Generalizing the Pythagorean Theorem: Geometric Interpretations of the Law of Cosines

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Generalizing the Pythagorean TheoremGeometric
Interpretations of the Law of Cosines

• Peter Gerrodette
• Anderson Union High School
• Anderson, CA

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Generalizing the Pythagorean TheoremGeometric
Interpretations of the Law of Cosines

• My name is Peter Gerrodette and Im a high school
  math teacher at Anderson Union High School.
• My web site/teacher page is located at CTAP 295
• My e-mail is pgerrodette_at_anderson.k12.ca.us
• This is a lesson wherein students will discover a
  useful tool for solving triangles from a
  geometric construction. This should provide a
  concrete justification for the algebra beyond the
  teachers because I said so.

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Generalizing the Pythagorean TheoremGeometric
Interpretations of the Law of Cosines
Expectations

• How to web-orient a lesson
• Learn how a web page is built
• Learn something about HTML
• Learn how to create links
• refine my plagiarism skills
• familiarize myself with Excel and Powerpoint
• confront my frustration as a Mac user in a PC
  world

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Generalizing the Pythagorean TheoremGeometric
Interpretations of the Law of Cosines
Outcomes
I learned the following

• Use an alias to avoid possible jail time
  resulting from performing numerous illegal
  operations on a PC.
• Downloading and uploading techniques in bilingual
  operating systems.
• Web page construction using a template and
  Composer.
• Linking objects, documents and applications to
  pages.
• Powerpoint and Excel KISS techniques.

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Generalizing the Pythagorean TheoremGeometric
Interpretations of the Law of Cosines
Successes
Personal and Projected

• Students love technology its a natural hook.
• Students appreciate that mathematics is more than
  a bunch of rules and formulas to be memorized
  use a line thats stronger than 2 lb. test.
• It works! Did they swallow the sinker?
• I made some new friends.
• New technologies arent as scary as some might
  think.

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Generalizing the Pythagorean TheoremGeometric
Interpretations of the Law of Cosines
Shortcomings

• The amount of time required to incorporate any
  technology into the curriculum is inversely
  proportional to my perception of how easy it will
  be to do so.
• I wont really be able to evaluate the
  effectiveness of this lesson until the Spring of
  2002.
• My new favorite refrain Sounds like a PC thing

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Generalizing the Pythagorean TheoremGeometric
Interpretations of the Law of Cosines
Student Data
This chart shows that all students
increased their knowledge from the Pre to the
Post-test which is not surprising since students
probably had no prior knowledge of the Law of
Cosines.
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Generalizing the Pythagorean TheoremGeometric
Interpretations of the Law of Cosines
Revisions

• To make my web page more accessible, I will need
  to learn how to convert a Geometers Sketchpad
  sketch into a sketch that utilizes JAVA. I hope
  to do this without having to learn JAVA itself.
• I need to link two more activities so that
  students can discover an alternate formula for
  the area of a triangle and also the Law of Sines.
• I can see a need to expand this work and download
  it to a more permanent home here at Andersons
  server.

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Generalizing the Pythagorean TheoremGeometric
Interpretations of the Law of Cosines
Summary

• This project helped me to see how using
  technology could enhance the learning of
  students. I have grown and now realize that Ive
  also opened a personal Pandoras Box. How many
  countless hours will I spend googling for
  animated gifs, jpegs, and JAVA scripts in the
  future? These however are just bells and whistles
  (or maybe theyre moo sounds Im hearing). What
  really matters is the dendrite growth that occurs
  in the minds of my students and their willingness
  to accept new challenges.