HOME PAGE History of mathematics' didactic What is the mental representation? Matematical mental representation Recording interview: René Thom, Dominique, Rosine... Write to me Author
 First process: switching signifieds To illustrate this process, here are excepts of an interview with an 18-year-old boy, Jean-Pierre, who is very good at maths.

 N: - What do maths mean to you? JP: - They allow me to escape, most of all they also allow me rigour, which is very important. Mathematical rigour is something fundamental. N: - What do you like about rigour? JP: - There's only one solution, either you're right or you're wrong. It's a sort of violence, you see where you get beaten, there's no half measure. N: - It's an all-or-nothing way. JP: - Yeah, while in physics, it's a middle way, it's the doldrums. I'm not being very nice with physicists... N: - This is the way you feel, this is what matters. JP: - Yeah, in maths, you can't really distort things, they can't be different. I've always liked rigour. When I was a kid, I remember, I would ask to be whipped. It's quite strange but I liked rigour, I liked all that is clear. N: - You would ask to be whipped? JP: - I remember one year when I was a kid, I must have been 6, I realized I didn't work enough, I said to my parents: "I can't work, I never do anything.", it was tragic, but as my marks were not too bad, they didn't say anything, but I felt I couldn't work, so I said to them: "Since I never do anything, whip me!" And they never did.

 In this interview, it appears that, in the pupil's mind, the signifier "rigour" is related to two different signifieds: mathematical rigour and physical rigour (whipping). He switches from one to the other as if they were the same. This switching of signifieds through a single signifier shows one of the mechanisms which allows interaction between the cognitive (mathematical rigour) and the emotional (whipping and all the imaginary that goes with it). Actually, mathematical rigour is substituted for the physical rigour which is expected, wished for. Mathematical rigour is a cognitive and emotional interaction which is going to become "motivating" for this boy.

 HOME PAGE History of mathematics' didactic What is the mental representation? Matematical mental representation Recording interview: René Thom, Dominique, Rosine... Write to me Author