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.
The only point I ever saw for them was the coolness factor. That was back in the 1980s, though. With today's tech, a dedicated calculator seems... at best, quaint.
When our name is on the back of your car, we're behind you all the way!
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.
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...
Glad I sold my 92 when I did.
Without music, life would be a mistake. --- Nietzsche
TI Calculators
How is this even a serious question? One point alone: a calculator's batteries last a HELL of a lot longer than a netbook's, even with very heavy use (we're talking months vs. hours).
But going further, a calculator is also a lot smaller and lighter than a netbook. There's nothing "crippled" about a graphing calculator (personally, I've worked through statistical analysis in my laboratory classes using my TI-83+ MUCH faster than my peers using a copy of Mathematica on laptops, but I know how to use the damn thing because I read the manual cover to cover).
Smells like flamebait, or somebody who hasn't actually used one of these devices.
You could ask instead: " Why do we allow automated calculating devices at all?"
But let's get real. The point is to let the student demonstrate that they understand
the (higher-level) concepts that are really being tested. The test is about "Do you
know how to determine X" (load on beam, area under curve), not about "can you multiply
100*pi^2), and not about "can you look up this on the internet".
There is a generation of scientisits that doesnt know how to use anything but them
I used to work in a company, with scientists aged 45 and above, they had linux clusters, powerful desktops with the latest software, but in the office, there HAS TO BE a scientific calculator lying on the desk somewhere.
Companies realize that there is still a minor need, and produces for that need accordingly.
But i assume that this will disappear.
The lunatic is in my head
To further the greed, even if they aren't getting kickbacks to increase sales of one line of calculators, they have no incentive to keep up with the tech and rewrite the books.Once they write one book, all they have to do to newer editions is charge the order that the problems are printed in. So its the same book, but different enough to force people to buy the new edition.
Do you really want students to have internet access during a test? I know how to solve a system of equations by hand (by reducing a matrix into RREF) but my Physics teacher and Mechanics teacher both lets us use a calculator to solve them on a test to save time. Are you saying they should let me use a computer that may or may not have an aircard (i.e. internet)?
The bigger concern is crippled calculators, who can't add or make change without electronic help.
Or you can just download the graphing calculator app for your smart phone.
.99
They only cost
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'Why are we teaching a generation of students to use crippled technology?'" Because we don't really want them using advanced technology on the exam in the first place. We want them to know the theory. Graphing calculators have limited uses (in my university, it is almost never actually useful) so they still require some thought before using them to solve a question. Advanced technology is advanced enough to solve problems without the student needing to know the theory in the first place, and advanced enough for teachers to not know how to shut off that functionality. That's all.
"...'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?'"
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? And no, I'm not talking about "show your work" when solving for seriously complex calculations, I'm talking about what 95% of high school students are "taught" and yet the system allows them to pass through with flying colors due to massive hardware "grants" from Texas Instruments.
Go ahead, take the calculator away for a week and see how much the average student has really learned.
we're teaching them concepts
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!
Seems to me a similar story was posted not too long ago. Summary of the discussion: graphical calculators serve as an anti-cheating tool, as they cannot be programmed, except that they can be programmed if you're smart enough, and therefore actually serve no purpose. The only practical solution seemed to be providing students with a school owned graphic calculator at the beginning of the test (thus taking away any opportunity to pre-program the calculator).
Our lumbering education system is slowly moving away from 'knowledge based education' to 'skills based education'. However, it will take a long time before the old-fashioned diehards retire and make room for some new thinkers.
I understand the difference between an emeritus professor, and a Wiki-expert, but outside my own field of expertise, why would I need to be anything more than a Wiki-expert?
Personally, I am excited about the prospect of having a plug in the back of my neck, and the opportunity to have large portions of my memory uploaded to the cloud. Leave me with my personal life experiences, and my core skills, and take the rest.
We are the borg. Prepare to be assimilated.
You heard it here first, folks. Teaching students to use anything but the latest netbooks or tablet is doing them a disservice, as no doubt once they enter the real world where all equipment is replaced every 3 years they will have no need of any skills beyond using voice control to ask Google Calculator to do unit conversions.
It's a digital device, unless the software and the hardware are married just right, the calculations are going to be off. Remember how hard it was to get basic math right in C, and it's significantly harder to do the higher level mathematics in a robust handheld form. I routinely use my trusty 83 to double check various calculations, and there is something to be said for having a single use instrument that performs without error.
...I used was a TI83 that I had to purchase for a math class when in college. I cost me almost 2 months of wages as a part-time student. I ended up selling it back to the bookstore when the class was over at more than 60% loss. Turned out we didn't use it for more than few stupid graphs of no value or relevance to real life, my education, of my future growth.
I remember that not purchasing it would have fed me for a month.
I've been so bitter about the experience that all along hoped that all graphical calculators would die a slow and painful death.
Speaking of which, looks like you can get the same experience on your phone: http://www.appcylon.com/
At least I was born with the wheel already invented.
I sit at my desk with 2x 24" monitors, Mathcad, matlab and maple, yet sometimes when I want to do certain things (simple arithmetic and symbolic calculus are the most typical items) I still reach for my TI-89.... some things are just faster on the calculator....
and I agree I wouldn't trust most of my classmates to have a full computer during a test.... but in electrical engineering if the tests can be done without a calculator then they aren't hard enough....
on a PC I could have every example and problem in the book done in a mathcad sheet and just do whatever slight alterations are needed to solve the problem... if the problem is so hard that you can't alter an example or problem from the book to complete it then 99.5% of the people would fail.
'Why are we teaching a generation of students to use crippled technology?'"
I was under the assumption that tests weren't about how good you were with technology or how quickly efficiently you could use technology to find/give you the answer, but rather that they were about being able to determine how well a student grasps the concepts, facts, and functions of the matter on which they are being tested. I thought these tests were supposed to be about the student, not about the technology.
The only thing necessary for evil to triumph is for it to be pitted against a slightly greater evil
One big reason to retain all of the simple tools, there is no interaction with the rest of the world, leaving more trust than any connected application or system would ever legitimately engender.
Why should a calculator need connectivity? These items were prevalent when products were completed prior to coming to market. There was no need for updates on 99% of finished products. There was no need for ads to be brought in, taking away value and usage time. There was no collection of personal information or usage data. They cannot be taken over from far away.
The same reason popcorn costs a fortune at the theatre. Artificial demand / scarcity, you can't bring in your own popcorn. And that had better be a TI-xx or you can't bring it in, either. No phones or laptops during the test, plz.
Pretty decent racket TI worked out with schools, I guess. I always preferred HP calcs anyway. RPN or death.
I really don't understand why those things are used! The only time I ever "needed" a graphing calculator was in high school. In college, not a single math class allowed calculators, at all. Even the calculus courses! The only thing I ever used my TI-83P for was loading it up with equations (in the notepad app) for physics. And in physics, the hard part is knowing which equation to solve given the problem, not how to do math. Most of the time we were allowed cheat sheets anyways. These things are useless. I would've posted the xkcd comic, but someone else beat me to it.
Why are we paying $100+ dollars for a device that performs on the level of a 2001 smartphone?
I'd imagine that most schools won't allow a person to bring a Netbook in school in place of a graphics calculator. Especially during a test.
That said one can't use a smarphone on a test. That is why over the past 10 years calculators have no been designed for he professional, but for the testing companies. Pro features are removed to make it acceptable for the standardized test. Ad copy basically focuses on this. I believe the TI nspire even has an interchanabled keyboard that limit functionality so it can be used on tests.
I don't see any reason to teach the calculator other than it is a necessary test taking skill. As long as the public gives credence to the AP exam, as long as states believe calculators are more important than basic skills, as long as calculator manufactures pay politicians to require calculators in the classroom, we will have them. OTOH, it is much more likely to get a kid o use a calculator to do work, rather than a computer where they go off and play WOW.
"She's a scientist and a lesbian. She's not going to let it slide." Orphan Black
I haven't run any exact tests, but I've gotten a TI-83+ running on solar panels, in full sunlight, rated at 6V, 100 mA (600 mW). I also have an Eee PC 701 that consumes roughly 26 watts of power when it runs directly off the wall charger. I'm not sure how efficient today's netbooks are, but that's a big difference.
priced like the textbook market and much like the old textbook system they are old fashion but are still uses and are very over priced.
