Calculators vs. PDAs in the Classroom 550
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?"
Calculatorama (Score:2, Insightful)
Cheating (Score:3, Insightful)
Re:other conflicts? (Score:2, Insightful)
Lets crawl before we walk... (Score:4, Insightful)
PDAs dont' have buttons! (Score:2, Insightful)
This is a good thing.. (Score:3, Insightful)
Kids these days get these glorious plotting computers that bypass the tedium and take you straight to the insight. They even have algorithms that do their algebra for them. And I am sure they have a much better high level understanding of what they're doing than I did even in college.
Actually I wouldn't be surprised if their ability to actually solve by hand some of this stuff is as good as ours simply because they understand it better than we did.
Math shouldn't be about rote memorization. (Score:2, Insightful)
Why stop there? (Score:3, Insightful)
Why stop there? Put a webMathematica [wolfram.com] server up, and access it though your PDA.
How about neither? (Score:1, Insightful)
Both are bad for learning (Score:3, Insightful)
PDAs are currently banned because they are "programmable". But so are all graphing calculators. On SATs, the only things that are banned are devices housing QWERTY keyboards, which most PDAs don't. Also, TIs can be programmed (and come with) more functionality than your average Palm. Even my Zaurus comes with only a 4-function calculator app!
Back on the topic of the CASIO, I left it at home nearly every other day of school, if even that infrequently. Yet I survived through every math and physics class often without it. Because of graphing calculators, most kids don't even know what a parabola looks like, let alone how to draw one. Most people even forget fractions and long division, and rather write the answer the calculator gives them, like "3.999999999" rather than "4".
Both calculators and PDAs are tools, and should
Re:I'm old :[ (Score:2, Insightful)
The response (Not an exact quote, but it stuck with me), "One needs a good imagination to study math, not a calculator or computer; paper & pencil are helpful when it comes to proofs."
Of course that was my point, but they assumed that I was like most other people today... thinking that a persons ability to use a computers or a calculators make them smart or able in the sciences/math/computer programming.
Ted Tschopp
Re:This is a good thing.. (Score:1, Insightful)
You must be joking. If I just push a button and the computer does the algebra, then exactly how am I learning algebra? All I learn is how to push a button. There is no way to really learn math other than to work exercises yourself. Not listening to lectures, not reading the book, and certainly not pressing a "solve" button on a calculator.
Re:Math shouldn't be about rote memorization. (Score:2, Insightful)
Actually a few things in math should be drilled into students by rote. That way they will know them without having to even think about them. The multiplication table is one such thing. Also the differences between all numbers from 0 to 100 (so I can get my change quickly in case the cash register is broken.)
If you don't remember a formula there is little chance of applying it is there? At least not until you have looked it up.
Re:Raising the bar (Score:2, Insightful)
Remember...somebody has to make the caluclator, PDA, compass, protracotr, or whatever tool ends up aiding in the job at hand.
Whatever... (Score:3, Insightful)
Nice troll...
I suppose the PDA is only a requirement if you want to be a marketdriod. For the rest of us, thinking is going to be considered a valuable ability. Right now, a PDA is just an interesting toy, and many people somehow manage to exist and lead productive, organized lives without one.
For what it is worth, I am all for banning calculators from the classroom. Far better to be able to demonstrate the process by which the student arrived at an answer than to pull some magic number out of the air and expect full marks.
I just graduated from university a couple of years ago and calculation devices of any type were strictly forbidden in my math, statistics, and CS classes. Sometimes it was a pain, but then the answer was rarely expressed as an integer anyways...
Re:"It helps us visualize what we're doing." (Score:4, Insightful)
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 (Score:4, Insightful)
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? (Score:4, Insightful)
We visualized landing on the moon before calculators. Get a grip, young man, and learn your trade before using crutches.
Visualisation (Re:Math shouldn't be about rote me) (Score:2, Insightful)
Also, make damn sure you leave the money I gave you on top of the register until I agree that it's the right amount of change. This prevents "I gave you a $20! No you didn't, you gave me a $10!" arguments.
How much of these arguments would have been stopped in advance if people in the US were able to see the difference on a 1, 5, 10, whatever note by checking the colour of it?
