EdObserver

We have gotten sloppy in our speech and we are paying the price. We have allowed common expressions to throw us off the track. How often do you hear someone challenge you to consider the value of something with the catch phrase “Do the math.” They mean do the arithmetic. It is a common practice for schools, from the third grade on, to group students in levels for Math. They mean arithmetic. I work with eighth graders and when they ask me in a pre-algebra class to help them with the math, often they mean the arithmetic.

Addition, subtraction, multiplication, and division are arithmetic skills. They are simple operations that must be mastered before a student can tackle problems that require reasoning. If you have ten fingers you can master adding and subtracting. But you must know your multiplication facts before you can move on to multiplication, division and mathematics.

If you are of a certain age you may remember this as your Times Table” and start to repeat in dull tones: “1 times 1 is 1; 1 times 2 is 2.” If you can go all the way to “12 times 12 is 144,” you may go to the head of the class – the head of almost any eighth grade class. Maybe you had a teacher who favored the recitation of the times table; each student repeating, learning by rote, until it becomes reflexive. There is no reasoning involved. 4 times 3 is 12. For me it was introduced on a “ditto sheet,” printed in purple, with each goup of ten lined up vertically. Every Monday a new set of ten was introduced. Every Tuesday we drilled. Every Wednesday a pre-test, every Thursday a test. All the while we still had an arithmetic lesson daily. I was absent the Monday and Tuesday we did the nine times table and had to catch up by Thursday. For years I had to pause when confronted with 9 x 6 and 9 x 7 just because I hadn’t drilled.

There is no magic to the technique, nothing that is asked of a student but to “repeat after me.” And the funny thing about it is that Great-great-grandma did it, Great-grandma did it, Nanna did it and maybe even Mom. But the chances are good that today’s students would roll their eyes if they were asked to sit there and drill. You would roll your eyes if you entered a math class and saw students who are struggling with this fundamental in eighth grade. If the idea of drill strikes you as something we threw out with ink wells, think of a professional football player. His team gets a new coaching staff. He gets a new play-book. He reads and learns the plays, shows up everyday for practice – and drills. He drills until he can do the plays with his eyes closed. And then in a game the quarterback,  lined up behind the center calls out: 6, 12, 18, 24…

Do you see the problem? An eighth grader is at the very least beginning algebra. If he doesn’t know his “multiplication facts” how can he solve the simplest of equations: 3x = 27? And how did he learn fractions in the sixth grade when he needed the multiplication table to find a least common denominator? The answer is simple: he didn’t. Then how did he pass?  And what happens now that our eighth grader is learning algebra but hasn’t mastered his multiplication facts – or fractions? Do the math.

This is a very serious problem and most Americans don’t know that it is a problem. There are at least two generations of us who think that all fourth graders capable of mastering their multiplication facts have. If you have no child in the school system, or even if you do, you may not know what, and what not, is expected of our students. Even if you know that high-schoolers working at the local Burger King can’t make change without a cash register prompt, have you ever asked why?

Consider a typical eighth grader who is just beginning algebra in what is now referred to as a “pre-algebra” class. He’s had a problem with fractions, and he already has a problem with the simple equation 3x = 27. Now he thinks that algebra is a problem for him – but all eighth graders have to take math. By the time he gets to high school and is in a real algebra class, he will have to tackle equations that require factoring. Someone will teach him how to do the mathematics and even when he understands and learns the process he won’t know how to do the arithmetic. If he doesn’t know his multiplication facts he can’t go on. He will become frustrated, say “algebra sucks” (Yes, that’s what he’ll say.) and do one of two things. He will struggle and possibly fail – he will never do well – or he will stop doing the work. There will be no homework to hand in, no class work will be completed.

Failing because you don’t do the work is easier on the psyche than failing because you can’t do the work. And what do you think a student does during a class in which he can’t do the class work? He talks, distracts others who can’t do the work, and antagonizes the teachers when they ask him to stop. And all the while he will think that he can’t do the math, when he can’t do the arithmetic!

Because he can’t do arithmetic he will stop taking math. He will complete the basic math requirement for graduation and that will be it. He will never know how far he could have gone. He will never realize that he may not have had a problem with math, just a problem with arithmetic. And his parents won’t know either.