Are Graphical Calculators Pointless?

An anonymous reader writes "Texas Instruments and Casio have recently released new flagship graphical calculators but what, exactly, is the point of using them? They are slow, with limited memory and a 'high-resolution' display that is no such thing. For $100 more than the NSpire CX CAS you could buy a netbook and fill it with cutting edge mathematical software such as Octave, Scilab, SAGE and so on. You could also use it for web browsing, email and a thousand other things. One argument heard for using these calculators is: 'They are limited enough to use in exams.' Sounds sensible, but it raises the question: 'Why are we teaching a generation of students to use crippled technology?'"

Comments

Obvious

[Anrego]

Why are we teaching a generation of students to use crippled technology?

Cause the large portion of students are untrustable cheating bastards? Ok, a little bit of hyperbole, but that really is the reason. In addition to web browsing, you could also load equation solvers and all manner of tools to enable one to cheat their way through math. The old way overpriced graphing calculators can be wiped before a test, and offer the right mixture of functionality and cripple that schools want.

The price I think is just a function of having a captive consumer base. They charge as much for something that should cost so very little because the people who need it are going to buy it.

And yes, I'm sure the ol` "in real life I'd google the answer anyway" point is going to come up, and while I agree for most traditional memorize and regurgitate type courses, I still think math should be tough with a reasonable distance from crutches, while at the same time not trying to pretend they don't exist either. Show them matlab, but make `em work it out on paper on the test.

Re:Obvious

[gman003]

The thing is, even the "standard" graphing calculators are now advanced enough to teach with. Smart teachers are now demanding students reformat their calculators before a test, because otherwise they (like me) would just write a BASIC program instead of memorizing a formula, or store notes as an image.

Of course, I wrote a BASIC program that mimicked the shell, except a) it did not actually reformat, just display a message that it did so, and b) like a rootkit, it displayed false values for stored data, in this case blanks. It wasn't flawless (the ON key would interrupt the program), but none of my teachers figured it out. Arguably, it was more work than memorizing the formulas in the first place. Also arguably, this was more useful to me than rote-learning the proof of the quadratic formula.

Re:Obvious

[arth1]

Quite often engineers have to create formulae.
And if all you can do is use a calculator to solve them, you're then helpless, and won't be more than a technician or programmer.

Yes, tools are good, but you should show that you understand what they do before you get to use them. Else, the only one you're cheating is yourself.

Re:Obvious

[PopeRatzo]

Also arguably, this was more useful to me than rote-learning the proof of the quadratic formula.

I would like to hear that argument.

I've had a student argue that the skills involved in plagiarizing a paper about Nabokov's Pale Fire were more valuable than reading the great novel and doing the thinking and writing involved in producing an original paper. I wonder why some 20 years old would think he had the merest grasp of what would or would not be "useful" to him.''

After all, learning to braze or cadweld a pipe could be much more useful than learning to solve a partial differential equation, if you wanted to be a plumber.

Looking back on my own education, the one quality I wish I'd had more of is humility.

Re:Obvious

[johnsnails]

As a mathematics teacher I always encouraged my students to show working as a means of giving them partial marks for partially correct answers. Very hard to award marks for working out that is not there even if I can see what they *probably* did wrong to get the mark they did.

Re:Obvious

[pclminion]

Today I'm a programmer, and I make more than twice what my idiot math teachers made, and probably have more fun doing it.

As a programmer, you must have experience with the following phenomenon: you come back to a piece of code you yourself wrote, a year or so later, and not only can you not remember how it works, you don't even remember that you're the one who wrote it. It's great and everything that you could turn the formulas into a computer program, but as a fellow programmer myself, I can tell you that I can turn all kinds of formulas into programs even if I don't understand the damn formulas.

The goal, which you apparently missed completely, was to learn math, not how to turn a formula into a computer program. There's simply no way around the fact that most of this stuff can only be mentally internalized by rote and repetition. It sucks, it's boring, it's also how learning happens. What you did, and your following smart-ass attempts to defend your case, had a quite foreseeable outcome. Although I commend your mother for going to bat for you. Seems like parents don't have the guts for that in most cases lately.

