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 two biggest players in the learning management system world, Blackboard and Angel, will soon be one company, since Blackboard has purchased Angel Learning, Inc. for $95 million.  From a superficial reading of the press release, it appears that Blackboard thinks of itself as having a more technologically innovative product, whereas Angel has a better track record with customers — and Blackboard has the money to pull off the purchase.

I can’t verify any of those claims, but I can say that we switched from Blackboard to Angel at my college a few years ago due to a general dissatisfaction with the quality of the product compared to the price we were paying. I don’t recall Blackboard as being particularly innovative, although admittedly that was 4-5 years ago. Angel has not been much of an improvement, and I’ve blogged before about the maddening UI design decisions that Angel has made. In going from Blackboard to Angel, we basically traded one set of deeply flawed LMS technology for another.

And now we have the situation where the current sub-par LMS technology maker is being bought out by the previous equally-but-differently-subpar LMS technology maker. So who knows what exactly we, the users at my college, are going to end up with. The best-case scenario is that we would get the best of both technologies. There are some things that Angel does  pretty well, well enough at least that I am no longer finding myself forced to roll my own LMS at Wikispaces just to retain my sanity. We shall see.

In the meanwhile, Jon Mott has some excellent thoughts about life post-LMS. I think he’s right that the basic problem isn’t the implementation of the technology (although, as I’ve noted, there are some big problems there with Angel and probably with Blackboard as well) but rather the paradigm on which the technology is based. It makes me wonder if the real LMS that best suits the modern college or university is already out there, in the form of previously-released tools that just need to be cobbled together rather than an expensive proprietary software package that tries to emulate those tools.

In a comment on an earlier post, I said I would try to blog about Flat World Knowledge and their business model soon. Here’s a 20-minute video that goes over this business model which allows textbooks to be free but still provides compensation to authors.

Again: Free textbooks can be done; it just requires a different approach than the one we’re used to.

With Harrison’s arrival on the 15th, I have had neither the time nor the raw material for blogging about math, education, or technology. Instead I’ve been mostly figuring out how to decrypt my new son’s little coded messages and trying to sleep when I can. But there is one tech item from my experience of the last week that I would like especially to highlight: the ongoing awesomeness of the iPod touch.

Originally I wanted an iPod touch to replace my aging third-generation Photo iPod. I figured the main purpose of an iPod is music playback, and having internet and video capability would be sort of nice too. But now I see that the iPod touch is a lot more than a music player: It’s a passport to new-parent sanity. Consider the following ways the iPod touch has been of use lately:

- I used the iPod touch to provide real-time updates of my wife’s delivery — well, at least right up to the point we went to the delivery room — for friends and family using Twitter and Facebook.  I was even able to make some short posts to our family blog, although blogging on the iPod screen keyboard really takes it out of you.

- I found out that while you’re in the hospital having a baby, the moments of genuine excitement are intense but sparse. Mostly there are lengthy periods when you’re just there in the hospital room with nothing to do. Fortunately before I came to the hospital with the Mrs. I stocked up the iPod with every LOST episode I owned and a whole bunch of podcasts, so when baby and mom were asleep and I wasn’t tired (ha! Remember when I wasn’t tired?) I could fend off the boredom.

- Although I have never actually done this, you could use the iPod in its originally intended mode, as a music player, to play back calming music to a newborn with one hand while holding the baby in the other.

- Perhaps the most frequent use of the iPod touch has been during my overnight shifts looking after the baby. These are usually from 8PM to midnight and involve trying to lay down in a quiet, dark room knowing that any attempted sleep is going to be interrupted by a suddenly hysterical baby. The first night we were home and I was on deck, I ended up rocking the baby in my left arm while seated and using my right hand to Twitter to the outside world. Now this has become something of a nightly live-blog of my exploits as parent-on-duty.  I use the tag #babyshift to highlight these posts.

Sometimes I report on what’s happening during my shift. Sometimes I throw out questions to the “audience” which turn in to good discussions about parenting tips and tricks. I’ve had very lively conversation threads during these times, while I Twitter one-handed in the rocking chair in our bedroom waiting for Harrison to settle into sleep. The “#babyshift show” has made what would normally be a tedious parenting task into something fun, even something to look forward to. You simply can’t overestimate the value of connecting to the outside world when your whole world is turned inward because of a new baby, no matter how wonderful that baby is. (Join me most nights between 8-9 PM by going to my Twitter page.)

So here’s to the iPod touch and the whole idea of mobile access to the Internet.

Sports Illustrated columnist Peter King has an interesting entry in his Monday Morning Quarterback article this week on how digital video has changed the NFL.

