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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?"
The downside of being a geek is you don't know whether to lose face admitting your system is down and you can't reach it -or- admit you really didn't do your homework, thus can't download it.
A feeling of having made the same mistake before: Deja Foobar
I always remember playing SimCity on my friends TI-86 during math class, does this mean I can play it on a PDA too?! Anyone else play SimCity on a TI? It was pretty damned good for a calc game.
In college, really poor, need a flatscreen.
The compass and protractor are as obsolete as the sextant. If a kid graduates from school and doesn't know how to work a PDA, he's going to quickly learn how to work a deep fryer.
Shutting down free speech with violence isn't fighting fascism. It IS fascism!
What? not 6 years ago I/we were required to graph the fuckers manually, and we actually explicitly forbidden from using snazzy ti calcs to do it.
Paper and pen help you visualize what you are doing, a calculator which draws everything for you, just makes you think you did it. No-one needs these to learn mathematics, atleast not before doing their master's thesis in a university.
There are already problems with students putting formulae into calculators. I would only think this would get worse with a PDA. With a calculator you can ask and see that the memory has been reset without much worry about lost data. A PDA stores other things though and so it would be alot harder to check that it has been cleared or that the student isn't using it to cheat.
Feminism is the radical notion that women are people.
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.
Why when I were a lad, we werent allowed to use calculators. (Only the rich kids had them anyway.) We had to do all of our plotting with protractors and compasses. It was tedius and we'd forget what we were doing while we were doing it because there were so many steps. Most understanding was lost while going through the motions, making mistakes and erasing holes into the paper. When we got to things like polar coordinate translation, or calculus, the steps become so complex that most of the students didnt have a clue about the big picture as they became mindless rote automatons emulating a tape head.
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.
Like, why not just go straight cellular and connect to the internet or your home beowulf cluster?
Why stop there? Put a webMathematica server up, and access it though your PDA.
I'd always wondered how long it would be before the companies that produce software like Mathematica and Maple would port their software to PDAs. When I went to college at Rose-Hulman IT we were all issued notebooks which ran Maple and CAD software. We used Maple in all of our Calc classes and were able to use it on tests once we proved our ability to do that particular type of problem by hand first. The CAD software could have easily been on higher power workstations. If Maple had been on our PDAs it would have lowered the cost of going to the college by a few thousand dollars (high end notebooks were really expensive back in '95, and sometimes still are)
The main problem is that PDAs were nearly non-existant at that time, but today I can see PDAs like the iPaq doing a grand job of running some of this higher end math software.
Of course cheating would run pretty rampant with wireless transmitting of email and text, not to mention the ability to store files with crib sheets on them. I'm still not sure how our profs back in the day thought they were ensuring that we didn't cheat on our calc exams back then. I think it was more of a matter of honor than anything.
Duris MUD - The best pkill MUD. Ever.
Among cruising sailors it is considered somewhat foolish not to pack a sextant and know how to use it. You'd hate to take a lightning strike 1000 miles from land and lose your GPS, RDF, Loran, or whatnot.
Maybe you'll be bad with the cheap sextant, but you should still get within 30 miles which will let you make landfall during daylight.
"When you have circles and ellipses, there is no way you'd be able to do this without a calculator," Jarvis said.
Ok...I know a lot of people don't need to summon Euclidian geometry from memory in everyday life, but the image of a kid in geometry class learning an equation thats been around for over 1000 years, and saying that level of math is impossible without a {graphing calculator, PDA} really saddens me. Especially since geometry is usually taught an at honors level - meaning the kids taking geometry are supposed to be the smart ones, on the fast track to college, etc. It makes me think that with all the technology readily available, kids will stop thinking and imagining and innovating.
I remember being in school when the TI's started to become popular. My feeling then was that ok, I've done these equations by hand...I've got a good handle on how to do that, and sometimes its a real PITA, so maybe sometimes its better to use the automated functions here. I still think that way -- I CAN configure SAMBA by hand, but there's a nice graphical tool that automates it, so that's simpler for me now.
I just hope with all the automation tools and short cuts technology can provide, we're not engineering out the human quality of wanting to know how things work.
So how do you tell kids today that yes, you can live without the latest gadget, and that it is important to master the fundamentals before you learn all the shortcuts?
I just graduated high school, yet never had a powerful graphing calculator (Casio's aren't terribly programmable). But everyone I knew who had a TI had no clue what more than half the functions on it did; they merely used them to play games (as the few who owned PDAs did). Unfortunately, their power is dulled by the fact that they are so slow; an equivalently-priced PDA can do the same types of calculations in 1/10th the time. (I can't wait to stick a Scheme interp. on my Zaurus!)
/not/ be used as learning tools. Kids learn to use them to do math, rather than the actual underlying concepts. Don't allow 4-function calculators until algebra; don't allow graphing calculators until calculus; don't allow scheme-based RPN symbolic integration magic twiddles until set theory!