I always ask myself why sometimes professors say "NO GRAPHING CALCULATORS". Okay...great, thanks. I understand. But why the hell are we being forced to downgrade our use of technology, and why can't you make questions in such a way so as to prevent (the large majority) of us from easily using the graphing calculator to find the answer?
'Why are we teaching a generation of students to use crippled technology?'
For the same reason it's good to teach your children good penmanship: you don't always have a computer around to do the work for you.
It's a standardised, task-specific device that costs half of the alternative suggested. This matters to schools and students (/parents). You can teach all kids in the class the same process, focusing on the math more than the device by having one universally required make and model of device. Also, the students can use it during exams with a lesser fear of cheating. This submission is just stupid.
In the early 90s I made my way through a pretty high power engineering program with just a simple "scientific" calculator. You want plots, bring colored pencils and DRAW them, punk.
There's no need for graphing calculators - they're for parents who think buying encyclopedias makes their kid smart.
I want to delete my account but Slashdot doesn't allow it.
I teach physics for a living. Different profs run their courses in different ways, but personally I feel that memorization is evil, so I give open-notes exams. Therefore I don't really care whether students use graphing calculators that can store all their equations for them. To me, the bigger issue is preventing students from accessing internet and cell networks. I don't want them communicating with someone outside the room who will help them on the exam. This is why I let them use a calculator on an exam but not a netbook. Outside the context of a test at school, my opinion is that graphical calculators are pointless because their price lies in between the price of a $10 calculator and a $600 netbook, but they are no more useful than a $10 calculator.
Find free books.
> 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.
Looks like you answered your own question. They're cheaper than anything else. Not everyone can afford a laptop.
Anyway, do you really think we're teaching a generation of students to use "crippled" technology? If there's anything the Y & Millenial generations have taught us, it's that young people catch on to new technology faster than everyone else. We're not teaching them anything about technology that they can't learn or un-learn on their own.
When I was in high school not that long ago, the graphing calculator was an integral part of the calculus curriculum. Back in '96, even the cheapest desktops were often beyond the pocketbook of my classmates, to say nothing of net/notebooks. I am unsure of the current pedagogic inclinations in math education, but others seem to be chiming in on this thread and at least a few are saying it is still important in the classroom. Beyond high school, however, my personal experience has been that HP graphic calculators were highly sought after in engineering circles. Those I've conversed with on the subject regarded the utility and power of those tools very highly - even the antiques still available on ebay. I guess if a tool is sufficiently well developed, it can be maximized to its full potential by any experienced user.
Stay sentient. Don't drink bad milk.
What is the probability you'd be in a situation professionally where you had enough time to boot up a laptop, install the relevant software, assume you already know how to use it, and do something productive with it and not get fired?
Solving simple differential equations or linear algebra in a pinch is exactly why I keep my calculator. The same calculator I used in school many moons ago. I've used Matlab and Mathematica, and can be moderately productive with them. But I'll always stick to my trust TI-89 for its utility and consistently error-free operation.
For me its the same thing as having a PC instead of a TV. Yeah, it works. But the startup cost (in time) and maintenance is non-negligible.
What are you people talking about? Graphing calculators are far quicker for most math problems *because* they are dedicated devices. Having a dedicated keyboard and character set just for mathematics means that functionality is quicker and easier to access. I refuse to do physics without my TI-86 on hand, although I'll admit the TI-89 that I use for most calculations can be frustrating at times. The NSpire series does seem a little dumbed down (I've never used one, though), so maybe a computer would be preferable to one of those devices.
I need the download code I faxed to doctor allcome
The only point I ever saw for them was the coolness factor. That was back in the 1980s, though. With today's tech, a dedicated calculator seems... at best, quaint.
OK, as the publisher of an iPhone calculator (Perpenso Calc RPN, 5 modes: Scientific Stats Business Hex Bill) I may be biased, but apps will eventually displace handhelds. It is just part of digital convergence, we will ultimately only be carrying around a single pocket sized electronic device.
Regarding web access during tests, things like "airplane mode" where all the wireless circuitry is disabled will do. It will take time for teachers/professors to catch up but a few years ago I had professors who were letting us use laptops with the caveat that wireless be disabled.
Math should not be taught with calculators, since calculators are simply tools to do math more quickly - once you already understand what's going on.
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?'"
The real question is - "Why aren't we teaching students to better understand by graphing themselves, rather than relying on a machine?"
Granted, it's a lot easier to use a machine to graph than going through the drudgery of drawing the graphs; but slogging through graphing is part of developing not just an understanding of the process, but a feel for the answer so you can recognize one that isn't right and look for your data entry errors.
I graded papers or engineering classes and would get (wrong) answers to 8 decimal points. After a while i felt like writing in big bold letters "DO YOU REALLY BELIEVE THIS ANSWER? BECAUSE IF YOU DO YOU NEED TO FIND A DIFFERENT COURSE OF STUDY!!!!"
An important part of math is getting a feel for the answer and about what it should be so you can recognize the odd ones and look to see if you made a mistake. Technology, while grand, often acts as crutch and people blindly believe it.
Of course, there's nothing like a sales clerk getting a price of one cent after discount and proceeding to explain it must be right because the register said so. Or staring blankly at you after ringing up $10.00 for a $5.05 and you hand them a nickel and the insist they can take it and give you a $5 bill back "because the register thinks I put in a ten." Oh well....
NoW, GET OFF MY LAWN!
I'm a consultant - I convert gibberish into cash-flow.
Your point is well made. Why use crippled hardware and software to teach mathematics? Why not teach higher level concepts with computers to 100 level students? The counter argument is that the student needs to work out the solution using algebra, theorems, and proofs, and the student needs to conceptualize the curve of the graph in general terms before tackling the problem. Often the software does not give exact or correct answers to a difficult problem, and it does not always show you the steps that it followed to get the solution. Until we get to the point of having decent software, teachers and engineers won't accept lame software.
Overpriced? Yes. But I don't think we should push for high school students to use devices with the power and modifiability of netbooks to replace what they're currently using graphing calculators to accomplish. When I was in high school, students spent enough time in class playing the handful of games that shipped with their TI-83/4's (or obtained them from a friend) that adding more opportunities for distraction isn't ultimately desirable for keeping attention in class and preventing cheating on exams. Sure, some people will always be looking for a means to distract themselves, but that's not an excuse to encourage it. I also found that most students (in general secondary school math/ science classes) had enough trouble learning anything beyond the basic functionalities of the devices that throwing many times more options on them wouldn't really add too much to their learning experience. A root issue was, of course, that the teachers often didn't know too much about the calculators' functionality themselves, and as such didn't effectively teach much beyond the basics. In many (if not most) of the type of classes that are required to use these calculators, the teaching emphasis is more on learning the mathematical concepts, not learning to use a device that will do it for you with greater efficiency. For the self-motivated students who are going to take advantage of what capabilities their devices have, a simpler device offers an easier learning curve and quicker route to mastery. One who is interested enough to learn most of a standard graphing calculator's functionality will most likely move on to expand that knowledge with full-fledged devices and software. An example, I had no exposure to programming as a child (as well as fairly limited internet exposure) and the BASIC language on my TI calculator was the first language I learned. It's simplicity left me wanting to do much more, and I went from there to assembly for the z80 architecture of my calc, and from there on to Java/ C++ and beyond. tl;dr - Calculators should be reduced (substantially) in price, but are primarily used by the average student, not a future mathematician/ scientist. Those who need more functionality will move on to it and won't be overwhelmed by an exhaustive feature/ functionality list at a younger age.
Pocket calculators are responsible for at least two generations of innumerate kids already. Netbooks with math software won't solve that problem in the future. There is no royal road to geometry, calculus, or arithmetic.
Not everyone likes to use a computer for everything. Sometimes having a small dedicated device that does one thing very very well is better than having an all in one solution that does everything. I will take my ti-92 and 83 before i lug around a netbook,a case and a power chord.
but it raises the question: 'Why are we teaching a generation of students to use crippled technology?'"
And the proposed alternative? Raise a generation of kids who can't do calculus by hand? Derivatives and Integrals and limits just come out of the magic computer box?
As it is, kids get no technology to learn elementary mathematics / arithmetic.
They get basic calculators in high school while they are learning algebra and trig and pre-calculus to do the grunt arithmetic. They get basic calculators once they know how to do what the calculators can do.
They get graphing calculators in college/university while they are learning calculus, differential equations and beyond to do the grunt algebra, trig, and arithmetic. They get graphing calculators once they know how to do what the graphing calculators can do.
