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 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!
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.
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.
You are welcome on my lawn.
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.
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).
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!
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.
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.
"Empathise with stupidity, and you're halfway to thinking like an idiot." - Iain M. Banks
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).