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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