Then they get computers, and they can use them to tackle advanced mathematics. And the math the computer does for them isn't magic box. They could do it themselves in principle, although they recognize that it would take man-lifetimes to do some of what they are asking it to do.
I think understanding what the tool is doing is crucial. A child being raised to farm should know how the earth should look when its turned properly, how much seed to distribute to an area, how much water is needed, what to harvest, when to harvest it, and how etc. He doesn't need wander around the yard with a scythe, or push a plow with oxen but he if you want to test that he knows these things you you can't give him a push button FarmingComputer9000 either with a buttons for "plow field", "plant seed", "irrigate", "harvest". That child may be able to operate the FarmingComputer9000... but he hasn't got a clue how to farm.
My TI-whatever had like 500 bytes of memory, and I could cram so many physics, economics, or statistics formulas into that space. Which begs the question of why I ever had to "memorize" any of that, since now I just look up whatever I need to use.
Godaddy is a scam and a ripoff.
Last year, for my birthday, I bought myself an old Sharp PCE-500 pocket computer. I love doing math on this thing. It remembers all the variables. It runs for over 40 hours on a set of batteries. It has an algaberic expression mode, but the main reason while I like it: The Keyboard; having a real scientific keyboard at your fingertips makes everything faster and easier than trying to make do with a laptop or desktop keyboard.
What am I to do when this thing dies?
https://www.youtube.com/c/BrendaEM
(First off, this is hardly news for nerds or stuff that matters, but...)
These devices have a very good place at a certain point in a child's learning experience. General purpose computing devices and more complex programs have their place on down the road, but at times when students are learning principles of algebra, geometry, and trigonometry, these devices provide a limited subset of functionality that focuses on the lessons at hand. Often the curriculum focus on teaching the principle, then teaching how to perform computations with the tool (the graphic calculator), and then combining the route knowledge of the tool with real-world or problem-solving applications. These types of scenarios are well suited for limited devices because most students don't yet have a complete cognitive framework to appreciate or use more complex modeling tools.
The question seems written from the point of view of a high school senior or college math student, where the utility of a simple graphing calculator is far less and may be more of a hindrance. It's important to note that not all students are part of the same audience for this type of technology.
I love my TI-81 that I've had since high school. I'm an engineer by day, and having a really fast way to calculate long formulas is incredibly handy. I almost never use the graphing functions anymore, but I love the 6 line display, the storage features, and the awesome ANS button. Oh yeah, and I've got the locations of all the function keys dedicated to muscle memory, so I can burn through equations so fast.
Computers are better for some things - I'm a regular user of Scilab and R, and they are both way better platforms on an actual computer. However, for run of the mill trig or arithmetic, a solid calculator still cannot be beat. Maybe the interesting question to ask is why aren't people selling sweet, multi-line calculators with multiple storage and scientific functions, just sans the graphing functions? I'd buy one of those in a heartbeat!
With a graphing calculate I can take it out, hit the "On" button, enter an equation, and get an answer very quickly. No need to boot up a computer, launch an application, etc. The battery life on a calculator is also and order of magnitude better. A graphing calculator is wayyyy less distracting. Yes they have drug wars...but they don't have facebook, /., and the other countless distractions that a netbook would provide. Lastly, 99.999999% of people will never need the tools on a graphic calculator OR the ones you described. Most peoples lives do not involve solving complex equations on a regular basis, if ever. So who cares if it is antiquated technology.
People say the same thing about tablets. You CAN get a cheaper device to do X. But Y is better suited for it.
I can code up a storm in Matlab. But if I need a 'back of the napkin' calculation. My TI-89 is there. Yes, it has made me a 'lazy engineer' because I don't care about units. I just put them in and let it deal with it. I've coded multi-hundred line applications using nothing but the TI-89's keyboards; I can probably type faster on its keyboard than most people can Text.
It fits in my backpack and if I need, a coat or sweatshirt pocket.
The battery life is measured in months. Not weeks, days or hours. You don't always need the power of Matlab.
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Yes. I know how to do it all by hand. I passed everything up through DE 2 without one. But like with most things, why recreate the wheel. I just need a short quick fast calculation. The TI-89 does it.
The only thing that pisses me off is the XKCD which is linked a few times. The speed, resolution and memory of a calculator is WAY behind the times. It took them until 2004 to add a USB port insisting on their 2.5mm plug format.
Some math exams are quite difficult as they are without calculators, such as the William Lowell Putnam competition, or even any of the American Mathematics Competitions (AMC, including AIME and USAMO). The existence of these exams proves the fact that, unless the purpose of an examination is to test one's ability to use such computational devices, there is no intrinsic reason why calculators should ever be REQUIRED for an exam.
The truth is, it takes work on the part of the test designer (often, the instructor) to write questions that are intended to test concepts in a way that do not require a computational aid. And educational publishers collude with the manufacturers of calculators to provide teaching materials that assume the possession and use of said calculators. So teachers, faced with the choice of a pre-approved, ready-made curriculum, versus having to design their own exams and fight for approval by bureaucratic school boards--assuming they even have the intellectual capacity to write their own material--choose the former. It is, again, the political and economic influence of large, powerful corporations dictating how math is taught, that is the reason why we push this crappy, overpriced technology on kids.
Now, that's not to say calculators don't have their uses. They absolutely do, but if the pedagogical goal is to show students how to use technology, then examinations must be written in a way that leverages, rather than inhibits, its use. Otherwise, it is entirely possible to construct exams in a way that require nothing except a pencil, paper, and a brain.
'Why are we teaching a generation of students to use crippled technology?'
Math courses should teach math, not technology. It takes work to develop mathematical understanding and intuition. How long does it take to teach someone to input a formula into a calculator and spit out the answer? That can be taught very quickly, preferably after the student already understands the underlying math.
Many (most?) people today don't need to know integrals or derivatives in their everyday lives. But as an engineering student, I often found myself wishing I'd spent more time learning and understanding the fundamentals. Instead, I used my calculator to produce answers quickly and spent the rest of my time playing Mario on my TI-89.
Is calculating a trajectory for his knife into your throat right now.
Teachers are lazy. They expect students to come up with original un-plagiarized answers to test questions the teacher/professor hasn't updated in 20 years and probably copied wholesale from a textbook somewhere. If you really want original answers, come up with some original questions.
There is no point to them; it just illustrates our very backward way of teaching math in schools. We need to stop teaching students "calculation" (memorizing formulas, remembering how to solve various types of integrals, etc) -- something computers are extremely good at, and instead teach students how to translate real world problems into equations that computers can calculate, and then how to interpret a computer's answers. These skills are far more important, and computers DON'T give you much of an advantage in these areas.
Conrad Wolfram (brother of Stephen Wolfram, of Wolfram Research Mathematica) did a great TED talk about this very subject.
mod up!
Why can students use a calculator on a test to begin with? And a graphing calculator!? Then you're just testing how well they can use the calculator - no wonder Americans suck at math.
You can't beat the user interface of a calculator though. It just turns on instantly, you don't have to stumble around with a mouse to activate the calculator program, the keys are all placed in a predictable location so that you don't even have to look when you punch in numbers.
Graphing Calculators can be used in high Stakes tests, Computers can't.
The HP-48 and TI-85 were a good value 15 years ago. Now they are nice, but way overpriced. Seriously, the old HP scientific calculators used to be really expensive. Now you can get a decent scientific calculator for $10-15. Why isn't the same true of graphing calculators?
I appreciate the value of purpose-built devices, and agree that a real calculator is nicer to use than software on a phone. But that is not why those calculators cost so much. They charge that just because they can, because it is a captive market.
Worse, there is no middle ground. I really don't need a graphing calculator; if I am doing graphing it is easier to bust out Matlab. On the other-hand, simple scientific calculators are more limiting than I would like. It'd be nice to have an calculator with a multiline display and plenty of memory for variables/stack, maybe with the ability to program commonly used functions, and preferably with an RPN option. In other words something on par with the HP-28, but in a more standard form factor. There really isn't anything out there like that though.
and a pencil sharpener for those number 2 pencils
There was probably a two year period -- late Junior year of high school through first semester of Engineering in college -- where a graphing calculator was kind of useful. Most tests didn't require anything more than an ordinary calculator (if even that). They were generally only concerned with one of the following at a time: 1) your ability to reason (you would prove/demonstrate something basic), 2) your ability to remember the general relationships (you just remember the formulas, the numbers will be ridged to make calculation easy), or your ability to actually set up and do the calculation (you can bring in a sheet of notes, or else a pre-printed note sheet would be given to everyone).
