Ideal for High School and College Level Curriculums
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Of Special InterestCommon Algebraic and Calculus Errors
What is Algebra
Simply put, Algebra is about finding the unknown or it is about putting real life problems into equations and then solving them. Unfortunately many textbooks go straight to the rules, procedures and formulas, forgetting that these are real life problems being solved.
Algebra is a branch of mathematics that substitutes letters for numbers. An algebraic equation represents a scale, what is done on one side of the scale with a number is also done to the other side of the scale. The numbers are the constants. Algebra can include real numbers, complex numbers, matrices, vectors etc.
Many people find arithmetic hard to learn, but most succeed, to varying degrees, though only after a lot of practice. It may be well you effort to read Common Algebraic and Calculus Errors for some helpful information. What makes it possible is that the basic building blocks of arithmetic, namely numbers, arise naturally in the world around us. For example, when we count things, measure things, buy things, make things, use the telephone, go to the bank, check the baseball scores, etc. Numbers may be abstract. You never saw, felt, heard or smelled the number 3, but they are tied closely to all the concrete things in the world we live in.
Algebra is thinking logically about numbers rather than computing with numbers. In algebra you are a second step of abstraction removed from the everyday world. Those x's and y's in algebraic equations represent numbers in general and not particular numbers. In algebra you use analytic, qualitative reasoning about numbers, whereas in arithmetic you use numerical, quantitative reasoning with numbers.
For example, you use algebraic thinking to write a macro to calculate the cells in a spreadsheet like Microsoft Excel. It doesn't matter whether the spreadsheet is for calculating scores in a sporting competition, keeping track of your finances or running a business, you need to think algebraically to set it up to do what you want; that means thinking about or across numbers, rather than in terms of numbers.
When students start to learn algebra, they inevitably try to solve problems by arithmetical thinking. That's a natural thing to do, given all the effort they have put into mastering arithmetic. When the algebra problems they meet are particularly simple, this approach works. In fact, the stronger a student is at arithmetic, the further they can progress in algebra using arithmetical thinking. Many students can solve the quadratic equation x2 = 2x + 15 using basic arithmetic, using no algebra at all.
Paradoxically, or so it may seem, however, those better students may find it harder to learn algebra. To succeed in algebra, except for all but the most basic examples, you have to stop thinking arithmetically and learn to think algebraically.
About this page
On the left, under the Suggested Topics is a list of topics typically found in most High School or College level Algebra curriculums. The difference is in the level of depth, scope and complexity of that topic. The list is provided to help you determine where you may need tutoring. Your particular topic may not be listed, but that does not imply that tutoring is unavailable. Just contact me and inquire if I can offer tutoring for your particular needs. I will promptly respond and you can decide what further action is required.
I have numerous texts on this subject and I am confident that whatever difficulties you are having in Algebra, I can be of assistance. I wish you the best of luck in your academic success and look forward to any inquiry you may send on how I may be able to help you.
Questions or concerns
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