The Algebra Tree
Algebra can seem like a confusing subject. It’s filled with various signs such as x,y and z and terms to remember such as variable, coefficient, term and polynomial. However, instead of getting bogged down with the “trees” of Algebra, I think it helps to look at the forest. What is the place of Algebra in Mathematics as a whole?
Having taught Mathematics for a number of years, I have found a good form for how the various Math subjects relate is a tree, with the most central part being Algebra. That’s why I call it the Algebra tree. Let me continue to explain.
First we have the roots of this tree and of Mathematics itself, which is Arithmetic. We learn Arithmetic in elementary school because it is basic for future Math learning. Addition, Subtraction, Multiplication and Division are central processes.
The base of this tree of Mathematics is Algebra. Algebra feeds on Arithmetic and goes beyond it. For example an important course of action in Algebra is to solve equations. However, this couldn’t be done without knowledge of Arithmetic, in particular, Addition, Subtraction, Multiplication and Division. Another Algebraic course of action is simplification of algebraic expressions. This again requires use of basic Arithmetic.
Where then do other disciplines of Math fit in to the Algebra tree? I would call them the branches. For example, there’s Geometry. In Geometry you deal a lot with Geometric figures such as circles, triangles and squares. However, to successfully solve related problems, you typically need to use Algebra. One example is for finding the area of a course of action, you need to solve an equation using a course of action learned in Algebra.
Another branch would be Trigonometry. Trigonometry focuses a great deal on relationships in triangles. It uses special concepts such as Sine, Cosine and Tangent. However you could not properly use such concepts without using your knowledge of Algebra.
A third branch would be Statistics. Statistics deals with tools for analyzing data that be used nearly such as in business and psychology. All the same, to use these tools you will need to use Algebra. For example, one tool for comparing two sets of data to see if they relate is called correlation. Two things you would expect to be correlated are persons’ heights and weights. The taller they are, typically the more they weigh. You can calculate a number called a correlation coefficient that provides an indication of the strength of this relationship. However the time of action for making this calculation requires Algebra.
So in summary, if you have trouble with Math and especially with Algebra, remember this tree of Math… the Algebra Tree.