## Are graphical calculators pointless?

I love mathematics and I also love gadgets so you’d think that I’d be overjoyed to learn that there are a couple of new graphical calculators on the block. You’d be wrong!

Late last year, Casio released the Prizm colour graphical calculator. It costs $130 and its spec is pitiful:

- 216*384 pixel display with 65,536 colours
- 16Mb memory
- The CPU is a SuperH 3 running at 58Mhz (according to this site)

More recently, Texas Instruments countered with its color offering, the TI-NSpire CX CAS. This one costs $162 (source) and its specs are also a bit on the weak side but quite a bit higher than the Casio.

- 320*240 pixels with 65,536 colours
- 100Mb memory
- CPU? I have no idea. Can anyone help?

If you are into retro-computing then those specs might appeal to you but they leave me cold. They are slow with limited memory and the ‘high-resolution’ display is no such thing. For $100 dollars more than the NSpire CX CAS I could buy a netbook and fill it with cutting edge mathematical software such as Octave, Scilab, SAGE and so on. I could also use it for web browsing,email and a thousand other things.

I (and many students) also have mobile phones with hardware that leave these calculators in the dust. Combined with software such as Spacetime or online services such as Wolfram Alpha, a mobile phone is infinitely more capable than these top of the line graphical calculators.

They also only ever seem to be used in schools and colleges. I spend a lot of time working with engineers, scientists and mathematicians and I hardly ever see a calculator such as the Casio Prizm or TI NSpire on their desks. They tend to have simple calculators for everyday use and will turn to a computer for anything more complicated such as plotting a graph or solving equations.

One argument I hear for using these calculators is ‘*They are limited enough to use in exams.*‘ Sounds sensible but then I get to thinking ‘* Why are we teaching a generation of students to use crippled technology?*‘ Why not go the whole hog and ban ALL technology in exams? Alternatively, supply locked down computers for exams that limit the software used by students. Surely we need experts in useful technology, not crippled technology?

So, I don’t get it. Why do so many people advocate the use of these calculators? They seem pointless! Am I missing something? Comments welcomed.

**Update 1: **I’ve been slashdotted! Check out the slashdot article for more comments.

**Update 2:** My favourite web-comic, xkcd, covered this subject a while ago.

**Other posts you may find useful / interesting**

I’d recommend using high-tech or low-tech but cutting out cripple-tech.

It could make sense to say “I want you to learn how to do this first on paper so you’ll understand it better, then you can use a computer.” I think students can understand that.

But what’s the point in saying it’s OK to use a crippled computer but not a real computer? What do students take away from that, other than school is an arbitrary game?

Many math teachers don’t really understand math, and they don’t know how to make a test question challenging without imposing some artificial restriction. They’re afraid students might explore on their own and come up with a way to make things easier. Is that so bad? In fact, isn’t that exactly what you want them to do?

I agree. I don’t even know why they are still in business sometimes (TI, I mean). I think it’s because of the superstition of high school teachers. You can enter in cheat notes into a TI-83, or 89, or whatever. They THINK you can’t, but how will they stop you? it would be better on a computer because they could apply policies and impose restrictions that really COULD stop you.

The only reason I enjoyed using a TI-82 calculator at school was the challenge of programming it. It was the most old-fashioned piece of technology I ever got my hands on, and as such it was extremely limited. This made it even more rewarding to make little programs for it, like an orbit simulator a fractal drawer etc.

But I agree that most school pupils would not find this kind of thing exciting, and it’s not a good reason to make kids buy one.

In my school we weren’t really taught how to use these things, more made to buy one, and then pick up on our own how to do stuff with it.

Anyway, I’d agree that it would be better to disallow calculators in exams, instead of this strange compromise. Reliance on a calculator seems to lead to laziness in pupils and they don’t catch the obvious mistakes from typing stuff in wrongly. In my maths degree I don’t remember once using a calculator, and of course they were banned in the exams.

