Tales from Charlie and Lala Land

What is it with these famous authors? They live in their big houses with thick, lush carpets and they hobnob with fellow literary stars, probably talking a lot about the good old days of going to incredibly expensive boarding schools and then of course, dahling, why are those ghastly teachers making innocent little children do tests all the time when they could be doing CREATIVE THINGS with paper mache instead?

Well, I teach those innocent little children and I’ve got some information for Lauren – they’re not so innocent and weak as she thinks. Last week, as I got up to walk over to a working wall in order to point at something, I bashed into a table and hurt my knee so bad it probably sounded like I was in the last stages of labour. Pretty much all of the kids laughed. Yes, that’s right – laughed. Because they’re feisty and urban and they knew that although I am the strictest teacher in the whole wide world, I do allow a bit of humour, so they just wend ahead and indulged in a bit o’ schadenfreude.

However, they’re not so good at reading and writing, yet.

The difference between me and this author is that I think that these children absolutely need to learn to read, write and add up whereas she seems to think that these expectations are just too much, never mind that we test them on these high standards. At the risk of rehashing many, many blogposts from the past, here are a few other reasons why I think SATs aren’t as evil as Lauren makes out:

  • Their existence ensures teachers keep focused on what matters – giving children the facilitating knowledge of how to read, write and add up
  • Preparation for them helps children to learn to cope and concentrate – two character traits that aren’t necessarily developed in the family home these days
  • Without the SATs results, parents would possibly be fobbed off with ‘progress’ reports and never know how far their child might be behind their peers (and at risk of not being able to access KS3 lessons)
  • For a few children, tests are actually a welcome respite from the noise and over-stimulating activity that feature to varying degrees in the typical primary school day

The fact is, if we take away all the testing, standards would slip and there would be far too many children arriving at secondary school completely unable to access their lessons not just because of the high level of content, but because the expectations (hard work, stamina, concentration, listening without interrupting) would be too much compared to what they were previously used to. As I have said before, children don’t magically mature during the 6 weeks holiday between year 6 and year 7 – no-one ‘naturally’ develops the ability to concentrate or work hard on something tricky – training is required and because children are not mature enough to choose to put themselves through the training, we, the adults, must ensure that they receive that training. The children who would benefit most from that training are those who aren’t receiving that kind of training at home.

Who’s with me?

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‘A bit like the army’ – and your problem is?

I’ve been super busy this week and haven’t really had a chance to look at twitter or the Echo chamber etc, but what’s this I see this morning? Oh yes, a previously failing school with a reputation in the community for terrible behaviour and terrible outcomes has been taken over by someone with a great reputation both as a teacher and as an expert in behaviour management and people are COMPLAINING? Good God. You literally couldn’t make it up.

Anyway, I’ve been meaning to write this by way of support for Barry, Great Yarmouth Charter Academy, Inspiration Trust and more importantly the children and families in that community who desperately want and need change in their local school. This blogpost is an attempt to give airtime for the kinds of people who don’t run to the local rag with their exaggerated complaints, but rather quietly attempt to bring up their children in the best way possible and want their local school to implement routine, structure, discipline – those facilitating systems that develop good character traits and of course enable teachers to teach and children to learn. After all, that’s what children go to school for – to learn. If the children aren’t behaving and paying attention, they ain’t learning; it’s as simple as that. It’s our job, as the adults, to help the children to learn.

One thing I’d really like the naysayers to understand is that in choosing to be the person who instills discipline, that person is committing to invest huge amounts of physical and emotional energy. Just as the already knackered parent must come to a decision to really push forward with bedtime routine for their children, digging deep to invest even though it would be so much easier to pretend to be one of these hippy ‘let-the-children-decide’ parents, the educator must dig deep to create whole-school policies, ensure that colleagues are committed and supported, and then personally make sure that policies are followed. Oh how easy it would be to just rock up and be one of those overly friendly, get-down-with-the-yoof types and just let the children (not) come to their own decisions about behaviour and uniform. Who is the most caring? Who loves the children the most? The educator-leader who takes the easy route for personal gain (fully knowing that all of his staff, the children and the wider community would ultimately suffer), or the educator-leader who digs deep, summons up enormous amounts of energy knowing that he would be on the receiving end of vitriol from virtue signallers?

New things are never perfect. So, the original behaviour policy needing a little refining. And your problem is? I would have thought that fellow educators were intelligent enough not to nit-pick at first, but to actually consider the meaning and purpose of it all, understanding that this is not about ‘controlling’ children, but about freeing them to learn, to be safe and to be happy. It’s amusing that the very same rock-throwers bang on about teaching children the skills of inference, yet can’t really do the same themselves. Hmmm, perhaps they need to have a little more knowledge about the research on how children learn best – when the atmosphere is calm, ordered and minds are open (not defaulting to ‘How can I mess about and get a laugh’).

‘A bit like the army’

I glimpsed this mid-week. Apparently, a school being a bit like the army at first is a bad thing. Is it really? For a start, the implication is that the Army itself is a bad thing. Let’s look at the evidence for and against ‘The Army’

For:

  • Young men who are perhaps on the verge of failing in life are taken in, cared for, transformed through routine, discipline, structure and fitness training and eventually turned into highly skilled heroes with respect for authority, willing to die for their country
  • Our country is protected

Against:

  • The army costs money

Of course, you might add ‘death’ to the list. But, there would be death anyway, particularly if we, the civilians, weren’t protected.

The first bullet point is really what resonates in my own mind – the transformative effect of discipline and routine. Anyone who chooses to take on that difficult role of putting in place something so transformative that has not been in place before deserves not vitriol, but support and praise.

Who’s with me?

Playing devil’s advocate: Zero choice for children at primary school

Caveat: this blog post is a sort of thought-journey and not in any way shape or form a ‘I think schools should be like this’ type of blog post. Join me in my pondering.

Has anyone questioned the received wisdom that choice is a good thing, especially for children? What if we just didn’t give them any choice at all?

