Bruno Buchberger

special activities

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.