0. P R E F A C E
On 26 January 1971, IOWO, the Institute for the Development o f Mathematics Instruction* was established as the executive arm o f the governmental Commission on Modernising the Mathematics Curriculum**. The end o f a five years period o f activities invites a review. IOWO is no research institute; its members do not regard themselves as researchers but as producers o f instruction, as engineers in the educational field, curriculum developers. Engineering needs background research and can produce research as fall out. Though b o t h o f them will be visible in the present account, its nucleus is our productive work, represented b y a few specimins, and embodies our views on mathematics as a human activity and on curriculum development as a classroom activity, guided by curriculum developers, in a continuous contact with all those interested in mathematics education. IOWOers are people rather than an abstract entity but their work is a collective achievement. So is the present volume, written b y individuals and edited by a team. All our national publications are meant to invite response from the field. I hope the present call will be heard abroad. HANS FREUDENTHAL
* Instituut voor de Ontwikkeling van het Wiskunde Onderwijs. ** Commissie Modernisering Leerplan Wiskunde.
Attention Children
This notice stands in the grounds o f a secondary school. The inscription may be interpreted in various ways: - Like the traffic sign: Be careful, there are chiMren around; As if to warn outsiders." Beware o f the children; - A s i f to warn the pupils o f the school: Don't approach the fence; As a reminder that anyone wishing to teach m u s t p a y attention to children, must observe them as they go through the learning process. -
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The IOWO staff had this last interpretation in mind when in a f e w intermezzos they described the learning behaviour o f children - often their own children. Most o f the learning happened in a unexpected way, in situations that were for the most part unprepared. Many more observations will have to be made before the experiences o f these unexpected learning processes can be more systematically used in instruction. Meanwhile along the road to better instruction look for the sign: Attention, children.
