By now, you’ve probably heard about Wolfram|Alpha, the “computational knowledge engine” that was recently rolled out by the makers of Mathematica. If you haven’t, here’s a good place to start. There is considerable debate among ed-tech people as to exactly what kind of impact Wolfram|Alpha, abbreviated W|A, is going to have in education. For me, W|A is still a little raw and gives back too many “*Wolfram|Alpha isn’t sure what to do with your input*” responses when given mathematically legitimate (at least they seem so to me) queries. But the potential is there for W|A to be a game-changing technological advance, doing for quantitative information what Google did for text and web-based information back in the 90’s. (W|A is already its own verb.)

One thing that seems clear is that, with technology available that is free and powerful and hardware-agnostic, technology that previously has ruled the ed-tech roost can’t survive for much longer. I’m thinking particularly of the graphing calculator. These have been a fixture in math education, especially at the pre-college level, for the better part of 20 years. But now here is W|A, which can graph functions, perform symbolic algebra and calculus computations, even solve differential equations and do number theory and statistics and all manner of interesting stuff besides, including but very much not limited to mathematics. In short, it does everything a graphing calculator does. But, importantly: W|A is free, runs on any web-enabled device (including, as I can attest to by experience, an iPod touch), is fast, is portable (see the links I just shared?), and — perhaps most importantly of all — has an army of developers who are constantly adding new features into the system.

You could spend $150 to get the latest and greatest from Texas Instruments, a handheld device that does what a graphing calculator does — but no more. (Here’s my first-hand take on the NSpire and details on what I see as its demerits.) Or, you could spend a little more than twice that much and get a netbook computer that gives you access to W|A as well as a suite of office tools and more. Computing hardware has become so small and cheap, and online quantitative tools so functional and powerful, that it’s very hard to see how graphing calculators can survive the next 5 years.

If graphing calculators do survive, it will be for one main reason: The AP exams. I was talking with a local high school AP Calculus teacher this week who impressed on me that she cannot afford to drop graphing calculators and move on to using netbooks or some other more sensible technology because, quite simply, there are questions on the AP Calculus exams that require the use of graphing calculators. Students have to have total fluency with graphing calculators — and not some other, calculator-like technology — in order to do as well as they possibly can on the exam, which is part of this teacher’s professional responsibility. The AP already succeeded in killing the TI-92 calculator — a really good technology for its time, when laptops still weighed 15 pounds and costs thousands of dollars — for no better reason than because it had a QWERTY keyboard. Today, the AP might succeed in keeping W|A and other similiarly useful, perhaps even transformative, technologies out of the hands of students pretty much for the same reasons, which is a real shame and quite backwards-looking.

But then again, I don’t know what the AP folks have in mind. Perhaps there are plans afoot to migrate the AP exams away from dependency on graphing calculators. It certainly wouldn’t take much for the AP folks to write their own lightweight graphing tool that does nothing more than plot functions, find intersection points, shade in areas, and do numerical integration (rarely are graphing calculators used on the AP free-response portion for more than these four things). Make it extremely basic, put it on the web, free for all to use, and provide it on specialized computers for students taking the exam. That way, students can learn how to use technology rather than learn how to use a graphing calculator, and both teachers and students can be freer to choose the extent and type of technology they want to use in their classes. And such a thing would probably have a longer shelf life than any TI calculator for sale or in production.

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The other potential alternative is an iPod Touch with some graphing software on it such as http://www.iphone-calc.com/wp/?page_id=67 .

Definitely a piece of school tech on the way out, along with those little voting gadgets.

By “voting devices”, you mean clickers? I hope you’re right.

Yes 🙂

I simply cannot image doing electrical circuits and a multitude of other engineering calculations on anything other than on an RPN enabled HP calculator. This, of course, is real world and not pedogogically motivated. I own both types of nSpires, plus the 83, 84, 85 and 89. Add to that many HP graphing calculators. Oh, and how about that xThink math journal for tablets? I also have derive, maple, mathematica, and matlab – all for hobby and learning pleasure.

