> 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