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

Raising the bar

[DNS-and-BIND]

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.

Re:Raising the bar

[sowellfan]

I had a Thermo professor at Univ. of Florida named Dr. Gater (most engineers who've graduated from UF in the last twenty or so years probably took Thermo I from him). In Thermo I, he wouldn't let students use the graphing type calculators (he might not have even let students use *any* calculators, but it's been a little while, I forget).

When students would whine about his restrictions, he would say something along the lines of, "What about when you're at the urinal, and an engineer at the next urinal over asks about how much sensible cooling you can get from that chiller? You can't use a calculator then." He was (and is) a terrific teacher, even if I dropped Thermo I once, got an F next, then a D+, then, finally a C+. My problem in his class was that I had become accustomed (in other classes) to not going to class (very often, at least), reading the appropriate material, coming to an understanding of the theory by doing a few problems, and then doing pretty well on the tests. Thermodynamics, unfortunately for my GPA, was entirely different (at least under Dr. Gater). You have to do lots of problems in order to truly understand the material, otherwise you're up a creek (and the knowledge is cumulative, so if you got lazy for a few weeks, you were screwed). Thermo II was entirely take home tests (any calculators allowed) and there was no chance to slow down or get lazy since you were always taking a test (you handed on in on Friday, and then he gave you another). I was extremely proud of my B+ (first time around).

On the subject at hand, though, it seems that most people here (especially those with experience as a math tutor, like myself) would agree that students should learn the basic skills without major calculator help. At a certain point (exactly when is up for debate), calculators can become effective learning tools. Most of us also agree that calculators are invaluable for getting the grunt work out of the way once it's second nature to you. Some people have indicated that, on a well designed test, a students math knowledge or ignorance will be exposed, whether he has a nice calculator or not. Unfortunately, it seems that in many, many (I dare say most) classrooms, the tests that are given aren't nearly up to that standard (as evidenced by the sheer ignorance of the people walking into math labs at community colleges around the country, even after they have passed Algebra classes at the college level). The most vocal defenders of calculators in the realms of educators will always point to teachers who are using calculators for truly enlightened teaching, as if they are typical examples, when we all should know that they are not.

Of course, we also can't forget that TI itself is one of the biggest proponents of this movement, and they have a huge financial stake in the matter. When you figure that nearly every high schooler in algebra is buying a $100 calculator, the numbers get pretty significant.

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

[jukal]

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.

And what when you move to higher dimentions?

[bluGill]

As one young math professior I had in college said I hope you sometime get the fun of working in at least 11 dimintions. He was a young guy (first you teaching), and was truely serious about that. Now I can deal with 2d graphics just fine, and 3d graphs are normally not a problem, though optical illusions sometimes are possible so I don't rely on them, but the one 4d graph I saw just threw my mind in a loop, and I decided not to bother with them again.

Maybe I'm not a visual person, but I can't deal with 4d graphs. I can deal with math in 11 dimentions if I have to, though I'm not good. The ability to work on 2d and 3d problems without a graph helps when you deal with problems that cannot be easially graphed.

Then again, all my college classes allowed calculators, but the time to enter numbers was longer than the time to calculate things in my head so I rarely used my HP-48 after my freshman year.

Re:I'm old :[

[Auckerman]

No kidding. I went my entire education (BA Chem) without once using a single graphing calculator. Now, In my spare time, I tutor college math: time and time again, my students have no true understanding of even the most basic of principles because they always had a computer to do it for them.

So now, If I tutor someone, I made them leave the calculator at home. Everyone to date ended up actually learning, rather than memorizing.

A couple of thoughts

[dlur]

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.

Does this horrify anyone else?

[goldenfield]

"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?

Exactly

[Wraithlyn]

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?"

It's not them I worry about...

[sykora]

It's not the kids that are smart enough to program things to help them cheat that I worry about graduating from school, it's the kids who don't know where the United States is on a map, can't read past a fourth grade level, and don't know which war won our (the US) independence from England that I am more concerned about (you know, the ones who end up on Jay Leno's "Jay Walking")- most of whom, in my experience, are not smart enough to figure out how to program a calculator or PDA to help them cheat at tests. JMHO

To a math major, this is scary...

[Eosha]

I am an avid user of both my Palm and my TI-86. However, I did not learn geometry, trig, or even calculus on either; I learned basic math with the same Euclidean rules that have stood for millenia.

I remember back in high school. One time out of curiousity I asked my (I think it was Algebra II) teacher if he could teach me how to find square roots without a calculator. He didn't know offhand, and so I went to EVERY MATHEMATICS TEACHER and NONE of them knew how to do it. I finally found one person who knew how: the ancient librarian. She taught me, and I'm grateful.

