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 > > > >