I reckon if an exam problem needs a calculator to be solved, then it isn’t a particularly nice problem. Beautiful problems just fall out, things cancel, and you don’t need to do big sums. The difficulty shouldn’t lie in the sums you are doing, but the problem solving you need to do.

I suspect there’s a large number of nervous people at Texas Instruments. Surely they know that their huge profit margins that they’ve enjoyed from selling the same TI-83 calculator for the same price for 15 years (while everything else got cheaper) won’t last forever. I think you’ve identified their best hope – that standardized tests allow students to use certain calculators but not a computer. Even so, TI is probably moving the right direction by selling nSpire software for PCs, although I doubt the testing companies will allow that given all the other capabilities found even in the cheapest netbooks.

If we look past standardized tests, then you’re right – let’s not only teach students how to use crippled technology. The day after WolframAlpha was live, I showed it to every one of my classes. And in every class I got the same question: “Aren’t you worried that we’ll use this to cheat on our homework?” My answer was the same: “No, my real worry is that if you don’t know how to use this you’ll be at a disadvantage when compared to a student who does.”

Amen! I managed to convince my department to leave them about 4 years ago (we are a 1:1 tablet computer school so really, what was the point?) and only introduce them because of the AP Calc exams. The ruling about QWERTY versus non-QWERTY keyboards is ridiculous; students are adaptable? Have they seen them text? I’d further what Matt said, either use rich problems requiring a computer or keep it standard with only a simple four function. In the interest of equity, obviously, the no/simple calculator would work best unless the College Board decides to push for better assessments.

I find it handy to have a “scientific calculator” at hand in a scientific lab. Of course we’ll load up Matlab to do any real data analysis, but often it’s quickest to just reach for my old but trusty TI-85 and punch in some numbers.

I agree on the subject of allowing students to have calculators: it largely makes them (us?) stupid. I was permitted to use one in my high school days, but once I hit university they were banned for 90% of my exams, and only used on assignments where there was computation that might need them.

Given that new ones (even really basic non-graphing ones) can compute matrix inverses, do reasonable probability calculations, and (for graphing) plot and explore, they really aren’t any simpler than a computer with MATLAB. The push seems to be that using them results in “intuition” as students “explore graphing”, but having seen some of today’s students attempt to use their calculators, it feels like instead they are being taught to mash buttons and ignore what the button actually does.

My vote for schools would be to eliminate calculators entirely until 10th or 11th grade, by which point you can assume that the basics have been taught (i.e. mental arithmetic, ability to recognize order of magnitude, etc.), and then introduce calculators to speed up computation and allow for more complicated problem-solving.

Having said all that: my favorite tool for calculation is not my laptop or desktop: it’s my beat-up old TI-83. It’s just graphical enough to let me type more complicated expressions and be able to find typos (and correct them), and simple enough that I have the number pad and can type quickly and efficiently. Doing numerical calculations on my laptop is misery without a number pad; the TI number pads are very well laid out in that respect.

I remember in college, I used to put equations into my graphing calculator before Diff. Eq. exams. Of course, it didn’t help, which goes to show that you either really know the material or you don’t, and no amount of technology is going to help in a 45-50 min. (or 2 hour if it’s a college final or midterm) exam.

There was a time when professionals WOULD use advanced programmable and graphing calculators. Mostly they were HP calcs (41, 42, 48-series.) Because, at the time, notebooks were either horribly expensive or severely limited; and they needed advanced calculations on the go. (And I never knew *ANY* ‘professional’ that used a TI or Casio. HP had that market cornered.)

But yeah, nowadays, ‘advanced calculations on the go’ can be done with cheap netbooks, or even smartphones. Hence the reason HP effectively abandoned the market. Oh, yeah, they have slightly-modernized clones of their old workhorses, but the latest HP 50G is basically just the old HP 48SX with a few software updates, and running on commodity chips for cheaper production, rather than custom ones.

