Ressursbok i geometri for lærerutdanningen

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need to build up layers of experience before they can master abstractions. … As
Whitehead has put it, "There is no royal road to learning through an airy path of
brilliant generalizations. … The problem of education is to make the pupil see the
wood by means of the trees". (S. 164)
Kline argumenterer for å holde terminologi og symbolbruk på et minimum.
"Symbols scare students."
Her kan det passe å nevne et intervju med hjerneforskeren Terrence
Sejnowski fra året 2000 [5]. Sejnowski trekker frem den reformen av matematikkundervisningen
som er tema for dette avsnittet: "Undervisningen i
mengdelære slo feil fordi menneskehjernen ikke fungerer slik. Etter det vi
vet i dag lærer hjernen først det konkrete og forankrer så det abstrakte i det.
... Mengdelæren forsøkte å gå nøyaktig den motsatte veien." Dette er en
autoritativ konstatering av noe som i en del år har vært gjeldende visdom.
- Hva med innholdet i matematikkfaget i skolen?
Fortunately, it is possible to teach most of the standard material of the traditional
curriculum with the proper motivation and exposition of its significance. Though
fortunate, this fact is not fortuitous [tilfeldig]. The standard material, except for a few
topics and possible reordering in algebra, is the material that has been found useful –
and this is why it has been taught in preference to many other possible topics.
However, one should not hesitate to depart from some of it if a richer and more vital
course can be fashioned. ...
There is nothing intrinsically wrong with set theory ... But it does not warrant time
on the elementary and high school levels. Arithmetic, algebra and geometry are far
more important, and set theory does not contribute to the learning of these subjects.
Analogous remarks apply to Boolean algebra, congruences, symbolic logic, matrices
and abstract algebra. (S. 165–66) [ Vår kursivering]
Kline kommenterer slagordet "Euclid must go!" slik:
Such a step would be tragic. Not only is synthetic geometry an essential part of
mathematics in which Euclidean geometry is the base, but geometry furnishes the
pictorial interpretation of much analytic work. Mathematicians usually think in terms
of pictures, and geometry not only furnishes the pictures but suggest new analytical
theorems. It is incredible that knowledgeable mathematicians should seek to oust synthetic
geometry. (S. 166)
Til slutt:
As far as mathematical content is concerned all of the desirable changes amount to no
more than minor modifications of the traditional curriculum, and all talk about modern
society requiring a totally new kind of mathematics is sheer nonsense. (S. 166)
Alt i alt foreslår altså Kline at innholdet i skolematematikken ikke
endres drastisk, men at fokus flyttes fra matematikk som studiet av abstrakte
strukturer til matematikkens kilder og dens anvendelser.
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Henvisninger 3
[1] Dieudonné, Jean A. "Should We Teach 'Modern' Mathematics?" American Scientist, 61 (1973), 16–19.
[2] Gjone, Gunnar. "Moderne matematikk" i skolen: Internasjonale reformbestrebelser og nasjonalt lære-
planarbeid. 2 b. Universitetsforlaget, Oslo, 1985.
[3] Feynman, Richard P. "New Textbooks for the 'New' Mathematics." Engineering and Science, 28 (1965),
9–15
[4] Freudenthal, Hans. Mathematics as an Educational Task. D. Reidel, Dordrecht, 1973.
[5] Klein, Stefan. "Training fürs Köpfchen: Wie Schulen lehren müssten. Ein Gespräch zur Neurobiologie des
Lernens mit dem Hirnforscher Terrence Sejnowski". Die Zeit 24 (8. juni 2000), 36.
[6] Kauke, Marion. Spielintelligenz: Spielend lernen – Spielen lehren? Spektrum Akademischer Verlag,
Heidelberg ⋅ Berlin ⋅ New York, 1992.
Øistein Bjørnestad 2005