Math: you have to begin at the beginning…

December 30, 2008

(Copyright 2008)

I once had an English teacher who admitted that she wasn’t good with spelling. Ouch! That’s kind of like having a math teacher who is not good with adding, subtracting, multiplying, and dividing.

As much as I liked that teacher – she was a character – she had no business being a teacher.

My eighth grade math teacher was a nice man, but I don’t think he should have been a teacher either.

The reason I say that is that he had a class full of not-good-at-math students and rather than teach us he threatened us with the warning that we would never make it when we got to high school and had to do algebra. Ha! I showed him. I didn’t take algebra in high school. I was too scared, too lazy, and the powers that be were too lenient. Had I gone through college straight out of high school in the late 1960s I would never have had to take algebra. While it was required for some majors, it was not required for others. I would have taken the others.

By the time I made it to the second half of my college studies California had upped its requirements and mandated that I at least pass intermediate algebra for what ended up being a BA degree in political science. Of course that meant I had to take beginning algebra first.

Actually I had tried to take beginning algebra through a night class while I was working at a newspaper. I couldn’t keep up with the homework demands, though. Later I took a summer course which as I remember was three hours per night, five nights per week for several weeks. The instructor warned everyone that they would not be able to hold down a job by day. We would be spending all day doing homework. He was right.

That cost me a lot. It would have been better to get it when I was supposed to, in high school.

Actually, these days they start teaching algebra in grade school. I think they introduce algebraic concepts before youngsters even know it is algebra or at least the building blocks for it. Anyway, I think this is good.

On the other hand, I keep reading that as a nation we are deficient in math and science (and, as most of us realize, those two subjects are virtually inseparable).

It seems that even though we were put on notice back in the 1950s when the Soviets launched Sputnik we might have a math and science problem, we haven’t come a long ways.

Well, in reality we were not behind or, if we were, not as far behind in the space program as we were led to believe. But I think the problem is that we still have not greatly improved our approach to math and science instruction.

I’ll just zero in on math here. Those who have a natural inborn talent with numbers usually progress despite any lack in instruction. They are interested enough to seek out the answers and go on to places where that is the specialty.

For the rest of us, it is catch as catch can, and it can be quite discouraging.

Anyone who has read some of my previous blogs is likely to notice that I’ve covered some of this ground before, but reminders in everyday life keep bringing me back. Today I saw a headline on Yahoo News that said our nation needs more math and science teachers (I think that headline has been running for several decades now).

Those of us who have managed to slip through life being a little more math deficient that we know we should be, might be tempted to console ourselves by saying, who needs it? We don’t do complex calculations and we have calculators and computers.

But of course all that means is that we cede our power over to those who do know what they are doing. No, most of us have no desire to be rocket scientists or number theoreticians, but we do want to know how good of a deal we are getting on that after-Christmas percentage markdown, our home mortgage (sorry, a bad word), or on those canned food items packed now in odd sizes.

Even the wizards of Wall Street were fooled by the mathematicians who used complex algorithms to split and bundle those mortgage securities that have thrown the whole nation into a financial catastrophe (well at least that was part of the problem).

I talked to my oldest brother, who worked with electronics and computers in the Navy and who later taught math.

He tells me that for instructors at the college level, one of the major problems is that their students did not get the basics down in elementary school. And before I go further I will say that what follows is a combination of what he told me and my own observations and opinion:

Elementary school teachers are often not comfortable with math themselves. Sometimes they teach the minimum and in the process fail to make sure their pupils are well grounded in the basic operations of arithmetic. Without that background it is impossible to succeed in algebra or higher math.

Teachers must make sure that their pupils or students understand fractions, really understand. They need to know how to manipulate fractions. They certainly need to be able to know the various notations used to represent fractions.

And here’s one I like: they need to understand word problems and understand what the individual words mean math wise in a problem. An example, the word “are” usually means an equal sign. I’ll just go off track here a little and mention that I once did a newspaper story about, well I don’t remember the education-speak term, but maybe “interdisciplinary learning”. At any rate, it goes something like this: you have to be able to read (English instruction) in order to do your arithmetic (word problems).

Still another one I like: teachers should devise and use word problems that fit their students’ familiar surroundings so they can identify with what is trying to be accomplished. I know I once did a photo-story about a college farm. One of the captions explained that the student was calibrating a fertilizer spreader. She told me she had to do an algebraic calculation to know how to set up the equipment. Now even allowing that in the real world things are often dumbed down enough that you don’t have to do the figuring yourself, you also have to know that someone did. And do you really want to always be in the dark? Equipment does not always work right and things don’t always fit the pre-programmed plan, and knowledge is power.

And I have always thought that a good way to teach fractions would be with rulers (measuring boards and such) and with wrenches, in order that one might have a visual and a real world application.

Let me just wrap up this tome with another anecdote from the tony walther file:

After doing graphing in algebra and working with those numbered pairs, I still did not see the real world connection (well yes there was map reading in the Army, but that’s a different story) and then years later I watched a school administrator calculate test scores, create her own numbered pairs, and proceed to do a graph showing a bell curve. Well I am too rusty to do that now (implying slyly that I could have done it before), but at least I have some mental picture of the process.

Just one more thing: if there is a math teacher reading this, please explain to your beginning students what algebra or whatever form of math you are using is for and what its practical applications might be. Also, test everyone to make sure that he or she actually understands the words used. When we define our terms, we can get somewhere.