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 had such a course? 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.
Ladnor Geissinger Math Prof at UNC Chapel Hill & Math Chair at IAT email: firstname.lastname@example.org or email@example.com phone: 919-405-1925 address: Institute for Academic Technology 2525 Meridian Parkway, Suite 400 Durham NC 27713 USA IAT phone: 919-560-5031 IAT fax: 919-560-5047 IAT web home page: www.iat.unc.edu LEARN NC home page: www.learnnc.org Mathwright Library: ike.engr.washington.edu/mathwright/