- During years 70 and 80, international congresses on mathematics' teaching were speaking only about "curricula", i.e., in some way : courses planing and contents : Should such subject be taught before or after such other subject ? Must or must not such area be taught ? That is now known as transition from savant knowledge to taught knowledge. In this whole process the student did not exist.

- Then came a didactic concerned by "epistemological obstacles". That means people become aware that in the history of mathematics some subjects were more challenging for researchers than some others : the focus was still on mathematics per se, the students were always absent but history and time were introduced, in other words mankind.

- Then the students appeared in didactics but only through their performances in problem solving. This was the time of statistical didactic; when, for the same problem, one was looking for the frequency of the different results, right or wrong.

- The student was look at as a black-box with the problem to be solved as an input and the produced solution as an output.

- Hypothesis on the internal performance of the black-box were then made in studying not only the results but also in trying to understand the various strategies used to produce the results. To do so the students' drafts were collected, if necessary, to figure out how they worked out the solution. Those drafts were then used to understand the various search strategies leading to the solution of the same problem. The student was still a mute black-box.

- Next didactical researchers became conscious of the students' speaking ability !

- They studied again the strategies but this time by asking the students how they solved the problem. They got "after the facts" explanations transcripts; very rationalized explanations to justify their process, but explanations allowing to become conscious of how important the student words were.

- A big step was made by a female didactical researcher (Viennot) who showed, by studying what the students were saying in physical sciences, that they followed a logic of their own, they were building "spontaneous theorems" who, although inaccurate, were useful in the problem solving process.

In other words, students were using "models" (some people say concepts) of the various physical processes, deductive mathematics logic was not the only one used in student reasoning but another logic existed.

- The only missing part was the student's unconscious in order to take into account all the complexity of the student's personality. That is what, following my personal research, researchers like Claudine Blanchard-Laville ; Benoît Mauret ; Jean Claude Lafon ; Nathalie Kaltenmark-Charraud ; Isabelle René etc..., are doing.

Others researchers show also that the student is not alone but that the group of students is important in the learning process, in other words individual psychism is influenced by group phenomena.

This history of mathematics' didactic is an example of the complexification work we all must do;

 Complexification:

 This very work will enlighten us to find the answers to the various questions we are asking ourselves about our teacher work. This evolution show also how important is the representation concept and to take into account unconscious in teaching mathematics.