Posted by
Antonio Cangiano in
Essential Math, Math Education, Suggested Reading on
September 9th, 2007 |
16 responses

**1. The Tenth Dimension**

**2. Outside in (Turning a sphere inside out)**

**3. Flatland the film (Trailer)**

The full movie is available on DVD, and of course, you can also get “Flatland: A Romance of Many Dimensions”, dirt cheap (a classic geek novel for less than 4 bucks). If you prefer, you could pick up the annotated hardcover version: “The Annotated Flatland: A Romance of Many Dimensions”. Highly recommended.

**4. Math Education: An Inconvenient Truth**

This short video shows what’s wrong with the current widely adopted methods of teaching mathematics (fortunately though, such practices have not caught on everywhere).

**5. Math Education: A University View**

You can consider this video a follow-up to the previous one. Clearly this education reform affects elementary school aged children, but the effects that it has on curricula at an early level also profoundly goes on to influences the education which is received by students at high school and even college levels.

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i’ve always wondered how much greater our analytical capabilities would be if this were a four (spatial) dimension universe, and our intuitions had evolved as such.

Great minds think alike!

Earlier today, I posted an article on Visualizing Pi!

[...] 5 Thought-Provoking Mathematical Videos [link][more] [...]

Traditional addition is great for big problems, but the method where 26 * 31 turns into 20 * 30 + 20 * 1 + 6 * 30 + 6 * 1 is the one I use in my head.

Having said that, the emphasis on calculators is very unfortunate. People should avoid relying on mysterious black boxes when possible.

I would also recommend ‘Flatland: The Movie.’ It’s another adaptation of Flatland that just came out on DVD, starring Martin Sheen and some other great actors. It’s 30 minutes long and is perfect for classroom use. It comes with worksheets for the teacher too, as well as the text of the book. There are some DVD extras that talk about higher dimensions too. Definitely consider this one – it’s at flatlandthemovie.com

[...] [Hat tip: Math Blog] [...]

The reasons for not liking “cluster” solutions:

- “parents don’t understand it”

Well, send the parents to school too!

knowing how to get to 26 * 31 = 20 * 30 + 20 * 1 + 6 * 30 + 6 * 1 means having skills manipulating the language of math. If you can do this, you dont need a calculator.

regarding the standard division algorithm, try doing *that* without pen and paper! hey, that “pen” thingy is a black box! don’t rely on that!

once you learn the division algorithm, all the use you will get from it is dividing. if you learn to divide dividing the problem into smaller and easier pieces, then you’ve learned a really valuable skill.

the first two videos where interesting. the one about teaching, very very very bad.

Thanks. Get huge collection at http://freevideolectures.com/mathematics.html

I agree with Leo Petr about using that in my head. I can multiply into the hundreds(xxx*xxx) in a couple seconds.

Teaching kids to only rely on calculators is… perhaps the stupidest and most foolish thing I have seen(except for what I’ve seen in some of my classes).

First, teach the kids how and why the math works(and how to do it quickly and easily in their heads), THEN let them have calculators because calculators can be faster and more precise for big numbers(if you enter it correctly… and have it set right(hexadecimal or binary!? Oh wait, you want normal? Darn)… and it isn’t a piece of crap like my current calculator that I just turned into scrap about an hour ago).

In my precalculus class(super easy because I’m reading Calculus by Michael Spivak(Thanks for recommending it!)), I finish most of the work in a quarter of the time everyone else does or less because I can multiply/divide into the hundreds places very quickly in my head.

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The turning a sphere inside-out was interesting and refreshing. I didn’t know that could be done with those rules(But you don’t know till you try).

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I’ve already seen The Tenth Dimension, and I think it’s a great concept. Like Mind, I also wonder what it would have been like had we been fourth dimensional and had developed our sciences as such…

[...] Thought-provoking Mathematical Videos [...]

English is not my native language and I’m not quite familiar with the US education system, so, please, bear with me.

I’m appalled by what is described in the videos about math education. When I first watched them, I thought it was a prank. A quick search on Google revealed that I was wrong. For me, there’s comfort in the fact that this nonsense hasn’t spread outside the United States yet.

