Emancipatory Aspects of Learning
(and Teaching) Mathematics
Department of Computer Science
Technion--Israel Institute of Technology
Mathematics, like the martial arts, provides us both with a
technique to face the world and to face ourselves.
I will explore a view of mathematics which has its testified
origins in Greek philosphy, Roman engineering and Arabic
science. It is the basis of the Renaissance
views of man, of the ethos of the autonomous individual
and the underlying assumption of secularism.
Here are some of its major points which should play
a vital role when we ask ourselves why we teach mathematics.
Mathematics deals with a controled virtual reality,
a landscape of mental images.
Virtual, because we create it unless we are die--hard platonists,
controled, because once we look at it, it does not change.
The mathematical challenge is to explore this landscape,
to map it out and to conquer it for exploitation (applications).
We are allowed and encouraged to use landmarks of
our predecessors, but we pride ourselves on being able to
remap and reconquer this landscape using our own capacities
and ingenuity if needed.
The personal challenge of a mathematician is to control
his/her hopes, feelings, weaknesses and fears in the face of the
mathematical terra incognita. We want to know what it looks like
there, and from there further on with the only goal to see.
Each mathematical victory consists also in a victory over ones
weaknesses. We reach a point on our own and the sole reward is
to be there and to be able to generously and humbly share our view
with our fellow travellers.
Competitiveness among mathematicians tries to turn
the other's weakness into our own strength. It makes us mean, petty
and greedy. We should always remember to serve Mathematics humbly
rather than use Her for our own purposes.
Even in teaching mathematics we can at least attempt to
teach the students the flavour of freedom and critical thought,
and to get them used to the idea of being treated as humans
empowered with the ability of understanding.
Roger Godement, Cours d'Alg`ebre, Hermann, Paris 1966.
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