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ERIC Number: EJ781150
Record Type: Journal
Publication Date: 2007-Nov
Pages: 2
Abstractor: ERIC
Reference Count: 0
ISBN: N/A
ISSN: ISSN-0025-5785
The Method of Jean Louis Nicolet
Gattegno, Caleb
Mathematics Teaching Incorporating Micromath, n205 p42-43 Nov 2007
Jean Louis Nicolet is a Swiss teacher of mathematics who found his subject so fascinating that he was puzzled as to why so many pupils could not share this enjoyment in their studies. He came to a conclusion which is now supported by the results of psychological research into the learning process: he suggested that the mind does not spontaneously adopt a logical approach to the study of a subject but rather acts intuitively on the material presented to it. "Intuition" is a dangerous word to use without further explanation; what Nicolet means by it is the direct apprehension of the situation and the unconscious associations with it which together leave traces in the mind for future analysis and rational consolidation. In this sense, intuition is the ready grasping of a situation in terms of knowledge already existing in the mind, which carries with it a high degree of conviction. Nicolet himself believes that everyone cannot know unless they use this intuitive process, though it is not sufficient by itself: it must be consolidated logically; in particular, by syllogistic proof. When applied to geometry, this proposition means that in each geometrical fact or set of facts (theorems and riders) there will be, for a given class of students, some intuitive basis which it is the job of the teacher to discover and use. Nicolet's approach was to animate the figures involved in a theorem and to try to view the result as a case standing out from an infinite number of possibilities; for example, the right angle when compared with acute and obtuse angles. These ideas might have remained impracticable had it not been for Nicolet's genius in translating them into film form. Nicolet realises the deep need in every man for beauty, and who sees beauty in every geometrical fact. He selected, for their simplicity, intrinsic elegance, range and importance some of the basic geometrical ideas; and, by applying to them his principles of intuitive apprehension, he developed the charming visual demonstrations on the screen. Thus, the use of Nicolet's films in this way opens an even more exciting prospect; it gives the teacher an opportunity to estimate the progress of his pupils, not just by the amount of ground they have covered, but by a more real assessment of their store of mathematical knowledge. The films reveal the meaning of geometry in a way that enables the pupils to talk about the facts as living reality instead of as textbook concepts labelled "maths" and pigeon-holed in a compartment of the mind throughout their school life and afterwards. Nicolet made his films for direct communication with the pupils and to stimulate their interest in mathematics; teachers will find that there are many new ways in which they can be used.
Association of Teachers of Mathematics. Unit 7 Prime Industrial Park, Shaftesbury Street, Derby, DE23 8YB, UK. Tel: +44-1332-346599; e-mail: admin@atm.org.uk; Web site: http://www.atm.org.uk/mt/index.html
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A