Re:Obvious

[reason]

I learnt a salutory lesson in high school back in the 1980s. Our maths teacher had given us dozens of simple functions and told us to graph them in polar coordinates. the first couple took me ages, calculating and plotting each point by hand. I felt comfortable that I knew how polar coordinates worked and felt I had no need to do each example in the problem set. So I wrote a simple BASIC program to do all the rest for me. I didn't bother to hide the fact, and handed in the results on dot matrix paper. My teacher queried it, and I explained that being able to write a programme to plot functions in polar coordinates proved that I understood the work. So he asked me what patterns I'd noticed. Off the top of my head, what would such-and-such a function look like? It was only then that I realised that in writing my programme, I hadn't just saved myself a lot of rote work, I'd skipped a lesson designed to force me to puzzle out the patterns. (Fortunately, it was a fairly simple set of patterns and it only took a moment's thought before I could answer the question, but if he hadn't asked, I might never have noticed and might have been reduced to plotting these things out one point at a time when exam time came).

Oh please, this comes up every six months

[PCM2]

This same topic seems to get re-submitted to Slashdot about twice a year.

Short answer: If you need 100MB for a calculator, I salute you. If 320*240 pixels with 65,536 colours is too small and low-res for you for a calculator, you should save your money for a trip to the eye doctor.

Can a netbook do more different things than a calculator can? Yes, yes it can. That is why a calculator is not called something else... like, say, a netcalcubooklator.

My cell phone lets me make phone calls and also play Angry Birds. Why is Uniden still selling phones that don't have built-in synchronization to Google Contacts?

My 24" widescreen LCD monitor can display six pages of a book at once at full resolution. How do Amazon and Barnes & Noble get away with selling devices that can only display one page at a time, are not backlit, and can't run Photoshop?

The answer is obvious: There is plenty of room in the world for purpose-built devices. The reasons why people like to use those devices will vary. I, for one, like having a compact calculator that is programmable and has plenty of easy-to-stab dedicated calculator buttons on the front (as opposed to messing around with LaTek formula input, or whatever other input method you'd use on a device with a keyboard or touchscreen). My calculator of choice is an HP 50G. The HP 48 emulator on my Android phone can do most of what the 50G can do (and probably a lot faster), but as an emulated calculator on a touchscreen device, it ain't the same.

Do I use my programmable calculator every day? No, no I do not. Do I resent spending $120 on a calculator, compared to the cost of the chemistry textbook I bought for the same class? No, no I do not.

Missing the point of math...

[interactive_civilian]

Meanwhile, I have not used the quadratic formula since I finished Calculus, let alone had to recite a proof of it. I have little doubt that knowing what the formula is and how to use it is relatively important. However, I would like to see a plausible theoretical situation in which one would need to recite a proof of the quadratic formula, without the use of any references.

There are a lot of posts like this, so apologies for singling you out... But, as a math teacher I have to say in response to the "but I never use this" ideas...

Though doing such things is required as class, mathematics is NOT and has never been about memorizing formulas, or even about using specific ones. Yes, we all know you probably don't use the quadratic formula in real life, nor to you have to find the rules for number sequences, nor do you have to find all of the number patterns you can in Pascal's triangle, nor do you have to use Pascal's triangle as a convenient shortcut for binomial expansions, nor do you have to do proofs using all of those uselessly memorized names and properties from your various classes, etc. Yes, you probably had to do all of these things and more in your math classes, but believe it or not, learning math is not really about these things.

Mathematics is (or should be) the class where you learn how to think logically, and use logical and critical thinking skills to solve problems. Not just math problems, but ANY kind of problem you are likely to encounter in life. No, you won't ever use pythagorean theorem to solve relationship problems in your love life, but the logical and critical thinking styles you gained in your mind from solving problems in math will apply to you finding reasonable and logical solutions in real life.

Not only are you learning how to think in math, but you are learning how to break down your thinking so you can check it step by step to make sure there are no flaws. THAT is why we math teachers make you show your work. I, for one, don't care if you get the correct answer or not. I care about how you arrived at your answer, if you can show me the process you used to get to it, and if, in the case of an incorrect answer, you can find the flaw in your thought process that lead to your mistake. Tell me the ability to explain your thinking or the process you intend to engage in to reach a particular outcome is not an important and necessary life skill!

The fact that we use mathematics to try to teach these things is a side effect of what math is. But math class is not just for learning math. It is the class where you exercise your brain so that logical thinking and sustained reasoning become easier in all aspects of life.

And that is why learning to prove the quadratic formula, rather than programming the answer into your calculator, is important.