The review shows Cosinus1 such that some equations of third degree to find a solution through the Origami and how far away it is likely that the need to reproduce the same pattern on pottery of different sizes able to germinate the laws of ‘dilation in the head of the Neolithic artist. The arts and mathematics are so historically lies2 and continue to give each other.
No creativity, no possible mathematical If talking about creation is obvious in the arts, the artist is essentially a creator, is not it unfair that the same term is used in creating the field of mathematics? From observing her daughter learning to read, Freinet had developed the idea of ??naturelle3 method. First applied to the learning of reading, the natural method was extended to language, drawing and writing, but math seemed a world apart.
Paul Le Bohec in a number of the Educator of 1972, the first showed the possibility of a natural method in mathematics, and he initiated the work from children’s productions. Before him and Freinet was the living calculation: that life was returning in the class gave many an opportunity to calculate, apply computational techniques which files had trained students. To apply the natural method to Paul mathematics introduced mathematical creations.
Later he experienced the natural method in many learning areas (sports, foreign languages, etc.), and throughout his various writings he showed the unity of the natural method (the role of creation, the experimental trial and error, etc.) in the humain4 behavior. The clinical approach permitted by scientific progress confirms the sensitive approach.
Recent brain studies show, through brain imaging techniques, the brain doing math uses several very different areas including two major ones: that of language for reasoning and calculation, that the vision for the search for solutions and approximate calculation. To do mathematics must make connections, see similarities, predict possible. Mathematicians forward by associations of ideas, mental images (Ah, I see …!), That generate new hypotheses.
The language takes over to formalize, define and defend the new concepts, new theorems. Thus hundreds of new mathematical theorems and objects appear every year. A mathematics education which would focus on mechanisms and reasoning would not form mathematicians but applied accounting. We must develop the ability to do mathematics in the objects and the world, to foresee, anticipate, imagine new connections, new relationships between these objects, new solutions.
We must develop creativity in mathematics. Do math from creations: the mathematical glance When the child makes a mathematical creation, there is no doubt not always a clear intention nor an aesthetic pleasure. However many examples of creations show that children seeking fun in the creations. This sought emotion can be an engine for learning. The authors of the above designs have certainly experienced this emotion.
If creativity is essential in the learning process, is it enough so far to put children at creating for them to learn? In the field of body control, the trial and error phase lead to new balances, new positions in space, new modes of travel. In the arts the trial and error phase lead to new productions.
Some of these advances are groping that, by trial / error method, able to move forward towards more efficiency, more expressive capabilities. In mathematics it is the same? The example below appeared on the site in October 2009. Coop’ICEM Theo shows his creation thus: «I made concentric circles. «. It means, for the words the geometric nature of its creation.
But when you read the comments dropped in surprise: It’s an optical illusion. Aaaaaa, not at all. It hurts the eyes. It hurts the eyes and it’s weird. If the people who were present a creation does not give a mathematical look, they do not do math.
But one would like to ask Theo: Why do you call your drawing «concentric circles»? How did you do as thick lines? The spaces between each circle are they still the same? How did you trace circles?
During the discussion in class, were you all agree? Why ? What did you understand homework helper
new math? If we changed the colors, the size of the circles, and if we added a sloping straight line … If we bent …
It is therefore not enough to produce designs for the class to do math. The aesthetic pleasure can be present in many cases. The fun math, according to Plato, is the satisfaction of completeness. A new theorem can therefore provide as much fun as a Rembrandt and a child can suddenly marvel at what he has just found.
What is dangerous, pedagogically, it is confusing mathematical creation and artistic creation. What makes it is in mathematics, is the look that arises on the object. Place speech in the construction of mathematical language actually presented any object, any production, can be approached in very different perspectives: historical, geographical, scientific, literary, artistic, psychological, … or mathematics.
This is why we ask the children to make a mathematical creation, to signify that it is about mathematics that we will exchange. With small is simply: «Find a good idea. «. When a child has a paving such presentation to the group: we will focus on the rhythm invented in the distribution of colors, even if the child will be sought aesthetic pleasure. The biggest rave rosettes.
They play all day compass. What may well please them? regularity, symmetry? the resemblance to a flower or a star, mastering a technical gesture? Probably a little at once.
But this gesture to draw a beautiful circle, this precautionary maintain the spacing of the compass, to postpone its tip carefully at the following location, only to find at the end, miraculously, we fall back on his steps … but the child can make tens of rosettes, rosettes pavements without doing math. The child learns that if he stops to marvel to ask why, how it is …
The road will be open to regular hexagons, with equilateral triangles, and for this it will probably exceed the curves to be interested in points. What if … To do mathematics, the child will talk, share with others, and also make connections. He may recall a mosaic set consisting of equilateral triangles, or kappla assembly into triangles, etc.
We do not do more math with rosettes with the living design situations: if we simply draw rosettes, it’s like when we solve a live calculation problem is stopped once the problem is resolved. When a CE1 this creation was presented, the children could talk about some regularities of some interrupted rhythms, incomplete paving, but the concerns of the class in the first quarter were others: «there is more red. «And the group to count the red elements. This act-it was enough to validate the claim?
They had to count as black, yellow … to understand that the statement was false. Mathematics is not always where the master awaits them, but they are present if only one cares. It seems to me important to state that mathematics is a special language, which develops speaking.
The concepts are opposed, are refined, are defined by the exchange. In classes that work in mathematical creations, so at the time of the exchange that mathematics are. If everyone uses its experience gained during the crucial time of personal research, however math does build for everyone in the exchange with others.
Remi Jacquet 1 Review Cosine No. 106 – June 2009 2 Review Tangent, Out thematic series 35, transformations, geometry in art. 3 Freinet, the natural method. 1.