Lately, I’ve been investigating the concept of the minimalist lifestyle. When I say ‘investigating’, I mean that I’m interested and think it’s a pretty radical way to dial down wasted time thinking about the pointless frouffery of life and instead concentrate on life itself*. I haven’t really done much about it though because I don’t think I can get rid of all my handbags. Yet. Even if we take a slightly less dramatic approach, this way of thinking and the lifestyle that goes with it is in stark contrast to the everyday experience of children because it is seen as a good thing to offer them lots of choice, especially in the classroom.

choice
Do I go for the ‘tricky’ challenge, or the ‘trickier’ challenge in today’s maths lesson?

Why do we do this?

Firstly, offering choice is an act of kindness and the underlying thinking is that by offering lots of choice and going the extra mile, children will also learn to think of others in a similar way while also developing ‘independence’ and ‘ownership of learning’. However, I think this just makes children choosy, never satisfied with what is on offer. Further, how would they learn to persevere if they are experiencing lots of opportunities to just ditch-and-run whenever things get a bit tough? The other aspect that I hadn’t considered until recently is that while we educators are trying to free up children’s working memories by ensuring knowledge is in long term memory (through direct teaching, practice, regular testing), we are then proceeding to clog up their freed-up working memories with ‘choice’. For example, a moment spent deliberating (and for some children, worrying) over which activity table to go to, which book to read or which maths worksheet to do is a moment spent not thinking about the meat and two veg of the lesson.

The very children who seem to be most adversely affected and the very children who we want to help the most; consider the struggling child who has put in maximum effort to listen, ask questions and take part during the input, and then just at the point where the child is desperately trying to hold onto the knowledge that the teacher has just imparted, hoping he can transport it to the table where he can write about it n’ stuff (before it falls out of his head), the teacher then asks the struggling child to choose a friend to sit with, a worksheet, an activity, the investigative equipment to use. All that knowledge pops out of his head as he grapples with the smorgasbord of educational choice. When he sits down, he has made his choices, but then has nothing to write about so what has he actually learned? Are we nuts, or what?

When I read this article about a democratic school in Germany, I initially thought about how they were seemingly creating the fussy customers of tomorrow, but after while I thought about all that choice and how it was taking away precious time for learning. Asking little children to mostly think about shitty things like whether to have fishfingers or nuggets for lunch takes away opportunities to just serve up a lunch and instead have a lovely conversation about the planets, or different types of jewels, or the world’s biggest gorilla etc. Then we could all just say thank you to the person who took the time to rustle up a delicious lunch for us. Two things have happened in this scenario: the children’s working memories have been freed up from the dross of life to think about awesome things and they have also learned to be grateful.

I don’t remember having any choice at all when I was at primary school or at home really, save for playtime. Have I been permanently mentally scarred as a result? No, not really; I didn’t know any different. Looking back to my old child life, I don’t think I would’ve wanted ‘choice’ either at home or in the classroom. To me, ‘choice’ was something to look forward to when I became a teenager and was granted a bit more freedom.

I get that teacher’s are minded to offer children choice, especially when Ofsted calls, the typical catchphrase being ‘Choose your challenge!’ I’ve even done it myself on numerous occasions, but it just seems to cause more problems. Anyway, I wonder if there is any teacher or school out there that has gone for a more minimalist approach to lesson content, teaching, children’s activities etc? In the meantime, perhaps it’s better to think twice about offering choice; is it stopping them from learning?

Who’s with me?

Do the children know what we’re going on about?

This blog post is about edu-lingo and it’s probably the one of the few times I will make a concession to the whole ‘child-centred’ thing. Now is a good time to write because I still feel sort of new to the profession (even though it’s been a few years now) and the initial ‘What is this person going on about?’ thoughts I had right at the start of my training still occasionally concern me, albeit these thoughts have gradually evolved into ‘Do the children even know what we’re going on about?’

Basically, I think we need to be careful when using language like ‘peer assessment’ and ‘reflect on growth’ because they might be a bit too, erm, businesslike? Don’t get me wrong, I’m all for new and rich vocabulary that is subject specific: awesome words like ‘trebuchet’ and ‘electromagnetism’ cannot be substituted and why would you want to anyway (knowledge is for everyone!)? But, using edu-lingo with children just seems wrong, unnecessary, out of touch, a little pompous even?

Take this random example of a flow chart of ‘How to Learn’ for a wall display for a year 8 class* (and there are many like it)

  • Learn a new skill
  • Practice the skill
  • Ask questions
  • Make mistakes
  • Analyse mistakes
  • Fix mistakes
  • Formative assessment
  • Formative feedback
  • Re-teaching and corrections
  • Practice/Study
  • Summative assessment
  • Reflect on growth

I doubt very much that something like this would appear in KS1, but something similar could easily be seen on a UKS2 wall in a classroom near you. Maybe it’s just me (and it probably is), but I’m uncomfortable with young people casually chatting about summative assessment – is it not a bit weird? I guess another example I could draw upon would be from my own background in financial services: I wouldn’t necessarily use the words ‘individual stake within a superannuation fund’ when ‘personal pension pot’ would be a bit better. Is this dumbing down? Well, I like to think there is a difference between ‘dumbing down’ and using plain English, or at least taking the time to explain specialised vocabulary before using it.

How would I tweak the above list to make it more end-user-friendly:

  • How to learn something new (like a skill, or some new information)
  • Take a test at the start so the teacher knows exactly what to teach
  • Look, listen and pay attention to the teacher
  • Ask questions
  • Practise
  • Probably make some mistakes
  • Look, listen and pay attention to the teacher’s corrections
  • Practise
  • Maybe use this new skill or knowledge in another lesson or for something different
  • Take a test at the end to see how much you have learned
  • More practice at regular intervals throughout the year
  • Ultimate test
  • Feel brainier/more intelligent

Actually, is it even necessary to put this on the wall anyway? Most children intuitively know all this and if they don’t, well, it’s probably because they’re very young and just need to put their trust in the teacher as the leader and expert. Anyway, do they really need to be bantering using the word ‘assessment’?

