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Topic: calculus for (secondary) math teachers
Replies: 3   Last Post: Jul 21, 1995 1:08 PM

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Andre TOOM

Posts: 549
Registered: 12/3/04
Re: calculus for (secondary) math teachers
Posted: Jul 20, 1995 12:00 PM
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On Wed, 19 Jul 1995, Tad Watanabe wrote:

> Should a college program for secondary math teachers include calculus
> courses? If so, what contents should there be? How should the course be
> taught? How much technology should be incorporated? If calculus is not
> needed, why not?
>
> After this one, maybe we can discuss about Algebraic Structure and Linear
> Algebra.


Of course, the more a teacher know, the better.
But let me mention some topics which a teacher (or anybody else)
should know BEFORE calculus and knowing which has a higher priority
in my opinion:

Geometry:
Similar figures, relations between angles and arcs.
Relations between segments in a right triangle.
Constructions with a straightedge and a compass.
Volumes and surface areas of cube, parallelepiped,
prism, cylinder, cone.
Problems on maxima and minima without calculus.
Arithmetics:
Divisibility and division with residues
Arithmetic and algebraic progressions
Long division
Periodicity of decimal representation of rationals
Irrationality of sqrt(2) and other roots
There are infinitely many prime numbers
The decomal and other systems
Criteria of divisibility by 3 and 9
Graphs and their application to algebraic problems

MOST IMPORTANT: When I write that a teacher should know
all this I mean that she or he must be able to solve
problems about this in a reasonable range.

A person who can solve problems about all this can be
a quite acceptable high school teacher even if he does not
know calculus.
A person who cannot solve problems at this level...
Well, in which sense can such a person `know' calculus ?
Andrei Toom








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