A Picture is Worth a Thousand Words

The NZ Herald reports on a maths teacher who has come up with a nice diagram on the basics of complex roots.

The article opens with:

Very few people wake excitedly every Sunday at 3am thinking about calculus.

which helps fuel the typical maths teacher stereotypes, but the idea seems novel. I’m unsure if his approach is really that new (educators love dressing up old ideas with fancy packaging and call it something creative and innovative) but it is spiffy enough in presentation. I’ll gladly let him have the benefit of the doubt.

The article has a picture of his model, but doesn’t explain in much detail as to what it means. Although, it is a moot point because most of the general public doesn’t have knowledge of what complex or imaginary numbers are. I think I’ve managed to work out the general gist of the concept from the picture. I’ll leave this as an exercise to the reader.

And whilst I’ve been thinking about the maths pedagogy behind this idea – I’ve completely forgotten the rarity of a newspaper article about maths. That isn’t about a “shortage” of teachers. This article shares a real gem of maths teaching knowledge. This image is powerful – it takes something so abstract and turns it into something concrete that can be visualised. I hope that this idea gets spread far and wide.

What makes this article important though is that teachers sometimes have the tendency to be lone rangers and can end up reinventing the wheel. The most effective teachers are savvy enough to copy the best ideas floating around and use them in their classroom.

A Possible Boon for Kiwi Academics Wanting to Cross the Ditch

The Australian reports that academics have been left off the list of skilled occupations for migrants to Australia, despite a shortage. An opinion piece in this paper points out that the list also excludes Mathematicians and Statisticians which are also skills in great demand in many places. If these reports are accurate, then it presents an opportunity for New Zealanders who want to work in Australia. If there really is a shortage, it will be worsened by the reduction in the number of people able to get these jobs because they can no longer leverage these skills to gain visas enabling them to live in Australia. So even though budgets are tight, more money will be on offer for these jobs. So basically these jobs with a premium are available to Australians with the right skills – or New Zealanders. New Zealand citizens will gain the benefit of having competitors for these jobs excluded.

One could even  say that this move is an indirect way of advancing the so called poaching of New Zealand academics by Australians that has been alleged by some.

Slow Uptake of New Curriculum

The NZ Herald reports on the front page that the uptake of the new curriculum document published in 2007 is slow indeed. Not that this is any surprise to me. In Mathematics, teachers will still be swearing by the burgundy bible, a common nickname for the older Mathematics in the New Zealand Curriculum, on account of the colour of its cover. I think it won’t establish a real foothold until a lot of teachers new to the profession today start to get promoted and put in more senior management roles. And by the time that happens, the next curriculum to supercede this one will have been published…

The new curriculum for all subjects at all levels from Years 1-13 is far more concise, now in a book half as thin as just the old maths curriculum. It does a lot more than convey than convey the subject matter – in fact it doesn’t even do a lot of that. The prescription of subject matter (and other parts) is very condensed, and the unpacking of its meaning and interpretation is left up to individual schools.

Mr Gall said the new curriculum required a big shift in thinking as it was not as focused on what was taught, but on how or why it was taught.

That is indeed one of the big shifts, in subjects such as history, there are no actual topics prescribed. In English, there is not one mention of Shakespeare.

The curriculum is considered to be “radical”, and it will be especially radical to those in the back to basics brigade. The preamble to the subject matter contains a framework including values, key competencies, learning areas (what I have referred to as the subject matter) and principles. Each of these frameworks are packed with plenty of buzzwords.

The new approach works for some subjects better than others. For example, in Music there is less about particular forms of music which makes it easier to include more than just Western European classical music. Some may scoff at any steps to “dumb down” the music curriculum but classical music doesn’t represent the diet of most people’s musical tastes, illustrated by classical record sales as merely single percentage digits of market share. But for subjects like maths, regardless of its now generic curriculum prescription, parents will still expect particular specific things like Pythagoras’ theorem or solving a quadratic equation. Those things are still in the curriculum, but specific mentions of specific skills are now rare. They will want the old stereotypes to be reinforced like I mentioned in an earlier post.

What is one very striking change is that maths is now called Mathematics and Statistics in the new curriculum. Statistics has now captured the attention of many and has quite a lot of resources dedicated to it – and the Statistical Enquiry Cycle is one of the subjects that has more rigourous treatment. This is a bit ironic at senior high school level as stats is seen to be less difficult than calculus.

Inverse Pride in Lack of Maths

The NZ Herald has a story about inverse pride in lack of maths skills, or sometimes more specifically, numeracy skills. This phenonmenon has been around for a long time. Many school children are scared of maths, even when they are capable enough of doing it. There also negative stereotypes of it being hard and only for “smart” or “nerdy” people. When I have taught lessons or have been a tutor often this is a far bigger barrier than any lack of ability amongst students.

What is even worse is that we seem to want these things to be reinforced. One professor at university told me about times when he’s done interviews with media wanting to speak to a “real” mathematician. As far as I can tell, real mathematicians when playing with ideas may do things like scribble some working on a piece of paper, run some numbers through a spreadsheet or write a few lines of computer code to run a simulation or generate some graphs to make sense of things. (They say a picture is worth a thousand words, well a graph is worth a thousand numbers).

What do the media want to see? Blackboards filled with complex partial differential equations (with lots of complicated looking Greek letters) and other fancy looking formulae which magically solves the problem. And even then, the whiteboard is the new blackboard.