For me, this makes me think about how I’d often have to explain, for example, the green ‘VF’ in a circle in the children’s books. Children of all ages, right up to year 6, would ask me what it meant, despite its use throughout the year and then when I would say that it stood for verbal feedback, they would give me a puzzled ‘Huh?’ in response. ‘Oh, verbal feedback means that I talked to you while you were writing that paragraph’ to which they would reply,

‘Sooooo, do I need to write it out again, or…..?’

I’ve asked fellow teachers whether they think it’s normal for children to tick off success criteria that includes ‘peer assessment’ on it, when the children don’t look at their friends and think ‘Oh, these are my¬†peers.’ Like I said, maybe it’s me. Another example could be the use of certain titles for lesson subjects and their corresponding wall displays. Do the little children really know what ‘PSHE’ means? Is it ‘Movement’ class, or is it just ‘Dance’?

The other side of this is communication with parents, not just teacher-parent conversations, but children actually being able to talk to their parents about what they are doing in school. The language problem can swing the other way and get too child-friendly with the use of, for example, ‘bus stop’ or ‘frog’ for calculation, when most parents would have used ‘short division’ and, well, they wouldn’t have spent too long using a written version of calculation that would/should normally happen inside their heads (and if it can’t happen in our heads, then they’d be deploying the column methods on paper, usually).

Anyway, I think we need to be careful about using edu-lingo with children.

Who’s with me?

* The person who originally published the picture on social media has asked for the image to be removed.

 

In defence of the anecdote

Every now and then I catch a vibe on edu-media that seems to imply that ordinary people shouldn’t take part in discussion or venture opinions because:

  • They’re not ‘professionals’ (i.e well-known enough)
  • They’re not ‘qualified’ enough (i.e possess strings of letters after their names)
  • Their ‘evidence’ for their opinion, even though they may cite additional supporting research, is merely anecdotal

This is a blog post for all those ordinary people who might feel intimidated into hushing up so that the big guns can continue their domination of the centre stage; this is a blog post that would like to defend and promote the ordinary human voice, however imperfect, as a useful addition to all the very valuable insights and clear direction that education research offers us. I hope this blog post finds someone, somewhere who would like to describe their classroom experiences by dipping their toes into the murky world of blogging! Newbie teacher-blogger, I’m talking to you.

authos-voice@2x

I’ll admit, it’s a pretty busy place, this world of blogging. There are so many voices all speaking at once and the odds are that one voice probably won’t shine through, but some of us are on the lookout you know, and some of us would be happy to give advice. I’m happy to help because I consider myself pretty ordinary and also I’ve had plenty of people help me which makes me feel very lucky indeed, so I need to return the favour to the blogging universe; you won’t find me pulling the ladder up any time soon!

I don’t accept or promote this attitude that you can only take part if you’re some kind of consultant, Ofsted inspector, headteacher, PhD researcher, specialist or educationalist who has published many books and I have been on the receiving on the end of this ‘Who are you? You are nothing!‘ attitude often. This is not to denigrate any of those excellent and intellectual people who have obtained their high status through years of hard work within their field of expertise because of course what they say has significant weighting and we should respect their opinion (and be prepared to be wrong as a result), but I also like to think that we need to allow some space for the other voices. You never know who might possess that nugget of inspiration, knowledge or insight and it could be you, dear newbie blogger, so be steadfast in your determination to contribute.

Likewise, with qualifications. I guess I’m biased here because I’m not a PhD although I would dearly love to be. I had to fight for my education slightly later in life, with the delay mainly caused by general poverty and, well, lack of housing; I studied for my degree while my children, then a toddler and a newborn, slept, so I’m grateful that I at least got a toe-hold in education. Most people know my story, so I won’t go into it, but you know what? The most intelligent people I know aren’t necessarily the most qualified: they’re simply incredibly well read and just love knowing stuff and being able to share it. Older, working class acquaintances are more likely to surprise me with some interesting knowledge, wisdom, insight, thoughtful interpretation or expertise, and from this, yes, personal anecdote I deduce that there are probably more ‘unqualified’ voices out there who could cut through the noise. If you think this might be you, then take this as encouragement to just wade in.

What if you make mistakes and say the wrong thing in the heat of the moment? Well, yes, if you’re not a professional writer who has had the fortune to have been socialised into the genteel world of academia, then you’re probably going to drop a few clangers at some point, maybe quite a few times, until you hone your message such that it is both subtle and powerful*. Lord knows I’ve put my foot in my mouth on more than one occasion and quite often go back to blog posts of mine and think ‘God, you’re such an arse! Why did you say it like that?’ but then it takes time to learn the ways of a new set of (mostly middle class and left-wing) people, plus, we’re only human after all and nobody starts writing like a pro without the requisite practice. There are many out there who have the intellect and patience to understand and like your message, even if your message is packaged in prose that is a bit rough round the edges and makes them wince occasionally.

The human ‘thing’ is the reason why I tend to reposte trite messages written on twitter or in blogs by people who have experienced some kind of great ‘revelation’ that edu-media is allegedly bollox and that they’re going to reject it all in favour of better things like reading big books, taking long walks looking at wonderful scenery and generally partaking in more civilised conversation with their own close friends, colleagues and family. The implication here that unenlightened people who remain on edu-media such as twitter (which is, after all, just fellow human beings from all walks of life having a debate in a public forum) are idiots in need of more balance in their life is somewhat pompous to say the least and I reject it because it is, essentially, a thinly veiled ‘I’m-better-than-you!’ guilt trip designed to shut people up. It’s OK to choose a raw, heated edu-debate over polite dinner party conversation about house prices once in a while and you are more than welcome to join in without feeling guilty. Also, amidst all those different voices are those who have a knack for digesting and offering up the results of educational research for ordinary teachers to absorb – I think we have an obligation to listen to and converse with these people. How else would we know about what was going on in classrooms around the world?

