Are you sitting comfortably? Then move.

Hello everyone!  The world turns and just gets more and more bizarre.  Here in the UK, the COVID-19 lockdown is still in effect... kinda.  Schools have 'reopened'... sort of.  People are being encouraged to go back to work... but only travel it is essential.  Basically, no-one seems to know the score.  Don't get me wrong, I'm sure far more intelligent people than me are at the helm and I wouldn't want their jobs for all the blanks in the Scrabble bag but it is tough to establish a new normal when the variables shift quite so frequently.

So what better time to talk about Vygotsky's gift: The Zones of Proximal Development!

Children don't learn from within their comfort zone
Children need to be guided out of their comfort zone
Children need to feel safe to take risks
Children who take risks learn


Our old buddy Lev Vygotsky (see here for previous musings) decided a long time ago that learning cannot happen when we are comfortable.  And no, I don't mean that you need to be kneeling on a bed of nails to read Shakespeare, you can be physically comfortable.  Vygotsky was talking about psychological discomfort (which makes sense given that he was a psychologist).  

Okay, Mr M, neat-o.  So what?  Why should I care?  How does that help me help my child?

I'm so glad you asked...



A while after Jean Piaget (another social scientist) established his key stages of development, Vygotsky decided that simply allowing time to elapse and expecting learning to happen wasn't enough.  Vygotsky argued that, in order to grow and learn, we must first leave out comfort zone of known things.  

This is a legacy that has impacted all areas of our everyday lives, not just education.  Would there be any fun in playing a video game that did not get progressively more difficult as you played though?  Would you be content to read a simple cloth book of first words with a soothing glass of shiraz of an evening?  As human beings, we derive pleasure from success; endorphins are released when we accomplish difficult goals (probably - I am not a biologist); we feel good when we grow.  

Again, so what?  How does this help me convince my child that completing their maths homework is good for them?

A fair question.  My answer is that in understanding Zones of Proximal Development (ZPD), we can use their influence to encourage children to take bigger risks; to be willing to make mistakes; to celebrate the missteps on their (forgive me) learning journey.

Let's stick with maths for the moment.  When I am teaching a class of Year 6 children (that's 5th grade for those of you who speak American), there will be a few children who are a little further behind the others.  There is no shame in that - we are all beautiful sunsets.  However, I still have to teach long division to the whole group.  So how do I use ZPD to do that?

Give them permission to not know

We start by establishing a comfort zone.  On the board, I'll write the most challenging question that I expect everyone to be able to answer by the end of the sessions (note, sessions; there's no guarantee that this will fit neatly into an hour).  Let's say it's What is 235.6 divided by 17?

Even to a confident child, this will look daunting the first time they see it.  Not only is it division by a double-digit number; not only is that double-digit number Prime; not only is there a 7 in it (kids dislike 7s in division); there's a bloomin' decimal in there as well!  If questions were Star Wars films, this would be Episode 9!

So I tell them that it's okay to not know the answer... yet.  I explain that they are here to learn how to solve the equation and discover the answer (remember, they are not here to know the answer.  If they know it outright; they haven't had to use their brains).  I invite them on a journey.  A happy little journey outside their comfort zone.  No-one is worried; everything is fine.

You've already come so far!

To teach something new, I go back to something old.  I go all the way back to How many 2s can I get out of 4?  Yes, with 10-year-olds. Yes, even with the confident ones.  Because it reminds them of how much they have already learned; of how many risks they have already taken.  I am a big fan of pointing out that at some point in their school career, how many 2s in 4 would have stumped them.  The fact that they are laughing at it now suggests that they will soon be laughing at what is 235.6 divided by 17?

And this is huge!  

It's also really important, so I'll spend some time ensuring that everyone knows that they know this stuff.  Next, we move through the various stages of learning division.  First, we grouped physical objects, then we grouped representative objects (dots on a page), then we grouped abstract concepts ('lots of' a number).  These stages are simple for these children.  All of them.  They know how to apply an abstract concept to an equation to solve for an unknown quantity because they can all tell me that there are 2 2s in 4.  

And we celebrate that.  These kids are brilliant.  They can do the maths!  Woohoo!


The more things change...

The very next thing I tell them (or remind them) is that the maths doesn't change.  The maths they need to apply to 235.6 divided by 17 is no different from the maths for how many 2s are in 4?  It is only the numbers that have changed.  So we'll write the problem up using the bus stop method and we'll approach it slowly, calmly and bravely.  The scenery hasn't changed but the sun has set and we are no longer in the pleasant clearing of how many 2s are in 4? We are now in the deep, dark wood of what is 235.6 divided by 17?  So remind them again and again, as many times as they need to hear it: it's okay, the numbers have changed but the maths is the same.  And you know the maths.

Then we walk it through.  How many 17s in 2?  Write in the 0, yes children, it's okay if our first answer is 0; we just carry that 2 and use it to make 23.  Now, how many 17s are in 23?  This is where I will choose a timid little lamb to be our champion (once at the start and once at the end, even if the end is just reading out the number.  They need to know that it is not scary and it is not incalculable).  This is maths they are very familiar with because it's essentially 23 - 17.  They'll get the answer and we'll move on in the same fashion until we get to the decimal point.

Pretend to panic



So far they've been guided through their ZPD and that's not truly experiencing it.  My mum used to tell me, you won't learn to drive until you've got your licence and you're on your own in the car.  It's the same for these kids.  They need to take the reins (I've lost track of my metaphors, it's true).  So I ask them what to do with the decimal point.  Taking suggestions and gently hinting at the right direction until they work it out for themselves.  

Now their ZPD is becoming more familiar.  Their comfort zone has grown.  They want to have a go on their own and take risks and prove that they have conquered long division.  So I let them.  I display the differentiated work and I let them choose their level of challenge.  

Yup.  They choose it.  

Some will be lazy and choose something that is too easy for them.  They're easily spotted and encouraged to move on.  Or, maybe they only seem confident.  Perhaps they need to try their skills on a practice range before heading out to join the hunt.  Again, let them.  

Some will gallop off and attempt things way beyond their comprehension.  Again, let them; just be there when they fall.  Work with them to answer the question they attempted and reassure them that it was a tricky one.  They'll adjust and self-correct.  Kids are resilient.

But what about us?

What do we, the grown-ups, do while the children are off mastering long division?  We learn to let go.  Just as they have been reaching beyond their comfort zone, so we have been reaching beyond ours.  It is a wonderful feeling to control a classroom.  To be the boss, the king, the shah and it is truly challenging to watch children make mistakes and only intervene when asked.  But that's what we have to do if they are ever going to learn and be independent.  And the more we do it, the easier it gets because our comfort zone grows to include that independence.

That kind of wandered into a weird medieval hunting metaphor.

To close, I am very excited to announce that I am working on a collaboration with the wonderful Molly (Mimmerr) @mimmerr, so that should be coming very soon (I'm off to write a bit of it now, in fact).  We'll be co-hosting so please check out her blog as well as this one.  

Also, for those of you keeping score, I am 1000 words away from only having my dissertation left!  So hopefully I'll be able to devote more time to my blog and my possible new podcast... we'll see.  



I hope this was either useful or at least mildly diverting for you.  As always, if you have any questions I can be reached using the links below or by leaving a comment (I read them all).  Wherever you are in the world, I hope this virus has left you and your loved ones alone.  Thanks for reading and I'll be back next week!

Carl Headley-Morris

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