Category Archives: Math on the web

The State of Education in America

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Anyone interested in education needs to watch this talk by Ken Robinson. Education will almost certainly change in fundamental ways in the next few decades–our current educational system is based on some faulty assumptions, as Ken Robinson points out.

On a related note, I recommend you check out this recent op-ed piece by G.V. Ramanathan, published last weekend. Here’s an excerpt:

How much math do we really need?

Twenty-seven years have passed since the publication of the report “A Nation at Risk,” which warned of dire consequences if we did not reform our educational system. This report, not unlike the Sputnik scare of the 1950s, offered tremendous opportunities to universities and colleges to create and sell mathematics education programs.

Unfortunately, the marketing of math has become similar to the marketing of creams to whiten teeth, gels to grow hair and regimens to build a beautiful body.

There are three steps to this kind of aggressive marketing. The first is to convince people that white teeth, a full head of hair and a sculpted physique are essential to a good life. The second is to embarrass those who do not possess them. The third is to make people think that, since a good life is their right, they must buy these products.

So it is with math education. A lot of effort and money has been spent to make mathematics seem essential to everybody’s daily life. There are even calculus textbooks showing how to calculate — I am not making this up and in fact I taught from such a book — the rate at which the fluid level in a martini glass will go down, assuming, of course, that one sips differentiably. Elementary math books have to be stuffed with such contrived applications; otherwise they won’t be published.

more…

Equations from photographs with new Casio calculator

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Excerpt from wired.com’s gadget lab:

If you’ve ever looked at the curve of a hill, the cables of a suspension bridge or the arc of a coastline and wondered, “I wonder what function would fit that line?” — congratulations, you’re a nerd. And Casio has a surprising new calculator that will answer your question.

Casio’s new Prizm calculator is to the graphing calculators of my school-days as the iPad is to the slates we scratched on with sticks of chalk. It has a color, 216×384 pixel display, 16MB of memory, a USB-port, and will do all of your math homework for you….

Any graphing calculator will let you input an equation and show you the result. Casio’s Prizm does this in reverse. The color screen will display a picture, and will draw a line over the top of any shape you like. It will then give you an equation for this line.

If that wasn’t amazing enough, that USB port lets you hook the calc up to a compatible Casio projector to show off the results on the big screen….

$130, available now.

That’s pretty amazing. I’m not sure it’s the most important feature of this new calculator, but it does highlight the fact that our TI-83’s haven’t changed significantly in 14 years. It’s surprising, given the advances in every other area of technology. Why isn’t your TI-83 calculator three or four times smaller and 20 times more powerful than the TI-83 of 14 years ago?

Google awards $2 million to AIMS

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News from the TED Prize blog:

Congratulations to the African Institute for Mathematical Sciences (AIMS) and 2008 TED Prize winner Neil Turok on winning $2 million in funding from Google’s Project 10^100. Project 10^100 (10 to the 100th power) was a call for ideas to divide a $10 million fund into five pieces that would help as many people as possible around the world. AIMS’ piece of the prize will be used to expand its network of science and math academies that promote graduate-level study in Africa.

Interestingly, Khan Academy, which I raved about in this post, has also been awarded a TED Prize. Click here for more info, and a nice video about it (sorry the news is a bit old!).

Great Carnival

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The 70th Carnival of Mathematics was posted this morning and has some fantastic links. I especially liked the news that wolframalpha.com now accepts \LaTeX syntax (I didn’t know that!). Also, it’s very cool that the golden ratio was used in the redesign of twitter.com (though some sources say the golden ratio isn’t all it’s cracked up to be). And there’s a link to my recent post on asymptote misconceptions.

Thanks, Daniel, for a great carnival!

What’s Algebra Good For?

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Learning high school math (Algebra included) is actually good for three reasons.

  1. Some students will actually use it (mathematicians, engineers, scientists, programmers, architects, etc.) Granted, this is probably less than 5% of students.
  2. It’s part of a liberal education. What will you ever “use” your history, biology, English, or art for? Most students will never directly use any of these. So what are we trying to pull on high school students? We’re trying to liberally educate you, so you can have intelligent conversation with the world around you.
  3. It’s fun. Math is a big game. And there’s nothing more satisfying then working on a problem that’s just perfect for you (not too hard, not too easy).

Could your math teacher be replaced by video?

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Before I get to the titular topic, let me share some links. I’ve been meaning to post links to a couple of online resources that are astonishingly thorough. I strongly encourage you to check all these out.

  • Drexel Math Forum — This site has been around for years, I’m just getting around to posting about it now. But if you’ve never been there, I highly recommend it. Almost any math question high school students could asked has been answered and cataloged on this site (including misconceptions about asymptotes like I posted about the other day).
  • Interact  Math — When you first link to this page you’ll be unimpressed. But select a book from the drop down menu and then pick a chapter and set of exercises. Then, click on an exercise and prepare to take an interactive tour of that problem. The site let’s you graph lines, type math equations, do multiple choice problems, and more. If you have trouble with the problem, it will interactively walk you through each step, asking you simpler questions along the way. What a fantastic resource! Unfortunately, almost none of our books are on the drop down list. That doesn’t keep it from being useful. Just find problems similar to what you’re struggling with and try those.
  • Khan Academy — A nonprofit organization started by Sal Khan, this site has 1800+ youtube instructional videos, nicely organized by course and topic. You can go learn everything from basic arithmetic to college level Calculus (and Differential Equations, Linear Algebra, Statistics, Biology, Chemistry, Physics, Economics…). Sal’s mission is to provide a world class education to anyone in the world for free. It’s very exciting to see how this site will grow, and possibly change how we do education.

Math Teaching by Video

Some of these sites, especially the Khan Academy, make me wonder how long our modern American school system will remain in its present form.  Will we always have a teacher in the front of the math classroom delivering instruction?

I’m not afraid of the idea that we (teachers) could be partially replaced by video lessons. It’s actually a pretty good idea. The very best instructional practices could be incorporated into a flawlessly edited video. Teachers wouldn’t make frustrating, careless mistakes, students could replay the videos at any time, and substitute teachers could easily run the class. Every school, even the poorest and most marginalized would be able to deliver top-notch, world class instruction.

And what would teachers do, then? Qualified teachers could turn their efforts toward more of “coaching” and “discussion leading” role, concentrating on one-on-one sessions, remediation, reteaching, providing feedback, grading, seminars, open forums, field trips, and inquiry-based instruction that supplements the more formal video presentations. And don’t forget blogging! 🙂 So much of a teacher’s time is currently spent preparing lessons and teaching them that they have very little time for all those other (more?) important aspects of teaching. All this time devoted to preparation is being spent by teachers everywhere. Imagine the possibilities if we devoted the bulk of our time to these other aspects instead of preparing instruction. Sounds really great to me.