And then we arrive at the anecdote. We all understand that an anecdote can never be statistically significant, but an anecdote could be the canary in the mine that triggers investigation, a search for further evidence that yields statistically significant insight that would never have been brought to light unless the person with their canary had the courage to pipe up. Anecdotes are also interesting to listen to, and the fact that they’re interesting doesn’t mean that they’re potentially dangerous thought-grenades with the potential to change minds in an instant, so if you’re a newbie blogger who is frightened to bring forth an anecdote lest you be accused of not being scientific, just let your anecdote out because sharing experiences promotes empathy which at least helps us all to feel connected and comforted. There is always the possibility that a pattern of similar anecdotes from various sources eventually causes collective concern and action.

The small voice armed only with an anecdote needs to be welcomed.

Who’s with me?

*Some of use are still trying to hone their message ūüėČ

Jo Boaler is wrong about maths facts and timed tests

This is a blog post about how I believe Jo Boaler is wrong when she asserts that learning maths facts off by heart and timed tests are detrimental to children’s well-being and mathematical ability. I’ve tried to take the time to read pretty much every piece of research she has linked to in her article and it’s been an interesting reading journey, not least because some of the research she cites seems to provide evidence that learning maths facts off by heart and the use of timed tests are actually beneficial to every aspect of mathematical competency (not just procedural fluency). To help me get my head around what she’s saying, I’ve summarised the entire article and analysed each part:

  1. The new UK curriculum requirement for children to learn times tables off by heart will lead to children being scared of and then turn away from maths

On the ground, I have seen the opposite: children are more confident, happier and definitely better mathematicians as a result of the new curriculum bringing back all the ‘old fashioned’ requirements such as knowing maths facts off by heart. I have worked to develop a system of fun, competitive, weekly timed tests with direct feedback and co-opting the language of sport in my classes and every year I have seen the ‘orange’ children on target tracker (particularly white, working class males/PP children) make accelerated progress and across entire classes there will be an improvement in confidence, ability to concentrate and persevere with increased love of mathematics as a result. It’s too early to say whether these same children will then, according to Boaler, turn away ‘in droves’ because the children who have, in my view, fully experienced the new curriculum are still only in LKS2. I predict that her prediction is wrong, but we will need more than my evidence alone, obviously.

2. Teachers in the US, despite the Common Core curriculum [allegedly] not requiring children to learn maths facts, have misinterpreted ‘fluency’ and are forcing children to learn maths facts off by heart

At this point, I worried that I didn’t understand the word ‘fluency’ and then Boaler started talking about ‘number sense’ which confused me a bit. The two are different; here are the definitions to help us all understand:

a) ‘Fluency’ usually means ‘procedural fluency‘: the ability to apply procedures accurately, efficiently, and flexibly [maths facts and algorithms need to be at ‘instant recall’ status i.e in long term memory for this to happen]

b) ‘Number sense’ is a phrase that is used to mean ‘conceptual fluency‘: understanding place value and the relationships between operations

Boaler seems to pit the two against each other, and if I am right in my interpretation, she is saying that teachers should really concentrate on the conceptual fluency (to me, this is the same as conceptual understanding, the ‘seeing’ of the calculation within the maths problem as well as the ‘picture’ of what is happening to the numbers) and that through concentrating on children’s understanding, the procedural fluency and learning of maths facts that are integral to procedural fluency will be developed indirectly and naturally.

This is sort of a chicken and egg situation, isn’t it? In my view, it is through procedural fluency that understanding is really developed, so I’m in the opposite camp to Boaler (who seems to be in the classic progressive camp). Of course, I’m not advocating that we don’t teach for understanding, but I could teach you how an engine works and then for a fleeting moment you might understand it, but until you take it apart and put it back together over and over will you really know the parts that go together, what might be missing and how it works (I might time you to see whether you know this off by heart – because you will be quick). I find that the children who don’t understand tend not to understand because they’re stuck at using fingers, repeated addition, stringing and they cannot see the mathematical wood for the trees – they haven’t practised enough and they haven’t committed number facts (sometimes including the fact of what a number is) to long term memory.

That US teachers are choosing to help children with their procedural fluency, even though the Common Core curriculum has [allegedly] de-emphasised learning maths facts and algorithms, is a good thing in my view and it also gives me comfort that I’m not the only maths teacher who take this view.

3. Example/proof of not needing some maths facts: why bother memorising 7 x 8 when you can work it out by, say, using 7 x 10 and then subtract 2 x 7

This was the author’s example of how the better mathematician has well developed conceptual fluency rather than relying on procedural fluency. Reality: the person who knows the two maths facts of 7 x 10 and 2 x 7 as well as the number bond 14 + 56 = 70 also tends to know the maths fact 7 x 8 = 56 off by heart. So, this was actually an example of someone with better procedural fluency being better at procedural fluency. The other glaring reality is that the young child who does not know 7 x 8, even if he/she does know the maths facts 7 x 10 and 2 x 7 (which is also unlikely since they’d probably use repeated addition to get there), will not necessarily see how to use them together because he also wouldn’t know the number bond 14 + 56 = 70 or even the two basic number bond facts (6 + 4 = 10 and 5 + 1 = 6) together to make 70 to then know that subtracting one from the other will arrive at the final result of 56. Already you’re feeling exhausted for the child and this is because we all know that noodling our way to 7 x 8 is inefficient and with each layer of calculation a little child is much more likely to make a mistake, possibly arriving at 57. Which is the wrong answer. I think this example is actually proof of the importance of knowing maths facts off by heart.

