Here's a trick question. The type of question that Chris Tarrant slides in to tempt the players in “Who Wants to Be a Millionnaire” or Oxbridge candidates get asked to fox them.
There's always a couple of obvious answers to choose between that give the appearance of being the right answer and then a couple of ringers that you dismiss immediately until, just as quickly, you begin to doubt the certainty with which you dismissed them.
So here's the trick question. What is the best way to learn Times Tables?
a) by rote
b) by reasoning
c) by social learning
d) subliminally
If you're a young teacher, chances are your training college will have taught you to answer (b).
If you are an older teacher or parent, your experience will probably lead you to opt for (a).
And either way, you'll be able to point to evidence to support your case.
So here's the first warning signal that you might be missing something vital. Conflicting research is always a clue, if ever there was one, that there is more to this question than meets the eye.
There is a gift of new understanding in this conflict if we look again, but what is it?
On the one hand therefore, supporting learning by rote we have schools minister Nick Gibb in a speech on 10th July this year, citing research by Carnegie Mellon University to support his view that “There are things that do need to be taught by rote, for example multiplication tables." Mr Gibb compares learning times tables to playing the piano, when children repeatedly practice scales and chords by heart. “The working memory is only so big and there are certain things you need to embed in your mind. When you play the piano, you have to acquire an automaticity to it and that comes with practice. The same comes with learning to read. All these things come with practice and that’s what multiplication tables are about." (See full article here)
In reply, we have Professor Peter Bryant of Oxford University on 20th July citing research at the university citing the importance of Maths reasoning as well: “Both arithmetic and maths reasoning are important and necessary, but we think there is a danger of maths reasoning moving out [with the introduction of the new curriculum].” His study showed that strong maths reasoning aged eight was a better predictor of being good at the subject aged 11 and 14 than strong arithmetic skills. He conceded however that “you can’t teach reasoning without children being able to calculate”. (See full article here)
So how do we resolve these conflicts?
The first obvious question to ask is are learning by reasoning and learning by rote, by definition, mutually exclusive? And less obviously, we should ask whether learning by reasoning and learning by rote are even the only or best ways to learn.
We all know for example that parents reading to children at home leads to higher literacy levels. Furthermore there is overwhelming evidence to prove it and all the research points to this same conclusion. But what's going on here is not just about literacy. The role model behaviour of parents in reading to their children provides multiple opportunities for close contact with reading and imitation of parental behaviour by their children. These positive learning practices, role model, close contact and imitation are what is meant by the term social learning and of course social learning is not applicable simply to literacy. The fact that skills and passions are often passed from generation to generation is testimony to the fact that social learning is an incredibly powerful, generic path to learning any subject, including numeracy and of course Times Tables. (Which is why I have invented Times Tables Plates, to provide social learning opportunities in numeracy, every mealtime, both at home and at school.)
So should (c) therefore be the answer to this trick question?
Well, now that we've evaluated all the options in detail, let's just see what we mean by subliminal learning. Most of us are aware of the perceived power of subliminal advertising. Research evidence is actually quite mixed but academic studies in recent years now support our perception that it is indeed a powerful way to learn something. Common sense also tells us that babies learn to speak, walk and to copy us in a more or less unconscious, subliminal manner based on instinct. None of us believes that babies go through a reasoning process before being able to speak. Marie Montessori built a whole way of teaching on these common sense observations, creating a variety of stimuli to learning using all the senses to maximise the potential to learn sub consciously and subliminally. Indeed, because learning how to speak, walk and behave are what distinguishes human beings from other creatures, should we perhaps conclude that subliminal, unconscious learning is the most powerful of all paths to learning? (Which is why once again I have invented Times Tables Plates, to provide sub conscious, subliminal learning opportunities in numeracy, every mealtime, both at home and at school.)
Should (d) therefore be the answer to our trick question?
Of course what I'm driving at is that none of these options are the best way to learn anything, including Times Tables. They are all important and I would imagine that most people would agree. Something important is being lost if anyone of these ways of learning is neglected. As ever it seems, a holistic approach seems to be the ideal approach.
Here are a few more questions to consider which I might address in a future blogs:
They've got to be better than boring blank plates and they might just be the serendipitous catalyst for wonderful conversations on numeracy around the dining table, and trigger social learning and subliminal learning both at school and at home, to set your children onto a path of improved reasoning, better understanding and above all, an enhanced desire, hunger and respect for the act of learning and questioning itself, driven by the role model behaviour of their parents, teachers and peers. And yes! all this simply because you put theMultiples' Times Table Plates on your dining tables.
c) by social learning
d) subliminally
If you're a young teacher, chances are your training college will have taught you to answer (b).
If you are an older teacher or parent, your experience will probably lead you to opt for (a).
And either way, you'll be able to point to evidence to support your case.
