We can only think about what we know and, no mater how intelligent we might be, we cannot think about something about which we are ignorant. But how well do we need to know things? Is there any point to memorising facts?
I had an interesting discussion with some primary maths teachers recently about the benefits of memorising certain basic maths facts. While pretty much everyone agreed that if children had memorised number bonds to ten and times tables then they would have an advantage when performing calculations, there was a difference of opinion on what was reasonable to expect. Some teachers suggested that 100% fluency of times tables up to 12 by the end of Year 4 should be an appropriate minimum standard, while others were worried that it would be unfair to expect all children to learn so much in such a short time. Maybe we should have a sliding scale of expectations?
Now, I’m neither a maths teacher nor a primary specialist, but I do know that the ability to store information in long-term memory is not correlated with intelligence. There may be all sorts of physical or cognitive impairments which make it hard for children to remember things but it’s not true to say that some children are not clever enough to remember their times tables. They may not appreciate the value of knowing the times tables and they may struggle able to apply this knowledge in unfamiliar contexts, but the ability to recall information is achievable for all but the most damaged.
If we couldn’t remember we wouldn’t be able to perform anything except the most automatic process such as breathing and blinking. Even something as basic as vision requires us to learn how to make sense of visual signals; babies have to learn depth perception before they can adequately interpret their environment. The thing is, we’re unaware of many of the things we’ve learned. Very few people are ever conscious of the cognitive process of interpreting visual signals, we just see. Similarly, very few skilled readers are aware of having memorised the vast number of phoneme/grapheme relationships require to read English fluently, we just read.
The advantage of having stored such background knowledge in long-term memory is that we no longer have to think about it. Working memory – the site of conscious thought – is a small workroom in which we process information from the environment as well as retrieve information from long-term memory. Our ability to pay attention is strictly limited – there’s perhaps an average capacity to hold on to about seven items at once before we start forgetting stuff and feeling overwhelmed. Those people who have a slightly larger than average working memory have an enormous educational advantage; those with smaller than average working memories are those who most need to store the basics in long-term memory. If we have to use up some our limited processing power to think about phoneme/grapheme relationships then we’ll have less space to think about the meaning of the words we’re decoding. Likewise, if we’re able to instantly recall that the product of 7 x 8 is 56 this means we have a lot more space to solve a calculation which we have not memorised the answer to than if we have to first go through the process of working out what seven eights might be.
Everything we do depends of information stored in long-term memory and the more we know, the easier we find it to think. The good news is, storing information in long-term memory – or learning – is something we’ve evolved to find easy. Almost everyone learns to see and speak and cooperate with others with relative ease. And a majority learn to read and perform basic calculations without too much trouble. But even those children who seem to have so much difficulty remembering times tables have no trouble remembering thousands of song lyrics, extensive lists of sports trivia or whatever else they’re interested in. The general rule seems to be, no one struggles to learn what they recognise as being worth learning.
So, what’s the best process by which children might be expected to learn such information? Clearly it’s possible to memorise a relatively small domain – such as the 12 times tables – by brute force, but this kind of rote learning seems not to work for many. I remember chanting times tables as a youngster and the experience left me cold. I found that in order to retrieve 7 x 8 I’d have to work my way through the rest of the seven times table first. I never got to the point where I just knew the answer was 56. This isn’t much of an advantage and I had no more working memory capacity to solve calculations as a result.
One of the teachers I spoke to said that although some children had memorised times tables, they were unable to perform multiplications slightly outside these narrow parameters. For instance, they might be able to reel of the 9 times table up to 9 x 12 but have no idea how to work out 14 x 9.
This is the difference between flexible and inflexible knowledge. If we asked children to memorise phoneme grapheme relationships without ever getting them to think about how these re used to build words and sentences, then it’s possible that they might struggle to apply their knowledge to the task of reading a text. Similarly if all children do is rote learn number facts without thinking about what they mean then they might not be able to use their knowledge very flexibly.
When considering whether it’s worth trying to get children to memorise facts there are at least three considerations:
- Do the facts to be memorised have sufficient utility to make the effort worthwhile. For the basics of reading and mathematics this should be obvious, but for other, less foundational knowledge, teachers will need to consider the opportunity cost of investing curriculum time in this way.
- Trying to learn a fact in the absence of meaning is not only harder; it’s more likely to result in narrow, inflexible knowledge. Hopefully no teacher would insist on rote memorisation without also drawing attention to patterns. It’s not enough to simply get students to memorise basic knowledge, they also have to think about what it might means and how it could be applied.
- How will the process be undertaken? The word memorisation implies arduous and repetitive drill, but much of what we memorise is not learned in this way. Low stakes, distributed retrieval practice may offer a way forward, as might specific programmes like Times Tables Rockstars.