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Phobic avoidance

 The statistical analysis lets us pick out a first group of statements:

Ql:- I feel there is something, that keeps me from getting at the problem, a barrier I can't get across.

 Q3:- At the start of a mathematical problem, I feel as if I'm in front of a black hole.

 Qll:- Doing maths is doing something which, to me, seems impossible.

QUESTIONNAIRE

 These three statements betray a certain anxiety towards mathematics.

The student cannot approach the mathematical object, something separates him or her from it - barrier, hole, or impossibility.

No blame is placed on mathematics itself, as in other cases described below.

I propose the following interpretation: the student is looking in this case, for a way of avoiding mathematics because of the anxiety it provokes.

The student self-protectively prefers to classify mathematics as impossible rather than confront it. This is a matter of the defence mechanism known as phobic avoidance

For example,

 

A girl from an arts stream speaks of a veil set up in front of her.

-<<It is as if there was a veil... which separates me from what is there, if... 1 look into space, I don't know, it's faraway... it has already given me this impression... evidently, 1 don't think immediately of maths, when I look at the stars; but there, I am aware that it represents something similar, I don't know. To look at something and then reach a time when you can no longer see, close your eyelids, there is the veil which prevents us from penetrating any further, from reaching it... I think it's that.>>

 

This girl envisages a distance between herself and mathematics like that between her and the starts. What she wants is to be able to "penetrate" further, but in practice, she bas set up a veil, which as in the Temple, separates the faithful from the Holy of Holies. The underlying ambivalence in such case was noted by Otto Fenichel:

<<Analysis always reveals that specifically avoided situations or inhibited functions have unconsciously an instinctive, sexual or aggressive, meaning. It is against this instinctive meaning that the defence is really directed. That which is avoided refers, either to a temptation to give in to the repressed urge or to a feared punishment, or to both at the same time. >>

 

Various mental representations

 

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History of mathematics' didactic
What is the mental representation?
Matematical mental representation
Recording interview: René Thom, Dominique, Rosine...
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