In my own classes I have found Professor Bruno Buchberger’s pedagogical model for teaching with technology – the black box/white box principle - to be a most helpful guide in finding my around the critically important questions of how and when to teach with technology.

The white-box phase of using technology is employed in the introduction of new concepts and skills. The technology is therefore used to discover patterns, make conjectures, test conjectures, and learn new algorithmic procedures. For example, in learning how to solve equations the solve button would not be used since this obviates the need to learn equivalence transformations. Once the student has mastered the concepts, manipulations, etc. inherent in a particular topic, the technology can then be used as a black/box for problem-solving, mathematical modeling, mathematical investigations, etc. where the emphasis is no longer on analytical or computational procedures but on “higher order” skills such as translating a real life problem into a mathematical system to be solved by the technology. This is where the “solve” function of the technology is indispensable in modern-day mathematics teaching.

To read more about Bruno Buchberger’s pedagogical model, click here.






							COMPUTER ALGEBRA SYSTEMS - TECHNOLOGY IN MATHEMATICS EDUCATION