Are Graphical Calculators Pointless? 636
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?'"
Size; runtime, harder to cheat (Score:2, Insightful)
They're small enough to be pocket portable ( smart phones could handle that , but awkward to type on to me
My ti-83 lasts forever on a battery set of easily replaced AA's
while it's not impossible to cheat; it is a lot harder to slip in hidden notes in a calculator.
Really, I thought the question is... (Score:5, Insightful)
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)
Oh please, this comes up every six months (Score:5, Insightful)
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.
Re:Obvious (Score:4, Insightful)
Personally, I think as far as math education should go, the more crippled, the better. The most advanced calculators make kids dependent on them when learning. Let's let them use calculators that can only give them the most basic info like a replacement for Trig tables or for basic calculation. Anything more and the kids will learn more about the calculator and less about the subject.
Re:Obvious (Score:2, Insightful)
I've always had the philosophy that you should take it one further and skip calculators altogether in math class. For harder K-12 math, there's no real calculations involved, just express your answer without evaluating the actual value of the square root of 5 or pi or sin(3), etc. Students shouldn't need any help doing basic arithmetic. Which is why they shouldn't need calculators for easier math either (if they need them, they deserve to fail). For classes in physics or chemistry, basic calculators should be acceptable since in those classes you're generally more concerned with the numerical answer.
Re:Obvious (Score:5, Insightful)
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 (Score:3, Insightful)
Honestly, the real reason for the demand for crippled technology is the idiocy and cluelessness of high school maths teachers. What's the problem with writing a TI-BASIC program to solve a formula?
When I was in high school (the mid-late 90's), the first thing I did when I understood a formula was to write a program on my calculator to solve it. (I did the same thing on my Debian box at home, but in C, just to make sure I wasn't being retardedized by BASIC). This was before the days of 'wipe your calculator before the test', so of course, I would use my program; I was here to learn math, not to repeatedly perform rote computation, right?
Wrong, evidently. I lost points on my exams for 'not showing my work', even though I included my code (which my teachers couldn't understand, apparently). Luckily, my mother got it. She went to every parent-teacher conference to defend my use of programming rather than repetitive, boring computation. The teachers argued, 'Well, if he just wrote a program, how do I know he understood the math.' She just looked at them. 'Really? How could he write a program without understanding the math?'
Eventually, it came down to, 'He has to show his work, that's the stupid rule because I'm a big stupid-head.' Luckily, I discovered this trick [xkcd.com] before the xkcd comic made it blatant.
In hindsight, it's not so bad. Today I'm a programmer, and I make more than twice what my idiot math teachers made, and probably have more fun doing it.
In other news, Conrad Wolfram agrees with me 100% [ted.com]. And I trust Stephen Wolfram's son over my high school math teachers any day of the week.
Re:Obvious (Score:5, Insightful)
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:Another viewpoint on calculators and exams... (Score:4, Insightful)
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.
Re:Obvious (Score:5, Insightful)
Because writing a fairly complicated program with the described functionality requires all of the skills, and more, involved in the proof of the quadratic formula (which is an especially trivial proof if you already know the formula). It's objectively more useful to learn, because it requires the same skills and other skills as well, not just differently useful (requiring different skills of unrelated application).
Re:Obvious (Score:5, Insightful)
In the real world, cheating would be called "collaboration".
Why, yes indeed. I worked in industry for many years, and I can tell you that no workers were more highly valued than those who were unable to do even the simplest things by themselves. "Let's collaborate!" they would say, and our hearts warmed instantly and we leapt into action, "helping" our valued coworkers, doing their work for them. In contrast, those with highly valuable skillsets, able to quickly solve difficult problems, those were as dirt to us. "Be off with you!" we'd cry, "and never dare to cross our path again!" Yes, as sweatyboatman says, nothing is more valuable in the real world than incompetence!
Re:Obvious (Score:4, Insightful)
Knowing WHAT formula to use is key.