There were some matrix and differential equations you could do, but for the most part it was as easy to solve them by hand as enter them into a calculator. You were being tested on the setup more than the answer itself. Even the differential equations class with the elective Maple/Matlab/Mathematica component to it didn't really demand a graphing calculator for the paper exams. The ability to set up a problem on even an advanced calculator is a minor, niche skill. You demonstrate mild proficiency, and if you ever need it again, it's not completely foreign to you. Otherwise, it serves little educational purpose. At the same time, there is not much benefit for non-STEM students learning specialized software. When they do, they learn something more domain-specific. Such as S as opposed to Matlab as opposed to Mathematica.
Love my HP 48sx and even my 15C. Tools, not toys.
For me, it's the fact that it's small, portable, and has a real keyboard.
If I have a bunch of numbers on paper to add up, I grab my HP-15C because I can set it right next to the paper, and I can use the keyboard to type the numbers on it much faster than doing it on my computer and having to look at the screen to compare with what's on the paper.
I have an RPN calculator on my smartphone, but it's not as usable as the calculator without a keyboard.
If I were doing graphics or anything more advanced, then I'd just use my computer. I have an old HP-48 which I never use because it's too complicated for anything non-trivial and for anything trivial, the HP-15C is better. When I bought it, it was great and I even wrote some programs to automate some tasks, but now it's much easier to use a real computer.
Let me be the first to say that the graphing calculators need to go. Mathematica etc. are infinitely more useful, informative, and powerful. Don't get me wrong - it's not that TI's aren't useful devices, but they've passed their prime. I grew up using a TI-82 for numerical and graphical stuff, with a hefty dose of doing stuff by hand - now I seem to use them just for quick number crunching.
Most universities have site license for two packages (sometimes more): either Mathematica or Maple, and Matlab (which is primarily numerical). I'd be astonished though if the high-school and down level had them (as they can be a bit pricey).
The one problem of course is that just like the calculators, computer software can be abused. I can only imagine getting printouts with special functions from calc1 students who have no idea what special functions are!
That said, I think scientific calculators are still useful for exam purposes (especially in physics/chemistry) and quick computation - but they're also cheap.
In school they still use pen and paper and learn about stuff thats on wikipedia. True story.
The question, in my mind, is why force children to learn, say, to compute arc length of parametric curves by hand. The concept is without doubt useful - but is the specific knowledge of the implementation critical? In fact, that might be a poor example - it has some thought and graphing correlation. Why force children, at the most basic calculus level, to memorize chain rule, product rule, tables of trigonometric identities? Why tie the concepts, with the specific implementation, particularly when in real world scenarios, most students (even engineers), will probably err on the side of computer aid in relatively simple mathematics.
Many of the above comments talked about cheating, and several mentioned mathematics at a level that, yes, could easily be solved without a calculator and probably should be. But above calculus one, where graphing calculators really begin to be "necessary", or at least widely used, is it truly that important, if we have a fool proof algorithm that a calculator or computer can do faster, easier, and with less mistakes, that someone who will not be reinventing mathematical formulas or questioning our perceptions thereof, memorize by rote the internal workings of the math they need to use? Particularly with the ease technology overcomes the issues, it can only cause students to resent the class, and indeed the subject as a whole -- which seems unfair, both to them and to the future.
The only functions I used that for that a regular calculator didn't have was to play games!
from 09 F9 11 02 9D 74 E3 5B D8 41 56 C5 63 56 88 C0
to 45 2F 6E 40 3C DF 10 71 4E 41 DF AA 25 7D 31 3F
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.
Calculators have one real use in a modern society, they are acceptable on many tests. This is why the calculator companies guard hacking them.
... if today is 1988 and you're a university freshman or highschool senior taking math and science courses.
Why is a generation of teachers insisting that students use crippled technology?
Very few people take math classes so they can go out and do more math, just like very few people take literature classes so they can go out and be literature experts. We take these classes so we'll have a base understanding of the process. Even students can figure this out quickly and know if they can just get through this horrible math class in any way possible they'll be able to move on to their real education. If it turns out they missed a few things along the way, the ability to learn and research on their own will provide the means to recapture the parts that turn out to be useful.
I have a TI-89 that I got for college Algebra in 2001--it's sitting in front of me as I write this. Lasts years on four AAA batteries, and let me do math fast, including the very useful dimensional analysis. My wife has a TI-83 that she uses for finances--the screen serves as a small paper-tape-esque display to let her see what she's doing. We love our TIs, since they do what they were designed to do, and they do it well and efficiently.
I've noticed that a lot of electronic devices designed to do specific things very well and efficiently can seem clunky and old-fashioned. I bought and installed a burglar alarm in my house in 2008--programmed from a numeric keypad with a 16*2 alpha display. But it does what it was designed to--sense a resistance change on a zone, reverse the polarity to the bells, and send a report out via the GSM modem. That doesn't require a 1024*768 color touchscreen or a 1 GHz processor--heck, the CPU's heatsink is about the size of a paper clip.
Through my entire math educational career (4 years of high school math, 6 semesters of college math, 2 PSATs, 1 SAT, 1 ACT, and 1 GRE), I progressed from a Casio scientific calculator to a TI-82 to a TI-89. Through 11 math teachers, TAs, and professors, only one demanded to inspect calculators and wipe them before allowing their use on exams--an extremely rude, highly ineffective, 50+%-failure-rate high-school math teacher who taught like it was 1971 and was somehow the math department head. I told her that she did not have permission to inspect the electronic contents of my calculator, thus forcing her to loan me a TI-82 from the school's arsenal.
I spent three years myself as a teacher--PC Support. While none of my exams ever required calculators, I had decided to myself that, should I ever find myself teaching a class where students bring calculators to the exam, I would not insist on wiping. If they can program their calculators (or even type notes into text files), they know what they're doing and deserve the fruits of their labor. Kind of like the students who bring in the one allowed page of notes for an exam and bring in an entire chapter scanned onto a page like microfiche.
I still have a fond memory from 1997. While taking Trig, another dinosaur math teacher (they were not in short supply) had a homework assignment: come to class with a list of 15 integer Pythagorean triples. A quick trip to QBASIC, I ran a from 0 to 100, nested b from 0 to 100, looked for integers, and sent the first 15 results to a text file. Prepended my name to the file, printed it, and appended the source code for good measure. Having fulfilled the assignment, she was forced to accept it, but she was nonetheless quite pissed off. I think that earned a phone call to my parents, who were by no means helicopter parents, but would have been in the principal's office if she had refused to accept the assignment out of spite.
I'm glad I made it through school before this idiocy of 'standard calculators' took hold and TI pushed HP out.
If they want to standardize on something, let them bring slide rules and/or a Curta. And stray off my lawn!
Have gnu, will travel.
I use my TI-89 all the time, including for non-school functions, so anti-cheating isn't the only reason to still use graphing calculators. When I'm working on a program, or looking at a graph, it's simply more convenient to use a small, hand held device rather than alt-tabbing to a calculator program. With the power of modern smart phones, I do agree with you that graphing calculators are on the way out. But we are not quite at that point yet. I haven't yet found an android program that includes all the functionality of the TI-89.
'Why are we teaching a generation of students to use crippled technology?'"
The same reason they made me use a slide ruler and log book and not use a calculator in exams. Cretins!
Yes. Let them use WolframAlpha and Wikipedia in their exams. It's not as if they will ever be required to do any thinking once they get out of school: why waste time developing useless skills?
Warning: this article may contain humor, sarcasm, parody, and perhaps even irony. Read at your own risk.
>> but it raises the question: 'Why are we teaching a generation of students to use crippled technology?'"
Well, we teach them to use their brains because that's all the best tool they have, as "crippled" as they might be! :-)
Even if you have notes you still have to work out the answers on your own.
These aren't so crippled. Back in my day as an undergraduate, you still used a slide rule.
As a current high school math student, I am on the “front lines” of this debate. My teacher teaches us to mash buttons, which I find boring. So I figure out how to do the same things in python on my netbook, using only the batteries included. I use my ti-83 for graphing, but that’s about it.