You are paying for the cost of the user interface and optimizations in the software of the calculator, which is irrelevant to the costs of other computing devices. If there is no margin on cost, they may as well pack up and go home.

Why do we all still use cellphones? Surely laptop computers loaded with voip/skype/who knows what else would do just as good of a job?

The TI calculators are great in that they’re specialized hardware built to do specific tasks. For the most part, the platform is a standard making writing text books and training materials easier.

I’ll agree that they’re not so necessary after formal education, when you have an opportunity to get something setup more suited to your day to day needs. But for educational use I doubt we see a multifunction netbook / cellphone solution in our schools anytime soon.

Also they’ve held that TI-83 price steady for far too long, but my 10 year old model missing faceplate and battery cover still works like a champ, so it’s hard to argue the quality.

All this when I have just received my HP 48GX.

No, you can’t have it.

I’ve noticed the decline in use of hand calculators by engineers. I graduated 16 years ago, and used an HP 48S to calculate problems by hand in college. No computers except for Fortran 77 programming in my fundamental engineering classes. Today’s graduates use computers and software much more. I think this has been to the detriment of their brain power, creativity, and problem solving skills. On lots of problems, I can get the answer really fast using my HP, while they peck away at some simulation program or big spreadsheet; I grasp the fundamentals and can get right to the solution, while they plod along entering data and then turning the crank, and their answer pops out like a jack-in-the-box. Just like a command-line unix interface is super-efficient and powerful compared to a windows interface, so is a hand calculator and good understanding better than computer software on many, many engineering problems. Sometimes a computer is necessary, such as for problems with lots of data or repetitions. But most of the time, a scientific calculator is the fastest tool.

Graphic calculators are a great resource for learning to program. I poured tons of time into programming my TI-83, it taught me the fundamentals of assembly programming and destroying alien invaders.

No really, they’re awesome. Anyone advocating mathcad + netbook just hasn’t owned a graphing calculator. It’s like a cellphone – people buy cellphones specifically to do tasks that could easily be done with a netbook. So why get the cellphone? BECAUSE IT’S AWESOME. That’s why.

@David Maas

I also totally forgot to mention that I learned that there’s a difference between (-1)^2 and -1^2 from a TI83.

Why not an iPod Touch?

960*640 pixels, 24-bit color

at least 8gb

1ghz ARM Cortex-A8 (underclocked to 800 MHZ)

$189

Sure it’s about $50 more than those calculators but it’s a similar form-factor and much more powerful.

As an added bonus: which one are you more likely to have in your pocket 5 yrs from now, an Apple iOS device or a TI calculator?

The answer to “Why are we teaching a generation of students to use crippled technology?” is very simple: because calculator manufacturers managed to make graphical calculators compulsory in high school math in America, so that they could make more money. There is really no other reason.

As for students, many of them already strongly feel that high school math classes have nothing in common with real life, so they don’t find it strange that schools make them buy those overpriced, antique machines. The geekier ones will have fun programming them in Basic and maybe assembler — they’re very hackable machines. But your average student will remain ignorant of 90% of their calculator’s capabilities (as are most teachers, in my experience).

Now I teach math in college. In my calculus classes, I use and teach the Maxima CAS extensively. Midterm exams are done without graphical calculators (I have to allow non-graphical calculators due to a department regulation, but always tell my students that no question on my exam requires a calculator). The final exam is in two parts: no graphical calculators in the first part, and the second part done in the computer lab where students can use Maxima to take care of the algebra, and can concentrate on modeling, qualitative analysis, and other, more interesting stuff.

That said, I’ll agree with a previous poster that a calculator, especially one that’s known inside and out, is still a superior tool for portable, short computations. I’m never far from my beloved HP 32Sii.

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.

These calculators don’t seem to me to be so crippled. Back in my day, we still were using a slide rule.