There is somthing about the handheld asthetic: instant on/off, dedicated physical buttons, long battery life, ease of use. etc. This plus perhaps TI marketing is why the PDA version of calculators never took off. You have to have mass mark acceptance plus lightening quick access – nothing but dedicated calculators comes close to this. The best engineering survival tool hardware of all time: HP42S. Today it would probably be MatLab on a laptop.

Should I sell my TI collection now??

Will, the HP calculators are a breed apart. I know engineers who still swear by their HP-10c’s, and if you try to get one off of eBay you will be looking at about $100. This is for a product that was discontinued 25 years ago! It’s like the Toyota Corolla of calculators.

I still get good use out of my TI-92.

I think migrating to computers (and the associated costs to AP, and difficulties in test administration) would only be worth it if there was some tangible in-test advantage — that is, it wasn’t just the same test on a different platform, but opened for the possibility for new kinds of mathematical manipulation and new kinds of questions.

Regarding the Inspire calculators, a colleague of mine has made roughly the same argument as you; I think there are adequate netbooks for $200. There is of course the practical concern of running a class where everyone has a computer. I trust adults enough to have a Facebook window open and still be paying attention, but at earlier age groups students will do anything to get distracted. (Including of course playing Yahtzee and so forth on their TI calculator, like they’ve been doing for 15 years now.) Counterarguments have been made that everything should be project-based now anyways, but it’s difficult — I know an experimental high school in the Midwest which has every part of curriculum project-based *except* mathematics.

In addition to the AP exam, we’ve got the ACT and SAT tests, so graphing calculators aren’t going away just yet.

I showed W|A to my seniors – and gave them time to play in the computer lab. They loved it – “Why didn’t you show this to us earlier?”

@Jackie, to what extent are GRAPHING calculators used on the ACT and SAT these days, as opposed to just SCIENTIFIC calculators (without a graphical display)?

I consider scientific calculators to be a very different kind of technology than graphing calculators from the educational perspective. Scientific calculators are cheap — the best one out there, the TI 30X, can be had at Amazon for $15 — portable, durable, and loaded with useful features and a pretty familiar and nice user interface. Get a good scientific calculator and you’ll carry it around for the rest of your life. Get a graphing calculator that’s 8-10x the price of a scientific calculator and has features which mimic, and are inferior to, computer technology that is only marginally more expensive, and you’re talking instant obsolescence.

I don’t know the nationwide statistics, but every student in our school is required to have a graphing calculator (TI83 or 84 -as TI89’s aren’t allowed on the ACT (but are allowed on the SAT)). I think this is true of many schools in the area.

I’d love to have a lab (or class set of laptops) with Mathematica or Maple or some type of software available to use every day, but I can’t see that happening any time soon.

But why are they required to have a *graphing* calculator? Why not just a scientific calculator, graphing functionality optional? The ACT and SAT don’t *require* graphing calculators now, do they?

Then one presumably can’t assign homework problems that require a graphing calculator?

I have directed students to gcalc.org when they end up in that situation, but some don’t have Internet access or even a computer. (Of course, if they had a netbook as you suggest above this wouldn’t as much a problem.)

I think it’s fair to point out that W|A isn’t really equivalent to a CAS like Mathematica or Maple in that you can’t perform a long sequence of computations or store your results. It would be very interesting to see a web based interface to Maple or Mathematica that had these features and could be used from the smart phones that will be very common in the next few years.

Of course these phones are powerful enough to run CAS software too, but having access to a server that could run very involved computations for me while I’m sitting at the local coffee house would be good. I’d even be willing to subscribe to such a service.

This is yet another example of a specialized application that might make perfect sense to implement in “software as a service” mode.

@Brian: Right. W|A is not — not yet, anyway — anywhere near an adequate substitute for a full-blown CAS. Although it also should be pointed out that a lot of the math functionality of W|A *is* a web interface to Mathematica — it just can’t access the full range of Mathematica functions right now. Who knows — in a year W|A might have a lot more functionality than it does now.

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