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

Generalizing the Pythagorean Theorem: Geometric Interpretations of the Law of Cosines. Peter Gerrodette Anderson Union High School Anderson, CA. Generalizing the Pythagorean Theorem: Geometric Interpretations of the Law of Cosines.

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

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  1. Generalizing the Pythagorean Theorem:Geometric Interpretations of the Law of Cosines Peter Gerrodette Anderson Union High School Anderson, CA CTAP 295 Teaching with Technology

  2. Generalizing the Pythagorean Theorem:Geometric Interpretations of the Law of Cosines • My name is Peter Gerrodette and I’m 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@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 teacher’s “because I said so”. CTAP 295 Teaching with Technology

  3. Generalizing the Pythagorean Theorem:Geometric 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 CTAP 295 Teaching with Technology

  4. Generalizing the Pythagorean Theorem:Geometric 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. CTAP 295 Teaching with Technology

  5. Generalizing the Pythagorean Theorem:Geometric Interpretations of the Law of Cosines Successes Personal and Projected • Students love technology; it’s a “natural” hook. • Students appreciate that mathematics is more than a bunch of rules and formulas to be memorized; use a line that’s stronger than 2 lb. test. • It works! Did they swallow the sinker? • I made some new friends. • New technologies aren’t as scary as some might think. CTAP 295 Teaching with Technology

  6. Generalizing the Pythagorean Theorem:Geometric 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 won’t really be able to evaluate the effectiveness of this lesson until the Spring of 2002. • My new favorite refrain: “Sounds like a PC thing” CTAP 295 Teaching with Technology

  7. Generalizing the Pythagorean Theorem:Geometric 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. CTAP 295 Teaching with Technology

  8. Generalizing the Pythagorean Theorem:Geometric Interpretations of the Law of Cosines Revisions • To make my web page more accessible, I will need to learn how to convert a Geometer’s 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 Anderson’s server. CTAP 295 Teaching with Technology

  9. Generalizing the Pythagorean Theorem:Geometric 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 I’ve also opened a personal Pandora’s 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 they’re moo sounds I’m hearing). What really matters is the dendrite growth that occurs in the minds of my students and their willingness to accept new challenges. CTAP 295 Teaching with Technology

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