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Topic: geometry for secondary teachers
Replies: 0

 Ladnor Geissinger Posts: 55 Registered: 12/4/04
geometry for secondary teachers
Posted: Oct 3, 1997 1:45 PM

I appreciate seeing many suggestions from the list about which geometry
book at least one person believes is good for a course for secondary
teachers. But it's hard to tell if the book recommended is simply the
latest to appear on the desk or if there is something more to it. I
don't see much which tries to make explicit what the students in the
course really need and why, nor what it is about the particular book
recommended that makes it especially appropriate -- I'm looking for a
rationale. I have some questions about that.

Many geometric topics or strands have been mentioned in notes to the
list: Euclidean Geom, constructions, axiomatics, transformational geom,
non-Euclidean geom, finite geom, solid geom, geom prob., coordinate
(Cartesian) geom in dim 2,3,?, complex plane. When you decide on the
course content and a book and then recommend it to others, what are your
reasons for choosing to include some subset of these topics? Is it
mainly a matter of what you think they will in fact have to teach and how
they will be expected to teach it -- or are other considerations more
important?
Do you choose synthetic Euclid geom and axiomatics because you think
that's the best way to both learn the needed geom and simultaneously
practice thinking and writing proofs?
Why would you choose non-Euclid or finite geoms? Is there some idea
here that's important for teachers, or just diversions from what has been
seen before?
Do you think they will find geom probability problems particularly
interesting and useful ?
Is the real point of choosing transformational geom to deepen their
understanding of function as a fundamental math object and a critical
element of high school math, while learning some geom?
Would you argue for Cartesian geom because Descartes' idea of combining
geom and algebra was the critical element that allowed the scientific
revolution to get rolling?
Would you argue for the complex plane as a good way to become comfortable
with using complex numbers [and why is that important?] while seeing a
slightly different version of coordinate geometry?
Would a course on Geometry, Vectors, and Matrices be just as appropriate
and useful -- are you assuming that these future teachers have already
What about some of the early uses of Cartesian geom -- statics,
mechanics? Or one view from theoretical mechanics that synthetic
geometry is a compact description of elementary notions of spatial
measurement -- early physics?

Maybe you have some references for me which outline or describe in detail
a rationale for what such a course should be.

Math Prof at UNC Chapel Hill & Math Chair at IAT
phone: 919-405-1925
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