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?

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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?

You cannot ask a question if you don’t have the right words

I’m seeing lots of the ‘What’s the point of teaching knowledge, why bother filling their heads up with lots of facts and surely it’s better to be helping children to develop curiosity and ability to ask questions anyway?’ type comments and articles floating about the edu-net at the moment.

To those people, aside from pulling a face, I have one great example that should hopefully highlight how silly it is to think that we should only teach ‘skills’ like ‘questioning’ over and above good-quality knowledge (and the vocab to go with it):

Car showrooms.

worldsworstcar
‘Slight dent at the front’ ‘I’ll take it!’

This morning, I’m off to look at a Japanese import MPV or two and I’ve already done my homework. Here are some of my questions that I have prepped:

  1. Are there later models on route through the import scheme that include 2.4l engine rather than 3.0 V6?
  2. What is the fuel consumption rate, MPG, roughly speaking?
  3. Do the vehicles have rust-proof treatment administered when they arrive in the UK?
  4. How easy is it to get insurance and is the insurance reasonable/pretty average for an MPV?
  5. What is the torque and can you tow a small caravan, for example?
  6. How long an MOT has it got?
  7. What’s the servicing interval?
  8. How easy is it to get replacement parts?
  9. I see the doors have an electric sliding mechanism, is there a manual override? What happens if there is a fault somewhere in the circuitry – is it easily fixed?
  10. Is there a cup holder?

OK the last one was a silly question.

These questions are all really specific and if I didn’t know about cars in general or Japanese import MPVs, then I wouldn’t be able to ask these really important questions. The odds are that some of those questions aren’t specific enough because even though I have spent some time researching and have quite a bit of general knowledge about automobiles, I am not an expert in Japanese import MPVs. But if I didn’t have the knowledge that I currently have, then I would be on route this morning to looking like an ignorant fool with just one question ready:

  1. Is it good?

As you can imagine, that particular question would make me very vulnerable indeed because it immediately exposes me as someone who cannot think critically about a car purchase (basic I don’t have any knowledge about it), and this is one reason why I advocate teaching children lots of knowledge – to let them go into the world without any subject specific knowledge is actually, in my view, tantamount to child abuse because it leaves them extremely vulnerable to persuasion by those with ulterior motives*.

Further, I have actually found my car knowledge journey to be quite interesting – but I would not be on this journey if I didn’t have those initial questions and the very particular vocabulary that is necessary for asking those questions. How did my car knowledge journey start? I was taught by my driving instructor, friends and family as I was growing up. Of course, I have done lots of reading since – but remember, I’m an adult who is capable of self-motivation, I am not a little child who would struggle to resist the urge to just go out and play instead.

If you are reading this thinking that I am advocating teaching children about cars and the car industry, you are completely wrong. My point is that to not have any knowledge completely inhibits the ability to ask questions or think critically about a particular subject. In the classroom, a child who cannot ask a question in Year 9 about a particular aspect of biology because he has not got the basic knowledge or vocabulary to think of that question, let alone ask it, will end up less curious, not more – how would he ever know about how amazing cell signalling is if he didn’t know enough about cells or even what a cell was?

So, the knowledge must come first if we want children to be able to ask questions and be more curious.

Who’s with me?

*History teaching (or lack, thereof) is a good example of this: many young people today are at risk of voting in regimes that have catastrophically failed in the past – regimes that cause economic disaster and lead to horrific consequences for ordinary people, particularly the poor

 

 

Everyone is passive

I was deeply concerned about this article centred around an epidemic of self-harm among girls at a boarding school; it made me wonder why children of wealthy parents who have nothing to worry about would be so mentally ill as to want to seriously injure or even kill themselves. This is not to say that their plight is nothing when it clearly is a big something – but, something’s not right here. Why is it that a family friend who had seen her own relatives set alight, burned alive and then had walked thousands of miles to try and get to Britain the most happy, positive and hard-working person I have ever known in so much better mental health than all these boarding school girls, for example?

