Don’t teach children to think like a scientist, but…

…do teach them something about how scientists think.

Agree, or disagree?

 

I’ve written before about the distinction between substantive and disciplinary knowledge.

It would be great if we could teach children to think like mathematicians, scientists, historians, by the end of Year 11…

…but it’s a virtually impossible goal for 100% of students, given the time available, since thinking in this way is a hallmark of expertise: enormous quantities of substantive knowledge, arranged differently even from that of novices who actually possess the same knowledge, and then framed by the disciplinary knowledge.

In this study by Chi et al., they don’t even categorise undergraduates as experts!  (they use advanced PhD students as experts, and find a marked difference in how they think, compared with undergraduates)

 

Probably the most egregious use of this ‘think like an x’ language that I’ve witnessed takes the form “You are all historians!” (for example,) explained to children literally before they’ve studied any history…!

Although the intent is noble in principle, it’s literally incredible, severely undermines the expertise of real historians, and teaches children that the title is meaningless, and nothing they need to work for, nothing to be earned.

I don’t think I deserve to be called a historian…  I think most adults don’t deserve to be called historians… so why on Earth would that be valid for school children?

Potential to be?  Sure.  Are?  No.

 

So that’s one extreme.

 

But looking to another extreme, most adults have no idea what professional mathematicians do.

How can you do maths all day… what would you do… add sums?  Solve random equations?

No.

 

Continuum 1

Two alternative outcomes

 

Yet, most people have some idea of what scientists do; some idea of how conduct experiments, even if they can’t ‘think like a scientist’ themselves, or conduct a series experiment of their own…

 

I think this happens because people are in the throes of believing our job is to teach kids to think like scientists, which involves lots of school time being given over to setting up experiments and trying to learn the discipline of science.

While I think the time afforded to this may be disproportionate to what yields educational gains, it does at least mean we get a population who understand something about how science works.

In maths, we do virtually none of this.  No investigations, derivations, studies of proof, or building of models… we learn the substantive knowledge with zero insight into how it is created.

This is a recognised problem, and some people have tried to solve it, but in my view they’ve mis-stepped.

They’ve fallen into the trap of thinking that our goal should be to teach children to ‘think like a mathematician,’ or that they can learn the substantive knowledge by discovering it for themselves, through investigation.

Instead, investigations might be better used to learn something about the investigative process, and likewise for proof – the goal isn’t to become proficient in either, but to have an awareness of how they operate, perhaps leading to future proficiency in higher level study.

 

So, what if we tweak the rhetoric.

 

Instead of ‘learn to think like x,’ instead, ‘learn how x thinks.’

 

It’s a subtle but important distinction.  It’s a kind of recognition without necessarily recall.  It’s knowing but not doing – no serious attempt to close the knowing-doing gap.

 

Continuum 2

A third way?

 

I think it’s more manageable, genuinely achievable, and would achieve something important.

It would advocate for a shift in how we distribute curriculum time, away from the massive amounts of it currently dumped into the diminished returns of history and science curricula, while equally perhaps shifting maths away from a zero time investment.

 

I’m interested in how people feel about this.

Teach children something about how scientists / historians / mathematicians think.

Like it?  Hate it?

 

 

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Why Maths Teachers Don’t Like Knowledge Organisers

TeacherTapp said this:

Blog 1

Blog 2

So I said this… (though I meant to say ‘knowledge’ – damnyouautocorrect ‘n all that)

Tweet 1

Then Laura said this…

Tweet 2

 

And so here’s my best, super-brief shot.

 

Point 1)  Knowledge comes in different forms

As a minimum:

  • Concepts
  • Facts
  • Processes

 

Point 2) Knowledge Organisers don’t really organise knowledge

They organise facts, and are very well-suited to doing so.

But they’re terrible for organising concepts and processes.

 

In this sense, Knowledge Organisers are really more ‘Fact Organisers‘ than Knowledge Organisers…

‘Knowledge’ Organiser suggests a broader remit than to what they’re really suited.

 

Point 3) Maths consists of very, very few facts

Most people think that maths is replete with factual knowledge… but actually, it’s subjects like English, the Humanities, and some sciences that are hefty in factual content.

