Geometry Proofs Made Easy
Posted on February 13, 2008
Filed Under Helping Parents Help Kids, Imagination, Improve Your Skills, Learning Tips, Math, Teaching Tips |
Remember geometry proofs? For many students, they are the basis of recurring nightmares.
Here is good news; they don’t have to be. Just do them as if you were telling a story. Huh? Bear with me.
If you were telling a story about your trip to a beach, is there any way you would mess things up like: “1. First I dried off with a towel, 2. then I dove into the water, 3. then I was wet and cold so I stepped out of the water.”?
Of course not; it isn’t logical. Well, the same applies to geometry proofs; they have to be logical. (By the way, logical thinking is precisely what geometry proofs are attempting to develop in children).
STORY METHOD: Doing a Casual Proof First
STORY METHOD. Before writing all the statements and reasons, just tell yourself a story. Make little notes and marks as needed on a simplified diagram (that you can freehand or trace from the original).
The story you tell yourself might go something like this: “This equals that (mark them), this bisects that (think: that creates two equal parts, so mark them equal), and at the end I’m trying to prove this triangle is congruent to that one.”
Now, add some detail to your story. Just go step by step doing what I like to call a casual proof. That means using almost no writing, just make light pencil marks and some abbreviated comments as you tell your story. Once you’ve finished the casual proof (story), now write each step, statement and reason. And, to make it easier to follow, as you go through the steps, darken the pencil marks you made on the casual diagram.
Why do it this way? Because once you start writing long, formal statements, it’s hard to concentrate on your logical overall plan. By doing a casual proof first, it is less likely that you will get lost.
And, for Pete’s sake (who the heck is Pete, anyway?), don’t write all the givens first. That’s not logical. Instead, write each one as you need it in your “story.” They don’t make logical sense all bunched up at the beginning of the proof. (The reason teachers tell students to put all the givens first, is to make sure the students don’t leave any out. That is easy to do by checking off each given as you use it).
And finally, relax in the formality when it comes to reasons. Instead of “When two straight lines intersect, they create pairs of vertical angles whose measures are congruent,” simplify the reasons. Make them short and punchy, like “All vertical angles are equal.” When you make the reasons simple and less formal, they are shorter and easier to remember.
Have fun doing proofs, after all, they are a lot like puzzles.
Linda & Al Silbert
authors of Why Bad Grades Happen to Good Kids
P.S. Do you know what geometry means? “Geo” means Earth, and “metry” means measuring. Geometry was created long ago to measure the earth, or pieces of land on the earth. Pretty cool.
Comments
2 Responses to “Geometry Proofs Made Easy”
Leave a Reply
A Teacher’s Life Blog Carnival - March 31, 2008
Welcome to the March 31, 2008 edition of A Teacher’s Life Blog Carnival.
For this edition, we have presented the carnival on our Lesson Plans site, which is dedicated to providing resources to teachers and parents of home schooled students. Af…
Great article. Sometimes students seem to think that “math” is just about numbers. You did a good job of making math be about thoughts and conclusions. Thanks for the reminder and insight!
Judy Armes,
The Homework Coach
www.HomeworkSuccessNetwork.com