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
Someone once asked Einstein how many feet were in a mile. His response? "I don't know. Why would I clutter up my brain with stuff like that when I can look it up in any reference book in two minutes?"
"Mind, as manifested by the capacity to make choices, is to some extent present in every electron." -Freeman Dyson
Too bad there are no more HP calcs.... RPN was awsome to use.
Circle: Use a compass. A compass is a simple tool that should be easier to learn than any calculator. (Adjust angle, stick pointy end into paper, draw.) And then all kinds of important tricks of geometry are possible, with just the compass - really only learnable with the compass in hand.
Elipse: put two pegs on paper, the chalk board, etc. Toss a loop of string around pegs. Pull loop of string tight with a pendic, chalk, etc. Draw with string kept tight. Lookie! an elipse! How hard was that?
I used my TI-85 to do all sorts of math, but I learned my math in books and on paper.
Evan - needs to hit preview before submitting
The compass and protractor are as obsolete as the sextant. If a kid graduates from school and doesn't know how to work a PDA, he's going to quickly learn how to work a deep fryer.
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...
*** Where are we going? And what's with this handbasket?
Also the differences between all numbers from 0 to 100 (so I can get my change quickly in case the cash register is broken.)
Wrong, WRONG, WRONG!!!!!
Disclaimer: I pulled graveyards at a 7-11 in 1982 and 1983.
Everyone should learn the PROPER way to make change. It pisses me off when some clueless idiot goes... "$7.47 is your change". That's not how to do it. let's say my bill was $2.53 and $7.47 *IS* my change. The correct way would be:
Say $2.53
Give Penny (say 54)
Give Penny (say 55)
Give dime (say 65)
Give dime (say 75)
Give quarter (say $3.00)
give dollar bill (say $4.00)
give dollar bill (say $5.00)
give five dollar bill (say $10.00, thank you).
That way, you know that you didn't screw up counting it, or that you didn't fsck up typeing in the amount given. 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.
Alas, making change is a lost art.
Fascism starts when the efficiency of the government becomes more important than the rights of the people.
... at all levels. In the early 90s I TA'd a course in statistical mechanics at Stanford. We got to the inevitable part where you have to calculate the expected wait time before all of the air in the room accidentally ends up under the desk. It turns out to be something like 10^130 seconds -- a very, very long time. The most common answer was "too long for my calculator", because after all most calculators can only go up to 9E99.
How annoying. You'd think they'd just switch to calculating the logarithm of the answer, or divide by 10^75, or something. But, no, "very big" was enough for most. These were Stanford students, too -- supposedly the cream of the (western half of the) nation's crop of students...
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-
"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.
If you can't do the math, no calculator can help you. Oh, it might make the difference between getting an 'F' and a 'D', but think back to your own math classes. Performing a finite integration to find the area under a curve between x=0 and x=18 is difficult enough.
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.
Above comment is personal opinion. Poster is not a spokesperson.
Unfortunately, TI hasn't officially provided much information, but having been involved in the TI dev scene quite a while, I've had the opportunity to play with beta versions of these apps quite a bit. They're slightly limited when compared to Palm because they don't have touchscreen input, although the 92+/Voyage 200 calculators have a full qwerty keyboard. The software is quite nice, and I've been using it full time since my Clie broke a few weeks ago. I'll have the Clie repaired under warrantee, but for the target demographics of TI's calculators (mostly students), the Organizer software is more than powerful enough to make somebody who purchases one of these calcs reconsider whether they need to carry around a PDA as well. And trust me, consolidating the two devices and freeing up a pocket is definitely something to look forward to.
-- Imagine how much more advanced our technology would be if we had eight fingers per hand.
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.
-- Imagine how much more advanced our technology would be if we had eight fingers per hand.
Frankly, anyone who would regard referencing forumulae as cheating is a poor excuse for a teacher. Who cares? Let the student look up the damn formula, already, like real people do here in the real world.
The best mathematics teacher I ever had was strict as hell, but when she gave tests she let students bring a single 3x5 card filled up with anything they thought they might need. Formulae, tables, reminders, tips--anything you could fit on there.
She also held timed open-book pop quizzes. Her reasoning was simple: the more time you needed to spend looking things up the less time you'd have to actually do the math. That policy encouraged students to remember those things they used most often without forcing them to fixate on memorizing every random thing that might be conceivably needed. Both policies also give students some reassurance that a random oversight or memory glitch won't mean failing a whole test.
Like, why not just go straight cellular and connect to the internet or your home beowulf cluster?
Can students use their cel phones to call their life-lines during exams?
Some people will spend far more than 4 years developing their mathematics education. Some will take the Algebra class that ends with the binomial theorom (or even just quadratics), scrape through it, and that's the end of math for them. Others will have multivar, partial diff, number theory, and advanced linear. Different strokes, different calculating tools used, different reasons for using them.
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*.
-fb Everything not expressly forbidden is now mandatory.
I was recently awarded the unpatent. Non-users of "the compass and geometry" must cease their inaction immediately, or I'll be forced to litigate.
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