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What is Algebra

Algebra is the study of the properties of numbers and the study of the things that we can do knowing those properties. Algebra is, or should be, a study in logic. Algebra is the process of using logic to draw conclusions from things we know to things that we do not know about until we apply algebraic reasoning. The laws of algebra can be written on a single sheet of paper. Everything that we do in algebra, we can do because of these rules.

If you gain the facility of algebraic reasoning, you will find that you have relatively little that you must memorize. You can easily derive what you need when you need it. There are some things that you must simply learn. You must learn the notation of algebra, how we write algebraic expressions and relations.

Much emphasis is placed on "higher order thinking skills" in the classrooms and textbooks of today. However, if you do not have the fundamental logic and algebraic tools with which to think, it is going to be very difficult for you to successfully achieve higher order thinking.

Word problems are very important. Your ability to work word problems demonstrates your ability to apply mathematics. In working an algebraic word problem, you first translate the language into algebraic expressions and relations. Then you must use the rules of mathematics in order find the solution required from those expressions and relations.

In general, word problems are applications of mathematics. Word problems are the bridge that allow us to relate mathematics to the real world.

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