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Learning Times Tables - 2014/12/14
Should primary school students be drilled on their times tables?
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.
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:
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.
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.
I've decided no longer to include comments directly via the Disqus (or any other) system. Instead, I'd be more than delighted to get emails from people who wish to make comments or engage in discussion. Comments will then be integrated into the page as and when they are appropriate.
If the number of emails/comments gets too large to handle then I might return to a semi-automated system. That's looking increasingly unlikely.
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