The only maths topics, up to GCSE, where facts really make a solid appearance, are:

  • number facts
    • number bonds
    • times tables
    • prime numbers
    • square / cube numbers
    • powers of 2
  • angle facts
  • formulae (arguably)

…really, that’s about it!

Maths is super-dense with concepts, and processes, but really only very few facts.

 

So whenever I, as a maths teacher, tried to build some kind of Knowledge Organiser, it fell apart very quickly (except in geometry and number!)

I tried to include the kinds of knowledge that pupils need, like what a prism is, or ‘how to do X,’ and because these aren’t factual in nature, the Knowledge Organiser became convoluted, complicated, and completely useless, very quickly.

 

Speaking with other maths teachers who’ve tried this – and also leaders in KO heavy schools who were trying to understand whether Knowledge Organisers are really useful in maths – I’ve tended to find the same experience repeated.

 

So there you have it.

 

I don’t think maths teachers are rejecting knowledge organisers because they want freedom to focus on problem-solving…

I think they’re rejecting them because they just aren’t well suited to the kinds of knowledge that dominate mathematics.

In other words… they’re just not very good for maths!

 

Conversely, languages are probably the most fact-heavy subject, so it would make sense that MFL teachers ‘really like’ Knowledge Organisers.

 

I have no evidence to support or deny this, but maybe TeacherTapp could find a clever way to uncover some, either way…!?

 

***

 

Incidentally, I’m in the middle of preparing a lengthy series that plummets into this in depth.

Watch this space!

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Where to Learn About Direct Instruction

I’m frequently asked for places to go to learn about Direct Instruction.

So, here’s a summary.

I’d probably suggest starting with ‘Psychology Learning Resources,’ for an intro / overview.

Then, The Components of Direct Instruction might be the best summary of the main principles.

 

Books

 

Other

 

That oughta do it!

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An angry blog post about Great Yarmouth Charter Academy

*** UPDATE ***

On Tuesday 13th March, Ofsted announced the results of their visit to Charter.

 

**************

On Thursday I spent a morning at Great Yarmouth Charter Academy, and like many people, I’m angry.

 

Angry that there aren’t more schools like this, which was one of the most inspiring school environments I’ve seen.

 

Here’s what I saw:

  • Everywhere teachers went, pupils greeting them with smiles and ‘good mornings’ that were heartwarming in their palpable sincerity
  • Corridors that were calm, and orderly
  • Behaviour in classrooms that was impeccable – amongst the best I have seen in any school, anywhere
  • Every child I spoke to was grateful for any help I offered, obviously excited to learn more, and determined – I sat and worked with some children who repeatedly made mistakes, but were unperturbed and keen to keep going until they understood every mistake they made, and then continued into success; not a hint of wanting to give up

 

Many of the staff I spoke to had been there for over a decade.  One had been there for fifteen years, and even went to the school as a pupil herself!  After more than a decade of abuse and ingratitude, she was ready to pack it in this year, but now, she never wants to leave, and has never been happier.

This was a common theme.  Teacher after teacher was joyful, welcoming, and said that they looked forward to coming into work every day – something that wasn’t true in the past.

One teacher said he couldn’t believe it: children who last year would swear at him every day, were now volunteering to hold the door for him, and wishing him a good day with a bright smile.

But what about the children?

Well, beyond what I’ve already said, I spoke with a Year 11 boy who achieved Grade 1 in his last mock exam, and recently achieved Grade 5.

I spoke with four Year 10 girls who told me that ‘everything’s changed’:

  • At lunch, there would be an enormous queue waiting to be served, while people ran screaming around the lunch hall
  • In the corridors pupils would be shouting and pushing people around
  • Classes were 30 minutes long, they explained, not by design, but just that’s all that was left once everyone finally turned up
  • Once there, no-one would learn because they were too busy using their rulers to fling the innards of glue sticks at one another, they said

But it’s not all good, they went on.  They miss the ‘freedom they used to have.’

If they were in charge, I asked, would they make the decision to sacrifice that freedom to have what they have now?

They paused for several seconds to genuinely puzzle this one through, then offered a tentative, yes… yes it’s important to do well in school… followed by an effusive ‘yeah definitely, it’s much better now!’ – it was like watching the full realisation of the positive changes dawn on them.

