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Mathematics in Everyday Events
Posted:
Aug 20, 1994 1:37 PM
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I am surprised by the twist this discussion took - saying that
applications (meaning?) interfers with the learning of abstract
(formal?) mathematics.
First - I can imagine teaching music through its applications to
everyday life (of the student). The Suzuki method teaching tunes (by ear),
long before scales and reading music. I am convinced that one reason
my son is now a student of music at university, rather than a student
of mathematics (or science) is because his music teacher (private)
responded to his interest in 'making music' of a popular sort,
rather than doing scales or 'good pieces' picked by the teacher.
Unfortunately, none of his mathematics or science teachers were as open.
(The computer science teacher was more open - hence his science fair
project on analyis of sound on a computer - and his current
program in Computers and Music).
I learned pure mathematics as a student (almost no geometry),
and only later turned to applied mathematics (geometry). The
idea of learning projective geometry without the underlying statics
(and kinematics - if you are careful) of Mobius et al seems absurd
after this experience. Why wouldn't we use the essential issues of,
say, computer graphics to motivate and illustrate aspects of
geometry?
These are neither gimics nor past issues. There is a great deal of
interest in geometry arising in applied areas such as computer
aided geometric design - and a number of unsolved problems, even
in plane Euclidean geometry. Many people not trained in mathematics
are discovering they NEED to know geometry. Current engineering text
LIE about known results because the students know too little geometry
to understand the real answers. I think this reality adds to the
enjoyment of geometry.
I suspect that many parts of mathematics are learned as
abstract pure mathematics, in part because we have forgotten the
original 'practical' issue. Pythagoris Theorem was the solution
to a practical problem - how do you add two squares using a straight
edge and compass. (Given that you trusted geometry more than algebra,
this is 'practical'.)
Yes - applications are not enough. They seldom generate the fundamental
insights which unify the pieces - and generate new applications.
I think the issue is to balance applications (and interest expressed by
the students) with theory that will build for later.
I teach (currently) at the undergraduate level. In courses such as
geometry - I make it part of every assignement that the students
write out some questions THEY had when they finished the assignement.
Sometimes these are integrated back into the class work. Sometimes
they become a private dialog with the student. Sometimes they become
the topic of a major project ( near the end of the course).
THis does not always work - but it works better that many of my
efforts to guess what is releveant to these students (who tend to
people wanting to become mathematics teachers!).
Walter Whiteley
York University
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