My scholarly background is in a social science discipline, not math. I have no particular pet theory on the right and proper way to teach math. Frankly, if someone convinced me that counting sheep were the most effective way to do it, I’d gladly requisition a flock or two and tell the soccer team to practice someplace else.
That said, it’s pretty clear at my college -- and at many, many others -- that lower-level math classes (especially developmental) are the most difficult academic obstacles many of our students face. The drop/fail rate in developmental math is embarrassingly and stubbornly high, and the national literature suggests that students who drop out because they feel overmatched in math are among the least likely ever to return. (The same does not hold true of developmental English, interestingly enough.)
In a discussion this week with someone who spends most of her time working with students who are struggling mightily in developmental math, I heard an argument I hadn’t given much thought previously: students who have passed algebra and even pre-calc in high school frequently crash and burn when they hit our developmental math, because the high schools let them use calculators and we don’t.
Among math people, the calculator/no calculator divide seems pretty strong. I’ll admit an uninformed sympathy with the ‘no calculator’ camp, just because I’ve had several experiences in which the ability to guesstimate the ballpark of a correct answer helped me recognize a ludicrous answer when I saw one. Calculators offer precision, but they’re just and only as precise as the numbers you put in. If you hit a number twice, or leave out a digit, or place the decimal point wrong, you’ll get a precisely wrong answer. If you can do the basic math in your head, you’ll have a better shot at recognizing when something is wildly off.
That said, part of me wonders if we’re sacrificing too much on the altar of pencil and paper. It’s great to be able to do addition in your head and long division on paper -- yes, I know, I’m old -- but is it worth flunking out huge cohorts of students because their high schools let them use calculators and we don’t?
At my job, I use statistics all the time. Most of the statistics I use are computer generated. Excel and its progeny (I’m an OpenOffice fan, myself) can crunch huge sets of numbers much faster than I ever could, leaving me free to do other things. Although I like knowing that, in a pinch, I could do a whole bunch of arithmetic myself, I typically don’t. And in most jobs, most people don’t. I agree that it would be better to have the ability than not to have it, but if the cost of holding the line against calculators is turning half a generation away from college, is it worth it?
At this point, the local high schools seem largely to have moved into the calculator camp. Wise and worldly readers, should we follow?
(Program note: next week the gang will be tromping through woods in another state. I’ll resume posting on Monday, August 2.)
