At 10:40 PM 3/25/2010, you wrote:
I'm teaching high school math to homeschoolers and I'm looking for how to make
geometry year meaningful.
I'm having a "crisis of confidence" because from my viewpoint, algebra was 10x
more useful for future math and science work.
The fact that geometry is considered a place to teach formal reasoning (and
not much more) is peculiar to the math standards in this
country. Properties of congruent triangles and other trivial stuff can be
dispatched with rather quickly (by the end of 6th grade in many
countries). I think after that, geometry, more than any other elementary
math subject, offers opportunities for creative problem solving. It also
teaches transformations and symmetry, invariants (loci of points), creative
straightedge and compass constructions, right triangle trigonometry,
spacial reasoning, etc. For a creative exploration approach consider
http://books.google.com/books?id=tDRJi-qlE18C&printsec=frontcover&dq=%22lines+and+curves%22&source=bl&ots=xPHqn0h_fk&sig=5Ve-5_pEsafkCAcRlDUfYvZFiOU&hl=en&ei=xNCsS6CLKMiVtgfb3KmrDw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CAYQ6AEwAA#v=onepage&q=&f=false.
Gary Litvin
www.skylit.com
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