Learning algebra is a lot like learning to drive a car, or swim, or ride a bike. You must learn concepts at the same time you are developing skills. There are pedals to push, gears to shift, lights to turn on and off, turn signals to manipulate, and a steering wheel to wrestle. Those are skills.
It’s also useful to learn what the brake pedal does, why you need to use your turn signals, what the clutch is good for, and which direction to steer when the car begins to skid. Those are concepts.
Most of the math you have been learning until this year is based in concepts of arithmetic. Arithmetic relates directly to real life. We add apples and oranges, we subtract money, we discover the area of a wall to learn how much paint will cover it. We might assume algebra is going to be like that, too.
But algebra is different. While it can, indeed, be useful in real life, much of it is simply a game that has no direct relationship to anything we can touch or count in our everyday life. Like many games, algebra has game pieces, moves, strategies, goals, and its own vocabulary. Usually, the object of the game is to discover some specific unknown by using available clues. Other times, the object is to translate recurring events into an equation.
Why must we learn this stuff? One answer is because it’s fun. There are many side benefits to many games. Tennis improves your eye-hand coordination. Racquetball is great aerobic exercise. Golf is meditative and social. Chess teaches concentration.
A side benefit of the algebra game is that it may allow you to become a chemist or electrical engineer. It may allow you to calculate interest rates and design cars and computer systems. Many people say that the thought processes they developed by learning algebra were more useful than any direct application. And, of course, if you want or need to learn more advanced math, algebra will be a prerequisite.
So I invite you to join me as we learn the rules and strategies that will make you winners in the game called algebra.