One final Year 10 girl became the star of show, when she came over to tell me about her personal transformation.  ‘Notorious,’ might be a word to describe her, ‘Every teacher knows who I am.’  She explained that she was in detention every day last year.  This year, instead, she received at least one Golden Ticket every day, equivalent to three merits, and awarded to only one pupil per lesson.  While she described herself as ‘loud,’ a more favourable estimation might describe her as ‘assertive;’ you could see her going far, if she could deliver the academic success, first.  She was now averaging only a single demerit per week.  She said she was finally learning; that she’d never learnt so much before.

This, again, was a common theme amongst pupils.  Every pupil I asked insisted they had never learnt so much before, and they were all excited by it.

 

So is there anything to be ‘concerned’ about?

Were teachers shouting?  Not that I heard – and given how settled the environment was, I think I would have if it were happening anywhere in the school.

Were pupils quivering in fear?  I’m not sure I’ve ever seen happier children at school…

Were pupils being put in isolation for McDonald’s haircuts?  Absolutely.  And I was in awe at the warmth headteacher Barry Smith was able to radiate while sternly telling an apologetic Year 11 pupil that, after his exam, he would have to go straight to isolation.  I wish I could do that, and the atmosphere of mutual respect was evident.

 

So throughout the day, when I thought about all the negative press I’d read, and the vitriol sprayed on Barry, I was angry.

It’s senseless.

 

But the other feeling I had today was hope.

Perhaps what stands out most at Charter is the feeling that… this is a pretty normal school.  KSA, Reach, Michaela et al. they’re all exceptional schools, and have proved that ‘poor kids’ can be successful at school.  But they’ve all done it with young, child-free teachers who regularly work 13 hour days, plus weekends – more than double the 1265 – to do ‘whatever it takes.’ (Albeit Michaela has tried to challenge that last one.)

Charter doesn’t have that.  It’s staffed by a typical school workforce, and so for me what it feels closest to isn’t those schools that were the crucible of many of the ideas it implements, but my second school placement, Bishop Challoner in Birmingham, an outstanding school that benefits from a privileged intake.  Unlike Charter, Bishop Challoner is not a school working in challenging circumstances, yet you’d struggle to tell the difference between the two.

 

So if they can do it at Great Yarmouth Charter Academy, if they can turn this school around and turn it into the next great success story, then it can be done anywhere.

 

And from what I’ve seen today, I believe they can, and they will.

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Mixed Ability, Sets, and Streams – a teacher’s perspective – Part 4

I’ve taught sets, mixed ability, and streams.

What follows isn’t any rigorous analysis, or appeal to research.  From what I’m aware of the research, the conclusions aren’t exactly conclusive: lower attainers benefit from mixed groupings, higher attainers suffer.  Mark McCourt reiterates this point, and takes it further by pointing out that those conclusions aren’t necessarily subject or key stage specific, while Lucy Rycroft-Smith suggested there was broadly no impact either way (MrBartonMaths Interview, roughly 52 min in.  Research Espresso.)

So, this has nothing to do with research, just my thoughts and feelings having had some experience of all three.

I’ve split it into four parts:

  1. Setting
  2. Mixed Ability
  3. Streaming
  4. Conclusion

 

This is Part 4 – Conclusion

***

Conclusion

My personal experience of teaching streams, a form of grouping that I don’t often see used, leads me to advocate for it strongly.

It seemed to eliminate nearly all the problems I perceived with setting, while also eliminating the extreme challenges I faced in teaching mixed ability.

 

I’m not entirely sure why any school that currently sets wouldn’t want to adopt streaming.  It’s an efficient way of organising pupils – you always know who should be in what group, and it makes form groups more meaningful than ‘the place you go to register in the morning.’

It eliminates the ‘get out clause’ of pupils and teachers working hard to form a working relationship, while avoiding the extreme difficulties that mixed ability grouping can present.

There’s sometimes an argument that a pupil might be terrible at English, but really good at maths, and it would be ‘unfair’ for them not to have the best maths experience by being placed in a lower group.  But, the myth of a ‘maths brain’ or ‘left/right’ dominance is entirely exploded; so while there may be some cost to streaming over setting, I think they are likely to be insignificant compared with the benefits. (see Cost-Benefit Analysis)

 

Even if a school wasn’t ready to make that change yet, I remain utterly, utterly perplexed as to why a school would deliberately stamp a number on each child’s face!  What possible advantage can there be to numbering sets, over naming them?

