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
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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
Continued from page 1
April 1, 2009

These advanced students seemed to have a better perspective on the geometry course partly because of their math background, but I also believe from a maturity standpoint, these student do better than the freshmen in geometry. Thus, the seniors and juniors in the primarily freshmen geometry course outpace the freshmen regularly and find the course easier than the freshmen.

One of the difficulties with offering geometry as a first year course is that it conflicts with the programs offered in science. In a number of high schools, chemistry is the second course in science. In our school, it was required of all students. Chemistry, if done properly, requires a command of algebra in solving formulas and in all sorts of measuring. Our students are usually taking chemistry when they are taking the first course in algebra and this results in watering down the chemistry a little, although one could teach the necessary algebra on an ad hoc basis, and get through adequately. Some of the science teachers have complained about this problem, and in our school, it is yet to be resolved.

One of the advantages of the freshman geometry course is that it allows the students to go through the next three years without an interruption in the algebra sequence, algebra, advanced-algebra, and college algebra. This ordering of courses makes it easier on the student since he does not need a substantial review of algebra in algebra- trigonometry and the algebra-trigonometry course can proceed much better.

Since high school physics is often a third or fourth year course, the student has enough algebra and geometry to meet the demands physics requires. It seems that more students have an easier time with algebra and pass it than geometry, however. This is possibly due to the adjustment factor in getting used to high school while at the same time adjusting to a course which is really very different than anything the freshman has encountered before in school.

Some educational psychologists have contended that Euclidian geometry, geometry using theorems and qualitative deductive proofs, is better given in 9th grade before algebra 1 because the young mind is structured to deal spatially with the universe rather than algebraically. However, in my opinion it is the deductive and qualitative nature of Euclidian geometry that is especially difficult for young students in high school even in the traditional second year.

Algebra 1 has many algorithms and is very straightforward. Most students, average or better, can, with help, use an example problem from the algebra text and apply it to relevant exercises. In traditional Euclidian geometry, there are no examples and exercises from which a young student can readily prove a theorem or corollary making mastery of the course much more difficult besides the requirement of having some command of basic algebra such as equation solving.

However, a newer course, which I call calculating geometry, emphasizing calculating such as the solving of the Pythagorean Theorem, alternate interior and vertical angles and volumes of cylinders and cones, for example, I believe, can work for a 9th year student provided the teacher is prepared to teach or review the necessary basic algebra such as squaring and cubing numbers, and fundamentals of equation solving. If the students are at-risk, basic calculators can be utilized to ameliorate the problems some students will have with decimals and division.

In summary, it has been my experience with 9th grade deductive Euclidian geometry given before Algebra 1 that there are difficulties with such a sequence. The standard high school geometry texts require a command of basic algebra and that the deductive qualitative method of roving theorems requires some maturity which is only beginning to develop in the students’ second year. 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.

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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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