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





History of mathematics didactics

This history is an illustration of the increased complexity of psychism's modeling


Mental representation  

What is the mental representation?

Reality goes across several filters and consequently we never reach to objectivity. We only have a feeling of reality (either concerning our pupils, our groups or our subject). What makes us looking at objects in an unobjective way? differently than others?

Actually, at all levers, either auditorilly or visualy we have a partial knowledge of a few wavelenghts, we only hear a few sounds. Greenlanders, as a matter of example give to qualify what is white thity different words. Language in itself, gives us shapes of things, any language teachers are well awase of that.


Making up mental representation


1) switching signifieds

2) the association chain

3) metaphor

4) mimicking speech  


Cognitive and emotional interactions

 Cognitive and emotional interactions are then halfway between the imaginary and the symbolic, they are situated in mixed elements like:

- representations (good/bad maths),

- symptoms (at the beginning of the year I always start with a migraine).


Matematical mental representation

Six mains mental representations


* structural law


- tools


* ideal object

* another world


* bad object


* object of phobie


Diagram of mathematical representations


Interactive questionnaire on the attitude toward mathematics


This questionnaire sums up a survey carried out on pupils of 15 to 18 years of age to study the relations existing between mathematics and affectivity.
Counting of the questionnaire
National comparisons:Great-Bretagne - Ontario - U.S.A - France - Belgium - Quebec

Defense mechanisms against mathematics:
Mathematical anxiety

Phantasy can be taken as the mental expression of instincts, but also as a means of escape - an escape from confronting external reality or the frustrated reality within  

- phobic avoidance
- repression
- projection
- reparation
- introjection
- narcissism

Recording interview with teacher:

Meeting René THOM


Field medal award

( Nobel prize for mathmatics) )

How the motivation of a discipline fits the personality

Dominique and maths/tool


Rosine and her confinement in mathematics


Brigitte and math: the mainstay of life


Recording interview with pupils

A 17-year-old boy from the arts


A 16-year-old girl from the scientific stream



Pr. Dr. Jacques Nimier

             I have started my carrer as a mathematics professor in a secondary school with students aged between 16 and 18 years old.

             During the first years of this time, I psychoanalised myself and went back to psychology studies.

             After my thesie about "The differents relations to maths" I teached communication to students in a Technology University Institute and then got the Chair of Clinic Psychology in the University of Reims and the direction of a Teacher Training Insitute (IUFM)

             From this day, I had the opportunity to create and animate training sessions called "face with violence" to thousand of teachers, and analysis groups about profesionnal practices where teachers or futures teachers could analyse the difficulties they have in their class or in training, specifiquely about violences and bullying.






The Death Camps-Drawings by a Survivor

Memoir from Beyong a Life







The Balint groups, or labor therapy groups, have the following goals for each trainer: Summary

*to widen their diagnostic appraisal to encompass the pedagogic condition,

• to clear up the pedagogic space stemming from the acknowledgment of their affective involvement • to spot and resolve the epistemological and pedagogical obstacles.

Their use has proven to close the gap between the knowledge about the psychological aspects, their implementation in the field of education and their availability in the micropractices.

The paper dwells on the theoretical foundations of such integration, which we illustrate with vignettes from the classroom clinics.


For read this speech

in spanish

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