I came across this Seymour Papert quote over the weekend, the best part of which is below. In context, Papert is speaking about effecting real change in the content of school mathematics, and he focuses particularly on the teaching of fractions:

One theory [among educators about why we should teach fractions in school] was that manipulating fractions was actually closer to what people needed back before there were calculators. So a lot of school math was useful once upon a time, but we now have calculators and so we don’t need it. But people say that surely we don’t want to be dependent on the calculator. To which I say, Look at this thing, these eyeglasses, that make a dramatic difference to my life and the life of everybody who reads or looks at any tiny detail. Once upon a time we would have been crippled, severely handicapped. Now we’ve got these and we don’t need to go …

Andrew Carol, an engineer at Apple, has rebuilt a model of the ancient Antikythera Mechanism entirely out of Lego blocks. Watch this amazing 3-minute video:

A fuller story behind all this is here. I feel like running out and buying out the entire stock of Lego from some unsuspecting toy store.

I was just talking with an older colleague of mine yesterday — he’s been teaching math at my college for over 50 years — about how technology has changed since he started, and I remarked that in many ways I’m more amazed by the mechanical calculator technology of the 50′s and 60′s than I am by modern digital computers. I remember my Dad bringing home an old mechanical calculator from his work and opening it up to reveal gears upon gears inside. Watching this video reminds me of that.

Interesting report here (via Reidar Mosvold) about American students’ misunderstanding of the “equals” sign and how that understanding might feed into a host of mathematical issues from elementary school all the way to calculus. According to researchers Robert M. Capraro and Mary Capraro at Texas A&M,

About 70 percent of middle grades students in the United States exhibit misconceptions, but nearly none of the international students in Korea and China have a misunderstanding about the equal sign, and Turkish students exhibited far less incidence of the misconception than the U.S. students.

Robert Capraro, in the video at the link above, makes an interesting point about the “=” sign being used as an operator. He makes a passing reference to calculators, and I wonder if calculators are partly to blame here. After all, if you want to calculate 3+5 on a typical modern calculator, what do…

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 …

One of the real treats of the ICTCM was the Saturday 8:00 AM session titled “Three Decades of Handheld Devices: How Mathematics Teaching Changed Along with Them” given by John Kenelly. Prof. Kenelly has a long history of involvement in the development of calculator technology, and he gave a fascinating talk full of good thoughts on the direction of handheld technologies today, war stories from the past, and good jokes. (Example of the latter: “Getting a spreadsheet to work on a calculator is like getting a dog to walk on its hind legs — it can be done, but it ain’t pretty!”)

I will try to say more about Prof. Kenelly’s ideas about the future of handheld technologies in a later post, but for now I wanted to share one of the really cool parts of his talk — the calculators themselves, some of which are now antiques. He had a bag full of these old-school devices (some of which are less…

One of the biggest conversation pieces here at the ICTCM is the Texas Instruments NSpire, their most recent entry in a long line of calculators. Here’s a firsthand look at it; click to enlarge, and then just take your time to look at the thing and think about it:

On the right there is a normal-sized TI-30-something scientific calculator. That should give you an idea of the scale. Here’s another shot with me holding it, which should also give an idea of the size of this thing; and another shot which gives a better view of the screen.

But let’s go back to that first photo. First of all, yes, the NSpire does actually have not one but two keyboards. They snap in and out; the one that’s un-snapped is just a duplicate of the TI-84′s keyboard. The one that’s snapped in is, well, let’s just say “busy”. The first thing you notice is that there are buttons between the buttons. The little…

It was a full day yesterday here at the ICTCM, and the day was capped off with a very enjoyable dinner with Maria Andersen and Scott Franklin, along with two of Maria’s friends who (if I understood Maria right) are soon-to-be math bloggers. I have photos and a video forthcoming.

Today will be no less busy:

8:00-8:45: Session on handheld calculating devices over the last 30 years and how they have changed teaching. Very interested in this talk; I’ll have more to say about some of the handheld technology I’m seeing here.

9:00-9:45: Session on using Maple 11 in the advanced calculus and modern algebra classroom.

9:45–10:30: Exhibit hall surfing.

11:30-12:05: Session on labs in mathematics classes.

12:30-1:15: Session on using Geometers Sketchpad alongside computer algebra systems.

Every semester before classes start, I get emails and phone calls from new students or their parents wanting to know about calculators. What calculator is required for your classes? What calculator should we get? I have a TI-**, can I use it in your class? And so on. A lot of these folks are trying to purchase technology, the uses of which are not entirely clear to them — and so they end up buying the wrong kind of device or spending a lot more money on a calculator than is really necessary.

From my vantage point as a college math prof — not beholden to any calculator company or big ed-tech advocacy group — here’s the scoop on what people really need to know about these things.

Fact 1: You probably don’t need a graphing calculator. Despite intense marketing for graphing calculators, the fact is that most settings do not require graphing capabilities from a calculator. In fact, the …

I am a mathematician and educator with interests in cryptology, computer science, and STEM education. I am affiliated with the Mathematics Department at Grand Valley State University in Allendale, Michigan. The views here are my own and are not necessarily shared by GVSU.

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