HOME PAGE History of mathematics' didactic What is the mental representation? Matematical mental representation Recording interview: René Thom, Dominique, Rosine... Write to me Author
 Third process: metaphor This 14-year-old girl has difficulties in mathematics. Here's what she says about maths:

Pupil: - <<It's grandiose... still it's relatively close to us, since we'll have to use it in the coming years... So, we should really learn how to use maths.

Nimier: - Grandiose and relatively close?

P: - Oh, yes, at the beginning, when I was 13, to me it seemed......it was really big.

N: - How big?

P: - It belonged to another world, a really vast one. You know, there were maths for this and maths for that. There was algebra, and geometry. It all seemed really big to me, so you had to take maths from a little parcel of this vastness. So you couldn't take everything, it scared me a bit, by the way.

N: - Why did it scare you?

P: - Because it was like that, it sort of made my head swim, I had never touched that, and now, you had to pick and gather maths, so you could not gather it all, we couldn't pick everything all at once.

N : - Like what? If you wanted to make a comparison....

P : - It's like a field of prunes....well.... prunes that you beat down, you know? They fall and then you have to gather them. And then, there's an impending storm, and then you have to pick them in a hurry, but you can't gather them all, and you try to take the biggest, but it's quite difficult.

N: - Because there is an impending storm?

P: - Yes, there is the storm.

N: - But what is that storm?

P: - The storm...it's French, it's time, it's the other subjects.

N: - All the things that bother you?

P: - Yes, if you only had maths to learn, you could do a good job. Yes, you could dedicate yourself entirely to this subject and then it would be all right.>>

 This pupil's speech expresses fantasies which she projects onto mathematics. Those fantasies appear through metaphors: a field of plums which are attractive since they are beaten down, a storm which is frightening. It is all expressed through a scenario which, in a way, gives a very positive image of maths: grandiose, to dedicate oneself entirely to maths.....Yet she fails in that subject (the storm?.....) Something bothers her. Her picture of maths is ambivalent. The cognitive and emotional interaction here appears in the metaphors she uses ( field of plums, storm ). Metaphor is like a third party between the cognitive and the emotional aspects, in that it creates a link beween them, and yet they do not merge totally into one another. Thus, it permits an interaction without any fusion.
 HOME PAGE History of mathematics' didactic What is the mental representation? Matematical mental representation Recording interview: René Thom, Dominique, Rosine... Write to me Author