Proof and visualization
The goal of the Letter is the stimulation of exchanges on certain current questions about the learning of mathematical proof. In no case is it an advanced contribution; it remains modest in content and editorial position. It is the letters and contributions which will constitute the substance.
The idea that recourse to images can facilitate the presentation of mathematical proofs is an ancient one; basically it is the idea that the concrete is more accessible than the abstract. It is undergoing a return of interest in the world of mathematics teaching, particularly as a result of the development of virtual realities to which computer science gives access. And after all, isn't a picture worth a thousand words? This point of view is reinforced by the attention being given to ancient mathematics, especially oriental mathematics, in which drawing was permitted to play an essential role in the communication of knowledge. But are things really that simple? Is visualization really a facilitator?
Tall, in his contribution to this question,
suggests that they are of interest in the
perspective of a progression in learning from the
concrete, and manipulation, to the more abstract,
and enunciation. He designates as the crucial
issue, which can be regarded as the lever for
progressing towards verbal proofs: "Difficulties
occur when the enactive or visual form of the proof
does not suggest an obvious sequence of deductions
to use for a formal proof, so that the individual
seems to 'know' that the theorem is true and yet
has no method of proving it" (ibid.).
The work of Claude
Tisseron on third degree polynomial functions
is such an example, probably reinforced in the case
he presents by the students' confidence in the
images produced by calculators and computers.
Contibutions to this theme will be published in the July/August Newsletter