It’s much easier to do something like:
csc = lambda x : 1/math.sin(x)
sec = lambda x : 1/math.cos(x)
cot = lambda x : 1/math.tan(x)
e = some_radian
for f in [sin, cos, tan, csc, sec, cot]:
print f(x)
And that was a whole problem in three lines. I believe it would be smaller in Haskell (seriously, I get so bored in there that I’m almost as good in Haskell as i am in Python). The only problems that I have are when the problems are designed to be boring, and I suddenly have a lack of doing them.
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.
It is good for kids to learn about history, but a slide rule would be a better way to do it. By the way, need a graphing calculator? There's an app for that -- http://www.appcylon.com/ !
I work in tech support for a major calculator manufacturer and it baffles my mind that so many people still use calculators. It also baffles my mind that people expect the damn things to work for 20+ years. We get calls for models from the 70s where the customers are irate because the calculator died and we won't send a replacement for free. Personally, I think it's a scam. The damn things cost $1.50 to make and we sell them for $60-$150.
Calculators are more programmable than most computers.
That sounds silly, and it is, but it's also pretty much true. Computers don't have BASIC anymore, and getting a C compiler is a deal, and most programming languages nowadays are set up for scripting. Then we can talk about the ludicrous battery life of a calculator or the ability for it to sit peaceably by, and we get into the real reason why a netbook is drama and a calculator is not. Calculators don't have to "boot". You never have to "reinstall the OS". Calculators won't catch malware from the stupid internet, etc.
Obviously you can't use a calculator for everything. But the things that calculators do, these things do really well.
If it was for me, I would make mandatory the use of slide rules, if the Apollo and Soyuz capsules were made by scientists wielding those analog calculators, kids can do with it as well. When in college I couldn't afford a calculator ( third world citizen...a Casio calculator was the equivalent of a month salary) so I became very proficient in the use of a 1950's era slide rule, ( I still have my trusty Faber Castell slide rule) they work extremely well, even for advanced calculus and geometry...
I learned programming on a TI-83+ calculator while I was bored during class in high school. I think this was BASIC, or maybe a simplified version of it? I had taken a class in C++ before, but programming on computers was intimidating, somehow. I'm most proud of a program inspired by Adobe Photoshop I created to make and save drawings. It had special brushes and shapes, could invert a picture, etc. but that was totally f*in sweet and it only took maybe 300 lines of menus and loops? It could also compress and uncompress images into Lists, since the calculator only allowed 8 images. Never ended up using it, of course...
Honestly given ten seconds of pondering, it should easily make sense. Seems to me the anti-gc crowd are just on about superiority complex of mathematical ability and/or utilization of lesser known math tools.
1) Near universal standardization. Text books and labs across dozens of disciplines rely on common graphing calculators, as do instructors. The industry invested on this tech and no one wants to re-write the curriculum to support alternative tech. Most calculators do most tasks the same way; it's standard. Also, the education hardly relies on functionality greater than what GC provide, so why go elsewhere? and the educators don't have to worry about who has Windows/Linux/etc or who has which software or who can afford to pay the extra $100 ... or who didn't download a virus that crippled their system and prevented their math software from loading, so on and so forth. It makes sense to package these functions in an isolated, portable, dedicated calculating machine which gives consistent and predictable results! Additionally, because of the standardization, everyone knows how to use these things, and the learning curve is negligible for just about anyone.
2) Cost. Yes, more expensive devices can offer superior calculating power. But the educational needs are well-met by the GC, so going the distance and paying more makes absolutely no sense. Plus, as every student knows, GC's are VERY recyclable and the recovery of cost is normally as much as 75% ! Try selling your netbook at the end of the semester, see how far that gets you.
3) Ease of Use. The OP suggested students and educators, perhaps professionals, rely too much on GC tech, then suggested using even more sophisticated math software as a replacement? Forget that learning curve! And what about portability, battery life? I can pack up my calculator and go anywhere with it, very easily. The thing is superior to any other alternative on this point alone.
4) Dedicated device. This kind of overlaps in what I've mentioned before, but it's a very important point. The GC is dedicated to one of a handful of purposes. Replacing it with a multi-purpose machine, and the latter becomes more valuable to me as it suits other important uses. Storing music, running other software, all this interferes with the "focus" afforded by simply having a GC next to my textbook - I learn less effectively! Also, running calculations are not likely to be interrupted or erroneous on the GC as they are on the other devices (e.g. netbook) due to software flaws, machine crashes (i.e. iTunes freezes up!) and so on. I lose or damage my netbook, and replacement cost is prohibitive; whereas a used cheap GC is very easy to find these days. Hell, I keep ROM backups and emulation software of my GC's for just that reason. Also, who is going to lend out a netbook? Who is going to study group around a desktop PC or pass around a heavy laptop low on battery life among eight other friends in the study hall? I've loaned out my GC's dozens of times, and expect just about everyone to have one somewhere, so study group is way easier, and at work we each have one and that's so much better than "let's go to my office and load up X math software"
5) Dedicated device. Hate to over-emphasize, but it's important. I use my GC to solve all kinds of random problems in a flash, you know little debates you get at work over whose algorithm is more efficient, where a quick visual is crucial. Explaining to colleagues that their mess of a word problem is just a system of equations, that a solution exists or can easily be obtained? GC does it in five minutes.
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
Well let's see, saying "You could spend just $100 more..." It's freaking $100 more! or, to put it another way, it more than doubles the cost of the calculator. Then it will have much shorter battery life, be a lot harder to fit in your pocket, and be less easy to enter calculations on (due to lack of specialized buttons), and be more complex to administer. (System updates, etc.). A calculator just works, and it works all the time every time. What's more, "Install GNU Octave" is not really a workable solution, compared to the built-in functionality of many of the existing calculators.
As for tests, if you are supposed to be learning math, then you need to make sure that the device you let the students use doesn't help them "remember" things they are supposed to have learned. It's all well and good to say "but in real life, they will have a computer...", but the reality is that if you follow down that path, then there is no need to ever "learn" anything. After all, when you want to build a nuclear power plant, you can just use Wikipedia and Google, right? For example "learning" finance might mean *understanding* time value of money, what it means, and how to calculate it. We let people use calculators to avoid multiplication errors with large inconvenient numbers, but want to make sure they are not reading "introduction to time value of money" during the test. (On the other hand, the recent trend by some professors has been to make the tests much more difficult, and say "go for it, open book, open notes, open everything" That way, if you haven't pre-studied the material, you simply don't have the time to look up and figure out everything during the test.).
Yes, graphical calculators have always been a gimmick, and completely pointless.
Professionals in engineering, science, or finance never use these things. A scientific or financial calculator, a spreadsheet, and possibly MATLAB are all you need.
Statistics is the only important math skill for non-engineering/math/etc majors. Honestly, I think its a travesty that calculus is a mainstay of the GE curriculum while basic statistics is not. Most students will derive zero value from their education in calculus. All students would derive huge value from a greater understanding of statistics. An understanding in statistics would make one a smarter consumer, a better-informed citizen, and a more productive worker (in nearly any job, from carpentry to law.)
I honestly believe that our entire math education in this country should be devoted to getting all students through a course on stats. They should be taught other subjects only as necessary to provide the foundation for stats.
As noted above, OT, but I'm curious
Other than the "because they're greedy and they can do it" answer, why the hell is the Ti-89 I bought in 1999 still the same price today? Hell, I actually paid less then than most places I see it listed now.
Way back when I started EE studies I (and everybody else) used a slide rule; finished the EE program with an HP-45 - expensive but worth every cent. Still have it and except for the NiCads it works just fine. Eventually bought an HP-15C which could live in a shirt pocket and run for years with out changing batteries. Still use that HP-15 every day - it looks beat to crap but has and continues to serve me well. I'm now retired, the HP-15C is on its third or fourth set of batteries and I would buy a new one if the idiots that replaced Bill and Dave at HP hadn't dropped it from production.
Old Fart
Graphing calculator? And exactly what pedagogical value does this buy you over a standard science, non graphing? Hopefully one would know the general shape of the equation. And just because it can solve some equations doesn't mean you can't make problems on the test that don need that.
I took the professional engineer exam about ten years ago, and there is nothing on that test you couldn't do with a slide rule and a decent math table book. Or an old SR50 or HP35
All we had back then was letters and signs! And it was all greek to me! >_
Seriously, can you solve a Laplace transform symbolically with a calculator or an iPad? Because if you can, you rock!
