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Learning Times Tables - 2014/12/14

Should primary school students be drilled on their times tables?

Note that I refer to these as "exchanges," and not "discussions." I always feel that discussions are intended to foster understanding and strive towards a mutually agreed position. "Exchanges" put me more accurately in mind of gunfire and battlefields, hence the use of the term.

That's a question guaranteed to create exchanges that generate much more heat than light. Indeed, I've just participated in one such exchange on twitter, and despite desperately trying to make myself and my position clear, it became obvious that there was somehow, somewhere, a complete disconnect.

Then I was sent a link to an article that rubbished the idea of learning tables, and I may see a chink of light. It may be that some people not only think about it completely differently from how I think about it, but even more, they don't mean remotely the same thing by the term "learning your tables."

Retracing the "conversation" on twitter I found traces of the same, fundamental, underlying disconnect.

Let me take you somewhere else first.

This question of "Barking at Print" was covered by Stephen L Burns in his 1988 short story "The Reading Lesson" published in the August 8 edition of "Analog Science Fiction/Science Fact"

I recently heard a child of about 8 or 9 reading some prose out loud. It was commendable just how well they could negotiate some of the more difficult words, and they read the piece without flaw. But there was something missing, and the phrase that came to mind was "barking at print." While it was true that they had read every word, got every phrase, and even had a good stab at inflection, it sounded like they were reciting without understanding, making the noises without having any idea what they were actually saying.

Just two weeks ago my wife said that she'd always wanted to learn the full text of the poem "Cargoes" by John Masefield, so I found the text, inserted it into the Spaced Repetition software I use, and three hours later we could both recite it.

It's true that as yet we had no feel for the rhythms, the pacing was wrong, the association of rhymes wasn't there, but we had it. But over the last two weeks we've been re-reciting it, each time getting more comfortable. Using it, becoming friends with it, learning the inner associations, and it is emerging as a full, performance piece.

But without that initial memorisation that would never have happened. Having the text not "to hand" but "to mind" has made it possible to use it, recite it, explore it, and become close to it, it a way that looking it up or re-reading it would never have done.

It seems to me that some people think that "learning your tables" is like that initial phase wherein we "bark at print." We learn the recitation with no meaning, no internal connections, no understanding, and no intent of subsequently using it, exploring it, playing with it, and becoming friends with it.

And it's true that if all you do is learn to spout meaningless syllables then all you'll be able to do is spout meaningless syllables. It's the follow-up and integration that converts that into something long-lasting and useful.

The piece I read was this one:

The image I get there is that of "barking at print." If that's what people think is meant by the phrase "learning your tables", then I'm 100% with those who claim that it's useless, and potentially deeply damaging.

But that's not what it means to me, nor to any of the teachers I've spoken with. They speak of knowing the tables, and being able to recall simple facts rapidly and confidently. They speak of being able to do simple "sums" as part of solving a problem without having to reach for a calculator at every other step.

Without the knowledge of simple multiplication facts, students are constantly interrupted as they try to solve problems, breaking flow, and preventing them from keeping the larger picture in mind.

So when we talk about learning your tables, are we talking about the same thing? Maybe not, and maybe that's the real source of the lack of consensus. Maybe that's why we are arguing - we're not really arguing about the same thing, we're talking past each other.

Maybe this is an issue of language.

So perhaps the thing to do is return to the real point:

Please, please, please, believe me when I say that I know that not every teacher believe exactly the same thing. Every teacher is different, and sweeping generalisations cannot and must not be applied to individuals. When I say these things, I may not be talking about you - don't for a moment think that I am. More, the secondary teachers I speak with generally have enormous respect for the work that Primary school teachers do. They know, as do I, that their workload is impossible, and there is no blame being levelled. They are making the observation that the students they see do not have the skills needed to progress as the curriculum demands.

What we need to do is equip the students with the tools they need. Secondary teachers I've spoken with say that the students they see don't know their simple arithmetical facts. They don't know that six times nine is fifty-four, and that inability is hampering their advancement. They're not ready to work on the next topic, because they simply can't do the problems. To learn a particular topic and gain mastery and/or fluency in it, they need to apply the things they've just learned. That means they need to work problems, and that requires that they exercise skills previously learned.

But often they don't have those previous skills.

The secondary school teachers might say that the students don't know their tables, but what they mean is that they don't have "to hand" the simple arithmetical tools.

I'm taking this quotation out of context, but I've had pretty much exactly this response in real life.

The primary school teachers I've spoken with say that drilling the tables is rubbish. One recently said "stuff your tables!" But maybe what they mean is that the meaningless spouting of memorised syllables is pointless.

Both are right.

But what do we do? How do we proceed? How do we help students gain mastery of the subject at whatever level they're up to?

For a start, we can reach a common consensus about what we are talking about.

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