🚀 go-pugleaf

Howard,

Thanks for your reply about constructions.

-> because of two more advanced theorems of geometry and the nice
-> connections between Euclidean contructions and transformations,
-> especially inversion.  The two theorems are the Mohr-Mascheroni
-> Construction Theoerem and the Poncelet-Steiner Construction Theorem.

Whooosh! Those whizzed right by me ;-) I am not in the least familiar
with those two theorems.

I appreciate that students may sometime encounter these types of things
in the study of higher math *if* they go on to it. But I wonder how much
time and frustration should the class as a whole spend on classic
construction given that the likelihood any one of the students in the
class would study such material is very small. (Remember, it is an
average ablility course).

Still, I am not having an easy time deciding on this one (or I wouldn't
have asked the question). Besides which, I don't think that I alone have
the decision to make. There are four other geometry teachers at the
school who will have some say in this.

Rick Heptworth, the guy who wrote the Mira booklet which I plugged in a
recent message, seemed quite comfortable with the idea of discarding the
traditional construction methods. However, he does use compasses in his
class for drawing circles and measuring congruent segments. Perhaps
simply by using the tools in this way they would get a sense of
familiarity with them so that the theorems you mentioned above would not
be too difficult for them to understand.

-> It would be useful and beneficial to students to explore the
-> equivalence of constructions they perform with "patty papers" and the
-> same constructions with compass and straight-edge.  For example,
-> constructing a perpendicular bisector.

THIS is something that I had considered previously. I am very certain
that I will do at least *some* such things with my honors classes. I
wonder how the other teachers will feel about trying to get the more
average students to work on seeing that kind of equivalence.

-> Please keep us informed, Sheila, as you struggle with revising and
-> reforming your geometry curriculum.  I'd certainly like to hear how
-> the students react to it.

Will do.

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

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