“Two mouse clicks,” said Tennessee defensive coordinator Jim Schwartz during a break in preparing to face Green Bay the other day, “and I have every two-point-conversion play the Packers have run since 2006, and I can watch them, one after the other. That’s how advanced our video systems are now. You’d be a fool not to use it for research.”

Schwartz prepped for Indianapolis two weeks ago by watching every red-zone snap of the Colts since the start of 2007 — 234 plays. He watched them in succession, without a break, just to see what habits the Colts had inside the 20. And last week, he looked at all 182 red-zone snaps of the Packers since the start of last season.

Some 25 years ago, teams would have had to splice film together to show that. Even 10 years ago, the computerization of video wasn’t the same as it is now. In the last four or five years, every team has been outfitted with similar video systems, which enables them to look at every commonality on tape within minutes — every third-and-eight-or-longer, for instance, that the opponent has run since the start of the 2006 season.

I could see something like “sports informatics” emerging as a very popular and lucrative field of study.

The National Assessment Governing Board has announced plans to develop a standardized test to gauge the technological literacy of K-12 students, according to a BusinessWeek article. They plan to deploy the test to a sample of students in grades 4, 8, and 12. The article doesn’t say what, exactly, is going to be on the test. But, interestingly, there are some hints in the article that the test will include mechanical and scientific concepts under the umbrella of “technology”. (Lest we forget, there are all kinds of technology out there besides cell phones and MySpace pages, and being really skilled in technology has to mean more than just the ability to twiddle buttons on a gadget.)

I’m not sure what the K-12 system in this country needs right now is one more standardized test. But on the other hand, it would be awfully nice — for once — to have a standard means of gathering statistically viable data on technological literacy, rather than relying upon unproven assumptions and anecdotal evidence. Or, as it says in the article:

Companies like Intel need people who not only know how to use a computer, but also have a sophisticated understanding of concepts like security, privacy, and intellectual property that will evolve with technology in coming years, [Paige] Kuni [of Intel] says. Her hope is that a national tech test will spur more schools to teach these skills since many educators just assume that kids are naturally tech-savvy and can pick this up on their own. “Adults in our society and in other countries assume that because kids are digital natives, they automatically know how to use technology in meaningful work,” Kuni says. “Just because a kid can use text messages doesn’t mean they know how to [do things like] analyze data deeply.”

I hope that the edu-blogosphere, especially that huge chunk of bloggers and conference-hoppers on the ed-tech side who are endlessly enraptured by the notion of the digital native, is listening to those emphasized quotes. We need to stop assuming that kids have these skills and start teaching them.

So this test could be of some real value to the education community. On the other hand, it seems a little naive of the NAGB to think, as the article says, that this test — no matter how well it measures technological literacy — can play a significant role in “revers[ing] the slide in U.S. test scores and enrollment in such subjects as science, math, and engineering, and ultimately address the more generally waning competitiveness of the U.S. in technology”. It seems that the NAGB people think that the existence of the standardized test will make classes which emphasize technology more prominent in the curriculum (“What’s assessed is what’s taught”, as Hofstra’s David Burghardt economically puts it).

Maybe . But when’s the last time a generation of young people got fired up about something because there was a big test on it? You can develop curricula and test it all you want, but when the popular culture still virtually criminalizes the idea of being smart among teenagers and younger kids — especially being smart in math and science — then it’s merely wishful thinking to expect a significant change in direction. But I’d love to be wrong on that.

[ht Joanne Jacobs]

The annual TED conference (TED = Technology, Entertainment, Design) bills itself as “bring[ing] together the world’s most fascinating thinkers and doers, who are challenged to give the talk of their lives (in 18 minutes).” You see presenters at TED along the lines of Al Gore, Jane Goodall, Freeman Dyson, Marvin Minsky, and on and on. Many of the best TED talks are available for free as video podcasts at the iTunes store or from TED’s website. I was quite surprised to find, among these “best of TED” talks, a 27-minute lecture from 1998 by Billy Graham. His talk was on “Technology, Faith, and Human Shortcomings”. Here it is, in its entirety. You should really watch the whole thing.

I think it takes a lot of guts for an evangelical Christian — to say nothing of a then-80-year old with Parkinson’s Disease — to walk into TED, into a crowd of people who by and large have precious little sympathy for your position, and talk with such ease and boldness. But Billy Graham has been around the block a few times and been into more hostile environments than that.

I happen to agree with Graham’s conclusions about Jesus Christ (although not every point of his Southern Baptist theology). But even if you don’t, listen to the questions he asks and the points he raises*. What about human evil, death, and suffering? Technology won’t solve these problems; what will?

(* …and don’t respond by reflexively hurling insults at Christians like depressingly many of the commenters at TED’s web site do. If you disagree with Christianity, fine, but step up to the plate and put forth a viable answer to the question rather than simply name-call like a 5-year old on the playground.)