Take the next step into evolution, colour your notes, and prevent confusion and unnecessary arguments caused by the fact that all your notes are the same colour.
After that it's only a matter of time before you adopt the metric system and your math will be easy again
Why so negative? (Score:1, Insightful)
Listen, we have technology for a reason. In order to advance society we have to continue from where the last generation left off. I mean come on, it's almost the same concept as open-source. What if you were not allowed to share information? So you want to build an airplane? "Figure it out yourself, then you'll be a real airplane builder". Give me a break, if we did that then progress would grind to a halt.
Computers for everyone on their desk, fine. Of course, kids still need to learn, but what they learn may be different than what we learned. They have the advanage of learning from our mistakes and then continuing on and advancing life as we know it.
Re:"It helps us visualize what we're doing." (Score:5, Insightful)
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.
Machines don't do math. (Score:3, Insightful)
Just require that the student show their steps in solving the problem. I don't care if the answer's right in a calculus class... I'm not there to teach arithmetic... were the steps used to solve the problem correct? Just because there was a silly addition error doesn't mean the whole problem get's no credit, and just because the answer's right doesn't mean it get's full credit either. A calculator can't help a student who doesn't know the intermediate steps to solving a complex math problem.
Calculators and Geometry (Score:5, Insightful)
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.
Re:"It helps us visualize what we're doing." (Score:2, Insightful)
As far as what level graphing calculars should be introduced... I say never. Allow whatever the students want for homework assignments (TI85s, PCs with Maple/Mathematica/Matlab, PDAs...), but exams should be strictly pencil and paper. At least for subjects where math is central - ie, physics/math/EE/ME.... (I suppose allowing intro calculus courses for general students to use graphing calculators is hurting nobody much).
OMG people like you are annoying (Score:1, Insightful)
Lowering the bar (Score:2, Insightful)
Perhaps, but one has to sense a decay in society when, as really happened to me, a cashier reaches for a calculator to figure out my 10% discount (when I commented she must have gone to a public school she simply said she wasn't very good at percentages, I don't think she ever had a clue why I knew the discount before she did). Or when the register at the burger joint has to have pictures of the food on it so the monkey operating it can function, and how it terribly confuses them, when you see your total is $2.78, if you give them and extra 3 pennies rather than just $3.
One gets the sense that the school system is skimming over the basics a little too quickly, and I've heard too many kids state that they shouldn't have to learn basic math because the calculator will do it.
Re:other conflicts? (Score:2, Insightful)
But erasing memory and all of this other crap is just darting around the real problem -- teachers aren't adapting to the tools available for the students. I'm sure if you were to dig up Newton he'd laugh at the people that used a book of logarithmic tables, let alone high-powered calculators. There will always be the people that gripe about "how good kids today have it" and "how the more archaic method of my education is the better way." That's not the answer -- the answer is that teachers need to design courses and exams around the tools. I had a chemistry teacher in college that let you have a calculator, gave you a sheet with ALL of the relavent formulae on it and even encouraged you to fill up your TI-8? with data. The exams were always designed to test your ability to think and apply what you should have learned. All of the cheats and formulae and math figures in the world wouldn't help on these tests if you didn't understand how to apply the knowledge.
So what if a kid has a calculator that can derive, integrate, draw circles and play games? Start designing cirricula around these new-fangled machines and find a way to test a student's application of the material. That will make calculators and PDAs and computers useless for "doing the work for you".
all curricula are not equal (Score:3, Insightful)
I'm in the latter category, where the calculator is pretty much irrelevant for the math classes.
I use the calculator for *arithmetic*, and hardly at all for *mathematics*.
Re:Why stop there? (Score:3, Insightful)
What you don't Visualise - You Lose (Score:3, Insightful)
whatever you get the machine to do for you - you pay for in letting your own ability to do it atrophy.
If you never learn it manually and always have a machine do it for you - then you're slave to the machine.
once you've Learned It without the machine, then the machine becomes an aid. but if you never actually learn it yourself, then you're slave to the machine.
once you know how to do it manually, then there's a place for letting the machine take the drudgery out of it for you - that's what computers are for after all.
but how many times have i been to a store, and the cashier didn't even know how to give correct change when the register doesn't tell them the right amount!?
john [earthlink.net]