Although for one or two decades mathematical
software for symbolic computation has been employed extensively in the
teaching of university mathematics, each respective course typically
emulates a traditional course without computers in treating a particular
topic such as differential calculus or linear algebra. We advocate an
holistic approach to the teaching and learning of mathematics involving
intensive use of contemporary software not only for pedagogical purposes
but especially for implementation by the users of mathematics. By
expecting a learner to employ computer software for almost all
mathematical operations, an instructor can emphasize the mathematical
concepts and principles, involving formal definitions, algebraic
derivations, numerical examples and especially graphical illustrations
and constructions, and then develop the implementation with selected
software. In this way not only does a student acquire a profound
understanding of those principles – and limitations of the software, but
he or she becomes proficient in applying the software for real problems
of a scale that would be impracticable in manual work. By eliminating
practically all repetitive drill and practice that is irrelevant when
the computer undertakes the calculations, an instructor becomes able to
cover a much enhanced range of topics within a given duration; for
instance, all material – from differential, integral and multivariate
calculus, linear algebra and differential equations to probability,
statistics and data analysis that typically occupies six or more
semester courses – might be covered within three semesters at a typical
pace. That content is all that a student is likely to need for a
technical career after completing an undergraduate programme in science
and engineering. We argue that contemporary students of engineering and
science who are not so equipped with a working knowledge of symbolic
mathematical software are not being prepared properly for a technical
career.
"The human mind is never performing its highest function when it is doing the work of a calculating machine." – Lord Kelvin
In this lecture we present examples of topics of which we demonstrate some benefits of teaching with mathematical software. |