From: Howard.Hansen@f101.n285.z1.fidonet.org (Howard Hansen)
Newsgroups: k12.ed.math
Subject: Revising Geometry curricu
Date: Tue, 08 Sep 92 23:40:00 PST
Organization: FidoNet node 1:285/101 - NE Dept. Education, Lincoln NE

Sheila,
Your ideas seem right on target as far as I can see, especially the idea
of deferring proof until later in the year (or at least introducing it
more slowly).  I hope that you have a copy of Discovering Geometry by
Michael Serra (also from Key Curriculum Press like the SketchPad).  His
ideas and yours articulate very well.  In fact, it seems that you have
arrived at many of his conclusions and methods from your own experience.
I used his text to teach high school geometry to college students who
had a deficiency.  I taught a traditional geometry for one year and
couldn't stand it.  I changed the course to start with learning
constructions (no software then) and based the course on Inquiry and
Discovery of properties, definitions etc.  Wow!! what a response.
Students were turned on and the conjectures flowed.  My real problem was
that it seemed to take too much time and I didn't feel I got through
enough material.  Serra's book helped me by introducing the idea of
cooperative groups--the whole class does not have to discover every
property, you can use the groups to discover individual pieces and then
put it together!!!  I also liked Serra's use of propositional logic
prior to geometric proof.  It seemed that students were able to quickly
grasp the more complicated proofs and most importantly they understood
the reason for doing them--they had made conjectures or generalizations
about most of the properties from specific cases and recognized the need
to prove for all cases.  One other thing on proof.  Serra's book does
this a little, but I think more is needed, that is since students have
just finished algebra, I like to use algebraic proofs at first wherever
possible along with the constructions and explorations early in the
course.  For example, the proof that an exterior angle of a triangle is
equal in measure to the sum of the two remote interior angles.  After
students have measured an acute, obtuse, and right triangle (my students
decided these had to be scalene for more generalized results) and foaund
this property, work through an algebraic proof.  Of course, your
suggestion about introducing coordinate (analytic) geometry early plays
right into this
Of course, if you need more ammunition for your board or
parents you can refer to the research of Belgians Pierre Van Hiele and
Dina Van Hiele-Geldorf and their theory of levels in the development of
geometric thought and the instructional process which is required to
move between levels. By the way this approach, using Serra's text and
other resources, was piloted in randomly selected classrooms in the
Lincoln Public Schools during 1990-91 school year.  The results are
reported in a Masters Thesis by Matt Larson at UNL.  The results were
significant and positive on both the achievement and affective measures
(students who took this course did better on the school-wide final and
were much more positive about their experience in geometry).  As a
result Lincoln Public Schools have adopted and use this approach in
teaching geometry, which follows first-year algebra. Well, sorry to
ramble, but when I saw your list and ideas I just got very enthusiastic
all over again and want to encourage you in your efforts.

Howard

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