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Hello Everyone,

Well a few weekends ago I attended the CMC Conference in Palm Springs
(CMC is California Mathematics Council--an affiliate of NCTM).

It was an exciting conference, and I thought I would share a little of
what I saw.

First of all, this thing called a MIRA is _quite_ interesting. We are
looking to incorporate them into our high school geometry course next
year in order to improve the course and increase student understanding.
Miras can be used to do ALL constructions that can be done with the
traditional straightedge and compass, but they are much easier with a
Mira. Plus, the Mira can do some constructions that you CAN'T do with a
straight edge and compass.

BUT what I found most interesting, was that a Mira can be used for so
much more than just geometry. You can also construct conic sections and
sine and cosine waves with the darn thing! I think Trig students using a
Mira to construct a  sine or cosine wave from the unit circle would have
a much clearer understanding of where those graphs come from and what
they mean. Also, the Mira can be used in lower level math classes to
construct fractional lenghts of line segments, and thereby one can model
addition, subtraction, and multiplication of fractions.

I also saw Michael Serra himself (author of _Discovering Geometry_). He
presented a session called "Patty Papers Geometry". The idea is to use
those little wax paper squares that go between hamburger patties to
teach principles of geometry. By folding, tracing, cutting, and using a
straightedge to connect points, you can do all constructions on these
little squares of paper. It's lots of fun and it's quicker than
traditional construction methods. Apparently Serra has another book
coming out around April of this year entitled (guess what?) _Patty Paper
Geometry_. Based on his excellent geometry text, plus this very exciting
session I attended at the conference, I would highly recommend this
book.

I also saw an interesting presentation on the TI-81 for use in class.
One of the programs this presentor had on his calculator will graph a
line at random and display it (you use the overhead device so all the
students in the classroom can see the graph). Then, you let the students
guess the coefficients A, B, and C in the equation Ax + By + C = 0 in
order to get the same line. After the students guess the A, B, and C you
enter them into the calculator and the calculator then graphs your guess
line and the original line. The students can then see both lines and
compare them and revise their guesses for A, B, and C. After they make
new guesses you can now enter these and the calculator will graph the
new guess line and the original line. Hopefully the new guess is closer
than the first guess. Anyway, this revision procedure can go on for as
long as the teacher likes, or when you think they get close enough to
the line have the calculator graph a new one and start over.

It is also possible to program the same type of thing for parabolas and
probably other types of graphs as well. If anyone would like some tips
for how to write such a program for the TI-81 (or even if you'd just
like for me to input the program here) let me know.

Sheila
coming to you from Diamond Bar, CA (in Los Angeles County)
                                                                 

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