Natasha is right that teachers cannot simply be chucked all the mental health hot potatoes simply because the taxpayer doesn’t deem CAMHS to be a worthwhile enough cause, but I don’t think there should be all these hot potatoes in the first place. I think part of the problem is that an underlying current of Western culture, this collective psychology that dominates, where everyone is waiting.

“I just want my child to be happy.”

How many times have we heard that one? Too many. But when you really think about it, it implies that happiness is something that comes to us if we just wait: let life take its course, let the opportunities come to us. For a lucky few (mainly the wealthy), those fulfilling opportunities will come. For the majority, happiness will never materialise the way it does in the movies. Many parents let their children choose the easy option in life of not working incredibly hard towards exams and in academic subjects (so many parents have told me that it’s more important their child is happy than becoming ‘mentally ill’ through having to work hard for exams); they are under the false impression that happiness is a fragile flower that, at any moment, could fall apart at a mere gust of wind, leaving the onlooker patiently waiting for the next flower to grow in its place.

flower

If happiness is something that just comes to us when we are waiting, then unhappiness is also something that just ‘happens’ to us too. The dangerous thinking here is that the unhappy person sees herself as a victim and never takes positive steps herself to brighten her own mood; one of the unintended consequences is that she never makes an effort to be a good friend to others (because, of course, it is her friends’ jobs to cheer her up, not the other way round) and then wonders why she ends up even more isolated, constantly thinking about how unhappy she is and how it is so unfair that everyone else seems to be happy. My friend whom I referred to earlier could’ve allowed herself to sink deep into a pit of despair, but she dug deep and chose to pursue a positive future for herself. Ah yes, it’s easy for her, isn’t it? She’s not a white Westerner and therefore must possess some kind of genetic advantage over us.

We’re all guilty of it. This passivity. We’re all waiting for everything: the perfect relationship, love, general happiness, a job that finally makes us feel worthwhile, a career path, to ‘find’ ourselves, the perfect lipstick, a mysterious affinity with an academic subject so that we don’t have to work so hard, readiness to settle down, the ‘right’ time to have a child. And if all these things that we are waiting for don’t arrive, then it’s everyone else’s fault, or perhaps just the fault of The Universe. Parents encourage their children to think like this right from day 1 by patiently waiting for their children to be ‘ready’ to behave, go to the toilet, use a knife and fork, read, write, develop good study habits, form a sleep routine, take in interest in others, choose to work hard, find the perfect extra curricular activity, choose to be kind and then if these things don’t happen naturally then that’s just the way it is, clearly some kind of SEN and therefore the responsibility of others to adjust their own lives to accommodate yet more people who are not ready to fully take part or be responsible adults in society.

Ask yourself this. What are you waiting for? I’ve long since realised that career, happiness, relationships are down to hard work and being proactive, but you know what? I’m still waiting for my wine habit to suddenly disappear, or for my body to suddenly want to go for a run. It’s never going to happen, but this whole waiting thing is so ingrained in my psyche that I am still having to root it out like the knotweed of my life that it is.

So, I recommend we all think about what we are waiting for and then we seriously need to think about how we are encouraging young and vulnerable people to wait for things that they absolutely could have control over and could choose to have. And that includes, sorry to burst a bubble here, happiness.

Who’s with me?

How about a completely different primary science SCITT training?

I should probably have blogged about what I’d do with maths first, but I got into a thing with this morning’s post about how children end up not really knowing much science at the end of KS2, so here are my thoughts on how SCITT science days for primary teachers should be run.

  1. Challenge misconceptions

I think the very first thing that should be done is to educate new teachers on how exactly a scientist is made. To get them to understand that scientists don’t go into their field of research because they really like doing things with micropipettes and liquid nitrogen in labs is the main order of the day. Teachers need to know that scientists are keen to research (which happens to involve experiments) because they want to KNOW more about that particular aspect of science, not because they want to blow stuff up. Then, of course, we need to let new teachers know that a child has no chance of becoming a scientist if he leaves primary school unable to access his secondary science lessons.

