Archive for the ‘education’ Category

Can a kid who writes “MoM” know why odd plus odd is always even?

April 2, 2009

Here’s some discussion of (primary) maths education from off the usual mathsblog trail. It’s the this post from John Holbo at Crooked Timber. He offers this excerpt from his daughters homework:

3. What do you get if you add two ODD numbers together? – an even number
4. Do you think this is always true? – yes
5. Why do you think so? My MoM Said So

The question is what she could possibly be expected to have put that would be better. Could a child so young be taught even a vague understanding of a better reason? Some informal “first draft” of what a proof is? Is it worth the effort to try?

On a side note, sorry for the not posting for a while.

Advertisements

Joel Feinstein is blogging

December 13, 2008

Hey look! Joel Feinstein, who was my PhD supervisor, has a blog on WordPress. He briefly had it on Blogger, but I explained to him how foolish that was.
He’s using it to write about undergraduate level teaching, which he does very clearly and readably with lots of good examples of how to present complicated, abstract concepts in a way that students can absorb.

Blogging is surprisingly hard: have some links.

July 28, 2008

I have a new found respect for people who write essays. I haven’t had to write an essay in years. But I have started writing a longish blog post on the awesome amounts of structure you can expect to find in a random real (and hence why numerology based on patterns in well known constants is such epic fail). It’s REALLY hard work.

Linking to other people’s posts is easier. The folks at ScienceBlogs seem to have gone crazy for “two cultures” stuff about what is expected general knowledge in the arts and humanities compared to in the science and maths.

So we have a physicist raising the old complaint that not knowing basic arts and humanities is treated as much more shameful than not knowing basic maths and science.
Then an science ethicist (foot in both camps) giving some thoughts on it and again

Then another philosopher of science discussing some of the post-modernism bashing that came up in the comments.

Lockhart, Jenkins and compulsory maths

July 15, 2008

I meant to post about this forever ago but I was kind of busy. I’m going to be talking about maths in school. I have very little teaching experience and none at a level below undergrad, so I’ll mostly be talking about how I wish I’d been taught.

Simon Jenkins’ doesn’t really know what maths is and thinks very little is lost by kids not doing it. Yemon Choi gave him a good kicking for that at the time, and he deserved it. Apart from his blinding arrogance about his own knowledge of the subject, he was happy to push a line of “It’s hard and the kids won’t need it so we should let it go” which I find it hard to believe he would be happy to apply to the works of Shakespeare, or to foreign languages (everyone speaks English these days, right). He implied that the only arguments for the importance of maths were (bad) economic ones or conservative calls for the brain to be beaten into shape, of the sort once used for arguing for teaching Latin. Well, no. There is very good argument for maths teaching as a path towards being able to share in the beauty of the subject. I believe that being familiar with a few proofs (infinity of primes, irrationality of root 2…) and having some concept of what makes them proofs (not too refined a concept, because I don’t think the philosophers of maths have settled on one) ought to on the list of things needed if you wish to call yourself “educated” or “cultured” just as being familiar with a few poems and knowing what makes them poems is.

Despite all this, there was (weirdly) the skeleton of a defensible position in Jenkins’ nonsense. First what I was taught in maths up to GCSE (Sir Simon’s “advanced” quadratic equations and such) really wasn’t the route to sharing in that beauty. It was an awful lot of memorizing algorithms for solving artificial and formulaic problems. I learned how to multiply matrices without knowing that it was composing any kind of function; just remember it’s rows by columns. It was kind of dull. and it makes maths seem boring, and mechanical and all the bad things that people think it is but it isn’t. It got slightly better at A-level but that was more down to good teachers than the curriculum. So yes, a lot of “maths” in schools could be cut away and I’m prepared to believe that neither students, nor the sciences, nor maths itself would suffer.

Another thing in Jenkins’ favour was mentioning Innumeracy by John Allen Paulos and Hardy’s apology. These are books you should be thinking of it you want to cut the tiresome, repetitive nonsense out of maths education. Unfortunately, Jenkins’ views on them were EPIC FAIL. He claimed that Paulos’ recommendation of a good knowledge of probability and statistics to avoid being tricked by numbers from pseudo-scientists, advertisers and politician came down to “simple concepts applied to daily life”. Well not really. Thinking critically about numerical data, knowing what they really tell you and what is random noise or sleight or hand, is something people are naturally VERY BAD at. Our brains didn’t evolve in a setting where big numbers were much of an issue; we can’t get a good intuition of them. That’s why national lotteries exist. It’s also why bad science reporting is so common and thus why Ben Goldacre is so frikkin awesome. So if we are going (collectively) to take Paulos cure for the con men it’s probably going to mean lots of class time.

Jenkin’s on Hardy was bad in a more subtle way. Surprisingly for someone so proud of his training in the humanities he took the Apology altogether too much at face value. It’s a lovely book, but it’s very much A Mathematicians Apology, a personal account of how one mathmo worked. Jenkins’ treats it as a description of all mathematics and thus is able to shrug the subject away as a game done for pleasure by men in ivory towers. Maths includes many things which are very useful. What the Apology shows (better than any other book I’ve read) is that it is also a beautiful, pleasurable activity. This brings me back around to where I started; it’s a shame if this beauty isn’t shared.

American teacher Paul Lockhart’s essay A Mathematician’s Lament gives a plausible way of actually sharing it. Instead of long hours of compulsory drilling in algorithms for solving simultaneous equations teach maths like music. Have a specialist maths teacher, who has actually DONE maths – not just learnt more of it a college, but done some – go from class to class doing little bits of maths with small groups. Show them how you make a conjecture, how you look for counter-examples and find simple proofs. By this method he had a 12-or-13-year-old come up with there own argument why a triangle drawn inside a semicircle always has a right angle; that AWESOME!!!1 He also say that if they really don’t respond to the patterns and proofs of mathematics they shouldn’t be forced to keep doing it because nothing kills the joy of creativity like a compulsory class (He doesn’t mention exempting stats and probability from this; I would since they are more “life skills” than a creative subject).

So, the maths Simon Jenkins did at school probably was as pointless as he said and many of the arguments given why it matters are asbad as he says- but he’s still a clueless arse.