Volume 4, Issue C ::: December 2000
A Conversation with FOB...
Low Tech: Calculators, Videos, and the Abacus
Technology can be both a tool and a source of motivation in a GED math
G. Andrew Page (Andy) taught mathematics to those preparing for the tests of General Educational Development (GED) at the Richard Arnold Adult Education Center Math Lab in Savannah, GA, for more than eight years. He used a number of "low tech" tools in his mathematics instruction, including calculators. We talked to him about why he did this and what tips he has for others interested in doing the same.
FOB: What made you decide to teach learners to use calculators?
GAP: Well, I was teaching general math, algebra, and basic geometry, to GED [General Educational Development] prep students who were pretty advanced, above a sixth grade level. They knew the four functions [addition, subtraction, multiplication, division] although they all didn't know their basic math facts automatically. It had been many years since some of them had been in the classroom. But, as I said, they knew the four functions, and some of them knew how to use calculators for those functions. Some of them were using calculators in their jobs.
Some people asked for them [calculators]; some brought them in, so I decided to teach them formally. This meant I had to get the same calculator for everyone, because sometimes calculators [from different manufacturers] label the functions differently. I got a grant to get everyone the same calculator.
FOB: Did you have to convince any of the students that it would be worthwhile to learn to use a calculator?
GAP: Oh, yes. I had several students who were resistant: they insisted on learning the old fashioned way. They wanted to be able to do it in their heads. They didn't want that tool.
I showed them the speed the calculator offers, and that the computation is not the important part. Especially with word problems, the calculator won't tell you the answer: garbage in, garbage out. I had to tell them that it was not cheating. We also compared it [calculator use] with computers: that computers supposedly simplify our lives, but if you don't know how to use them, they don't. The underlying message was that I am going to teach you to use it effectively.
FOB: Did their peers help your cause?
GAP: They encouraged each other. I had one guy who worked as a maintenance worker. His company wanted him to carry a calculator around in his shirt pocket.
FOB: Any drawbacks to calculator use in the classroom?
GAP: You don't want calculator abuse. [Students shouldn't use calculators] for things like 6 x 7, for example. It's incumbent upon teachers to facilitate a classroom where you don't have calculator abuse. You have to be proactive, to model which problems they should use the calculator for and which they shouldn't. Show the importance and logic of estimation, ask why we use division, why we use multiplication. Until they know, learning has not taken place. When they can tell you why, that really helps them.
FOB: Is there a "right time" in which to introduce calculator use?
GAP: Using the Socratic method, asking why, I model a computational algorithm, then I show a word problem relating to that, then we work a similar problem with a calculator. I allow time for [learners] to offer real world problems that they have encountered. Usually these dealt with personal finance, such as figuring sales tax or computing the simple interest on a loan. Sometimes I show that the brain would be faster than a calculator: mental math. But we need to get away from drill and kill. Math is not just about computation, it's about thinking and exploring.
It's good for the teacher to show an example. Savannah is on the Atlantic. I go to the beach. I wonder, "How far is it to the horizon?" You can do this any place you have a flat surface in front of you. You take the square root of the height and multiply it by 1.4. Would you want to do that by hand? We would do it estimating, then we do it on the calculator, getting the square root of the height using a function key.
Function keys on a calculator look intimidating. The students were excited when they learned the use of a new function key: the x-squared key, for example. Instead of 6 x 6 you just hit x-squared. They could be very adventurous. I would hear "I always wondered what that meant."
FOB: What tips do you have for math teachers?
GAP: One of the things about calculators is the "coolness." This connects to my philosophy of teaching: whatever it is, however you do it, make it fun. Show interesting things. There's no aspect of math you can't apply to the real world, so find it and show it.
I taught the abacus; that's a tool, too. I would show them different algorithms for multiplying. I showed that video of the man who can do mental math in his head. I didn't want them to become technology dependent to the point where they can't think by themselves. Technology is both a tool and a motivator.