No, really - I'm not being sarcastic here - if you can tool yourself past obstacles using the collective wisdom of mankind relayed through whatever device, you are the future and better than me. I just wish I could.
and a note that says "get off my lawn"
As a math geek, former teacher and owner of a dozen different graphing calculators, I feel I have to add my two cents.
I'm from the era where you weren't allowed to use any calculators on tests. Not that I would have needed one anyway (as a math geek). Calculators were cool (for math geeks) in the '80s, and some of them are still cool.
But there are some skills that come up later in math that many people these days don't know or never even learned. Long division can be used with polynomials instead of just numbers, but it's a lot harder to teach polynomial long division if they don't remember long division in the first place. And try to get anyone these days to work out a square root by hand. (Yes, there are polynomial square roots too - but how can you teach that?)
I do appreciate that the Casio will give you an exact answer for SQRT(5+2*SQRT(6)) - namely, SQRT(3) + SQRT(2). I could get that myself, but it's not something we ever taught.
I appreciate that my students have no excuse for multiplying wrong. Okay, they might enter a number wrong and get a wrong answer for that reason, but they're supposed to check their work. People of my generation should know if an answer makes sense or not - we had to learn to estimate so that we knew if we had made a mistake (because it was so easy to make one). It is still easy to make mistakes, even if the mistakes are now different ... I worry that people who grew up on calculators don't know when they get a wrong answer.
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
Yeah, sure you can get that netbook, and get the cutting edge software, but can you use it on the SAT. Nope - so its not all that useful for a learning tool anymore, is it.
You should use a type of calculator you plan on using for your long term educational career. My good old TI-85 got me through 6 years of school, and I still have it 10 years later.
Seriously, wtf is wrong with companies?
Every electronic device does NOT need to access the web, email, have a camera, or do anything other then what it's purpose is.
Why does a calculator need to access the web, check email, etc? We have fucking computers, netbooks, laptops, smartphones, and of course, tablet pc's that do that already.
Enough is enough.
Be seeing you...
I remember being told some years ago "graphing calculators are pointless toys; do toy problems by hand/ with a $5 calculator and use a system with real computing power to run Mathematica or Matlab for serious problems." With the emergence of dual-core A9 chips, it is now entirely feasible to have considerably more computing power in a graphing calculator than desktops had when I was told that.
The sad story here is that there has been rather little progress in the calculator market since the introduction of the HP48 in 1990.
To really be equivalent you need MATLAB or Mathematic, which both cost more than the TI's calculator. Octave and SCILAB are way too technical to be used by your average student.
“Common sense is not so common.” — Voltaire
When I was taking chemistry in college, calculators were banned from exams. That was partly because they were new enough back then that not everybody had them (pocket calculators had gone from nonexistent to $400 to $150 to $100 over about four years), while everybody could afford a plastic slide-rule, and partly because in chemistry you were expected to know what the calculations you were doing actually meant, and partly because you seldom had measurements that needed more accuracy than a slide rule anyway.
When I was in grad school in the late 70s, my time-series professor didn't believe in wasting valuable computer time graphing numbers. We should be doing that by hand on graph paper and only use the computer for Real Computing. Of course, I'd usually crunch the numbers on the IBM 5150 and have it graph them on its crude thermal printer, and then copy the graph by hand. Things have changed a lot.
Bill Stewart
New Fast-Compression-only CPR http://preview.tinyurl.com/dy575ks
People have a lot of experience with these devices, and form factor, battery life, and software work well in the classroom.
Long term, they are going to be replaced not by netbooks, but by tablets. But tablet prices are still a lot higher.
The more you understand Pure and Applied Mathematics the more your understanding of say Mechanical Engineering becomes. Take Heat Transfer as one example, or Fluid Dynamics. When you know the Mathematics and see the applied theories of each specialty in your undergraduate days you discover the only time you need the Calculator is for saving a few minutes during examinations necessary to solve the reduced equation you derived where you input the boundary conditions. The computer comes in when you're doing your lab research projects and your data capturing tens of thousands to millions of data points for you to later process.
...use the calculator - we'd prefer you to get to the correct answer than have a simple adding/subtraction error. This was detailed over and over and over in numerous so called 'college prep' highschool math classes that I had. Then fast forward to college - the calculus department was the only department that seemed to have it in for calculators. Well screw them - I don't need to show off to the world that I don't need a calculator. On the other hand my clients prefer not waiting for me to complete the long division and amortization by hand and prefer the quick calculator method. I really wish I would have learned some more REAL world applications using the calculator. Nothing like REAL world application instead of theoretical (for those of us who prefer that).
College...what I really learned: How to spend a whole lot of money and put myself in 30+ years of debt in just a matter of months.
Why do we let them use graphing calculators in the first place, even for exams. You don't /need/ a graphing calculator for any but the most insane of math, which can easily be done using Mathematica or similar equipment. And none of that math is anything you'll see in high school.
Scientific calculators are useful, and that's about it. I am not gifted at math and I can imagine functions in my head even though I'm not even a visual learner. I think graphic calculators are like providing kids with a crutch for their math. Instead of teaching them to be literate and sure of the math I see high school seniors who still can't distribute in basic algebra.
Right now I'm taking accelerated multivariable calculus in college. I still don't need a graphing calculator and very rarely must I pull out a regular calculator.
My HP48G graphical calculator was frikkin fantastic. It could store whole text essays, copies of past exams and came with a fake-reset application that made it appear as though it had been reset but actually just made a hidden directory and moved the contents of the system into that. Imagine how many exams this helped out in!
That's bloody useful, I can tell you!
:-P
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.
Will that be solved once we can record each students screen activity? I would not consider that privacy problem since it is exam.
I don't think there should be ANY calculators used in any math test on any subject, beyond elementary school. Teaching mathematics is supposed to be teaching analytical problem solving, through tools developed over thousands of years. Anyone who studies it should be able to figure out on his own where to apply it in day to day life, business, video games, whatever. Teaching math is not teaching someone to calculate. Elementary school takes care of that. Teaching math should be a glorious expedition in rationality, pushing the limits of the students problem solving capabilities. Not to teach someone how to become a slower and less accurate version Wolfram Alpha.
In all seriousness, any calculation based question is silly. It is like having an English exam, with points on quality of calligraphy. Technique should be strong enough to study the real thing. Not a goal onto itself. Especially when any smartphone can have better mathematical technique than the greatest geniuses of all times.
tl;dr: If it requires a calculator, there's no use teaching it.
You see, education of all sorts is about two things: training the the big natural neural network (NNN) that most of us carry with us on our shoulders, and verifying that people's NNN is up to a certain quality standard.
The programming is done to make sure that people's NNN's are capable of providing the right answer in real-life situations, while the verifying part is there to allow people to show to prospective employers that their NNN is of a certain grade, *before* they are let loose in a place where they can do harm, say, a hospital, an aircraft, a law office, a laboratory, or even an office.
With me so far? Ok, then for the last step. It's neigh impossible to measure the performance of someone's NNN in an exam if they can use their laptops or graphical calculators as crib-sheets or to get enough hints about the solution that they can guess the answer instead of deriving it, or looking it up on the Internet, asking someone else, or even paying someone to provide the answer.
It is for that very reason that we have e.g. closed-book exams, and exams that people are debarred from taking home.
In the same vein as the question about "Why are we teaching a generation of students to use crippled technology?" we might ask: why are we debarring a generation of students from using their friends and relatives to pass their exams and from buying their thesis on the Internet? And that question has the same answer.
Graphing Calculators are good because they are in fact limited machines.
No Professor in their right mind would allow a student to use his/her Phone or any other device on a test because these devices have internet access.
Graphing Calculators shine because they do one thing, only one thing and they do it well.
I raised the very same question here;
http://slashdot.org/comments.pl?sid=2068726&cid=35718426
I'm glad to hear its not me and that more people can't see the point of using these voluntarily.
Hivemind harvest in progress..
At university here graphical calculators are forbidden at exams in the engineering bachelor, students can only use a simple calculator.
There are many reasons why this move was made: calculators got too powerful (half of the students was actually using a computer that looked like a calculator at the exams), students get unequal chances at exams, the actual goal of an exam was sometimes missed (i.e. testing the skills of the students). If an exam requires more complicated calculations or simulations, then the university should just provide a computer class with appropriate software during the exam.
It is although quite an abrupt change for new students at university, who were used to using graphical calculators in their previous schools. Most students seem to accept the measure and find it quite normal...