Partial credit for an incomplete answer.
Knowing what formula, what it means, what assumptions it requires, and what limitations it has, is key. That means memorizing its details.
Simply programming the solution into your calculator doesn't teach you anything but what the formula is. It doesn't demonstrate any knowledge of when/why/how to use the formula.
It's the same level of knowledge that has a student saying the answer to a problem is "1" when he uses an RPN calculator. He had the formula written down in front of him, but wasn't smart enough to realize the vastly wrong answer when he thought he was using it correctly. (He pressed an additional ENTER and wound up dividing one number by itself.) This problem dealt with the concentration of hydrogen ions in a buffer solution, and it should have been obvious that '1' was a completely ridiculous answer. (The real answer was around 10e-6.)
Except you get out in the real world and the last thing you want is your engineer pulling formulae from their (faulty) memory when they are already available in the computers they will be using.
No, the last thing you want is your engineer picking an equation to use because it looks like it might apply and it has been programmed into the computer for him. The correct problem solving method means knowing the problem to be solved first and then solving it, not picking from a list of problems that have already been solved and reproducing it.
Calling these calculators "crippled" is wrong. They are limited in function, deliberately. (car analogy) It is like calling a VW bug "crippled" because it isn't doing the job of a 1/4 ton pickup truck. (/car analogy).
They are smaller, cheaper and lighter than a computer (even a netbook, and much cheaper than an iPad). They are harder to use to cheat, and unfortunately, that is an issue that makes them better for classwork than those full computers with fancy software. They are just the right level to remove the tedium of doing basic math (which should have been mastered by now) while leaving the requirement to think through the problem to know what basic math needs to be applied.
Re:Obvious (Score:4, Insightful)
Wow, it would have been at least marginally clever if he'd claimed Zemblan diplomatic immunity...
One might point your student to Laughter in the Dark: you know, the Nabokov novel about the dilettante who's self-satisfaction and self-deception are his undoing.
Standardize the calculators (Score:4, Insightful)
Re:Obvious (Score:5, Insightful)
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.
I think you are missing the point (Score:3, Insightful)
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.
Re:Missing the point of math... (Score:5, Insightful)
It's never about critical thinking. It's never about solving real life problems. It's always about passing the next test or quiz.
And, again, you miss the point. I apologize if I didn't make that clear. It's not about directly solving real life problems. It's about learning the STYLE AND WAY OF THINKING LOGICALLY in order to solve real life problems.
The way math classes make you do this is by doing math problems, because math problems can only be solved by logical thinking and a logical application of mathematical properties. Doing this again and again, building in complexity over the years, doesn't just teach you to solve math problems, it teaches you HOW TO THINK about any problem. Just like muscular exercise builds up muscles that are used repetitively for some task that you want to be stronger at doing, the kinds of problems you do in math are brain exercises that build up, through repetitive use, the pathways that are useful for logical thinking.
I'm sorry if your teachers didn't make this explicitly clear to you. A lot of teachers don't. I, for one, do explain this to my students, because I understand very well that the level of math we are doing is not very interesting, the types of problems we solve with it are very contrived and not realistic (because the math required to solve "real" problems is way beyond these basics, but you must master the basics if you want to learn to do the advanced stuff), and a lot of the actual things we do in class are not very applicable themselves in real life. For most people, math is not exciting or interesting. But learning it gives the gifts of clear and logical thinking and the ability for sustained chains of reasoning.
I'm sure not many of my students get this, even though I have explained it to them, but that's simply a product of them being young and inexperienced with the world. If even a few of them come out of this class as clearer, more rational thinkers, then I've done my job well.
Re:Obvious (Score:5, Insightful)
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).
