Een historisch-didactisch onderzoek van het meetkundeonderwijs aan kinderen van vier tot veertien jaar in Nederland gedurende de negentiende en twintigste eeuw.

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Utrecht, April 26, 1999. Time 12:45.

De handelseditie van het proefschrift

Te bestellen bij het Freudenthal Instituut, Tiberdreef 4, 3561 GG Utrecht, telefoon 030-261 16 11, fax 030-266 04 30, e-mail ank@fi.uu.nl prijs

In conclusion, the following ten recommendations have been made.

1. More detailed historical sociological research, especially on the Wiskobas group of the Seventies, should be done into the life and work of prominent individuals in mathematics education mentioned in this study.

2. Renewed historical didactic research is needed into mathematics education in the Netherlands during the nineteenth and twentieth century.

3. The importance of Fröbel and Haanstra for Dutch nursery education should be investigated.

4. Prior to education development projects, a historical-didactic analysis should be undertaken.

5. A conference should be convened with a number of experts with the aim of reaching a consensus on basic goals, content and form of a realistic primary school geometry curriculum.

6. A comprehensible description of a programme should be included in the school textbooks.

7. For primary schools, geometry tests other than multiple choice tests should be developed.

8. Short in-service courses in realistic geometry should be developed for mathematics coordinators in primary schools.

9. Geometric reasoning in children of four to fourteen years old should be studied. The connection between logic and spatial intelligence, the effects of specific geometry teaching, the differences between boys and girls and the use of geometry computer programmes should also be examined.

10. Geometry curricula in primary and secondary schools should be coordinated.

Pestalozzi pioneered the idea of introducing geometry as a foundation subject for young children, side by side with language and arithmetic. Fröbel managed to construct geometric material and activities suitable for the youngest children. It is only in the last few decades that geometry topics have been available that can be used in an informal geometry curriculum for children aged four to fourteen. The author of this study is of the firm opinion that putting such a curriculum into practice in primary schools would contribute to the development of spatial reasoning in children and that this would be good preparation for more formal geometry. Implementation will only succeed, however, if geometry is given a substantive position in the primary school curriculum and if sufficient emphasis is placed on pre- and in-service training of teachers.

1. The literal meaning of vormleer is `the study of shapes'.

2. Pestalozzi's conception of Anschauung was wide-ranging. `Intuitive perception' could be a translation of the German word, but this does not cover all meanings. In this study the term is restricted to (1) the physical observation of concrete (mathematical) objects and shapes, (2) their (drawn) representations (figures), (3) the perception of a mental image of such an object, and (4) the mental operations involving these mental images.

3. We speak of Anschaulichkeit of a problem or more generally of a text when it is posed in such a form that it gives the opportunity to create mental images and visual understanding. Usually this is done by means of drawings, schemes, diagrams or other visual aids.

4. `Vision geometry' is based on looking at (observing), perceiving, representing and explaining spatial objects and spatial phenomena, in which the idea of the straight line as a vision line (sighting) and a light ray plays a central role.