I did Maths and Further Maths A-levels 10 years ago (...DAMN I'M GETTING OLD). I was not allowed to use the calculator in exams, and was discouraged from using it in lessons because I would not be able to use it in exams.
A simple £10 scientific calculator still had all the functionality I needed and I was allowed to use that in my exams...
At university, despite me already owning the specific model of "receommended" calculator that the university said we could use in exams, I still had to spend money buying one of the calculators that they supplied with their own logo sparypainted on the back because "I might have tampered with my current calculator". What was to stop me buying this calculator with the logo and "tampering" with that?
These calculators are pointless because you cannot use them in the very environment(s) in which they are most useful. Not because they lack funcitonality in any specific area.
we need display-less calculators that will beep the result in morse code..
The real question should be, at least in high school and MOST college math courses, why are students using a calculator at all? I took two years of AP calc in high school. On the first day of AP calc AB the teacher made us take out our calculators. "You spent a bunch of money on those didn't you?" he asked before continuing "Take em home. I don't ever want to see them again. You bring a calculator into this class, you fail. You do NOT need a calculator to do any of the math through calculus." We hated him for it, but he was absolutely correct.
I've always found graphical calculators completely pointless. A PC or laptop can run rings around a graphical calculator.
The only reason a graphical calculator sells because the schools want a limited device used for tests. Plotting functions can easily be done on paper, during an exam.
On the other hand. Getting a good calculator remains invaluable. I've bought a HP 32S-II calculator the day before the EMC (ElectroMagnetic Compatibility) exam. My 4th Casio FX-82D had broken down that year and I ead that HP makes decent calculators and that RPN rocks.
EMC is a fairly complex subject and you need to solve a lot of equations. The day I bought the calculator, I was pulling my hair out, trying to find out how the damn thing worked.
Because, I heard that using an RPN calculator allowed you to work faster. However, learning to use an RPN calculator takes a while. Not funny when you have an exam with a lot of equations the next day. On the day of the exam however, I was able to work with the HP 32S-II quite comfortably and was on average 20 minutes faster than the rest of the class.
The reason that RPN works faster remains the fact that you can skip all the intermediate solutions of the equations after you written out the correct algebraic solution to the problem. So that's a real life safer there, during exams, because you have to type a lot less.
Using a real calculator still has benefits nowadays. The tactile feedback from a real calculator allows you to work much faster than using a touchscreen of your phone.
So for graphing and complex mathematics I will use my computer. For simple algebra I will keep on using my trusty HP 32S-II for a long time.
I personally think teachers are placing too much into trust into the calculator. hey I started on a slide rule because it taught me that there is more than one way to skin a cat. Not that I promote skinning cats or using slide rules instead of calculators, but knowing how the damn thing works can really do a hell of a lot in how one uses their technology. Calculators are easy and work most of the time. If teachers really wanted to be jerks they could give problems that involve lots of work and have the student show their process. Write out each step and explain it, thus showing an understanding of the material and a certain comfort level with it. Instead of training them to automatically punch every problem into a piece of software spit out an answer.
I've thought of buying a TI calculator, because it would be hand to have. I don't go to school, I work for a living, and I don't do much in the way of advanced math. What's more, I actually work as tech support for an engineering department at a university. This implies two things:
1) I'm a geek with lots of computers. I have a desktop, laptop, desktop at work, etc. I have no lack of access to not just computers, but high end computers.
2) I can get all the math software for free. The full version of Matlab? No problem, I can install that on any system I want straight off our server.
Yet I have toyed with the idea of getting a graphing calculator. Why would I do that? Because they are good at what they do. Matlab is a pain in the ass to use, it is a very complicated program when all you need is some simple math done. Not only that, it isn't as though getting out a laptop, firing that up, and running Matlab is the fastest thing in the universe.
It would be nice to have something small that I can turn on and do calculations with. However I don't want a simple calculator, I want to see the whole problem I've entered, to be able to go back and change it if I realize something is wrong.
A graphing calculator does that extremely well. It is useful at what it does and acting like $100ish is some massive fee is silly.
As you say, purpose built devices are useful. As another example at work we have oscilloscopes for classes, unsurprisingly. I don't remember the precise models for they are Tektronix MSO and DPO 3000 series. These things do pretty much everything. You want to measure something, they can measure it. However, we still have a bunch of multi-meters too. Why would we have those? You can measure things like voltage and resistance with an advanced scope, if you know how. Well the reason is because the meters are easy. Just push the "DC volts" button and touch the terminals to your item, you get a result. The scopes are far more complex.
When I need to see if a laptop power supply is broken, I do not go fetch a scope, I fetch a multi-meter. The scope would work, but the meter is easier.
It is ridiculous: math in school is still taught to a large part as if computers would still not exist and in exams one has to show how well one can perform tedious and completely useless calculations a computer can do millions of times faster. This goes for simple arithmetics just as for stuff like solving quadratical equations or performing calculations with polynoms.
Most of what is asked in exams does not help to show if a student understands what mathematical thinking is all about. Given some exercise and and algorithmic memory an average student can pass these exams without even understanding what she is doing.
Instead, math education should be about teaching how mathematical insight is gained, how to think in a mathematical way, how to find interesting problems and find proofs for them etc.
I believe that what makes math boring or hated by many students is exactly that attitude that students have to learn how to become little computers like monks calculating endless logarithmic tables in past centuries.
All you are talking about is saving time. But exams are set up such that when they are to be made without a graphing calculator, they can be made without running out of time (unless you are really bad, in which case running out of time is part of the reason you get a low grade, caused by being bad, so deserved). So this is just bogus.
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.
my hp48 has gotten me through hell and back, through high school, through the army, through university and it's about to get me though a master's.
it's tough, it's nearly faultless (single digits of bugs) very documented, huge library of software.
did i say it is tough? 13 years later the keyboard does not even look new (no label fading) it feels new.
even if i find a new GX for 300, i would still buy one, just to display it to people who have no idea what a well engineered device is.
yeah the new 50g is faster, but it's comparatively worthless.
Calculators have their undeniable uses, but they do not make mental arithmetic obsolete, as some people seem to think. There are always times where it is more efficient to simply think for a split second, than to plug it into the calculator.
You know, there is a difference between trolling and pointing out the flaws in your reasoning. Just saying.
Just to chime in a bit on the graphing calculators for exams issue, if the exams in your class can be trivially passed by somebody who just wrote a few notes down on a calculator, then what the hell is the point of that class in the first place? It might as well not exist at all. Furthermore, in the real world, you will pretty much always have access to a graphing calculator (or something vastly more capable), so what is the point in hobbling students for such artificial reasons?
The answer, it seems to me, is to do one of two things:
1. Force students to show all of their work. This way they might be able to use a calculator's equation solver to check the answer, but they actually have to know how to do it to get any credit.
2. Focus on understanding instead of memorization. If you force your students to actually think, no amount of written-down formulas or equation solvers will give them the answer. In fact, better to assume that many of the students will have access to this sort of technology, and craft the exams so that it makes no difference whatsoever.
Again, in the real world, the students will have access to tables and whatnot to find whatever you might otherwise want them to memorize in a test. All they need to know is how to look things up quickly, and with practice they'll memorize anything and everything that they actually make use of frequently. The stuff they don't make use of frequently they'll forget anyway, so what's the point?
Anyway, all that said, graphing calculators are still quite useful to me from time to time. I obviously won't do any serious calculation on them, but my trusty old TI-89 is very useful for checking my work (e.g. ensuring that a program I wrote to compute some numerical result works as advertised). It's also very useful for getting quick answers to simple calculations that are just a bit too complex for the Google calculator. Sure, it'd be nice if it had a faster processor, but for the most part I'm limited by inputting the formulas, not the processing time.
Just like you would rather use a specialized trouble code scanner for a car (even though you can use a laptop) I can see the usability benefits of a calculator over a netbook. Like almost every multifunction device, the netbook suffers from being adequate at a lot, but being good at very little.
a. Much less fragile than a Netbook
b. The specialization means less time wasted fiddling with settings and configurations than actually using it
c. No issues with crashing/updates/version conflicts.
The main reason that a basic calculator is only allowed in exams is because of people using the advanced functions to cheat.
