No one disputes how important it is, in today's world, to prepare
students to un- derstand mathematics as well as to use and communicate
mathematics in their future lives. That task is very difficult, however.
Refocusing curricula on funda- mental concepts, producing new teaching
materials, and designing teaching units based on 'mathematicians' common
sense' (or on logic) have not resulted in a better understanding of
mathematics by more students. The failure of such efforts has raised
questions suggesting that what was missing at the outset of these
proposals, designs, and productions was a more profound knowledge of the
phenomena of learning and teaching mathematics in socially established
and culturally, politically, and economically justified institutions -
namely, schools. Such knowledge cannot be built by mere juxtaposition of
theories in disci- plines such as psychology, sociology, and
mathematics. Psychological theories focus on the individual learner.
Theories of sociology of education look at the general laws of
curriculum development, the specifics of pedagogic discourse as opposed
to scientific discourse in general, the different possible pedagogic
rela- tions between the teacher and the taught, and other general
problems in the inter- face between education and society. Mathematics,
aside from its theoretical contents, can be looked at from historical
and epistemological points of view, clarifying the genetic development
of its concepts, methods, and theories. This view can shed some light on
the meaning of mathematical concepts and on the difficulties students
have in teaching approaches that disregard the genetic development of
these concepts.
