Back to Algebra for
Adults.
Algebra for Adults:
Part 1, Introduction:
November 25, 2002:
This is the first of a series of essays I will be presenting on
algebra basics. Much like my previous math series, which became
our latest publication, "Math for Moms and pops," I
will produce a progressive set of guides outlining the basics
of algebra. As always, these essays will be saved in our archives
as we go along. This will make reviewing and catching up easy
enough. I will also post the lists of the rules, terms, and operators
in the archives.
Why Algebra? Most of us will never have to know algebra to get along, but it is sometimes helpful to know the basic operations. For example, the challenge of working out proportions and ratios will yield to simple algebra solutions. Besides, it is fun. It's a challenge not unlike working out puzzles. More important to some folks, these studies will be useful in understanding what your kids are trying to learn in school. So let us go a little ways into algebra.
This is algebra for people who did not get it the first time. I will not fault anyone who has suffered that problem. I was there. I remember one school teacher in particular who thought she was teaching beginning algebra. The truth is, Mrs. Postmortem who is long since dead, did not know how to teach anything. Most of us had at least one Mrs. Postmortem in our early educational experience. No wonder we did not learn.
Because of poor teachers and many other reasons Algebra is a frightening concept for many people, even more so than long division. The truth is, algebra is simply a tool for making math more powerful. It is nothing more that a way of making mathematics more powerful by giving us formal symbolic procedures for problem solving. Of course, since it is mathematics and math is logical, we can proceed logically.
First, let me say I will endeavor to assume nothing about you except a good mind and a desire to discover algebra. I have found that many people who write text books make assumptions about their reader's levels of knowledge which are simply not true. The only reason that most text books are useful at all is because there is usually an instructor present to fill in the huge gaps. Most textbook writers rely on that instructor being present and sluff off their responsibility to present information clearly. I believe that is disgraceful.
To write a good self study guide, you must assume nothing except a reasonable command of the language being used. It is extremely difficult for a highly skilled and trained person to descend to the knowledge level of the neophyte. They are simply so far removed from the time that they were so ignorant they can no longer identify with it. Also, I will try not to wear the mantle of the overbearing master working with the simpleton. I will try to assume only you good mind and your good intentions.
With these assumptions, we can begin by reviewing the eight basic operations of arithmetic. The simple fact is, If you do not understand basic math, you cannot understand algebra, for it is based in math. The step from math to algebra is a logical progression. In fact, as I said, algebra is nothing more that a symbolic way of doing math. So once we understand math, we can take the next step.
For those who do not need a review of math, I will not be insulted if you skip the next three exercises. For those who need more than just a review of math, there are two ways to proceed. One way is to purchase our book, "Math for Moms and Pops" by me, William E. Steinman. It is designed for adults who want to understand basic math. If you do not need quite so much detail and guidance, the Schaum's Outline books are outstanding resources. Any good bookstore will have these.
With a review of math under our belts, we can begin the transition from math to algebra. Here we can emphasize the use of algebra to make math more powerful for solving life's problems. We do this by formalizing how we solve for unknown quantities. We have already solved for unknowns in our study of math. In algebra we will simply formalize the procedures. We will still be doing math and all of the rules will still apply, but we will discover more powerful methods of manipulating numbers.
As we go along, I will emphasize that algebra is just arithmetic from a different perspective. In basic algebra, the only difference is that we will represent an unknown quantity with some kind of symbol. As I said, In basic math we have unknowns, but we do not formally represent them. When we find the area of a rectangle by multiplying the width times the length, the unknown is the area.
We are always solving for unknowns in mathematics. That's what math is about, solving problems for unknowns. Even in counting we are really solving for the next number in the sequence. In algebra, we use alphabetic characters to represent unknown quantities. That allows us to represent a problem as an equation. Then we can solve the equation for the unknown by doing regular arithmetic.
Once we understand how to represent problems with equations, we can get into the manipulations of equations to solve whatever problem we have at hand. In our look at equations we will learn about equalities. Then we will use all of the tools from basic math to solve our problems.
That is enough for an introduction. In the next essay, I will
begin with the review of counting, basic addition, and subtraction.
From there, I will cover the other basic operations which are
multiplication, division, fractions, decimals, and percents.
Back to Algebra for Adults.
|
|
|
|