Calculators vs. PDAs in the Classroom

TheMatt writes "CNN.com is reporting about a new conflict perhaps emerging in classrooms: calculators v. PDAs. The article talks about how TI seems to be making their latest calculator more PDA-like, while PDAs are gaining TI-like functionality. A comment on current math education is this quote from the article: "When you have circles and ellipses, there is no way you'd be able to do this without a calculator," Jarvis said. "It helps us visualize what we're doing." Were the compass and geometry uninvented?"

Comments

Lets crawl before we walk...

[Yoda2]

I have no problem with "aids" such as graphing calculators and PDAs in the classroom as long as the "ole fashioned" ways (i.e. by hand on paper) are taught/learned first. We've become a society (in the US at least) where most people have to carry around tip charts in order to function in restaurants.

Re:"It helps us visualize what we're doing."

[mattbelcher]

atleast not before doing their master's thesis in a university.

Actually, at the early level is when calculators and other graphing aids are *most* useful. In my experience, the further along I got in math, the less I used my calculator (and the smaller the books got). I see calculators as a memory aid, sort of like the periodic table. A long-time mathematician doesn't need to turn to his graphing calulator to see what a sine curve looks like, just like a long-time chemist doesn't need to look up the atomic weight of nitrogen. Those things are a crutch for beginners.

It's a Tool

[HardCase]

Was the compass and geometry uninvented?

Back in the day, my Dad got a degree in civil engineering. He was allowed to use a slide rule for many of his classes, even in high school. His dad thought this was inherently bad because it defeated the idea of learning to do the math by hand. Naturally, geometry, trigonometry and calculus didn't lend themselves (graphically) to a slide rule, but he could perform arithmetic calculations like a maniac.

When I went to high school, slide rules were out and calculators were pretty damn expensive, so in high school, everything was done by hand. I can do arithmetic calculations in my head like a maniac.

After about 18 years, I went back to college and got my electrical engineering degree. Not only were calculators cheap, but computers were cheap, too. I took Trig, three semesters of calculus, one of differential equations and one of statistics. I used the calculator and computer in each one.

Did it help? Damn straight! Did it hurt? No.

Here's what I think: the mathematical fundamentals that I learned were aided by the electronic tools. Sure, any monkey can poke the keys on a calculator or type in a Mathematica or Maple function, but, fundamentally, the student must have some degree of knowledge of the basics of what he's doing to know that the answer that comes out of the box is the one he wants. I don't know how many times I poked the buttons and watched the calculator or computer toss out the wrong answer because I typed something wrong. But I knew that the answer was wrong because my knowledge of math was such that I could estimate to a reasonable degree what the answer should be.

I do have to admit, though, that the string and two nail method of drawing an ellipse does drive home the idea of visualizing how the ellipse works (major and minor axes), but I'm most definitely a cheerleader for using calculators and computers to overcome the mundane mechanics of math. Not only that, but modern calculators like my TI-92 Plus do a great job of graphically modeling things like surface integrals. Computer programs do it even better. Tools like that allow students to progress many times further in their math "careers" than they might have if they didn't have those resources.

Fundamentally, though, and I suppose this is what you meant by the calculators and geometry comment, it's vital that a well developed, solid knowledge base is developed in the basics so that the resources become tools and not crutches.

-h-

Visualize WHAT?

[YrWrstNtmr]

"When you have circles and ellipses, there is no way you'd be able to do this without a calculator," Jarvis said. "It helps us visualize what we're doing."

We visualized landing on the moon before calculators. Get a grip, young man, and learn your trade before using crutches.

Re:"It helps us visualize what we're doing."

[MrResistor]

Actually, at the early level is when calculators and other graphing aids are *most* useful.

I'm a college level math tutor, and I can't even begin to say how wrong that is. Kids don't learn math by using a calculator any more than they learn to spell by using a spell checker or learn grammar through a grammar checker. I've tutored countless students who's teachers thought as you do, and none of them knew a god damned thing about math, despite the fact that they got 'A's all through high school.

When kids are first learning math is exactly the time when you absolutely don't want them using calculators! They need to learn how to do things by hand first, without having to rely on anything else to do it. Then, when you hand them a calculator, it's just a way to do things faster, to get the busy work out of the way so they can focus on more advanced concepts.

In my opinion, graphing calculators should be allowed only at the calculus level and above. Below that level, they can only be a crutch. Scientific calculators should be allowed for Trigonometry and intermediate Algebra, and absolutely no calculators at all at a lower level than that.

Calculators and Geometry

[SMN]

Speaking as someone who's had a TI-89 with full CAS since taking Algebra II, they can be a great help as an _aid_ to learning. I had one when learning the formulae for circles, ellipses, etc, and yes, it was great to be able to play around with changing the numbers in whatever spots and see how the graph changed. I've always been a math person, but near real-time visualization of the concepts definitely helps a lot of people learn.

That said, this is dependent on the student using the calculator only as an _aid_ to learning, not a replacement for it. After I bought mine, I watched as students in courses as simple as (remedial) Algebra I bought 89s, and the calculators solved the problems for them. Then even students in the honors sequence bought them when first getting to limits -- and I do know quite a few students who didn't know how to do limits by hand, yes passed tests solely by using their calculators.

But for someone like me, who actually learns the concepts before resorting to the calculator, it's a great help. Got a tricky integral for homework that you're having trouble with? Check the calculator's answer, and often the "form" of the answer will hint at how to solve it, and the next time you have a problem like that, you'll know how to solve it. Does your homework have even-numbered problems that don't have answers in the back of the book? Use the calculator to check your answers, and if you know you got one wrong, you can go back and figure out why.

Fast forward a few years, and I've just finished up Multivariable Calculus and Linear Algebra at a well-known US university, and the calculator was still a great help. Test and Quizzes were all done by hand, so a calculator won't get you through the course. But I can now check my homework bit-by-bit as I go through it, so a little mistake in matrix multiplication in the first step of a long problem won't result in a completely wrong answer 20-minutes later. It's saved me a lot of time and a lot of frustration, and of course I learn where I commonly make mistakes and can correct them. And you can extend the geometry comment made by this teacher to higher level math, like graphing quadratic forms -- after solving one, I could graph it and see the eigenvectors/principal axes, the signular values, etc. And I was able to take some of those 3d shapes that I had to integrate to find the volume and use the 3d grapher to see what they look like. And the calculator has quite a bit of differential equation functionality that I don't fully know how to use yet, but no doubt it will come in useful in the future.

So the calculators in and of themselves aren't bad; it's those who abuse and overuse them. Can anything be done about that? Well, having calculators banned on all tests did wonders for my math-by-hand skills. Let students use the calculators when learning the concepts, but when it comes to testing their application of those concepts, make sure you're testing the student and not the calculator.