Just to put the effects of this into sharp relief for a moment, when I first visited Eton, I observed a Year 11 class, set 12… of 13.  I sat down next to a very polite pupil, who then almost immediately felt the need to apologise: “I must apologise… I’m afraid we’re not exactly the creme de la creme.”

Now, Eton is obviously a highly selective school, so to be clear what this means, I asked the teacher what GCSE grades these pupils were expected to achieve.  Apparently not all of them would get A*s, but they’d all get As at least.

Now on the one hand, I really want to see what the hell their top set is doing!  Moving them into these sets, I am certain, means that those top sets must be progressing in a way that is very special indeed, and entirely appropriate to the value of helping everyone reach their potential.

But why the numbers?  Set 12 of 13?  Christ, no wonder, that poor boy felt underwhelmed by his own accomplishments; where in almost any non-selective school that group would probably represent the ‘arrogant’ top set.

img

Even at Eton, numbered sets can leave pupils feeling inadequate

 

So why not just name the damned classes?  In a school, with 6-8 sets, or more, you can guarantee that they wouldn’t figure out the ‘ranking.’

 

A final point worth making about mixed ability grouping, in my fifth year of teaching, and third at KSA, I again took on a mixed ability Year 9 group.  Throughout the year the experience was relatively similar to my first efforts; somewhat improved thanks to two more years in the classroom, but there were four pupils with whom I felt trapped – completely unable and unequipped to help them learn anything.

Until, the very end of the year.  With all my other classes having left after the exams, I finally had the time to think through how to apply everything I’d learnt to our final sequence of study together.  I wrote about it here (My Best Planning.)

The success of that experience gave me hope that there is some way to teach a completely mixed group successfully, and certainly Mark McCourt’s experience of teaching mixed ability sounds wholly positive, albeit he caveats this heavily by recognising that it’s difficult to do well, and so perhaps shouldn’t be attempted lightly, and without pouring huge resource into a department to help them learn how to do it; huge enough that this might be a real, insurmountable barrier to mixed ability teaching in many schools.

 

And so, on balance, considering only my personal experience and having heard no strong argument to the contrary, for now, I continue to strongly advocate for streaming as the lesser known and best of all options, in the best of all possible worlds.

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Mixed Ability, Sets, and Streams – a teacher’s perspective – Part 3

I’ve taught sets, mixed ability, and streams.

What follows isn’t any rigorous analysis, or appeal to research.  From what I’m aware of the research, the conclusions aren’t exactly conclusive: lower attainers benefit from mixed groupings, higher attainers suffer.  Mark McCourt reiterates this point, and takes it further by pointing out that those conclusions aren’t necessarily subject or key stage specific, while Lucy Rycroft-Smith suggested there was broadly no impact either way (MrBartonMaths Interview, roughly 52 min in.  Research Espresso.)

So, this has nothing to do with research, just my thoughts and feelings having had some experience of all three.

I’ve split it into four parts:

  1. Setting
  2. Mixed Ability
  3. Streaming
  4. Conclusion

 

This is Part 3 – Streaming

***

 

The whole thing left me looking forward desperately to…

Streams

Once in Year 10, the classes that pupils at KSA have been in for three years are finally shaken up.

They are placed into new ‘streams,’ with roughly 30 in the top stream, 20 in the middle stream, and a 14 in the bottom stream.

These streams operate largely like the mixed ability classes from their earlier year – this is their form group, and they are in these classes for all of their core subjects.

That means: maths, science, English, and MFL.

Optional subjects like art, P.E., music and the humanities, were taught in different groups.

The streams still have names; they are not numbered, and they are never referred to as ‘top’ or ‘bottom’ set by any of the teachers.

 

This, for me, was the best option, in the best of all possible worlds.

 

Most all of the issues with setting didn’t manifest.  True, in a school so small the pupils were savvy enough to realise that there was a ‘top/middle/bottom’ group, and figure out which one they were in; but it wasn’t emphasised and all-encompassing in the way that it was in my first school.

