|INTRO TO THE ALGEBRA MATHROOM|
There are three posters on the wall in my tutoring room.
One of them is my favorite quote from Albert Einstein which says:
Everything should be made as simple as possible,
But not simpler.
That's what Algebra is all about -- making things as simple as possible.
I bet you find that hard to believe if you're a High School student struggling to understand why the symbol for the set of Integers is Z, and what's so sane about Rational numbers anyway? And can someone please tell me why we invert and multiply when we're supposed to be dividing by a fraction?
I know, I know. It all sounds so complicated -- but it doesn't have to be. There are a few good tricks you can learn to apply that will make your life as an Algebra student a lot easier. One of them is what I printed on the second poster. It says:
WHEN ALL ELSE FAILS,
You see, I've often said that Algebra is a code for reality. Doesn't it look like a code -- with all those squiggles, numbers above the line, numbers below the line -- letters with and without strange accent marks -- it couldn't be anything but a code!
Algebra is a set of instructions, calculating tools and information used to explore one of the elementary building blocks of human intellectual pursuit -- numbers.
I went to Granny's retirement party two years ago. There I saw Reuben and his wife Norma -- former colleagues I hadn't seen for a long time. I, in my usual blatant way, declared: "The first thing everybody looks at when they wake up is numbers!"
Norma shook her head. "No," she said. "The first thing I look at when I open my eyes is Reuben." I couldn't disagree with her. I'd never woken up beside her so, we talked a short while until I drifted to another part of the house for some food.
Not 5 minutes had passed when, there was Norma beside me with a sheepish grin on her face. "You were right," she said. "I do look at the numbers first. I look at the clock to see if there's enough time before work to spend a few minutes cuddling with Reuben in our comfy, warm bed."
It's true! Think about it. What would anyone do without numbers??? And here's a worse thought: what would we do without Arabic numbers??? Can you imagine doing a simple division problem with Roman Numerals???? I think not! It might hurt your brain.
Without numbers, you wouldn't know what bus to take, what number to call, what highway will lead you home. And what would we do with all those number key pads?? Numbers rule our lives.
But, see, the thing about numbers is -- you gotta get 'em right! Dial the wrong number -- you don't get your pizza. Take the wrong bus -- you end up in the boonies. So numbers -- to be useful instead of a pain in the backside -- must be used with precision. That takes us to the 3rd poster.
Often, while I'm tutoring a student who is working on a question, gets a wrong answer -- and -- when I say the answer is wrong -- he says "Yeah, but it's close"
That's when I respond with:
CLOSE IS ONLY GOOD
IN HORSESHOES & HAND GRENADES
Especially in hand grenades!!
When doing Algebra, you can't be satisfied with close! It has to be right on! That's why we have to follow the instructions. Mathematics is the only human endeavour in which we can achieve perfection, therefore that must be the objective at all times. Can you imagine if the guys who sent those astronauts to the moon had only come close in their calculations?
Ask those two Air Canada pilots how they feel about precision? These two fellows had to land a 767 loaded with three hundred or so people without any power because the fellows who had filled up the tanks in Montreal before this plane was to fly across the country to Vancouver, decided to come close in their estimation of the amount of fuel the plane needed. Some of them also assumed mistakenly, that the plane could refuel in Ottawa when it stopped to pick up passengers. So, halfway across the country, this plane runs out of fuel. No fuel means no power. No fuel -- the plane crashes -- everybody dies. As luck would have it, the co-pilot had flown jets during World War II and had landed planes on a long runway near Gimly Manitoba. He wasn't sure if that airstrip was still there but he figured it was their only hope.
After radio contact with the Winnipeg airport he was informed that the air strip was still there and he was given directions to it. He was also given a Godspeed or twelve because those guys in the tower knew the plane was out of fuel and probably wouldn't make it.
Well, these two pilots managed to direct that fuelless plane to this long unused landing strip. Thing was however, the runway was now used as a drag strip for noisy, high-powered cars. Let's think about this for a minute. The plane, with no fuel, makes no noise. They have one chance on that plane. To land on that tarmac. However, that tarmac is covered with thundering dragsters out for an afternoon's adventure.
Luckily, one of those dragsters saw the incoming plane, used his horn to alert the others, and the strip was cleared in time for the plane to land. No one was hurt. Actually, one woman twisted her ankle after sliding down the chute to safety. That was because with no power, it was impossible to get the front landing gear to lock in place. So when the plane landed, the tail was way up in the air but the nose was on the runway.
How do you think these two pilots felt about "coming close"? With Algebra, as with jet fuel, close is not good enough. Algebra demands precision. And one more thing:
Algebra also demands efficiency. Yes, if you're not in a hurry, you have to go to Toronto, you decide to go via San Francisco so that it takes you 2 1/2 weeks to get from Montreal to Toronto when it really should take you about five hours, that's okay. But, when you're doing math, the objective is to get from where you are to where you want to be in the fastest most direct way possible. If a question can be done in three steps, there is no reason to do it in five. If you're doing an equation with four terms to transpose, why write four lines of text instead of one?? Do a bulk transpose!! and get it over with.
Yes, math is nit-picking -- but we don't have to turn into sniggling idiots, now do we? Your math teacher isn't doing you a service when he/she insists you use two lines to square a binomial when it can be done in one. Eventually, you're going to be doing Calculus, where you can't waste time thinking about the algebraic operations you perform in your calculations. You've got bigger fish to fry. Learn to be efficient from the outset and you'll be glad about it later.
And, finally, the most important habit you can make to help you do Algebra.
LEARN THE WORDS!!!
Actually, don't only learn the words --- speak the words, as often as you can. Once the terms become a natural part of your vocabulary, they take on new meaning -- and in math that's important.
So, learn the rules, follow the instructions precisely and efficiently and most importantly, talk the math while doing the math -- you'll have no trouble doing well in Algebra.
(MathRoom Musings Index)
(all content of the MathRoom Lessons © Tammy the Tutor; 2002 - 2006).