This is a list of approved calculators put out by the The National Council of Examiners for Engineering and Surveying:
http://ppi2pass.com/ppi/PPIInfo_pg_myppi-faqs-calc.html
I know this isn't the case for all universities but in my class you can have your graphing calculator with you and when it's armed with a CAS such as the TI-89 then it's a great companion during tests, I could never bring a netbook in. As for them being slow, not really! I mean whats slow in comparison, doing a bode plot by hand or having the calculator spit one out, Solving multiple linear multi variable equations in state space, or having your calculator spit it. There not really that slow, in fact there pretty fast and there a huge help when you don't want to spend a hour to solve a questions your calculator could do in under a minute.
The point is so they don't type every damn question into WolframAlpha and actually learn rather than have a computer give them all the answers. Honestly, it's no wonder there is a fear that computers will enslave humans. When nobody can understand the algorithm, that algorithm becomes mystery, then magical, then mystical. Call me grouchy, but I wouldn't let you use calculators at all if I were a teacher! Learn to utilize that brain and you'll out pace a calculator user at least all the way up to polynomials. Then again, I think speed is NOT emphasized enough. The kids who prize speed tend to also get more right answers. Practice with your kids! Make them tabulate the grocery bill (plus tax!) in their heads at the super market as soon as they learn to count. Ask them story problems, and let them figure out how to figure it out by themselves! Kids who figure out how to solve the problem without being shown how to solve the problem become good at learning how to learn instead of learning how to memorize. Simple little tricks to make little Susie #1 in math... so STFU about calculators! **grumble*grumble*when I was your age!*grumble*grumble***
I8-D
Easy to whine on slashdot...difficult to demand change of your federal/state governments and local school boards.
When I start coding, I often find that I don't completely understand things that I thought I did. While calling eig() from a matlab prompt does not require understanding much linear algebra. I think writing code often is a better way to clarify and demonstrate understanding than working examples.
I agree completely. Working as an engineer (and as a student) I find my self always returning to my venerable HP 15C. While it may be useful to have some programmable 'macro' level functions (parallel resistor formula, Volts to dBm conversion, etc.), entering and graphing equations or programming anything in general is generally a waste of time.
Anyone doing serious work will be using Octave, Matlab, Mathematica, Maple, etc., or even Excel.
Anyone "not there yet" should be graphing by hand and using a basic calculator (if any) for gnarly calculations.
In a related rant-
Calculators should basically be banned from lower level math classes, at least until students demonstrate proficiency with arithmetic and can check their own work.
The argument that introducing young students to calculators is of some benefit is entirely misguided, coming from educators that have not much experience in math in the first place. We find the results of this calculator reliance in a huge number of college students that have no clue how to check their own work, what results to expect, when they've made an error or not, to the point where they're basically mathematically illiterate.
Teachers and professors should be smart enough to craft problems with 'nice numbers' that are easily worked by hand, eliminating any need for calculators in class or on exams in the first place.
Of course! Super Mario!
http://www.youtube.com/watch?v=JfKN73qaC0A
The American high school math curriculum is intentionally designed to cover pointless and uninteresting subjects.
Why, for instance, do we shove trigonometry down every student's throat? Almost every trigonometry student knows they'll never use an arc tangent again in their life. What they do learn that math is tedious and irrelevant agony, best avoided whenever possible.
Meanwhile, high school students don't learn math which has real-world benefits for almost every citizen. If more people understood compound interest and exponential growth, they'd know how mortgages work (and why zero-down and negative amortization mortgages are catastrophes waiting to happen). If more people understood probability, they'd know how insurance works and how to choose medical treatments. Both of these subjects would help tremendously when people are choosing retirement investments. (The replacement of pensions with personal investment accounts means almost every American needs to grasp these concepts or suffer misery when they hope to retire.) For both compound interest and probability, students could solve real, interesting problems that they will face later in life, and learn to think logically at the same time. Instead, we give them pointless math that couldn't turn Americans into math-haters more effectively if math teachers deliberately conspired to do so.
How did the American math curriculum get so bad?
1. If you don't need the other features of a netbook, that's still $100 wasted.
2. Does the $100 include those 3 software packages?
3. What 1000 things are you thinking of? I really can't think of a 1000 things I would want to do on a netbook. Some things, sure. But do they justify the $100, maybe not.
Ironically, most CS majors were failed physics students, who couldn't handle both concrete and abstract applications of mathematics at the same time..
When I was a kid I didn't understand why teachers didn't let us use calculators in algebra. Now that I am trying to teach children math I understand completely. I had the following conversation with a child just a few days ago:
ME: What does 'percent' mean?
KID: Out of one hundred.
ME: Ok, so what's 20% of 100?
KID : (Blank stare)
ME: If 'percent' means 'out of one hundred' what percentage is 20 'out of one hundred'?
KID: Five?
ME: No, that's 100 divided by 20. I'm asking you to convert 20 out of 100 to a percentage.
KID: (Blank stare)
ME: Let's try this again. What does 'percent' mean again?
KID: Out of one hundred.
ME: Ok, so what might be a different way to say '20 out of one hundred'?
KID: 20 over 100?
ME: Yes that's one way. How about as a percentage?
KID: (Blank stare)
ME: (Pulls pistol out of drawer, puts it in mouth, and pulls trigger)
My point is that kids learn to hunt and peck numbers into a calculator without understanding why it works. I have no problem letting kids use a calculator after they understand the arithmetic they are working on.
Why are we teaching students how to use calculators?
Interesting article, but still need to learn how to walk before you can learn how to run. Software isn't much help if you don't understand the fundamentals of what it's doing. Some professional licensing examinations prohibit the use of programmable / graphing calculators (e.g. NCEES Fundamentals of Engineering {EIT} and most state Professional Engineer / Professional Surveyor {PE/PS} examinations), so you better know how to work the problems by hand.
First, crippled technology might be a little bit extreme. It's really that is just has a very focused operating scope. After that though, the real thing is that students really should learn basics. Sure, you might be able to buy a program to solve any problem for you later on in life but what if you are hired to design that program? Of course you can go do tons of research at the time but for many people math is not a "simple" subject, they need a lot of exposure to really learn it and being able to do a "high level" view or understanding the details can both be very useful. Besides, if you keep going with the "well you can get a computer to do....." you could eventually extend that to "Well, you could get a computer to breath for you, run your heart, and tell you what you're going to eat today". Just because you can get a computer to do something doesn't mean it's a great idea. From what I remember of college a few years back many students were already doing everything they could to not have to really learn a subject anyways, why make it easy?
I don't have time to make a sig
I would take issue with the author's perspective of "only" a hundred dollars more. For many families the graphing calculator is a stretch and to effectively double the cost would be extremely burdensome. This perspective I find somewhat elitist and out-of-touch with the situation in many of the school systems in the U.S.
a) Cutting edge and well documented mathematical programs are matlab and mathematica. I am *not* going to use software in an exam where the exact range of the current functionality is not documented (and i use octave regularly).
b) What do i expect a student to know when he arrives in the lab where i am working? I expect him to be able to make *simple* estimations and caclulation in hois head or using a pencil, and he should know where the limits of sowftware are. Nothing which can be tested using a test which requires a calculator.
My university allowed most graphical calculators, as long as the couldn’t be networked. The reasoning is that the test-assignments should be designed in such a way that you don’t need a calculator. As one is supposed to show all intermediate steps, having a calculator (which only shows the final answer) is not very useful. It can be useful for verifying results, though. To take away this advantage some om my teachers would give the answer to the question. This was also advantageous in multi-part questions as it would prevent students from continuing to use a wrong answer in the subsequent parts.
Even as a working professional, I still have my TI-83+ readily available in a desk drawer at work despite having tools like MATLAB and Octave available on my desktop machine. Why? When I just need to do a few quick calculations it's loads faster than booting up a program on my PC (or netbook, assuming these things are on in the first place) and, because of various classes that involved math (calculus, statistics, various electrical and computer engineering courses) I'm very familiar with the functions it provides. In contrast, if I used a MATLAB/Octave environment I'd have to go searching for special purpose statistical and mathematical functions that your standard scientific calculator readily provides. Personally, I much prefer using my graphing calculator in most situations. This isn't an argument against calculators in the classroom, but graphing calculators are far from pointless.
It allows me to see more stack entries. Err, wait . . . TI calculators have a stack, right?
it doesnt matter how you succeed? at the end of the day microsoft gets the money anyway ? you think they ever cheat ? probably not, how could they have made it in life if they were to do such evil deeds ?
Free speech was meant to be free for all... how can anyone grow up in a nanny state ?
We're not suppose to be teaching them technology - we're suppose to be teaching them mathematical concepts.
Coder's Stone: The programming language quick ref for iPad