So here's the first warning signal that you might be missing something vital. Conflicting research is always a clue, if ever there was one, that there is more to this question than meets the eye.
There is a gift of new understanding in this conflict if we look again, but what is it?
On the one hand therefore, supporting learning by rote we have schools minister Nick Gibb in a speech on 10th July this year, citing research by Carnegie Mellon University to support his view that “There are things that do need to be taught by rote, for example multiplication tables." Mr Gibb compares learning times tables to playing the piano, when children repeatedly practice scales and chords by heart. “The working memory is only so big and there are certain things you need to embed in your mind. When you play the piano, you have to acquire an automaticity to it and that comes with practice. The same comes with learning to read. All these things come with practice and that’s what multiplication tables are about." (See full article here)
In reply, we have Professor Peter Bryant of Oxford University on 20th July citing research at the university citing the importance of Maths reasoning as well: “Both arithmetic and maths reasoning are important and necessary, but we think there is a danger of maths reasoning moving out [with the introduction of the new curriculum].” His study showed that strong maths reasoning aged eight was a better predictor of being good at the subject aged 11 and 14 than strong arithmetic skills. He conceded however that “you can’t teach reasoning without children being able to calculate”. (See full article here)
So how do we resolve these conflicts?
The first obvious question to ask is are learning by reasoning and learning by rote, by definition, mutually exclusive? And less obviously, we should ask whether learning by reasoning and learning by rote are even the only or best ways to learn.
We all know for example that parents reading to children at home leads to higher literacy levels. Furthermore there is overwhelming evidence to prove it and all the research points to this same conclusion. But what's going on here is not just about literacy. The role model behaviour of parents in reading to their children provides multiple opportunities for close contact with reading and imitation of parental behaviour by their children. These positive learning practices, role model, close contact and imitation are what is meant by the term social learning and of course social learning is not applicable simply to literacy. The fact that skills and passions are often passed from generation to generation is testimony to the fact that social learning is an incredibly powerful, generic path to learning any subject, including numeracy and of course Times Tables. (Which is why I have invented Times Tables Plates, to provide social learning opportunities in numeracy, every mealtime, both at home and at school.)
So should (c) therefore be the answer to this trick question?
Well, now that we've evaluated all the options in detail, let's just see what we mean by subliminal learning. Most of us are aware of the perceived power of subliminal advertising. Research evidence is actually quite mixed but academic studies in recent years now support our perception that it is indeed a powerful way to learn something. Common sense also tells us that babies learn to speak, walk and to copy us in a more or less unconscious, subliminal manner based on instinct. None of us believes that babies go through a reasoning process before being able to speak. Marie Montessori built a whole way of teaching on these common sense observations, creating a variety of stimuli to learning using all the senses to maximise the potential to learn sub consciously and subliminally. Indeed, because learning how to speak, walk and behave are what distinguishes human beings from other creatures, should we perhaps conclude that subliminal, unconscious learning is the most powerful of all paths to learning? (Which is why once again I have invented Times Tables Plates, to provide sub conscious, subliminal learning opportunities in numeracy, every mealtime, both at home and at school.)
Should (d) therefore be the answer to our trick question?
Of course what I'm driving at is that none of these options are the best way to learn anything, including Times Tables. They are all important and I would imagine that most people would agree. Something important is being lost if anyone of these ways of learning is neglected. As ever it seems, a holistic approach seems to be the ideal approach.
Here are a few more questions to consider which I might address in a future blogs:
- How much do you care that you have an holistic numeracy strategy or not?
- What is your strategy to implement such an holistic numeracy approach?
- Who is responsible for designing and implementing an holistic strategy?
- How receptive are your teachers to implementing an holistic approach in spirit, not just the word?
- How receptive are children to embrace each strand of the holistic approach?
- Does such an holistic approach require more than just teacher inputs and teacher facilitation?
- Does such an holistic approach require an element of teacher leadership and authority, for rote learning for example?
- Will teachers resist any leadership/authority role?
- Do teachers, school managers and children require a formal, school-wide emotional literacy framework in order to manage teachers' dichotomous, emotional roles, that is to say between their emotionally neutral 'input and facilitation' roles, and their emotionally charged 'leadership and authority' roles (required for rote learning for example)?
- What support can parents provide in building such a community wide holistic approach?
- Would the emotional literacy framework assist in managing and developing the school/home partnership?
They've got to be better than boring blank plates and they might just be the serendipitous catalyst for wonderful conversations on numeracy around the dining table, and trigger social learning and subliminal learning both at school and at home, to set your children onto a path of improved reasoning, better understanding and above all, an enhanced desire, hunger and respect for the act of learning and questioning itself, driven by the role model behaviour of their parents, teachers and peers. And yes! all this simply because you put theMultiples' Times Table Plates on your dining tables.
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