4. Dr Boaler, professor of mathematics, did just fine without having to learn maths facts off by heart and naturally developed ‘number sense’ because her school developed the ‘whole child’

Unfortunately, a population study n = 1 does not qualify as statistically significant. I know many who were well and truly failed by progressive education and the maths ‘teaching’ that went with it – yet even today you will see year 6s struggling with the basics, forever stuck at repeated addition and inefficient methods like grid method, the complete lack of systemisation in their calculations and how this manifests as a scatter-gun approach to layout in their maths books, even number formation would be awry, yet they were being praised for ‘creativity’ in trying to find an answer, thus demonstrating their ‘understanding’ (the answers were wrong, by the way). All it takes is one teacher or a maths lead who has bought in to the whole ‘You don’t need to have instant recall or be quick with your algorithms because it’s all about the understanding‘ (because it justifies her own grade C maths GCSE) to let a child spend a year meandering through the leaves and branches of numbers, never to see the full mathematical forest in all it’s glory because they don’t know, off by heart, that certain leaves and branches make trees. Perhaps Boaler was lucky then? I don’t think so. Luck has nothing to do with this, so let’s just read on.

5. A study showed that low achievers have no number sense, and tend to resort to counting back in order to solve problems like 21-16, but higher achievers do have number sense and are able to do 20 – 15 + 1 instead, for example [thus showing that you don’t need to know maths facts off by heart] (research link: 404 error!)

Again, you could argue that ‘higher achievers’ have better procedural fluency because they know their number bonds to 20 off by heart as well as having done enough practice to know and apply – 1 + 1 = 0 each side of the equation. This is pretty much the same situation as point 3.

6. Problem solving is the best way to develop ‘number sense’ and indirectly learn maths facts off by heart (Feikes & Schwingendorf, 2008)

Now, this is where things got really interesting because I read the research (I’ve linked them all, this one above is on p.83) she cited as evidence for this claim. The study looked at how children begin their maths journey well before attending school by ‘compressing’ the concept of number. In lay man’s terms this means, for example, that a 4 year old initially knows there are 5 pencils in front of him because he counts them one by one, and then he eventually is able to look at the 5 pencils and instantly ‘see’ that their are 5 without even counting. It then goes on to state that through practice of addition, a child then might used his compressed concept of number (ie know what ‘5’ means) to add 4 + 5 initially by adding 5 + 5 and then -1, but then eventually he just knows that 4 + 5 = 9 off by heart as well. The premise of the paper wasn’t to imply that problem solving helps children to develop conceptual understanding and then naturally acquire key maths facts off by heart (which is what Jo inferred), but rather to make early years teachers aware of how children learn those crucial early maths facts (eg what ‘5’ is), to think about their teaching of early maths and to provide lots of opportunities for children to learn these early maths facts off by heart with manipulatives and plenty of counting practice until they are able to just glance at 5 pencils and say ‘There are 5’. If anything this paper supports the use of lots of plain arithmetic practice in order to put basic maths facts into long term memory.

7. Lack of ‘number sense’ is the reason why the Hubble Telescope once missed some stars – and number sense is inhibited by too much rote memorisation [therefore the dude in charge spent too much time learning maths facts?]

OK this is ridiculous. People make mistakes, even the good people at NASA.

8. Some people are better than others at memorising maths facts – but they’re not necessarily better at maths, nor do they have higher IQs¬†(Supekar et al, 2013) because maths facts are only a small part of maths learning

Again, interesting to read the research here because it seems that Boaler is implying that research is tells us that learning maths facts off by heart isn’t that important and that those who take the time to memorise maths facts aren’t always going to be better mathematicians as a result. As ever, the devil is in the detail: the study looked at whether differences in morphology and connectivity in different parts of the brain affected how a child responds to individual maths tutoring. It turns out it does, but the study doesn’t imply that children shouldn’t be required to learn maths facts, since all the children in the study experienced an improvement in mathematical ability via ‘a¬†significant shift in arithmetic problem-solving strategies from counting to fact retrieval,¬†it was just that the children varied in degree of improvement. Other factors such as IQ, working memory, behavioural measures had no bearing – it was all down to variations in the regions of the brain associated with long term memory. I certainly didn’t take away the message of ‘Don’t bother getting children to learn maths facts off by heart’! What I did take away was the message that all children can become good mathematicians, it’s just that some need more time to practise and more teaching in order to make the same progress as others. But, you know what else I found in this research (and this is where my eyes popped out)? Take a look at this golden nugget:

the proof

So, the very same people who conducted this study about differences in the brain had also established that learning maths facts off by heart and doing timed/speeded practice leads to significant improvements in:

  • automatic retrieval
  • arithmetic fluency
  • procedural fluency
  • reasoning
  • problem solving

The method of the study, understandably, used these findings as the basis of structuring the tutoring sessions as a ‘program focused on number knowledge tutoring with speeded practice on efficient counting strategies‘. At this point, I did wonder why a professor of mathematics, someone who has adopted a position against the learning of maths facts off by heart and the use of timed/speeded tests, would refer to a research paper that clearly provides evidence in favour of rote memorisation of maths facts and the use of timed/speeded tests?

9. The best way to develop fluency is to develop number sense by working with numbers in different ways (problem solving), not by learning maths facts off by heart (Parish 2014, p 159)

Boaler still maintains her position by citing another study in support of problem solving as way of learning maths facts off by heart, only it’s not a study, but a resource called ‘Number Talks’ that guides teachers in their teaching for conceptual understanding through problem solving using open ended questions for children to discuss. I did have a look at it and you know what? I quite liked it – but then I remembered that I’m pretty confident and do this sort of thing with children anyway (I’m fond of an array or a bar model), encouraging children to fully explain the reasoning behind their calculations and then demonstrate (I do this when we mark our weekly arithmetic tests) by coming to the class board. But, you know who’s sat there looking bamboozled? It’s the kid who doesn’t know any maths facts off by heart, so as soon as her friend launches into an explanation which begins with ‘Well, I know that 10 lots of 7 apples are 70 apples and 2 lots of 7 apples are 14…..’ she’s lost because she didn’t know 10 x 7 = 70 off by heart – that’s definitely not learning through problem solving. The resource itself is not evidence that children can just problem solve their way to procedural fluency.

