Ok, here it goes. The first sessions I'm blogging about happened during Valentine's Day :) During the Math II courses (Algebra), I reviewed how to factorize in order to perform operations of rational expressions. The first class went smoothly. I asked students about the purpose of identifying how to factorize a expression. During my High School and College years there was not a single teacher who told me about the cognitive processes involved while factoring. Well, here is my take. While we try to factorize an expression in order to simplify it, we are developing an EXTREMELY IMPORTANT technique. Its name??? ATTENTION TO DETAIL. Why is it so important? Well, it is not only important. It is actually EVERYTHING. Think about your favorite movie. Your favorite song. Your favorite book. Think about the experience of using an iPod Touch, a Blackberry, or updating your Facebook status. Think about the clothes designed by your favorite fashion designer. They are all made up of tiny details that provide a wonderful experience. For example, you have a date, and you try to impress that girl or that guy... most surely you will use a strong perfume/cologne. Attention to detail is one of those concepts closely related to beauty, happiness and perfection. Knowing how to factorize is all about details... (is it a sum of cubes? a square trinomial?), and details mean everything.
The Trigonometry courses today were quite hectic since I had to review logarithmic and exponential equations, and explain concepts related to angles. An important fact that I like to stress in angles, and which makes students think is the fact that "the concept of a straight line is the proof of mankind's dominion upon nature". Think about it. Do you see any straight lines in nature? Is a tree trunk perfectly straight? The flow of a river? The sun? Grass? A flower? Animal fur? There are no straight lines in nature. Thus, mankind develops the straight line concept to build and master nature.
The songs I played today during each course (quite Valentine-ish):
Nickelback--Photograph
The Calling--Wherever you will go
Goo Goo Dolls--Iris
Savage Garden--Crash and Burn
Radiohead--Fake Plastic Trees
Oasis--Sunday Morning Call
Coldplay--Green Eyes
U2 feat. Mary J. Blige--One
Aerosmith--I Don't Want To Miss a Thing
Snow Patrol--Chasing Cars
I like that idea of how the straight line represents our higher-level of understanding nature. There's so much detail and chaos in nature that we could never dream of accounting for all of it. That's why abstractions are so awesome, and so powerful!
ResponderEliminarAlso, it might be interesting to use the last five minutes of a class about lines to slip in some non-Euclidean geometry. Make them understand that while a straight line is straight in a flat universe, it's not in an spherical one. Then watch calmly as their minds are blown :)
Jorge, as a former military man specifically in the United States Coast Guard, one concept ABOVE ALL was literally "drilled" into us: it was attention to detail. At sea thing happen as quickly as they do on land, and you can't just pull over to the side of the next wave. If you miss even the smallest of details, you will die as a punishment - and sadly, all of your shipmates with you. With such a price to pay, attention to detail was job ONE in the USCG!
ResponderEliminarSemper Paratus, my friend, and an excellent blog!
Tom
Chelo!!! Thanks for the insight related to non-Euclidean geometry. I will definitely take it into account, since it will give them a tiny tease of what calculus is all about. The only problem of baking their noodles so soon is... baking their noodles so soon hehehehe!!! Take care!!!
ResponderEliminar