@John

Because on a real computer, you can google every answer/solutions/theories and possibly even the exact questions and answers.

If you don’t know already, your blog entry has appeared on slashdot. You can find many interesting comments there: http://science.slashdot.org/story/11/04/11/2246231/Are-Graphical-Calculators-Pointless.

Just thought you might want to know.

Are there any netbooks or smartphones that will run uncounted hours without having to suck up to a wall socket? I just asked my son what the battery life of his (heavily used) 2 year old TI is, his answer being “I don’t know, I’ve never replaced the batteries.”

How about the feature of instant availability, with immediate access to desired functionality, guaranteed unless you’ve dropped the unit in beer?

Existence is a marvelous virtue. A netbook with a dead battery might as well not exist, a smartphone that requires 30 seconds to reach a state of being able to add two numbers is arguably crippled compared to a calculator.

All the same, this is a thought provoking post!

Hi Mike

Here’s the answer: running Doom!

http://www.engadget.com/2011/02/21/ti-nspire-calculator-yes-it-plays-doom/

In the UK and Ireland the highest level of technology allowed in a University exam (that I’ve seen, doing Engineering and Computer Science courses) is a scientific calculator.

I bought a graphing calculator some years ago to see how US exams might be different. My first though was “This can find roots, local minim, invert matrices; US college graduates must know fewer equations off by heart”. Then I saw the counter point, why did I know these equations off by heart, I would never realistically need them in an industry situation.

The gap between skills taught in University and those necessary in the field’s you’re attempting to enter is growing, most strongly (I feel) in Sci/Eng courses. While services like the Khan Academy provide an accessible way to access knowledge, a University qualification will always be useful for an employer. It shows that you’ve done some base level in the field; not just in the areas you enjoyed, but all areas. However, if, as a company, you need to put a fresh grad in 6 months training to bring them up to speed, you may seek new dependable metrics of competence.

Professional qualifications may become more important (Cisco Certified, Red Hat Certification, &c.), but most tend to aim at SysAdmin roles at the moment. It’d be nice to see a professional developer certification.

The best badge of developer competence I can think of is a high Project Euler score.

See also: http://xkcd.com/768/

Why the merlion?

Back when I was in school we bought, through the school, “scientific calculators” with an eight digit display (ti30stat in my case). A couple of years later the focus shifted to “graphical” calculators. I’d guess that if you wait until those people are the grumpy 40- to 50-somethings that make up the senior engineering corps, you’ll see more graphing calculators on desks. But maybe not. As a replacement for log tables a pocket calculator is marvelous. After that it gets clunky.

Personally I don’t really see the point of teaching math with graphing calculators; graphing something yourself oughtn’t take much time and should give you better insight into the numbers than watching the machine do it for you gives you. In that respect I’m vaguely wistful they didn’t also teach basic slide rule skills.

One of the hallmarks of a good engineer is the ability to quickly figure out if something is feasible at all, and for that you need a couple well-placed guesses and assessments, provided you know what’s important and what you can ignore. The fancier the modelling, the less that “fingerspitzengefuehl” comes into play.

What are we teaching for, anyway? No, not saying we shouldn’t teach. But we should have a clear idea whatever for.

Couldn’t agree more! Totally pointless toys. Expensive toys at that.

Plus, in all my schooling and career to date I have never ever felt the need to have my calculator plot anything for me. The only reasonable and useful plots are on big monitors or dead-trees (if you need to scrawl over them while discussing with others – or yourself).

I guess the captive – and inexperienced – audience of school/college kids get tricked into spending money on a flashy gadget that is not as useful as it looks. At a guess, kids whose parents are in engineering/science do not get sucked into this arms race, either. Heck, all the way to uni I was content with my dad’s HP-25, and through uni a HP-15C. Then, as a SW engineer a HP-16C came in handy (but not as much as you’d think), and these days, having taken the red pill a RPN calculator on my Android phone serves just as well.