Any SCITT tutor would need to be very diplomatic because in letting teachers know how a scientist is made, they are also letting them know that, actually, the primary science teacher is really setting the child up to have that spark of interest well after they have forgotten who their primary science teacher was. I think this aspect should be on any primary teaching course because we should not have huge egos – it is better to be prepared to step back knowing that every child has a chance to really love that subject but it will and should be the secondary science teacher whom the child remembers as the one who made them feel like they want to become scientists.

nutty-professor-9067265
Mr Smith was ready to get those kids doing science

2.  Teach teachers how the world of science works.

This would make teachers realise that the experiment is but a mere part of the collective evolution of science knowledge. Through this, teachers also need to end up fully understanding that it is science knowledge and vocabulary that children need, like a scaffold, not endless experiments.

3. Initiate new teachers into the best of current research in how children learn and retain what they have learned. This is where teachers are given no-nonsense information about how to put knowledge at the centre of planning and teaching, how to make sure that children receive the information (ie they are paying attention) and then how to make sure that children are given opportunities to remember such as with regular quizzes and tests. Of course, a plethora of experiments that help to consolidate knowledge should form part of this training too.

4. Ensure that the new teachers know the new curriculum inside and out

This would be a test/exam and it would show that teachers know what they need to teach.

5. Let them see some real science teaching.

And I mean real, not the whizz-bang lessons teachers are shown on video. If they could just watch about ten science lessons then they would really feel like they had an idea about what they were doing! They would also understand that even when no experiment is done, science lessons can still be fascinating for children. Further, this should be proper fly-on-the-wall experiences. What is it with SCITT training that requires new teachers to constantly work with a group or with the children with SEN during input such that they never get to see the bigger picture of a lesson? This really does my head in: they’re not TAs! Let them watch the teacher and see how the children react!

6. Let them know that they have a responsibility to work with the literacy coordinator to ensure that the children they teach are fluent readers and have access to a plethora of interesting science books.

And that’s it really.

Who’s with me?

When do the children see the adults talking?

Every year, the tally of children rocking up to reception year with speech and language deficits seems to increase; some have an American accent (!), some have no clear consonant sounds, some have a severely limited vocabulary and some don’t speak at all. I think pretty much everyone is in agreement about the positive effects of sharing civilised conversation and food at the dinner table on children’s emotional and intellectual development (research shows it is better for building vocabulary than reading to children*) and how lack of dinner table conversation may impact on development, but have we taken the opportunity to look at the life of a disadvantaged child to see when exactly they might have any kind of adult conversation modeled to them? For some children I fear are not seeing or hearing civilised conversation at all. What’s going on?

  • Even where communal dining experiences happen, children are now allowed to interject, talk over or even dominate the topics of conversation (this is, I think, more prevalent among middle class families) which effectively prevents them from learning to politely sit and listen and maybe pick up the plethora of subtle words, phrases and concepts from adults who are conversing around them.
  • When eating out, children are quite often given an iPad or a phone to entertain themselves with, so they are effectively sent into a conversation-less and self-absorbed bubble. Even teenagers are allowed to opt out in this scenario.
  • Adults tend not to talk on the phone and instead prefer to use some kind of text messaging app/service. I’m pretty sure that I would’ve learned so much from hearing my mum gossip away on the phone, but I’ll admit that my own children never hear me on the phone (I avoid it, partly because I’ve been conditioned to ‘put the children first’ and always be at their service).
  • Nobody goes to church any more, or even regularly attends village gatherings, so children don’t get to regularly see or hear any kind of script for conversing with various types of people (strangers, close friends and family). What do people regularly do? Shopping. Not much conversation there, other than “Do you have this in my size?” and generally treating fellow man like The Help.
  • Single-parenthood. For a while, a couple of years ago, I was on my own; I’m very sure that my children would’ve suffered from not seeing any kind of regular intellectual or caring adult conversation modeled to them (although I always engage my own children at the dinner table) during that time. This must be the case for the hundreds of thousands of children who (mainly) live with one parent (usually the mum). That one parent must also experience some kind of conversational-ability attrition rate due to the fact that they are tied to looking after their children 24-7, sometimes without any respite at all.
  • Even at nurseries and playgroups, years ago you would let your little ones go and play with all the toys or join in with singing while you sat with a cup of coffee and nattered to a fellow mum, knowing full well that a few toddlers around you would be eavesdropping, but nowadays (actually, this might just be my observation) it seems as if every mum must forgo that coffee and a natter and join in with the singing and playing down on the floor (which knackers your knees!). Upshot: no adult conversation to be heard.
  • In the classroom, the TA is either not there (as in my case) or has been brow-beaten into maximising ‘teaching and learning’ by shoe-horning interventions into every crevice of the day. The upshot is that they never see the teacher and TA ask each other how they are. Further, at lunchtime, I’m flapping about with meetings, clubs and preparing for the afternoon such that I never stop to have even the briefest of conversations with a colleague. Essentially, the children in my class could just see a servile automaton constantly teaching and handing out worksheets/scaffolds etc and I’m sure many other children up and down the country are experiencing the same thing.

