The time for submissions to ACARA’s review has ended. Which means it’s now time for machinations and clandestine transactions. One hopes that our Glorious Mathematical Leaders know who they are dealing with and how to deal with them.* In the main, we’ll get back to posting on other topics.** Still, there are ACARA irritants remaining, things left unwritten, and when we’re sufficiently irritated we’ll post on it.
One constant irritant has the been the “it’s all there” defenses of ACARA’s draft. Yes, so it goes, there is an increased emphasis on inquiry/modelling/whatever, but not at the expense of basic skills.
“We absolutely have to focus on problem solving [but there should also be] an equal focus on building fluency”.
So, it’s not “strategies/efficiency/skills/content” versus “problem solving/reasoning/exploring/thinking”:
“Great Maths teachers do both!”
See? The problem isn’t with the ACARA draft curriculum. The problem is that you’re not a great maths teacher.
Well, no. The simple answer to the claim that “we can have everything” is that, no, we cannot. Great teachers do not pretend that they can do everything; great teachers have a proper appreciation of their limitations. Great teachers also appreciate the limitations of their students, and the limitations of temporal reality. They appreciate that it is simply impossible to have an increased focus on B not detract from the focus on A.
That is not to deny that the certain mathematical topics and certain aspects of mathematical teaching should not be thoughtfully linked. Of course they should. It is always worth reflecting on how an activity or exercise might be linked to past and future lessons, to revisit some numerical trickiness or to subtly flag some future concept. The small act of choosing a coefficient of 7 rather 12, including or not a troublesome square root, can create or encourage a spark of recall or recognition or wonder. But none of this comes for free. None of it instills magic in the educational pudding. If an exercise or activity contains more to think about, then the student will require more time to think about it.
In brief mathematics teaching is not a zero sum game, but it is close. You may want to have the kids to spend an hour discovering – or “discovering” – Pythagoras’s theorem; but that is an hour you will not have to spend on something else. You may think it is worth the cost,*** but do not pretend that there is no cost. Do not pretend that it is free.
Moreover, if you want to make mathematics teaching as close as possible to a zero sum game, the fail-safe way to do it is to add in a mountain of real-world exploration, as is done in ACARA’s draft. There is then effectively no feedback to mathematics, and the addition of this absurd Everest of non-mathematics must of necessity result in the equivalent mountainous subtraction of mathematics.
The draft mathematics curriculum is a con, and an old and familiar and obvious con. The world has always been full of hucksters selling the “you can have it all” line. ACARA’s hucksters are no different.
*) Some mathematicians are more equal than others.
**) Thanks to GooberBrain Gladys and our consequent homeschooling, it is difficult to find time for anything right now.
***) It is not.
I mostly used “drill” in my career teaching in juvenile justice centers, but it wasn’t empty drill. It was visual and historical and took student from not knowing much pre-algebra to deriving the quadratic formula. Was I robbing Jo and Gladys to pay Peter? Check out my new Youtube site: “Marc Roth: Math for Social Justice”. Thanks for the free publicity, Marty. Next time I’ll pay you instead of Peter.
Hi, Marc. I’m not bothered by a bit of self-promotion in the comments. Note, I’m not arguing whether drill, empty or otherwise, is preferable. (It is.) What I’m arguing is much more straight-forward: if you spend more time on B then it takes away from A.
As a slightly off-topic remark, all this is very applicable to VCAA’s stupid SAC system …
Indeed it is.
I actually don’t find this point off-topic at all.
If you increase the emphasis on problem-solving (and whatever ACARA actually means by that – I’m not even sure they know themselves) it makes sense that there will be an increased focus on SACs with “problem solving” and “unfamiliar situations” come VCE.
Which could be really, really bad.