Slashdot Mirror
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?'"
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.
but it raises the question: 'Why are we teaching a generation of students to use crippled technology?'"
because Texas Instruments has lobbied very successfully to keep it that way.
technology that has barely advanced since the early 90's and probably only costs $10 or so to make being sold for $100-$150 to every student
to protect that kind of profit I would bribe a bunch of school districts too!
Snowden and Manning are heroes.
Why are we having exams that require a calculator?
I did all of calculus and most of linear so far(sufficiently complex equations were done to allow for matlab use, but the test stuff could be done without), and even statistics(yay longhand division!) without one just fine, and most problems can easily be done without them if the proper setup numbers are used.
Also, they are NOT crippled enough. Even when i was in middle school there were program packs to download your textbook onto your ti-83 (I had a ti-80 and i could still type the formulas by hand) so they are still too advanced to not cheat with. And don't tell me you can just wipe the memory, any sufficiently smart cheater would have a ti with a different spare battery. You can find easy DIY's for those online nowadays easy.
Allow a calculator with a 10 key, if they need to graph something, then they should be able to figure it out enough by hand and not need a calculator.
All testing with a graphing calculator does is let more students pass because they don't need to learn, they just need to throw thier notes on the calculator memory. (Yes you'd have references in real life, but the point of most math tests is it's so basic you shouldn't NEED references, it should be the core material you know by heart)
You never realize how much manually made unmanaged "linked" lists suck, till you have src.link.link.link.link...
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.
Breakfast served all day!
What's the point in "teaching" math if you let the calculator do 90% of the work?
What's the point in "teaching" math if you let the decimal system and all that clever carry-the-one shit do all the work? I mean seriously, students need to learn what addition really is -- make them put 198 beans into a pot, then put another 61 beans in the pot, then count the beans to get the answer.
Being a human is about being smart, not being dumb. Forcing a student to do addition on paper when the student is studying partial differential equations is nothing but an insult. By that point I think they've earned the right to not continually have to prove that they can add two numbers together.
As an undergrad taking physics I had this bad habit of forgetting my calculator, especially on test day. I'd end up doing longhand division and taking up half the paper and leaving less room to write the actual answer. The professor started asking me what the hell I was smoking.
You made your point about the keyboard being difficult to use quite eloquently.
What's the point in "teaching" wood shop, if you let a power drill do 90% of the work when drilling holes?
Students should have to do it using hand screws, lest they become dependant on the newfangled lctricity!!
Crippled technology? Hell, why do we even allow calculators to be used in ANY exam? What's the point in "teaching" math if you let the calculator do 90% of the work?
Because calculators are a tool used by practitioners of mathematics, and students benefit from learning to use the tool to facilitate their work? Because arithmetic is simple, and it would be wasteful to just be constantly re-testing all that particular type of "work" on every test?
Don't take testing of students' ability to use a calculator for granted.... many students fail, even with advanced calculators fully allowed. To be successful in life, you have to learn how to use a calculator, and if math classes don't teach this and test you on it, many students won't get the required skill.
It turns out that in real math classes you actually have to have some idea what you are doing to be successful even with a calculator. This couldn't be more true than with word problems that sometimes involve many steps and pages of work, and require advanced problem solving --- the more work the calculator can do, the more time the student has to do work on the real math (problem solving), AND, therefore the more complex the problem can be, and the larger the amount of material that can be tested (the more advanced the thought that can be required of the student).
In other words use of a calculator is not harmful, and actually beneficial, if the examination method is effective, and accounts for the students' access to a calculator. Strategy for using the calculator in an appropriate way is also a problem solving consideration -- if the student uses their calculator inefficiently, or doesn't take a good problem solving approach, they will run out of time before they finish the exam. The introduction of this strategy element allows the exam to be made more challenging, and therefore.... taking the exam more rewarding / more educational an experience.
If you can't use a calculator, you won't go very far in modern maths. If you can use a calculator, 98% of the students will have their needs met; the 2% who go into advanced maths for maths sake are such geeks they will not be harmed by learning to use a calculator.
A basic scientific calculator should be so cheap these days that they could just be added to the instructors budget and handed out to students and returned to the instructor during a test. I see no reason in this day and age where basic calculators shouldn't be as readily available as say, a pen.
The question is not "should graphing calculators exist" but "should $100 graphing calculators exist?"
If a low-end netbook cost 5 times as much as a graphing calculator instead of twice as much, we wouldn't be asking this question.
If it weren't for virtual "vendor lock in" dictated by testing agencies, book publishers, and other "high influence" players giving TI a near-monopoly, the price of these fancy not-a-computer graphing calculators would be more like $25-$50 instead of $80-$130. Oh, and netbooks would still cost the same as they do now.
Knowledge is how to play a game, intelligence is how to win, wisdom is knowing what game to play.
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.
"Empathise with stupidity, and you're halfway to thinking like an idiot." - Iain M. Banks
In fact it was open book, open note, open teacher. You could go ask the teacher for help. He wouldn't give you the answer, but he'd help steer you on the right course. I learned more in that class than in any other. Now of course people are quick to say "No you didn't, you just liked it because it was easy." Actually it was not easy, but my appreciation for how much I'd learned came not from that class, but after.
So first thing to understand is that I'm good at math, but not stellar. I was never the stereotypical "Better than everyone at math and loving it," geek. I did well, got to advanced (but not advanced placement) math classes, usually got Bs and As and so on, but I was no super math whiz, and while I didn't hate it, I didn't really like it that much.
It was a precalc class, taken my senior year of high school. So in university I started in Calc 1 as you'd expect. At the beginning of the second class, the teacher gave us a precalc test. It was to be fully graded, though not counted. He said he was doing this first to get a feeling for how much precalc he needed to cover since it often got taught wrong, and also to help people who might not be ready for Calc 1. If you bombed the test he didn't kick you out, but suggested that you might wish to transfer to precalc since it was unlikely you'd do well.
I just aced that test, near 100%, by far the highest score in the class. He came up and asked me where Id' learned precalc, since it was so rare to find someone with such a solid knowledge of it.
Never before or since had I learned so much in a math class, and he allowed calculators, the book, any notes, and asking him questions. The tests were about learning how to do the math, how it worked, not about making sure you could do the fiddly stuff in your head.