One commentator (lucio) defends the current situation by saying that parents should go back to school in order to keep up with their children. Well, the lady featured in the first video did that and she found out she performed better than her younger colleagues who recently graduated from high school. So, it appears that lucio’s prescription doesn’t work. The second argument is that learning how to divide a problem into smaller pieces is a valuable skill. It’s easy to apply that method to small numbers. However, try to do that with big numbers (eg. 436728652675 and 52718876) and you’ll be overwhelmed. That method suspiciously looks like a botched implementation of the euclidean algorithm. However, that’s beside the point. What the videos depict is an inability to master the skills that previous generations took for granted. It is a system that ignores the advice given by eminent mathematicians of the past : to become proficient in maths, one must solve a lot of problems, not dwell in fantasy. If learning maths means planning a virtual world tour or manipulating little cubes, then teachers should all become travel agents or toy sellers.

No matter what young people think, the results speak for themselves : nowadays, college professors have to repair the damage caused by the New Age school system. We can debate this subject all day long; the fact remains that somebody must build and maintain the infrastucture we rely on in our daily lives. That is where fuzzy maths fall short.

I have to agree with derson above and disagree with lucio. I teach Math in 6th grade in Japan. We actually use a 7th grade text book in order to elevate the Math level for our students. I do teach the 26 * 31 = 20 * 30 + 20 * 1 + 6 * 30 + 6 * 1 method. In fact in traditional math it is called the Associative property of Multiplication. But it only really works after students already have a foundation in traditional Algorithms. How can you do “Mental Math” and divide 360 by 2 if you have not experience long division?

The Second video was even more terrifying because my entire life I have always envisioned math as a series of interrelated skills that build on each other in a hierarchy. How can students understand higher math without this hierarchy? It is ineffective. Should we teach other lessons like this?

I was going to teach you the basics of architecture, but I want you to discover it for yourself.

Ridiculous. You give an objective. Ask reflective questions and use metaphors and related examples, then practice, correct, guide and perfect.

I enjoyed watching the first video on mathematics education. I found it enlightening. I have a PhD in Mathematics but when it comes to real world calculations I use a calculator, and when I don’t have a calculator, I use methods like partial sums, partial quotients and the “cluster” method. I find the cluster method particularly useful and made great use of it just the other day when drawing up a plan for our kitchen remodelling. I seldom use the full blown “standard” multiplication algorithm and I can’t remember when a last did a “standard” long division. The standard algorithms are algorithms for machines. The other methods are what you use when you actually want to understand the numbers you’re working with. (Eg. you’re exploiting distributivity of multiplication over addition (it’s not “associativity” as John says above). You still absolutely need to know your multiplication tables up to 10, but otherwise the “alternative” algorithms seem like really good ways to get the job of arithmetic done in the real world. And once you know a bunch of different methods (including, say, the Russian peasant algorithm), the cluster method lets you pick and choose different methods to combine them. For example, someone schooled in the standard algorithm, when faced with 24*57 and 24*60 (like might happen when computing the area of the counter for the new kitchen…) would have to perform two long multiplications but someone schooled in the cluster method would reuse the result of one computation in the other. Much more efficient I think.

Those cluster algorithms looks different than commonly used “long multiplication”, but they’re the same, only constructed differently. You still have to multiplicate digits to get the partial results and then add them up to get the answer.

Hmm.. But it reminded be about something called “Vedic maths”, that is, mathematical methods founded in ancient Vedic texts. Here’s a little sample of those techniques [it's a tutorial]:

http://www.vedicmaths.org/Introduction/Tutorial/Tutorial.asp

I see they’re based on the core features of the decimal system and the modular arithmetics.

Those who set the curricula should read Isaac Asimov’s short story set in the future about the Scientist who discovers a “new” way that people (not machines) can perform calculations…

An exciting ‘discovery’ using a writing implement and paper!!

Naturally, his ‘discovery’ in not well received by the establishment – surprise !!

I use a slide rule, myself!!

Batteries *not* included or needed…

seems quite reasonable to me. i don’t find these approaches objectionable. this video is an example of what happens when someone who is not a math educator seeks to become a critic.