Down under, the Australians are going through many of the same arguments about mathematics education that we are here in the US. In this column from The Age, Marty Ross — who holds a PhD in mathematics from Stanford — lambastes the Australian mathematics education community in ways that might seem eerily familiar to those who follow the similar issues in America. Quote:
[H]ere is an exercise from a current Victorian year 9 maths text: a farmer has 2C cows and 3H horses. The exercise is to find the square of the sum of the farmer’s animals.
The Victorian texts are not uniformly that pointless or that bad. But not much is good. Definitions are clumsy, problems are contrived, natural connections and beautiful insights are overlooked. The texts do not reflect a mathematical culture.
It is not just the textbooks. Teachers are poorly trained; the curriculum is moribund, rife with silly, contrived applications; and everywhere there is pointless calculation. And calculators – the cane toads of education.
Is there still proof? Proof is the source of the power of mathematics, the reasoning and the understanding: it’s what holds the discipline together. But it is practically dead. The very little proof that remains is meaningless and ritualised: maths as Latin Mass.
How did it get this bad? Primarily, it results from the failure to involve mathematicians, the people for whom mathematics is their life’s blood. The simple fact is, many of those responsible for mathematics education do not know sufficient mathematics to do the job.
There are lots more “ouch” moments in the article. Ross concludes by saying:
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.
Mathematicians do mathematics because it is fun and it is beautiful. If the curriculum is not written in that spirit, and if teachers are not trained in that spirit, then we are doomed. We will have yet another generation devoted to gradgrinding students into hating mathematics.
I’ll agree on many of these points — especially why mathematicians are motivated to do mathematics, the criticism about the lack of proof in the math curriculum, and to some extent Ross’ critiques of the mathematical background of mathematics education people. But what do you think — is Ross’ assertion that fun and beauty form the proper basis for a mathematics curriculum really sound? I mean, I’d like all my students to know about the infinitude of primes too, but does that sort of thing make a reasonable organizing principle for an entire curriculum?