Calculators are a tremendous help for solving things faster and more accurately. But if you don't understand what the calculator's doing, what good does it do you when you have to modify it a bit to fit a given situation?

What kind of an "educational" system is this where so many people are utterly incapable of standing on their own two feet without the support of calculators?

This is a really disturbing trend in math, and education in general. And it's only getting worse thus far.

-eosha

When you don't know what to do, walk fast and look worried.

Calculators aren't the end of math

[moonrakerelite]

I can't understand what everyone is complaining about. Graphing calculators/ PDA's, although incorporated heavily into the curriculum, are only tools, not a means to pass off the thinking to a machine. I'm sure a similar debate took place when electronic calculators came into the school system, but what needs to be realized is their advantages. Work can be double checked easily, tedious processes sped up. Sure, some wise-guy could secretly hide L'Hopital's rule, or some trig identities in his calculator. But what is the problem, as long as he shows he knows how and when to use them? The easiest way to combat this is by teachers shying away from multiple choice math exams, and forcing students to show their work. Then, instead of spending time memorizing formulas, students can concentrate on the actual mathematic process. However, this is not to say that a student should not be self reliant. Anyone (Except some apparent technophobes) have other ideas on how to integrate (Pun not intended) these tools into schools?

How my school does it....

[chronos2266]

I just graduated from high school. My mathematics classes have been using graphing calculators as a standard since sophomore year when I took Alegebra 2. We still are required to learn all of the formulas, and how to compute them by hand. Most of our tests have a calculator part and a non calculator part. The key steps in the calculator part do not deal with calculators at all. For example, when I took calculus BC my senior year, we would have to write out the integral first before using the calculator to evaluate it. This demonstrates the knowledge being tested as well as calculator proficency(which was required by the Advanced Placement tests we took at the end of the year).
People that say you need to be doing it the old fashioned way just think we are using only calculators and nothing else. That is not even close to the truth. Calculators are a valuable aid in a high school mathematics class and I could not even imagine what I would have missed out on if they were not utilized during classes.

It's not cheating.

[5KVGhost]

There are already problems with students putting formulae into calculators.

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.

Tis are more useful for programming than graphs

[ddd2k]

quite alot ppl think that TI-calcs ruin the learning process when students become too dependent on trying to find the anwsers with graphs. but im doing calculus in high school and use graphs mainly to check for anwsers. What most people are missing out on is the programming capabilities on the TIs. you can create simple programs that will compute functions otherwise extremely long and pointless. the language is very simple, (and if you want, u can always use ASM)and useful. Like in a couple seconds i can generate 4 lines of code that will fill a list or matrix with a sequence of numbers and generate the product of say every 3rd element. I also made a program that calculates the area of any triangle formed by the intersection of 3 lines. In doing so, it not only makes your life easier but also help you grasp the concepts when you program them. Its different from programming at home since i can do this when i get bored on math class or somethin. In this perspective, the TIs are far superior to the PDAs and do not make students dumber.

Re:I'm old :[

[lordaych]

In elementary school, I was an arithematic whiz. In middle school, I had no problem getting through "Pre-Algebra" and first-year "Algebra." In high school, I got suspended for five days for using cannabis on school grounds. I thought it was a ridiculous "punishment," but it ended up hurting me big time. I missed the entire week where we learned how to factor polynomials, and it took me a "D" in first year Calculus 4 years later to realize what I'd failed to learn. I ended up getting a big fat "D" in that high school Algebra class, too, although I did manage to pull a 107% (extra credit, of course) on one test that involved graphing. I had a TI-85. Other than that, it became a massive crutch (with games to distract you, to boot) and I regret ever having gotten it at that age.

I regretted getting a TI-89 in college, too. It seemed to hurt me rather than help me. When I go back, I'll stick with a TI-83 or lower. Heh.

Re:Calculators and Geometry

[sean23007]

That's true, when you don't have a calculator you do tend to get better at doing it by hand. On the first day of Calc 2 my TI-85 was stolen, and I couldn't afford to buy a new one. So what was my only option? Do everything in my head, of course. I got damn good at visualizing integrals and differential functions in my head, and I never learned how to do it on a calculator. I went on to take the ACT and SAT without a calculator, and I think I did better without it. After all, pretty soon you get to the point where it takes longer to plug something into the calculator than it does to do it in your head. It all comes down to which you do more often. I'd rather be independent of the calculator.