Some pupils voluntarily practice mathematics out of the classroom. Such a "different" approach, generally based upon a mathematical research work, has, or course, a didactical interest. But, furthermore, the clinical anlysis of non-directive pupils' interviews shows how much the engagement itself is significant. Because of the voluntariness, the commitment takes place in an identity dynamics and contribute to the psychic construction : to accept an unknown and absorbing work, you need indeed to believe that you will find some interest in it. But this interest, psychical* and symbolical before being didactical, is only present in some special social, psychical* and educational background, as we can show it by analyzing here three interviews.
* or "psychological" ?