Thursday, 28 January 2016

How did you learn your times tables?

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.


  1. It's interesting what curve balls life can throw at a person. As a student in school I rather unconsciously divided kids into 3 groups:the smart kids, the regular kids and the bad kids. There was this boy Pat who was a bad kid. His parents ran a successful
    business, he lived in a beautiful home, and he was obviously sharp
    and bright. Pat was a class clown and never did well in school. After elementary school I never thought much about him again, not until I had two children and they were sharp and bright but could not do well in school. As a parent, I watched as my little girl was absolutely imploding before it even came into my radar that there was such a thing as learning differences and learning disabilities. It seems to me that people who make the sorts of decrees that you are discussing just have no comprehension or motivation to grasp the concept that there is such a thing as different processing speeds and varying abilities to cement certain kinds of facts into memory. Even as a parent, being an intimate witness for years to these struggles, it's still surprising what a challenge it is to empathize with minds that are so different than my own. And I can tell you for certain that most of the teachers who didn't understand my childrens' learning differences wouldn't or counldn't budge in terms of opening their minds to the concepts that some children think differently. For some wonderful reason you survived, but the fact that you are still writing about it certainly attests to how deeply this misunderstanding of your abilities touched you. You write, of the computerized and times-restricted test that "For the flunkies, there will undoubtedly be some sort of penalty." Yes, but the worst penalties include the hijacking of children's futures. A few years ago I heard that my old schoolmate Pat was he in jail. Last I heard he was dead.

  2. Thanks for replying and sharing this story.

    It’s disheartening to hear about the stubbornness of some of your children’s teachers. I have met many teachers who are not bound by such uncompromising attitudes, and who do accept that kids learn and process things in different ways. I hope your children had some of those as well.

    It’s also sad to hear what happened to your schoolmate Pat.

    In the end, some problems in schools are caused by what is poorly mandated from above, like that UK times-table test, and that can harm the children and hobble even the best of teachers.

  3. IT was the teachers who were willing to really look at how their own practices impacted the students and who were willing to share their insights with me that made all the difference with my own kids. My children still carry the shame that others, who were not so insightful, where able to dole out. I have noticed that the attitudes, or decrees, that come from above have a way of changing the learning cultures. The attitudes of the principles and superintendents resonated far. I wonder how much the attitudes of the secretary of state for education shape the classroom culture.

  4. Ah. Nice to hear that there were at least some caring teachers at your children’s schools. Please encourage them.

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  6. I want to clarify that it wasn't my intention to rant about my children's teachers.What I meant to lament is how difficult it is for many, probably most, people to understand learning differences. "Even as a parent, being an intimate witness for years to these struggles, it's still surprising what a challenge it is to empathize with minds that are so different than my
    own." This is important to talk about because there are people in power who make decisions that ultimately do real harm to children. Broad decrees like the one you reference perpetuate a culture that alienate too many students.I am glad you are writing about this. I want to encourage this kinds of discourse.

  7. I also believe that there are great differences in how children think and learn, and that our school systems need to accommodate these differences.

    Part of the problem may be that many people with power and influence over education are in their positions because of qualifications that have very little to do with K-12 education. They are prone to creating “one-size-fits-all” policies that end up creating misery for both teachers and students. Ultimately both teachers and leave the classrooms, if not physically, then certainly emotionally.

  8. should have said "both teachers and students"