We interrupt this blogging hiatus to throw out a question that came up while I was grading today. The item being graded was a homework set in the intro-to-proof course that I teach. One paper brought up two instances of the same issue.

• The student was writing a proof that hinged on arguing that both sin(t) and cos(t) are positive on the interval 0 < t < π/2. The “normal” way to argue this is just to appeal to the unit circle and note that in this interval, you’re remaining in the first quadrant and so both sin(t) and cos(t) are positive. But what the student did was to draw graphs of sin(t) and cos(t) in Maple, using the plot options to restrict the domain; the student then just said something to the effect of “The graph shows that both sin(t) and cos(t) are positive.”
• Another proof was of a proposition claiming that there cannot exist three consecutive natural numbers such that the cube of the largest is equal to the sum of the cubes of the other two. The “normal” way to prove this is by contradiction, assuming that there are three consecutive natural numbers with the stated property. Setting up the equation representing that property leads to a certain third-degree polynomial P(x), and the problem boils down to showing that this polynomial has no roots in the natural numbers. In the contradiction proof, you’d assume P(x) does have a natural number root, and then proceed to plug that root into P(x) and chug until a contradiction is reached. (Often a proof like that would proceed by cases, one case being that the root is even and the other that the root is odd.) The student set up the contradiction correctly and made it to the polynomial. But then, rather than proceeding in cases or making use of some other logical deduction method, the student just used the solver on a graphing calculator to get only one root for the polynomial, that root being something like 4.7702 (clearly non-integer) and so there was the contradiction.

So what the student did was to substitute “normal” methods of proof — meaning, methods of proof that go straight from logic — with machine calculations. Those calculations are convincing and there were no errors made in performing them, and there seemed to be no hidden “gotchas” in what the student did (such as, “That graph looks like it’s positive, but how do you know it’s positive?”). So I gave full credit, but put a note asking the student not to depend on technology when writing (otherwise exemplary) proofs.

But it raises an important question in today’s tech-saturated mathematics curriculum: Just how much technology is acceptable in a mathematical proof? This question has its apotheosis in the controversy surrounding the machine proof of the Four-Color Theorem but I’m finding a central use of (a reliance upon?) technology to be more and more common in undergraduate proof-centered classes. What do you think? (This gives me an opportunity to show off WordPress’ nifty new polling feature.)

So I’m plotting out my tactical plans for research and scholarship over the next year right now — my imagination being stoked by the completion of my Statement of Scholarship — and I’d like to go deeper into educational technology on a number of levels. I’d like not only to stay abreast of the rapidly-changing face of the technology being used in schools, but also the social implications of that technology, the legal issues behind it, and the technical nuts/bolts/bits of how this stuff works in the first place (including the computer network/programming side of things).

I’m just a user and a self-appointed pundit of ed tech, so I have no idea exactly where to start if I want really to go deeper on this subject. I do know that I’m going to swallow hard and read Digital Natives, Digital Immigrants by Prensky carefully (as opposed to skimmig it as I have done in the past) even though I disbelieve in nearly everything I’ve drawn out of that essay. And I have Friedman’s The World is Flat, which seems to be a seminal work among School 2.0 people, on my bookshelf at work waiting to be read. But what other suggestions would you readers have?

Remember, I’m looking not to become a mindless School 2.0 zombie (that takes no effort at all) but a person who is fluent with all the important aspects of ed tech, including the “tech”.

My interest in the new iPhone has never reached critical mass, but after finding out that I can get 15% off AT&T cell phone plans through my work, I started thinking again. The basic family plan, after discount, would be $100 per month, which is more than what we’re paying now ($60/month) but possibly worth it if the iPhone is as great as some say. But my interest tanked again when I saw the coverage map near my house:

The finger on the map is roughly where I live. The orange color indicates “good” coverage, which according to AT&T means that it “should be sufficient for on-street or in-the-open coverage, most in-vehicle coverage and possibly some in-building coverage”. If I stray over to the other side of our subdivision into the yellow, it’s only “moderate”. Most of where I live and work is no better than “good”.

Sorry: But if I’m going to drop $300 on the phone and $1200 per year on the service, I want a little better than being able to maybe-sort-of use the iPhone inside my house and only a relative degree of certainty I can use it at all, even standing out in the front yard.

It reinforces my conception that iPhones are for city folks and people who travel a lot, who make up a large and vocal portion of the pro-iPhone blogosphere and who don’t have to worry about whether they’ve got cell phone tower coverage in the first place. As for the rest of us, well, I don’t think the network is ready for us yet.

Or am I missing some important point here?