10. Maths testing causes the life-long, debilitating condition called maths anxiety (research link yielded 404: error)

I don’t think there’s a special condition called maths anxiety, just ‘anxiety’. I used to have anxiety about performing as a musician; doing more performances made me a better musician and helped me get over said anxiety. If someone had made a big deal out of it, sent me for therapy, generally pussy-footed around me and made me feel like I had something terribly, irreversibly wrong with me, some sort of ‘condition’ like extreme asthma that I should be ever vigilant and frightened of, then I would have avoided performances and never got over that anxiety. I think it’s the same with maths testing – help the child by teaching them and letting them practise, don’t make a massive fuss about maths tests like you’re about to send the child to war (in fact, they’re fun, like a quiz!) and let the child get over their anxiety in their own time because it’s definitely¬†not a life-long condition. ‘sake.

11. Stressed students can’t use their working memory and therefore can’t access maths facts – they ‘leave’ mathematics as a result (Beilock, 2011; Ramirez, et al, 2013)

The first reference is a book that quite clearly states that with practice, and using certain mental strategies, you can overcome performance anxiety (and its tendency to befuddle the working memory) and do really well in your chosen field – nothing about abandoning maths or that performances should be avoided. The second reference, which referred to previous research that found that worrying about a maths test diminished working memory and attention available for the maths (if you’re thinking about how worried you are, you’re not thinking about the maths), was for a study that found that maths anxiety was correlated with lack of self-control of emotions and concentration as well as lack of maths facts committed to long term memory (which is where the maths facts should be anyway). Previous research had also found that maths anxiety didn’t necessarily impair performance because sometimes it leads to better concentration, and for those who had more working memory available (because they had committed facts and algorithms to long term memory) the anxiety actually had a positive effect. The study itself does go on to recommend making tests less anxiety-promoting by avoiding timed elements even though it identifies weak maths ability and low working memory (because of distraction of the anxiety itself) as being risk factors for poor performance due to maths anxiety (surely we should target the risk factors?). It certainly doesn’t say that as a result of tests, children have maths anxiety and then ‘leave’ mathematics. What I took away was that children need to make sure that they have instant recall of maths facts and also to find thoughts and methods that help with control of emotion and concentration in order to avoid the vicious circle of maths anxiety in the first place.

12. Putting pressure on children to recall maths facts at speed will not reduce maths anxiety (Silva & White, 2013; National Numeracy, 2014/404 error).

The first reference is to quite a long publication about the results of intensive courses in remedial maths for young people in the US looking to go to college. It’s quite long, but a central jist was that (and the excellent work of one of my favourite researchers, Stigler, was cited for this) they found that these young people had internalised that they weren’t good at maths and as a result, had poor work ethic and tended to give up quite easily when faced with a bit of struggle – hence doing badly in maths. A contrasting example was provided in that students in the Far East were known to persevere more because they believed that getting better at maths required practice, hard work, concentration (and being ‘good’ at maths was open to all, and they are indeed very good at maths). Part of the program was about getting student to really understand how hard work leads to success (through a bit of struggle – which they were made to push through) and the course content also attempted to get students to understand the purpose of maths in the real world as well as work with each other a bit more. There was nothing that I could see stating that getting children to learn maths facts off by heart (and therefore being speedier at recall) resulted in no change in maths anxiety or that testing was causing maths anxiety, because the ‘study’ wasn’t really focusing on that. If anything, it highlighted that maths anxiety is a problem arising from student mindset, not because of tests or ‘pressure’ to learn maths facts.

13. The best problem solvers use both numerical/symbolic and spatial/intuitive reasoning neural pathways (Park & Brannon, 2013)

This research seems to support the notion that visual aids are a great way to get children to understand a problem and then they tend to do much better. I found this paper a bit much, but I certainly didn’t infer a message that using different parts of the brain for solving problems diminishes the importance of the parts of the brain associated with long term memory and quick recall of maths facts.

14. Studies have shown that you can learn maths facts two ways – by memorisation, or by ‘strategies’, but the latter produces superior performance¬†(Delazer et al, 2005)

The research does indeed state that drills vs. ‘strategies’ involve different parts of the brain, but then of course that makes sense really; I bet I’d use different parts of the brain to look at and listen to the sea compared to thinking about the sea as if it were written in musical notation. I had to really work hard to understand this paper, but it did eventually dawn on me that yes, while the drill and strategy people initially used different parts of the brain, the research also showed that both methods caused the ‘thinker’ to retrieve and use previously existing networks of arithmetic processing and memory – so everybody relied on their long term memory after all in order to perform the calculations. Surely this is evidence for committing maths facts to memory?

Maths is the only subject where children get upset, have to do timed tests and are made to work towards instant recall (be speedy). Why? 

I think Boaler is trying to imply here that maths people need to learn from and be like teachers of other subjects? Clearly Boaler has never experienced being the fat kid in a dance class then.

15. It is a misconception that maths is about getting correct answers or about calculating, when actually it’s all about methods and reasoning¬†(Boaler, 2013)

Her article which she references in support of this statement talks about ‘mathematical democratization’ through making maths lessons more about problem solving, reasoning, enquiry, creativity and encouraging the use of software to help with problem solving (avoiding having to rely on long term memory to do the calculations) – apparently lessons that are focused on procedural fluency are racist and sexist! I don’t think any mathematician thinks that maths is only about getting correct answers and calculating, or that this area is mutually exclusive to methods and reasoning – it’s about both sides of the coin, but actually the former is really, really important as a foundation – otherwise you wouldn’t know if your methods and reasoning were on the right track?

16. Conrad Wolfram, of Wolfram-Alpha, says we need to see the breadth of mathematics.

I looked up the website. Awesome, but I couldn’t see his quote. Do check out the website though; you won’t regret it.

17. Mathematicians, including the top mathematician Laurent Schwarz, tend to be quite slow at maths; this is because they’re taking the time to calculate in an intelligent way, so why do we try to get children to be speedy?