Full disclosure: I do own an HP-50G, but then I also own the whole Voyager series, and a good few others; in other words I’m a HP collector, and if I weren’t one I’d never have even thought about the HP-50G. Oh, and I have turned it on the whole of twice. :)

I work in the domain of cryptography, for a major governemnent of Europe. I still use a HP calculator. I got a HP48GX with two cards : one 128 Mb and one 1 Mbit card. I love RPL and it’s small, easy to program and works fine. Having a limited tool compared to a computer brought me to find innovative and very effective ways to break various ciphers, where I do think I would have burned much more time with a laptop.

But it is true that I am considering replacing it. But what laptop does offer as much hours of work as my calculator ? The various laptops I saw offer 3 hours, sometimes 3h30 and when I use them to crunch numbers, it’s usually well below 3 hours ? I work 10 to 12 hours per day. 3 hours is a big no-no.

Calculators are limited, because they help students and at the same time we don’t want those to be too powerful so exams would become too easy, and most work done by the calculator instead of the student. This is why they are limited, and expensive because specialized for exams. Do not mix those calculators with those the mathematicians and engineers do use, most of the time we use Mathematica and a powerful PC or a simple SSH connection to a cluster of computers loaded with a front end, Mathematica and tokens…

I am considering replacing the HP48. It will probably be a very light netbook with 10 hours or so of battery life. A cheap 3G key so I can SSH to a cluster of computers running Linux with Mathematica loaded on them for number crunching. I still have the HP48 to check “ranges of numbers” more quickly than my own head and pencil/paper can do.

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.

@Dan Haskin

Most high school math teachers (in decently funded schools) have a teacher set of calculators. They are bright yellow and come with a device that clears all the data from them.

Of course when I went to school, we didn’t even have google (that’s sad) so we didn’t have a lot of ways of downloading programs. That’s all kids do these days. We actually had to write the program. I think my teachers had the opinion that if you are smart enough to write the program you’re smart enough to use the program on the test\homework.

On many places even graphical calculators aren’t allowed. In my uni, we are barely allowed to use function calculators (is that the term..?), and even then only the low-end calculators. I have a calculator which can convert 2/4 -> 1/2, and because of that functionality, I’m not allowed to use it.

Just a quick thought. I dare you to drop a netbook or iPod touch or iPad from the second story of any building and do the same with a ti-whatever. The ti will still work fine. Although not indestructible, it is definitely tough.

@Dan Haskin

TI also makes some pretty High quality MCU’s and other semiconductors, while they’re known for they’re calculators, its not the only thing that keeps them afloat.

Using technology in exams —

There are many professional exams such as for the financial industry that pretty much require using a calculator. However there is no graphing and the technology is 20 yrs old these financial calculators have even less memory and less features than a scientific calculator and cost $100 USD. Why – calculators are an investment, and when treated as such, engineering majors who get a graphing calculator because they cannot use a netbook in a test, or a finanace guy taking a test like the CFA level 1, or a mathematician taking an actuary exam need these tools. It is short sighted to believe that you need fast mathematical software to cruch numbers on a test, test are designed to be completed in a limited timeframe. Why use a computer to save all of the .05 of a second difference, do you actually get frustrated knowing it’s wasting half a second of your life calculating an answer that would take you 1/2 an hour by hand???

If the problem is so complex it takes a computer to solve thats normally given as homework.

My university allowed most graphical calculators, as long as the can’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.

@Raylion I’ve taken a LOT of exams in mathematics and physics over the years. All I have ever needed is a $10 scientific calculator.

Couldn’t agree more. I have always asked why I am not being taught the tools that I will use as an engineer. I agree that theory is important, but not teaching me these other tools is not good.

Why use crippled tech ? Because (hold on to your hat) people cheat. If you have been reading the surveys of students, in the last few months, they use the all to common approach of ‘if we can get by with it, do it.’ ‘Hey Teach, can I use my cell phone for a calculator on the test?’ Really means, “Hey Teach, I can I IM, Twit, email my questions to my friend in the next room or next row, so I can get a better grade with their answer?’