Re:Missing the point of math... (Score:4, Insightful)
It's not the logic of solving problems you should be teaching. Anyone can do that, easily, with or without math. We call them arts grads. It's the quantitative analysis that's important. Ok so you aren't using the quadratic formula in your love life. It's the wrong tool. A statistical analysis of activities engaged in, money invested, the probability of loss due to breakup etc. are all very legitimate mathematical tools in to assess the risk/rewards involved in any relationship. Moreover you need to be confident in the validity of the tools you use to solve a problem. Take something simple, like choosing the specific shade of blue in the google logo, or the background on your corporate letterhead. Now, you can use a 'logical' approach, and feel good about appropriate contrast or the 'tone' the colour conveys. Or you can use survey people (how many is significant?), quantize the various options (how do you quantize them?), and view it as an optimization problem to pick the the optimal colour for the problem you are solving. The latter is the correct (if somewhat expensive) way to choose, the former is what you have arts majors for. If you are a 5 person company, the arts major approach is all fine and good. If you are nokia, google or IBM you damn well better have some actual analysis behind your choice of what font to use, what colour to use etc. because even subtle variations effect perception of your brand, and when you're a company worth 10's of billions of dollars, fractional percent shifts in the value of your brand equate to millions of dollars.
Most of what we learned in math, that seemed basically useless to everyone who wasn't going to be an engineer or a physicist (I was originally a physicist), ended up 15 years later hitting me in the head as a game developer. Quantitatively defining fun, defining the world all of those things are both mathy, and require a lot formal proofs of either correctness or at least derivations of whatever it is you're trying to solve. Computers simulate the world through math, and mathematical approximation, so by extension any field which requires computer models necessarily relies on math to build those tools accurately. The better you are at math, the better the models will be. If you want them to be fast, have good cache hit ratios, minimize memory use, etc. then you can come to a computer scientist. I note that I'm really a developer, not a designer. The designers come up with all these ideas on what would be fun, and I have to find a way to analytically assess them. Is this UI placement better or worse than that one? Is this area too hard or too easy? Solving those problems regularly requires derivations and proofs, and the developers have to come up with them themselves (they aren't just in a book somewhere I can look up), well ok, some tools are in books. But most of them are situational at best.
Do I use the quadratic formula? Not so much at the moment. Do I use its proof and derivation on a regular basis, absolutely. I'm working with a hex grid pathfinding algorithm, and I work with some curvalinear coordinate systems (not all of which are your standard spherical or cylindrical) to attach visual effects to various things. Not far off from where I thought I'd be 15 years ago (hex grids were all the rage in the 90's wargaming scene).
Applying numbers to real problems, either for simulator or for actual analysis, whether its' physical simulation or finance or the like, developing and understanding what your toolkit is, how to use it, and where it will fail is the point of teaching math. If your goal is a 'logical approach to problem solving' you're either on a course for people who won't ever be capable of using math to solve problems, or you're doing it wrong. How do you quantize it, how do you analyse it, how do you prove that your answer is optimal, or if it is intractably hard to optimize it, how efficient is it, and what approximations did you take to get here?
Re:Obvious (Score:4, Insightful)
With THIS you have grasped what many people just fail to see. Intuition should become part of every learning in life. I have a friend who has gotten nothing but high distinctions throughout her entire engineering degree. She is a mathematical genius. You drop a circuit in front of her she can solve all the steady state values in a minute, she can also quickly give you any gain or AC analysis.
But she can't grasp what a circuit does. If you put a drawing of an amplifier with some reactive components in the feedback loop in front of her she can't simply come out and say low pass or high pass. Put a powersupply circuit and she won't within a second answer if it's a buck or boost, if the capacitor is used to smooth output ripple, etc.
People miss this fundamental learning in all degrees. So you know how to write a quick sort, good for you, so do I with 2seconds of googling. But do you know when to use the quicksort on a dataset instantly and intuitively without googling for "What is the best sorting algorithm?"
Details can always be worked out or looked up. Conceptual vision and intuition however are the lifeblood of most professions, and people often miss this part about rote learning.