When I was a kid, I liked playing ice hockey. I was actually not very good at it — no Connor McDavid here! But I did acquire the basic skills. For example, I figured out how to lift the puck. (For you non-hockey players, that means shooting the puck in such a way that it flies off the ice into the air. It’s a essential skill if you want to be able to score goals.)
I practiced that skill a lot. Whatever I did, it worked. I could lift the puck consistently without thinking about it. I haven’t shot a puck for many decades, but whenever I imagine doing so, I swear can feel the memory in my triceps.
Of course, I really did not "figure out" how to lift the puck. I did not know the theory behind the lifting action. And to the extent that the skill was necessary, I didn’t need to understand the theory.
The lesson is this:
When learning something new that you will need for later use, master the mechanics first. You can learn why it works later.
* * * Warning: possible straw man ahead * * *
It’s a useful lesson. It helps me understand the approach to mathematics teaching advocated by the back-to-basics people: You can be successful by
learning the how without understanding the why. Just learn the essential basic facts and algorithms. Don’t worry about why the puck flies into the air — just practice shooting enough so that you can lift it consistently and effortlessly.
Reasonable advice? Maybe. But, no matter how hard I practiced, I could not always
"lift" the multiplication tables. As far as the basic multiplication facts are concerned, I do not have what some people call
rote recall — I do not have the ability to rapidly and effortlessly retrieve all of the basic learned facts from memory.
A great chunk of my own elementary math education was founded on the contrary belief, that rote recall is, in fact, achievable by everyone — that all it takes is practice. Accordingly, my classmates and I were regularly drilled and tested on the multiplication tables. I did not do well, and I argued with my teachers. Ultimately, I was
punished for my inability to memorize the 12 x tables.
I don’t believe that my recall difficulties are exceptional. The more blogs I read, the more I suspect that there are many people who, no matter how much they practice, will never possess rote recall of the basic arithmetic facts. In that sense, those people
can never know the basic facts.
So, it was with interest that I read that Nikki Morgan, the secretary of state for education in the UK,
has decreed that:
"we are introducing a new check to ensure all pupils know their times tables by age 11"
An
interesting post by @thatboycanteach asks what it means to "know" the times tables. Like me, he suffers from what might be described as
rote recall deficiency. And like me, he survived (and even thrived) by using various work-arounds to compensate.
The UK times-table test will be computerized and time-restricted. It looks like it will be based on pure rote recall. For the flunkies, there will undoubtedly be some sort of penalty. It’s unlikely that they will be physically punished like I was, but even non-corporeal punishment can inflict great stress and harm and, in the end, may prevent them from learning mathematics.
What is of concern to me in Alberta is that, however sincere the back-to-basics people may be, they seem to be basing their reform efforts on the very thing that caused me difficulties, namely, the belief that all students can and must achieve rote recall, that this is the only way to know the basic facts.
That is the conclusion that I draw from reading their petitions and press releases. If I’m wrong, if I am raising a straw man, it is difficult to understand why they also want to banish the teaching of alternate approaches to the basic facts and algorithms that are needed so that people like me can compensate for our deficiencies.