I’m tired of elementary teachers telling me proudly that their students use calculators in class. Especially, when I get them a few years later and they can’t answer questions like ‘What is -2 times -2?’ No joke, I worked with a student (11 grade) that could not answer this today!. He offered to try to answer IF I got him a calculator.

I teach high school Computer Science, so I’m not anti-technology; just anti-inappropriate-technology.

There was a time when Chemistry and Physics teachers “back-calculated” their questions so students did not need a calculator. Oppps, that did require the teachers to really understand the concepts they were teaching and to do some work. It is easier now to say ‘use your calculators (and share/borrow your ansers.)’

How many parts on new planes would not fit, even though the computer said they would? How many auto-recalls happen, even though the computer said all was fine?

It is NOT the computer’s fault. People (and engineers) need to be able to think; not just push buttons.

Expensive toys.

I bought my last calculator, a HP-48GX, in 1994.

It’s batteries last forever(ish) and it’s easier to grab than fire up a PC’s calculator or Mathematica. It’s ridonkulously overpowered for the unit conversions that it spends most of its time these days doing.

It does double duty as a tetris / minesweeper machine when the desktop’s busy.

I was recently forced into purchasing a dated Casio graphical calculator, the Classpad 330.

The calculator comes with a whopping 5.3mb of flash ROM, a 160×240 pixel touch screen capable of displaying UP TO TWO COLOURS, and an SDK that only works on Windows all powered by four bulky AA size batteries that go flat in two weeks. But hold the phone, I got all this for just $200! Yep, that’s right, for the price of a substantial ARM tablet or netbook I got this outdated piece of garbage. Obviously Casio are making HUGE profits from these calculators given their rubbishy specs.

The cheating argument against netbooks is garbage. I keep a full set of self written reference material for all maths-based subjects on my calculator (though I don’t use them during tests as a matter of principle), and if I wanted an application (like dc or bc or lua) I’d port it from Linux (using their SDK through Wine, of course :)). The calculator does EVERYTHING a netbook could do in the cheating department, albeit a bit slower.

But at the end of the day, I’m happy to use expensive and outdated technology because I know that the alternative won’t be a sensible ARM tablet or netbook. The alternative will be a 17″ x86 laptop running Windows Vista SP1; and if the threat of having to use Microsoft products isn’t enough to keep you in the dark ages, I don’t know what is.

And @Bob I: conduct all assessment in a giant, soundproof, airtight, windowless Faraday cage. Problem solved.

You know, this presents a very interesting opportunity. Even the newer calculators are vastly underpowered compared with Android phones that are two years old, and those old throwaway phones can be found at much cheaper prices. The opportunity here is that someone could sell old Android phones as next gen graphing calculators. Just preload it with math apps, disable wifi (updates would occur via desktop), and sell for $150 a pop. You could develop math apps that close to what engineers would use, and sell those on the Android market to offset the cost of including them in your graphing calculator. Then, at least kids won’t be using crippled software/hardware.

Of course the toughest part would be for College Board to accept new technology over the TI calculators they’ve been allowing for years.

@George

I’m just glad that I wasn’t educated in the US and forced to buy an overpriced, underpowered piece of technology just to be able to sit some outdated tests ;)

it was made for a function… if u think it is “underpowered” look for Arduino, that stuff can do almost anithing and is not even half power than the calculator… so, if we go for power, then all of your iphone/ipad/blackberry/(any smarthphone) is obsolete because there is more powerfull computers in the market, and so those hipotetical computer are obsolete because there is oter hipotetical computers (for a lot more money) in the marquet and so those will be obsolete, becose there is oter 7000 millon more powerfull and usefull computers on the world and everybody has one…

Arduino is low powered and cheap – a combination I am happy with.