Second process:The association chain. The pupil interviewed here is a 15-year-old girl, not really good at maths, but not really bad either. What surprised me straight away in her interview is that she considered algebra and geometry quite separately. <<Pupil: - Algebra, that was awful. It was all new. I did well in geometry because I had a good grounding, and it was all right, I could understand. And right from the beginning, I refused to learn algebra... Why algebra? I've been asking myself since I was 13. I found geometry classes really interesting, I never got bored, I was really into it. While in algebra, I could have brought my pillow with me.... We could feel that the teacher didn't put her heart into her work, and what's more, the poor woman had a voice that put you to sleep. From time to time, she would scream and wake us all up... N: - A voice... What did that voice remind you of? P: - What did it remind me of?....... N: - A voice that put you to sleep.... P: - Yes, that's true, it must have reminded me of something I had been through, something I knew..... or which had probably been particularly unpleasant, I guess. N: - What was that? P: - What was it?.....I don't know. I know, for sure, but I can't explain it to myself, but I try to understand myself. Sometimes it's difficult and sometimes I feel ashamed all by myself, but... N: - Why ashamed? P: - Ashamed of trying to know yourself. You end up realising you have a lot of faults..... Well, you have to learn to put up with yourself, that's all. N: - There are characteristics.... P: - Yes, I tried to understand myself... That voice.....? It must be related to something or someone that struck me or that I found unpleasant... N: - Someone? P: - Because of her voice, I don't know. It was a bit like a droning, she spoke, not very loud besides, it was very soft. Oh! I think it must have been related to something else.... But I can't believe that's it..... N: - What are you thinking of? Even if it isn't, it doesn't matter. P: - All right, because my father and my mother disagreed a lot, and we all slept in the same bedroom. I remember all those nights when I couldn't sleep, because I heard the arguments that went on, and I heard it all while I was half asleep..... and everytime I arrived in maths, when I heard this woman's voice..... Well, I don't know.... I thought about that and I don't know, it made about the same noise, the same droning. So it made me nervous. So in geometry, I ended up cutting myself off from the rest, I was alone with my drawing. Whereas in algebra, I heard that voice....  In this interview, an association chain appears: pillow / that puts you to sleep / wake up / scream..... This sequence is made by the pupil without her being aware of it. Often, much more is said than what one is aware of. This association chain shows the relationship between past events, which were emotionally unpleasant, and a rational speech on mathematics. In other words, there now exists a cognitive and emotional interaction for this pupil, between this memory which is heavy with unpleasant emotions and a cognitive element, here mathematics or, more precisely, algebra. The cognitive and the emotional, here, cannot be separated. They are like the two sides of a coin. The pupil's representation of algebra originated in this process. What is important here is to see that this relationship occurs through an interaction between two speeches, one of which is conscious and belongs to the cognitive field, while the other (in the association chain) is unconscious and bears imaginary and emotional elements. Those two speeches intermingle and interact constantly. Mental representation Making up representation Various representation Defense mechanisms Questionnaire Counting diagram of mathematical representations HOME PAGE Author My bibliography Cognitive and emotional interactions History of mathematics' didactic. Rosine and her confinement in mathematics Write me Sommaire français