Wednesday, April 04, 2007
Kids don't learn arithmetic anymore. Adults are forgetting everything they ever knew about it because calculators will do the computations for them. Fractions, signed numbers, decimals, etc, etc, etc can all be done on these little machines. After all, most of us use a remote to change the station when we are watching television and we certainly use a washer-dryer to launder our clothes instead of beating them with a rock on a river bank, so why not replace our brains with little machines that can be purchased for less than $20?
I don't have a problem with calculators if they are used to enhance learning, not replace it. Kids need to understand how operations with signed numbers work before they just start pressing buttons to hopefully arrive at a correct answer. They need to understand what happens when they find a percent of a number, know whether the answer should come out larger or smaller than the original number. They should know that multiplying by pi will give a number slightly larger than three times the original number. Too many times I have seen kids come up with totally insane answers and write them down because that is what the calculator gave them.
I do believe that arithmetic shouldn't hold anyone back. Not mastering fractions should not be equated with the inability to solve an equation. After years of trying, kids should be able to move ahead with a calculator if that is the only way, and I do mean the only way.
Calculators do have a place in higher mathematics. By freeing the individual from tedious calculations, more difficult conceptual problems can be studied. But, even in the higher level classes we are doing our students a big disservice by allowing a calculator on every exam. For example, kids no longer know trigonometric relations of quandrantal angles or of the special angles, and some of the beauty of math is being left behind. We used to teach them to find sin 15 by using sin(A - B) formula. Now, they just want to get the answer from their calculators.
The AP calculus exam is divided into four parts. Parts II and III allow calculator use. Parts I and IV do not. The calculator parts are the most difficult parts because of the concepts that are being tested. In my class, to prepare for this exam, I give both calculator and non calculator exams. At first, the kids whine about not being able to use the calculator. THEY HATE DOING ARITHMETIC! THEY DO NOT REMEMBER SIMPLE TRIG RATIOS! They soon find that the arithmetic they are being forced to do is the easiest part of the exam. I find that I have to show them silly calculation tricks to make the arithmetic easier, things that they should have learned (and are more than capable of learning) a long time ago.
So, what is the answer to all this? I don't want to do away with calculators. I just think calculators need to be used sensibly. Teaching must include calculator and non calculator questions. Exams must sometimes be calculator exams and other times be calculator free exams.
Mathematics is more than arithmetic, but, an understanding of arithmetic is vital to being successful with it. Technology must be used, but, it must not be used to the exclusion of everything else.