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

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Tad Watanabe

Posts: 442
Registered: 12/6/04
Re: calculus for (secondary) math teachers
Posted: Jul 20, 1995 3:46 PM
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Do you have a list of topics for Algebra? How about something from
Probability/Statistics? Or, they don't come BEFORE calculus?

Also, I'm curious, why you list divisibility tests for 3 and 9
specifically but not others, like 4 and 8.

Tad Watanabe
Towson State University
Towson, Maryland

Still beliving I have a life...

On Thu, 20 Jul 1995, Andrei TOOM wrote:

> 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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