 

Pupils were placed in these sets based on their performance in maths, English and science exams at the end of Year 9, but upon taking the exams, this was never mentioned by teachers – there was never any threat that pupils had better revise hard ‘lest they find themselves in the dreadful bottom set!’

The party line was always that groups were chosen based on teacher judgement about what would work best for each individual pupil, taking into account many factors; and this was true.  The groupings were heavily informed by the exam results, but not determined by them alone, and two of these groups, representing 75% of the year, followed identical curricula.

 

There were still never any ‘set changes,’ and while some arrogance could creep into the top stream, and some disillusionment in the bottom, by and large the cultural effects were far weaker than I’d seen with sets.  I often saw pupils who were very low attaining, in the bottom stream, work as hard as anyone in any other group – they were as determined as anyone to be successful.  They didn’t see themselves as ‘dumb,’ and ‘not very smart.’

 

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Mixed Ability, Sets, and Streams – a teacher’s perspective – Part 2

I’ve taught sets, mixed ability, and streams.

What follows isn’t any rigorous analysis, or appeal to research.  From what I’m aware of the research, the conclusions aren’t exactly conclusive: lower attainers benefit from mixed groupings, higher attainers suffer.  Mark McCourt reiterates this point, and takes it further by pointing out that those conclusions aren’t necessarily subject or key stage specific, while Lucy Rycroft-Smith suggested there was broadly no impact either way (MrBartonMaths Interview, roughly 52 min in.  Research Espresso.)

So, this has nothing to do with research, just my thoughts and feelings having had some experience of all three.

I’ve split it into four parts:

  1. Setting
  2. Mixed Ability
  3. Streaming
  4. Conclusion

 

This is Part 2 – Mixed Ability

***

 

…so, yeah, sets sucked in a lot of ways.

Mixed Ability

But fortunately KSA had mixed ability groupings for all subjects in Years 7 to 9.  Children joined the school, were put into their form of 20-22 pupils, and took every single lesson with that group.

I taught Year 9, all of Year 9 – three groups of ~20 children each.

At first, I adored mixed ability teaching.

Literally every problem I listed above had evaporated.

 

There were absolutely no ‘set’ changes… indeed, it would hardly make sense.

You couldn’t even move classes to get away from a pupil, or vice versa.  If I teach every group in Year 9, then moving classes isn’t going to make a difference!  And I can think of one or two cases where I certainly would have fallen into the trap of begging for the pupil to move to another class, had I been in my previous school.

In one of those cases, we went on to have a hugely positive relationship after three years, and I’m deeply proud of that pupil’s achievements.

The other case is less of a resounding success story, but we struggled through, we got along as best we could, things did improve, and we certainly did better than we would have in a school where we could have ‘gotten away from each other.’

 

Each form has a name, not a number denoting their ability.  Gone the self-concept based on the set you’re in.

 

Gone, the horrible language of low-expectation.

 

But.

 

After a few months, the darker side of mixed ability teaching started to rear up.

I often felt trapped.  I had super-smart wannabe mathmos in a group with pupils who couldn’t add and subtract negative numbers accurately.

The top end asked deeply insightful and interesting questions, but responding to them meant that 2/3 or more were shut out of the class for the next few minutes.

By my standards, the bottom end failed, failed, and failed almost every lesson, and I couldn’t go slowly and deliberately enough to cater to them without boring, to the point of insurrection, a different 2/3 of the class.

 

Across a year, I was deeply confused, and if my preferences were like a needle in a metre, pointing to either ‘sets’ or ‘mixed,’ it was swinging wildly back and forth, month after month.

Meter

Sets, or Mixed Ability?

 

Even though my teaching, and the outcomes, were undeniably better than they had been in the previous two years – thanks to the excellent discipline systems at KSA, its outstanding culture of high aspirations, and being a teacher in my third year – by the end of the year I was deeply dissatisfied with the experience.

I felt that I couldn’t teach the top end to the limits of their potential, and I was consistently failing the bottom end, while the middle sorta chugged along relatively unnoticed.

And these were classes of 20… I could hardly imagine what it would be like with traditional classes of 30!

 

The whole thing left me looking forward desperately to…

 

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