A firm understanding of concepts is enhanced by a firm understanding of the vocabulary used to describe them. While true understanding ultimately goes beyond the words, it is also true that words are an excellent way by which to gain understanding.

About The Number Man

Ralph Schatzki has taught high school algebra, and geometry, as well as trigonometry and statistics.

Referred to as "Mr.Ralph" at Ruamruedee Internatioal School Bangkok, a pretigious school where he taught for many years, he prides himself in being able to identify areas on which students need improvement and in giving them the tools they need to succeed at math.

A firm understanding of concepts is enhanced by a firm understanding of the vocabulary used to describe them. While true understanding ultimately goes beyond the words, it is also true that words are an excellent way by which to gain understanding. Certainly, teachers use words to convey ideas, and even though you might be able to intuit the ideas, knowing the vocabulary never hurts. Of course, if you can't figure out concepts on your own, words become even more important.


At their basest level, words are random. Why is blue "blue," or dog "dog?" They could just as easily be "florp" and "toobye," in which case you might walk your florp under the clear toobye sky. A lot of mathematical terms make just as little (or, just as much) sense, and you'll need to put a little effort in in order to know what the words mean.


For instance, the difference between a "coefficient" and a "constant" is subtle, but when your teacher is explaining something and rattles off one of these words, you don't have the luxury of stopping time in order to make sure you understand. You have to know what it means, and I don't mean simply memorized. If I say "blue," you instantly imagine the color, and if I say "dog" an image pops into your head. The same thing has to happen when I say "coefficient," and this means you have to be diligent about achieving a thorough understanding of the terms used in your class.


Now, I know you have better things to do with your life. Who doesn't? We'd all like to be playing a video game or going out for soft-serve. But when you are on solid ground, work becomes anything but, and your life is full of sunshine. That's better than a video game, and probably even better than soft-serve.


So, what's the difference between "coefficient" and "constant?" Well, a constant is simply a value that doesn't change- hence, it is constant. 6 is always 6, -41 is always -41. So, 6 and -41 are "constants." A "coefficient" is the constant portion of a monomial (uh-oh, there's another word I don't know!). For example, in the term 3x, 3 is the


Hey, don't blame me: I didn't make all this stuff up!


A lot of the words you should know - not simply memorize - are: integer, rational, real, natural, whole, cardinal, ordinal, equation, expression, term, monomial, polynomial, constant, coefficient, solution, variable, prime, composite... The list goes on and on.


So, when your teacher uses a word you don't know, or if you come across one in your textbook, stop to make sure you know what that word really means. It's extra work now, but it will pay huge dividends later on.

Any math problem? Ralph will be happy to help you find your way. Please use the box provided to put in your math questions. We will make sure that you will receive your answers quickly. This service is free of charge and operates on a first come first serve basis.

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Math Tutorial links

• Introduction
• Finding your own way
• Knowing The Words Pre-Algebra, Algebra
• Variables and Equations - Pre-algebra, Algebra
• Postulate , aka Axiom, what is it? - Geometry
• Math Made Easy The Number Man Ralph Schatzki

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