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.

You can’t learn to drive, or ride a bike, or swim, without practicing. Skills improve with practice.

You can’t learn math without practicing either. Most math books acknowledge this as they throw you m the water and encourage you not to drown while you’re practicing. Concepts are explained in one terse sentence, often framed in a blue box. If that sentence doesn’t make sense to you immediately, you’ll have plenty of time to think about it while you’re dog-paddling your way through three pages of problems. Sometimes it still won’t make sense to you.

It’s difficult to learn anything by being placed in the middle of a bunch of technicalities. Some math writers have forgotten this. If they designed a course in bread baking, the students would spend the first three weeks doing nothing but measuring flour. This would be followed by a unit on measuring the temperature of water. Then students would grow yeast. This would take longer than anticipated, so the last chapter, which was to actually bake a loaf of bread, would have to be postponed to the next course.

People who learn best by reading, who like to understand concepts before they dive in, have been ignored by the world of math books. English teachers, historians, psychologists and other bright, reading-oriented folks tend to react to traditional exercise-intensive books the way vampires react to Arizona at noon. They’re polite, but can usually think of someplace they’d rather be.

This book is different. You won’t get much chance to practice. Instead, you’ll get an overview of important concepts, such as “don’t inhale under water.” Our theory is that tidbits like that may prove more valuable if you understand them before you ever get wet.

You’ll still need to practice. But perhaps, if we’ve done our job well, the whole experience will make more sense. It won’t be frightening and confusing. Perhaps, while you’re taking a traditional class, instead of feeling panic, you’ll remember to hold your breath and move your legs like a frog.

Of course, the other students in your algebra class may find that distracting.

What is It?

Algebra is a game. Like many games, it 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. Every time we deduce how many tacos we can buy by remembering how much we’ve spent, and how much change we probably have in our pocket, we are practicing algebra.
Sometimes the object is to translate recurring events into an equation. Paychecks are figured by multiplying hours-worked by wages-per-hour, then subtract