Tuesday, May 19, 2009

fail: education of teachers

Imagine you're teaching a class, and you give them a basic test to check that they know the minimal information they need to understand the subject. And 75% of your class flunks this test.

That's bad.

And that's what recently happened to a group of teaching candidates given a basic math test to evaluate their qualifications to be licensed educators.

If this situation happened with a group of students, I would not blame the students. Once failure reaches a certain ubiquity, it's clear that the expectations of the test are no long aligned with the accessibility of the information. Something has gone wrong with the education itself, not the students.

And so, in a highly cyclic fashion, we have an education problem that re-invents itself as the product of the previous generation proves itself poorly prepared to take the reins of the next.

How can we break out of the cycle? I suggest we begin by universally recognizing the problem. Follow up by providing motivation for smart people to go into teaching - make teaching a more respectable, reasonable, and decently-paying career (I'm saddened to realize that I can add "safety" to the list of things many teachers currently lack in their jobs). It's not easy, and I'm resisting the temptation to pontificate further on the tip of this iceberg.

Here's the short article about the abysmal candidate performance:


You might notice the sample math problem they show. Yes, it would probably be trick for many very young students, but frankly it's easy for anyone who knows a little math. If your job is not only to understand basic math, but to teach it, then questions like this are more than reasonable.

Monday, April 6, 2009

chocolate is good for math

It's true!

A recent study revealed that consuming cocoa-derived flavanols (naturally occurring in chocolate products) helped subjects attain improved performance in simple mental math:


As a mathematician, I must note that what they were really studying is basically just arithmetic, so claiming chocolate helps with all math from this study is akin to saying you'd be a better poet simply because you're better at spelling. Maybe some correlation, but it's a stretch.

In case you don't want to give yourself another excuse to consume vast quantities of cocoa, here are a few other items (according to this website) which also contain flavanols: red apples, apricots, and green and black tea.

Friday, March 27, 2009

youtube edu

Yesterday google announced the release of the youtube edu channel:


This is a subset of youtube videos devoted to education, primarily for college students.

Clearly, this is a good idea. Education is evolving to work better with modern resources (ie the internet), and this is another step in the direction of connecting great teachers with motivated students.

If mathskool were a business competing with youtube edu, this would concern me greatly :) But it has always been a key element of mathskool that it is a completely free and open service. If youtube makes a better service, it simply raises the standard. I plan to continue contributing to mathskool in my free time, in the hopes that any new features will be useful to students, and at very least encourage others to consider similar ideas or improvements. And the videos have always been hosted on youtube from the start, so that they still gain overall exposure and continue to help students through either site.

It's also important to note that youtube edu is focused on a different audience (college level), whereas mathskool is focused on middle/high school. In addition, the culture of youtube is less interactive than the vision of mathskool. Of course, youtube already has a great community of users, which is an as-yet-unmet prerequisite for a truly interactive mathskool community.

Keep up the good work, open educators!

Saturday, February 28, 2009

Thoughts on math curriculum

This article is written concerning the national Australian math curriculum, but I very much appreciate the author's perspective on how we think about math education:
What do I want from a national curriculum? I want a dodecahedron in every classroom, and beautiful diagrams to ponder. I want students to know why there are infinitely many prime numbers, and for them to realise no one knows about twin-primes. I want them to know what the golden mean is, and why it is irrational, and why we care. I want pattern and play and beauty. And I want the times tables.

Is teaching any of the above useful? It is exactly as useful as teaching Harry Potter and Shakespeare.

Ok - I actually think some of the most beautiful mathematics happens to also be very useful - in this regard, I don't totally agree with the author (Marty Ross). Understanding the structure of the primes and related ideas gives us many cryptographic tools, for example. Understanding the meaning of irrational or transcendental numbers lets us know when certain things are impossible - we won't waste our time searching for an algorithm to square the circle (using the traditional construction tools, that is). And that just scratches the surface.

But the analogy to popular and influential works - Harry Potter and Shakespeare - is something I think many educators and students don't recognize. It is obvious that the large majority of careers don't rely on a profound understanding of Shakespeare, and yet we feel that an education without such crucial literary components is incomplete. Why do so many people seem to consider the beauty and value of the world knowledge of math to be inferior? Some may argue that math lacks the cultural saturation of great works of art, and I would have to agree. And yet, math is everywhere, and not because we write stories about it, but because it describes the raw logic and flow of the world around us. To borrow a phrase from Robert Osserman, math is the poetry of the universe.

Tuesday, January 27, 2009


Who knows best about what's good and bad about the present and potential future of mathskool.com? You, the users!

That's why I just added a link from the top of the mathskool.com headers to our own uservoice page. This is a very nice user feedback system for collecting and discussing ideas and bug reports. Every time you have an idea, type it into uservoice, and they automatically search for similar ideas. This way you avoid duplicate ideas, and you can vote in the main thread representing your idea. As the mathskool web builder, I can also provide plenty of feedback on these ideas - marking things as planned, started, completed, or not going to implement in some cases. It's a nice interface, and I'm glad I can give users a very friendly way to express their thoughts on the site.

Saturday, January 24, 2009

one in a million?

This article:


recently claimed that the odds of the same pick-3 lottery ticket happening two days in a row - which did happen this past Monday and Tuesday - are one-in-a-million, so that it was a rather surprising occurrence. The choices allow ten numbers in each of three places, and order matters. So there are 1000 choices of ticket. But that means, whatever yesterday's winning numbers were, the odds they're the same today is 1 in a 1000, not 1 in a million. We'd actually expect this to happen about once in three years - not such a wild coincidence after all.

The fact that this article was published at all is a little scary to me. This is very basic probability theory - even if math is a journalist's weak point, I would imagine you could double-check such a key fact with someone else who knew their stuff. In an ideal world, responsible members of the media would have at least a better intuition for something like this.

Of course, I'm not so worried about trivial inaccuracies in novelty news, so much as I am about a general lack of educated reporting - the kind of thing that has lead many folks (at least in the US) to doubt the legitimacy or human-influence on global warming, for example. This is an area on which the scientific community has been in virtual consensus for many years, contrary to the impression you might receive from certain media outlets. Any good disseminator of knowledge cites their sources, so I'll back that up with a quote from the Doran/Zimmerman 2009 report on scientific opinion of global warming:
It seems that the debate on the authenticity of global warming and the role played by human activity is largely nonexistent among those who understand the nuances and scientific basis of long-term climate processes.
If you're curious, there's more on this wikipedia page.

Monday, January 12, 2009

math is the best!

A recent article by a career expert at careercast.com ranks mathematician as the best overall job. Cool.

I sometimes forget how much nicer it is to be a mathematician / programmer than some of the lower-ranked alternatives, such as taxi driver or lumberjack.

Unfortunately, I'm not sure this article could effectively change a lot of young students' minds about how much they like math. If you ask a kid if they'd rather do some math or take a chainsaw to a tree, I think most would choose the chainsaw. It seems to reduce to the more profound problem of making life choices in the context of youth - your first glimpses of the various options (such as careers) can be fleeting and misleading, and the school culture of your peers adds pressure to base decisions on status more than intrinsic merit.

Here's a Wall-Street Journal article about the jobs rankings: