I recently read a blog from a math teacher whose main area of concern is elementary math and literacy. I had to laugh at the example he used--why do we use the word "borrow" in subtraction when we don't intend to give it back? This is a point well-taken. We tend, in mathematics, to use terms from everyday speech, but in mathematics, these terms often have very different meanings. This can be and often is a source of confusion for many Algebra students; and, unfortunately, students often don't even realize they have confused the meanings of a term, and the teacher doesn't catch it is until too late. By "too late" I mean that the mistake has been practiced and has become ingrained in your brain as a fact. These mistakes are difficult to fix. It is better to avoid these than try to fix them.
One term from your elementary days that still causes students difficulty is the term "value"--especially with respect to fractions. If I asked you, "Is 3/4 > 1/2" what you say? You and almost everyone else would say "Yes." In reality, the answer is "not necessarily." The problem here is that fraction symbols do not actually have a VALUE until you know the "of what." Is 3/4 of an inch greater than 1/2 of a foot? Of course not, you say? Why not? You just told me 3/4 > 1/2.
Now that you are thinking a little bit more about it, you realize that fractions can only be compared IF they are fractions of the SAME THING. So why have math books had homework sections with instructions to "compare the fractions?" Because someone assumed you knew that fractions can only be compared if they are of the same thing, and they left out an important part of the instructions. "Compare these fractions on a number line" or "Assume these fractions are of they same thing" would be appropriate directions. On a number line, 3/4 and 1/2 represent parts of the same size unit. We math teachers tend to assume that every student is picturing the same thing or understanding a definition the same way that we intend; but you and I both know this isn't always true.
In Algebra, there are two huge examples of extremely important concepts that students often get confused with their everyday meanings--or at the least, cannot really explain what the math meaning actually is. These two concepts are: "solve" as in solve an equation and "factor" as in factor this expression.
You know what it means to solve a puzzle or to solve a problem you are having making free throws in basketball; but what does it mean to solve an equation? To find the answer, you say? How do you know when you have an answer? It works? What does that mean? Very few Algebra students can actually say in words--with any real understanding--that to solve an equation means to find values for the variables that make the equation TRUE.
You know that washing hands is an important "factor" in slowing the spread of disease; but how does this apply to factoring an expression like a^2 - ab? The mathematics meaning of "factor" is totally different from the everyday meaning. In Algebra, to factor means to "re-write as multiplication." What? Well, a^2 - ab in factored form is a(a-b) since when you multiply a and (a - b) you get a^2 - ab.
All of mathematics--not just Algebra--is full of these terms with different meanings in the everyday world than in the mathematical world. For your own success, you must always memorize math definitions immediately, practice these definitions, and even discuss with yourself and with your teacher the differences in meanings. It is OK--in fact, important--to know that a term has several different meanings. It is equally important that you understand each of the meanings and know when to use which meaning.
If you get confused, or are ever in doubt, ASK YOUR TEACHER! It is the teacher's responsibility to teach you. We math teachers are not perfect human beings, even if we like to think we are. We often ASSUME more than we should. DO NOT BE AFRAID TO ASK QUESTIONS. That is your responsibility. Ours is to answer your questions.
Shirley Slick, "The Slick Tips Lady," is a retired high school math teacher and tutor with degrees in Mathematics and Psychology and additional training in brain-based learning/teaching. Her goals: (1) to help parents help their children with math, (2) to help eliminate the horrendous Algebra failure rate, and (3) to inform the general public about problematic issues related to the field of education. For your free copy of "10 Slick Tips for Improving Your Child's Study Habits," visit her website at http://myslicktips.com/
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