PhD Curriculum for
Symbolic Computation / Mathematics
for Computer Science / The
"Thinking, Speaking, Writing" Course / The
White-Box - Black-Box Principle
Special Didactic Activities/
The White-Box / Black-Box Principle for Using Symbolic Computation
Systems in Math Education:
Although math software systems, in particular those based on advance
symbolic computation techniques, are now heavily considered for
improving and supporting math teaching all over the world, there
is still a lot of confusion about their appropriate use in math
teaching. There seems to exist an unbridgeable disagreement between
those who believe that these systems must not be used in teaching
in order not to "spoil the abilities of the students"
and those who believe that, with the availability of these systems,
teaching the mathematical techniques covered by theses systems is
not any more necessary and , rather we should confine ourselves
to teach how to use of these systems.
For bridging this disagreement I introduced, in 1989, the "White-Box
/ Black-Box Principle" for the didactics of using symbolic
computation systems in math teaching: I am advocating that, in the
"white-box" phase of teaching a particular mathematical
topic (i.e. the phase in which the topic is new to the students),
the pertinent parts of the SC systems should not be used, while
in the "black-box" phase (in which the students completely
master the new topic), it is essential for modern teaching of math
to use these systems. The principle is recursive because, what was
"white-box" in a particular phase of teaching becomes
"black-box" in a later stage and new topics become "white-box"
that use earlier "black boxes" as building blocks.
Quite some authors in math didactics refer now to this principle
and a couple of didactics textbooks appeared that are based on this
principle. Also, in several Austrian high-schools, based on my advide
didactical experiments incorporating this principle were pursued.