April 2009
Vol 6 No 4

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Teachers.Net Gazette Vol.6 No.4 April 2009

Cover Story by Alfie Kohn
When “21st-Century Schooling” Just Isn’t Good Enough: A Modest Proposal
Are we serious about educating students for the global competitive economy of the future?

Earth Day Special Article:
GE Project Plant-A-Bulb
Give the planet the gift of flowers for Earth Day....

Harry & Rosemary Wong: Effective Teaching
The Tools for Success

»Actively Involve Every Reader—Ten Easy Ideas! Sue Gruber
»Motivating Children Leah Davies
»Multiple Working Hypotheses Todd R. Nelson
»Eliciting vs. Punishments Marvin Marshall
»The Busy Educator's Monthly Five Marjan Glavac
»Tattle Tales and Classroom Helpers Barbara Pressman
»Tips for Travel to France or Italy with Students Josette Bonafino
»Too Much Parent Involvement? Can It Be? Dorothy Rich
»Return to Sender & The Neon Necklace Rick Morris
»Be Your Own Mentor: Reflect Hal Portner

»Getting Your Students' Work Published Alan Haskvitz
»At Risk Students: Victims of Miseducation and Failure Bill Page
»Teachers – Healing Broken Lives Graysen Walles
»Get Smart! Doodle! Tim Newlin
»A Dozen Ways to Build a Caring Classroom Community Susan Fitzell
»April 2009 Writing Prompts James Wayne
»Using Photographs To Inspire Writing VI Hank Kellner
»Quality in School Systems Panamalai R. Guruprasad
»Problems With 9th Grade Euclidian Geometry Stewart E. Brekke
»Multisensory/Kinesthetic Alphabet ActivitiesJeanine Horner

»Apple Seeds: Inspiring Quotes Barb Stutesman
»Today Is... Daily Commemoration Ron Victoria
»The Lighter Side of Teaching
»Teacher Blogs Showcase
»Guided Reading in Kindergarten (printable)
»Printables - Happy Earth Day, Reduce, Reuse, Recycle, We’ve Got the Whole World in Our Hands, Portable Word Wall, Earth Day Every Day Award, Bringing Choices to Light, and April - May Calendar
»Photo Tour: 3rd Grade Classroom, Red Creek, NY
»Lessons, Activities, Theme ideas: Earth Day, Mother’s Day, Paul Revere, Spring, Easter, more!
»Featured Lesson: Outdoor Activities/Nature
»Meet Bill Martin Jr. and Brown Bear, Brown Bear, Creative Quotes from Shakespeare, Massive Ant Colony Uncovered! AMAZING science!, Tim Hawkins - Cletus Take the Reel, Lovefield, and Dolphin Bubbles: An Amazing Behavior
»Live on Teachers.Net: April 2009
»Newsdesk: Events & Opportunities for Teachers
»Wisdom for the pain? Why Did You Do It? Why Pursue National Board Certification?


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Editor in Chief: Kathleen Alape Carpenter
Layout Editor: Mary Miehl

Cover Story by Alfie Kohn

Effective Teaching by Harry & Rosemary Wong

Contributors this month: Alfie Kohn, Graysen Walles, Hal Portner, Sue Gruber, Leah Davies, Todd R. Nelson, Marvin Marshall, Marjan Glavac, Barbara Pressman, Josette Bonafino, Rick Morris, Bill Page, Tim Newlin, Susan Fitzell, Alan Haskvitz, James Wayne, Hank Kellner, Dorothy Rich, Barb Stutesman, Ron Victoria, Stewart E. Brekke, Panamalai R. Guruprasad, Jeanine Horner, Marie Smith, Carol Goodrow, Jennifer Goldstein, and YENDOR.

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Stewart E Brekke

Archive | Biography | Resources | Discussion

Problems With 9th Grade Euclidian Geometry

A 9th grade course in calculating geometry is realistic provided the student has some basic algebra in elementary school or the fundamentals of algebra are taught as needed in the geometry course.
by Stewart E Brekke, MS in Ed, MA
April 1, 2009

Students usually take high school geometry in the second year unless they have had an algebra course in the last year of junior high. In our school, Robeson High School, all students would take geometry as the first course in high school math and then take algebra, algebra- trigonometry in the third year and a fourth year math course. Our school, a neighborhood school taking all students, required that every student take four years of math and science.

A freshman taking geometry without algebra first usually encounters a book that assumes a first year of algebra. All the texts for high school geometry that I have seen require a background in algebra. In fact, the more recent the text the more the book is filled with problems that require basic algebra to solve.

I have found however that at least in the introductory chapters of the current geometry, texts demand only a rudimentary knowledge of algebra which is mainly solving simple equations. After dealing with some of the non-algebraic material in the geometry book, I determined that spending about a week introducing students to the rudiments of algebra such as solving equations in one unknown and some basic work on signed numbers and like terms is sufficient to get them ready to solve the problems in the text. I try to do two concepts a period such as using the addition property and using the subtraction property of equations and with a week’s work capability of the students can be achieved.

The problems with algebra also enter into the lessons on the Pythagorean Theorem. For students with no algebra background, we must spend time learning to solve equations, squaring numbers, taking square roots, and reviewing the addition and subtraction properties of equations. Usually, the elementary math background covers some of these topics, but without the algebra course, most students would have difficulty. Therefore, the time taken on the Pythagorean Theorem is about three or four days including the algebra basics.

One of the most difficult problems encountered in a first year high school geometry course is the newness the deductive method and qualitative method of proof of the theorems, postulates and corollaries. I have found that freshmen are not used to this type of thinking at all.

For most of their lives, high school freshmen have been used to calculating, as have most adults, and when they encounter a course that is mainly composed of words and deductions, it takes them some time to learn the methodology involved in reasoning in proofs, for example. In this respect, I have to provide simple proofs as drills on ditto paper to get the students into the mental framework for dealing with harder proofs which involve more complex reasoning. Because the newer texts have many more problems involving algebra and calculating, the problems the students have with the verbal-deductions are a little lessened at present, although some of the proofs involve algebra.

My impression is that a first mathematics course in high school such as a Euclidian Geometry course with deductive proofs must be watered down because of its difficulty for new high school students. When a student has a year of algebra behind him, it seems to make a difference in the student’s performance. Although our first year requirement of geometry puts all freshmen in the course, we received transfers from other schools, and other students who for one reason or another have had at least one year of algebra and sometimes even algebra-trigonometry.

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About Stewart E Brekke...

Stewart E Brekke, MS in Ed, MA retired from Chicago Public Schools where he taught high school physics and chemistry.

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