It amazes me that while we espouse the benefits of learning a new language through ‘immersion‘, we collectively conspire to immerse our youngest generations in nothing at all. We then teach them how to read and write (using systematic synthetic phonics instruction – the best way to learn to read), but they do not understand the words or phrases and they have fewer words, phrases and facts in their heads to write. Nursery and playgroup leaders can only do so much, as can EYFS reception year teachers. What can be done? What do we need?

  • A massive, collective realisation of how we are effectively going backwards as a species in terms of emotional and cultural intelligence.
  • A campaign to ‘bring back conversation’ to our daily lives (‘Conversation is not just for Christmas dinner, it’s for life!).
  • Non-patronising information for parents about the importance of not limiting adult conversation when looking after children.
  • Subtle opportunities for children to hear adults at school be nice to each other and talk about interesting things – perhaps more break times or even not being so frantic about deploying the TA.
  • We could even go as far as to have teachers sat near to children at lunches, but my fear in this case would be that teachers would be minded to only talk to children about what the children want to talk about which doesn’t exactly teach them how to take turns, be nice or hear a bigger range of vocabulary and phrases. In many cases, teachers would just end up doing constant behaviour management (“Stop throwing the fork on the floor!”) which would be depressing and exhausting.

I did see one EYFS reception year in a private school integrate snack time as part of their ‘whole-child’ education. The children were taught a script for serving each other juice/milk (out of jugs!) and plain biscuits while the teachers sat with them asking them about their day, expecting the children to do the same back. At lunch, the children were sat with a teacher being shown how to sit up straight, use a knife and fork properly and, again, have civilised conversation. It helped that the class sizes were much smaller. In state schools I have only ever seen rushed snack times where the adults run around waiting on the children hand and foot and the children might have the whiteboards out or some kind of instructional video on. Very interesting. I guess if Ofsted came though, they would see ‘No wasted opportunities for teaching and learning’.

dinner2

It does help if you are actually teaching, rather than getting children to constantly [not] discover, do group-work etc because at least that way the ratio of adult talk to child-talk is better, even if they’re not hearing any kind of day-to-day vocabulary and phrases. However, if behaviour is poor then children are only really hearing short snippets of interesting sentences punctuated with relentless reminders to ‘do the right thing’ such as refraining from poking each other, playing with rulers, fiddling with shoes, talking over the teacher, calling out, making silly noises, humming, using the mini WBs for cartoon practice etc combined with regular praise for those children who are doing the right thing.

Anyway, the least we can do is be aware of how children need to hear at least a little bit of adult, civilised conversation.

Who’s with me?

*I’m not saying we shouldn’t read to children, in case anyone gets the Venn diagrams in their heads mixed up. In fact, we should read lots of stories to children!