Q&A #918

Geometry Textbook "Discovering Geometry" by Michael Serra

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From: Murrel (for Teacher2Teacher Service)
Date: Dec 20, 1998 at 09:37:34
Subject: Re: Geometry Textbook

When I returned to teaching in 1989 after being away from mathematics at the
senior high level for almost 10 years, the only thing that moved in my
classroom was me...writing on the chalkboards that covered 3 of 4 walls in my
classroom!  To make a long story short, in 1992 I "discovered" Discovering
Geometry and was given permission to pilot the book in my classroom. I had
two geometry classes, one was taught with the traditional text -- emphasis on
2-column proof from the beginning--the other was taught with DG.  At the end
of the year, my students took a critical skills test on geometry
content...the test had been written much like a criterion referenced test and
in the traditional content. My DG students scored 16% higher than the
traditional class.  After that year, I found Sketchpad and Patty Papers and
other ways to enhance the teaching of geometry. My colleague who taught the
rest of the geometry classes at my school came to me after that first year
and said, "I don't know what you are doing in geometry, but I want to do it
next year." Together we taught all students coming through our curriculum
with the discovery method and cooperative learning. Two years later, the
counselor came to me and said, "Whatever you two are doing in geometry must
be working." She showed me the test scores for our juniors that year (which
would have been the first class of students to have all been taught using DG)
and their logical reasoning scores were +23 over national norms!

I attribute that success to the investigation based curriculum.  My students
are involved in their own learning during 70-90% of their class time and in
my opinion, that makes the difference! They are not sleeping...they are not
day dreaming...they are busy talking geometry!  I will never go back to
teaching any class using "talk and chalk" methods! I love being a facilitator
of learning...the "guide on the side, not the sage on the stage" philosophy
had worked for me and students in my classroom.  I have used DG with bright
9th graders who challenged me with their conjectures and the depth with which
they understood geometric concepts and I have used DG with juniors and senior
who are typically so unmotivated. I have had great success in both
situations...I still have students who do not achieve the 70% passing grade,
but I will continue to believe they know more geometry from this approach
than they would from the traditional curriculum.

I use Geometer's Sketchpad during class time and at the end of the class take
10 minutes or so to summarize and help students transfer what they have
learned to applications... I cannot lecture and investigate and it took me a
long time to realize that the investigations take the place of the lecture.
My students work in pairs or threes at the computer and when they finish an
investigation, each student gets a copy for their notebook. They turn these
in at the end of the unit for assessment. During the closure for an
investigation, I try to be certain each student writes "my conjectures" along
with their own which have been typed into the Sketchpad document. These serve
as their notes for the day.

Roya was right on target when she said time management was the most important
part of teaching with DG.  I rarely get to the formal proofs at the end of
the text with my juniors and seniors, but I firmly believe those students are
prepared to deal with proof if they are in a curriculum where they will need
it...more so than students in my traditional classes in the past who only
memorized steps without any understanding of the geometry concepts involved.
With careful management, you can get to the proofs with honors classes. They
often wonder what all the "fuss about proof" was when it is so clear for them
after having using inductive reasoning and always justifying their
conjectures...verbal proof is always a part of our discussions when we arrive
at conjectures.

You might be interested in some of the research of the Van Hiele's on levels
of geometric reasoning...the fact that our students enter geometry at a 0-1
level of reasoning and we begin teaching at a level 3-4.

Hope I have been able to give you some insight into how much DG has meant to
me and my students....good luck!

 -Murrel, for the Teacher2Teacher service

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