called realistic approach that is developed and promoted by Freudenthal and his institute and that strongly influenced the national mathematics program for students of age 12-16.
However, Aad Goddijn will present another development that seems to originate from a sort of nostalgia for ancient geometry, inherent in the deductive method. To avoid any misunderstanding: It is meant for a relatively small group of students (age 16-18), who are heading for a study of one of the exact sciences. The properties and relations between angles and circles form a locally organized system of definitions and theorems where the students can have nice experiences with the characteristic method of mathematics at University. Combined with sophisticated software (Cabri or Sketchpad) and with up to date applications in geography and archeology (diagrams of Voronoi) this seems to be a promising domain for the new mathematics curriculum at pre-university level. I admit, it is an example of a rather accidental choice of a topic. But the enthusiasm of teachers and students indicates that we can continue with this stuff for at least a decade. The most important thing is the new impulse to discover heuristics for mathematical proof in an inspiring environment and the experience of the power of the human brains.
Another inspiring story is the example given by Susan Picker from New York who talks about experiences in high school with a relatively modern subject, namely coding theory as a part of discrete mathematics. Also from other experiments we know that problems from discrete mathematics are very attractive and challenging for students of all ages. The advantage of discrete mathematics compared with continuous mathematics is the conceptual simplicity which makes students feel rather comfortable. Moreover, it is a very rich domain with many interesting applications.
Between the two examples mentioned above, continuous and ancient, discrete and modern, there are many interesting contributions in WG 13. The presentations in this working group will provide an impression of what is going in South Africa, Iran, Australia, Hungary,... Some presentations will focus on relatively small domains, other ones will try to outline a complete program. They will give a local and instantaneous picture of the process of permanently rethinking mathematics education.
To structure the program we made a division in three strands (algebra/calculus; geometry; discrete mathematics) and two age-groups (12-16 and 16-19). The participants may choose for one age-group or one strand. I have no doubt that the different contributions will be a good starting point for animated discussions.
Nobody will expect that ICME will invent or define a model for a mathematics curriculum for the next 25 years. Noticing new movements considering social needs and technology progress, will be the aim of WG 13.
I hope all participants of WG 13 will gain many inspiring ideas to bring home to their country.
Especially I want to express my gratitude to Mieke Abels and Michiel Doorman from the Freudenthal Institute, who gave great support by preparing the program and composing this book.
Martin Kindt
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