This statement confuses two things: problem solving, and recall of maths facts and algorithms. The latter needs to be quick because being quick is a proxy for said math facts and algorithms being tucked away in long term memory. No one is advocating rushing a student on a maths problem and yes, the slower ones tend to arrive at the correct answer whereas the quick ones are more likely to miss something crucial (like the second step – very common in UKS2). You can bet that the ‘slower’ problem solvers’ brains are working very quickly at shuffling those number facts like it’s a game of light-speed tetris. Conclusion here: the fact that mathematicians like to deliberate over a problem does not mean we need to almost encourage children to be slow at their recall of maths facts and algorithms.

18. Fluency is not based on speed of recall or memorisation of maths facts, in fact, the lowest achievers focus on memorising maths facts [and they are not fluent] (Boaler & Zoido, in press)

This is a confused and confusing statement because the article that is linked refers to children struggling with maths facts in their working memory – it’s a sort of circular reference back to the article I am writing about and she states again that conceptual understanding and the ‘joy’ of problem solving should trump procedural fluency (an emphasis on which damages mental health?). Yet, from looking at the other research above that she cites, we can quite clearly see that committing maths facts to long term memory is a great way to positively influence procedural fluency and conceptual understanding.

19. Michael Rosen is leading a cause in the UK to stop children from being tested and stressed out about tests – teachers making young children learn maths facts off by heart is contributing to this maths anxiety

This is primarily about baseline tests in EYFS reception year (children don’t even know they’re doing it) and SATs testing in schools, not about regular maths tests. In fact, we could easily draw a conclusion from this that children need more, low-stakes testing so that when it comes to the official tests, they take them in their stride.

20. Learning of maths facts should be developed through exploration with numbers

No it shouldn’t, but exploration with numbers can really help consolidate understanding. Pretty much all the research cited stated that committing maths facts to memory and doing timed tests helps with all aspects of mathematical competence, including problem solving.

21. ‘Number talks’: a package of engaging maths problems to be discussed in groups, using different strategies – helps children to learn maths facts

See point 9. Children who don’t know their maths facts end up confused.

22. When we emphasize memorization and testing in the name of fluency we are harming children, we are risking the future of our ever-quantitative society and we are threatening the discipline of mathematics

Actually, on all those counts, not we are not. In fact, it’s the complete opposite and I have to thank Boaler at this point for introducing me to so much in the way of great research that proves that learning maths facts off by heart and doing timed tests is a great way for young children to become better, and therefore more confident and happy, mathematicians.

Who’s with me?

Little children do not need to be ‘critical thinkers’

I read this really interesting article this morning and it got me thinking about primary schools in the UK. You know that I have written before about feeling like I’ve landed in an alien world (when I enrolled on that SCITT course a few years ago); I still feel the same way sometimes and quite often my face is like this whenever someone mentions ‘creativity’ and ‘critical thinking’:

confused pirate

The article I link to repeats the great wisdom that in order to be a critical thinker you need to know a lot about that particular subject (likewise with creativity). Of course I agree, but in contrast to many educators, I think even the earliest years of education need to be about transmission of subject specific knowledge and vocabulary. I’m going to be bold and say that I think we actually need to be encouraging our youngest children to be ‘uncritical’ thinkers (ie, mostly in ‘receive’ mode) and for teachers to really know what they’re talking about.

Oh my God! She’s trying say that little children shouldn’t be allowed to think for themselves!

No, I didn’t say that, but I do think it’s a bit weird that you’re trying to treat my own offspring like they’re little professors – you can get them to be curious all you like, but they’re not going to magically come up with the theory of relativity all by themselves.

In the staff room, for example, I reckon I could venture a few critical thoughts about the sustainability of final salary pension schemes, but that’s because I know a lot about pensions including the rules, regulations, taxation (personal and corporate), investment, administration and the process of winding up (almost inevitable, unless underwritten by the State). Over the years, I have collected various jigsaw pieces of knowledge about a variety of subjects, but that’s just because I am older and a bit more experienced; I’m nothing special though. However, what seems to be different about the adults in the school staffroom compared to the average office is how educators with no knowledge whatsoever about a subject seem to think they can talk about it like they are an expert even though they are talking complete bollox (‘Yeah, well maybe if the bankers didn’t get paid squillions, we’d have more money for pensions’), so my face ends up looking like this:

What-are-you-talking-about

It could just be a unique experience to me, although there have been a number of occasions which has led me to think this is a ‘pattern’ and it’s hard not to take it personally because these situations are incredibly insulting, but I sometimes wonder whether this is symptomatic of a general attitude in education that you don’t need to be an expert in a subject in order to be a ‘critical thinker’ and have an opinion on everything because, according to many educators, ‘critical thinking’ can be taught and tiny little children can be ‘critical thinkers’ too, even when both child and adult in the situation know hardly anything about that subject. So, I get told by supremely confident people all sorts of wrong stuff about all sorts of subjects, and then when I come back with, say, some actual science (for example, no, there aren’t only 3 states of matter), I just get a ‘Well that’s what you think. Everyone is entitled to their own opinion’. I worry that this attitude where even if you don’t know the salient facts about a subject, you can still go ahead and think ‘critically’ about it, could transfer into the classroom with the following results:

a) children copy the same kind of behaviour – perhaps feeling entitled to rudely interrupt in order to spout opinion and ongoing commentary about anything and everything

b) children think they don’t need to know about a subject because they’ve been given tacit permission to comment or ‘think critically’ without having done the hard graft of background research (or been taught much about it), so they don’t try as hard to learn the facts or take that much of an interest in that subject

c) children are taught misconceptions, stereotypes or outright wrong’uns by teachers who are convinced of their own expertise, despite their not having learned enough enough about that subject themselves (the worst examples I have seen are in maths and science lessons, but music, history and RE can throw up a few clangers and I can’t be the only person who has winced at the ‘modelling’ of poor French pronunciation)

d) children grow up thinking that they do not need to listen to or respect experts/elders

But all that’s OK isn’t it? So long as they’re curious and asking lots of questions, that’s all that matters, right?

