Saturday, March 20, 2010
Message To Jia
Jia said... (see comment section)
Would you have any words of advice for a freshman student at Townsend Harris High School who is failing geometry despite tutoring from her teacher?
My best words of advice for someone taking geometry is to look at the words for clues. Unlike other fields of mathematics, the answers will be right in front of you if you know where to look. Let me give you an example. Suppose you see the word perpendicular. The first thing that should come to mind is a right angle or an angle that contains 90 degrees. If you are doing a proof, you've now found two angles that are congruent and if you are doing an algebraic expression, you know the equation to write. We just finished a unit on circles. When you see diameter, think semi circle, or 180 degrees. While the measure of the central angle is equal to the measure of its intercepted arc, all other angles are half of something. Common sense should tell you the further from the center you go, the smaller the angle is , so inscribed angles are measured by half their intercepted arcs and angles outside the circle are measured by half the difference of their intercepted arcs. Angles formed by two chords are vertical angles so it makes sense to find their measure by finding the average of their intercepted arcs.
When tackling a proof, always use colored pens to mark your diagrams. Start from the beginning and do as much as you can, going down. When you can't do anymore, go the the bottom (what you have to prove) and work your way back up. You will end up meeting almost in the middle and at most miss one step.
I hope these words help. It is hard giving advice in writing. You are a student at Townsend Harris High School, one of the most selective schools in the city. You must be extremely bright or they would have never allowed you to become part of their student body. Stop stressing about what you don't know and start concentrating on what you do know. Think of the math words as the word you are learning in your Latin or Greek class. I'm sure once you stop agonizing things will get better. Good luck.