If I’m honest, this whole situation, especially the last point above because it potentially turns children against their own parents, makes me very sad. Perhaps this is the root cause of how our youngest generation arrived at the collective decision that we’re all, allegedly, now living in a ‘post-truth’ world – the reality is that no one knows very much and instead of finding out more, perhaps from those who do know about that particular subject or via going to the library and reading an actual book, they just make stuff up. This means that in the West we’ve potentially managed the unique feat of completely closing the minds of our youngest generation to any and all wisdom and expertise. This is in stark contrast to the almost universal commandment in the Far East that young people have a duty to listen to, learn from and respect their elders and their collective wisdom.

I think this process of ‘closing of minds’ starts in EYFS school reception year (where they are immersed in themselves as it were) and continues all the way to the end of year 6.

By the time the children arrive at year 7, they have had many years of ‘What would you like to find out about the Tudors?’ and ‘What do you think causes earthquakes?’ Even if teachers then go on to properly teach any particular subject complete with all the juicy facts, the children are still introduced to every lesson and lesson sequence with questions like this, causing them to think they they can go ahead and make up any old crud in their heads while believing that they’re being incredibly insightful, with the most disadvantaged children being disadvantaged even further by their limited background knowledge and experience (‘I’d like to find out if the children in the Tudor times played football or had video games!’). Many primary educators would read this and feel offended by these accusations, but believe me when I say that many, many parents up and down this country have had to correct misconceptions, stereotypes and untruths that their children have been taught at school:

  • Kind Henry VIII was some kind of mad, fat, woman-hating tyrant (actually, it is notable that as a young man he taught himself to dance, read and write music, speak many languages, understand the structure and military capabilities of all the surrounding countries, write poetry and worked hard to become excellent at sport – the guy was tall, fit, clearly incredibly intelligent, had charisma)
  • All children in Africa live in mud huts, wear masks and hunt with spears (actually, no, Africa is a continent and most of it is really quite developed)
  • The Victorians hated children and beat them constantly (actually, no, they were deeply concerned about the welfare and education of children – by the end of Victoria’s reign, the welfare of children had improved and almost all children were in school till the age of 12)
  • Grid method is how you do multiplication (actually, no, let me show you this whizzy method called long multiplication that takes a fraction of the time and is also way easier)
  • Butter is bad for you (actually, no, real butter helps you to absorb the fat soluble vitamins A, D, E and K and you can’t really get everything you need just from vegetables and fruits)
  • If you believe, you can achieve (actually, no, you need to have a goal and consistently work hard towards it)

Does the profession not find this embarrassing? Do educators assume that every parent is an idiot who will glibly accept whatever the child has been ‘taught’ at school when in fact most parents have some kind of relative expertise somewhere – whether it be general knowledge (because parents are typically older and more worldly experienced that the average primary teacher), knowledge honed through progressing through academia or having a specialist interest as a hobby, knowledge gleaned from reading lots of books and newspapers, or knowledge honed via the workplace (IT or financial services, working in foreign countries and having a better understanding of different cultures, knowing that only hard work and not ‘luck’ leads to rewards).

So, there we have it: children who are being encouraged to think critically even though they don’t know enough (because the teachers don’t know enough) when in fact younger children need to be encouraged to think uncritically (ie, just listen and learn) and be taught by experts.

What’s the answer?

Thankfully, the tied is turning and many primary schools are getting on board with the whole knowledge thing, working together to ensure that the children are receiving a great immersion in fascinating, linked-up facts in all their lessons. Knowledge organisers are being shared, experts are helping teachers with their resources, planning and teaching, and children are being given those wonderful opportunities to feel successful and like they’re really learning whenever they are tested. Although this isn’t the reason why knowledge is at the forefront of curriculum planning in many schools, children will experience a subtle shift in their mindset such that they will understand that the main job of a teacher is to teach and that their task is to listen and to¬†learn.¬†I think this is a good thing because little children need to be uncritical thinkers until they are old enough and wise enough (ie have learned lots about that subject).

There is much more that can be done though: textbooks written by experts and with ‘background information’ for teachers to bone up on, national/state tests of knowledge (start with science in year 6, please) for each year group; this will also cause parents to take an interest and to want their children to do well. Larger schools and academy trusts have the advantage that human resources can be pooled in order to provide expert-led lessons for children. The people at the DfE are talking about knowledge and the ‘substance’ of what is taught, but much of what they say is directed at secondary schools when we (those of us who have read our ED Hirsch) know that attention needs to be paid to what goes on behind the closed doors of the primary school down the road.

Perhaps many primary teachers need to accept that the joy of having a truly intellectual conversation with a young person that spurs them onto further interest in a subject is a joy reserved for the secondary teacher, and that in order for that conversation to take place someday in the future (when the child has long forgotten our names and faces), it is our job to lay the foundations of knowledge and vocabulary to enable it otherwise that conversation many never take place. Don’t get me wrong, I’ve had conversations with children about how much dark matter there is in the universe, but at the back of my mind I’m thinking about making sure they are damn good at maths, can write a decent report and have the basic science knowledge so that one day they can tell the world¬†about dark matter, but it will be their physics teacher and the subject itself that they will cite as being their inspiration and that is absolutely the right thing.

But what if these little ‘uncritical’ thinkers are taught a lie and just accept it?

They shouldn’t be taught lies though, should they? As adults, it’s our job to make sure that we know enough and are teaching them the facts. Further, is it appropriate to be treating little children like they’re mini-professors, constantly asking them to think critically about a subject they know little about, just as we try to get them to pretend to be expert scientists by doing lots of experiments, hoping that by pretending to be experts they will, de facto, become experts?

So, let’s expect the little children to be uncritical thinkers and let’s make sure we’re giving them lots of knowledge.

Who’s with me?