Punctuated Equilibrium, Progress and Schools

Punctuated Equilibrium is a theory in evolutionary biology that seems to fit well with progress in students’ learning.

What is Punctuated Equilibrium

Punctuated Equilibrium was first proposed in the 1970s by Nile’s Elderedge and Stephen Jay Gould. They argued that while most of us think that evolution happens gradually, the fossil record showed  evolution happens in spurts. Stasis (or equilibrium) is the norm, then there are bursts of activity (the equilibrium is punctured) and then stasis reigns again.

There is a helpful post here explaining it in more detail but the difference between gradualism and punctuated equilibrium can be shown as per the below

As a model, it has been attacked by Dawkins and Bennett. They called Punctuated Equilibrium “evolution by jerks” (to which Stephen Jay Gould’s response was that Gradualism was “evolution by creeps”).

That said, the punctuated equilibrium dynamic seems to happen outside of the natural world too. In industry, there is often stasis, then a new environment (often triggered by an innovation) leads to a burst of new prototypes before these are whittled down to a smaller handful of product categories.  Bicycles seem to be a good example of this. As BicycleHistory says:

Between 1817 when Nicéphore Niépce created his first velocipede and 1880 when first “safety bicycles” became highly popular across Europe, bicycle designs were highly varied

It seems is might be a useful lens through which to assess learning too

Punctuated Progress

David Didau has written a number of good posts about the myth of progress.  He points out that, as in Hugh Macleod’s Gaping Void Cartoon, while we act like progress is linear, it’s more confusing that that.

It’s a great diagram for pointing out the shortfalls of thinking about progress as linear, but it doesn’t help much in terms of “where next”. I’m curious to know if the punctuated equilibrium model is more helpful.

There are some obvious ones such as that if progress is characterised by periods of stasis, then there will be lessons in which students are not performing substantially differently.  Threshold concepts look to be a tidy fit with the model and I’m going to have a further read to see how these might help. If anyone has any pointers, I’d love to hear.

Praxis – The Rarest of the Three

Aristotle divided human activities into three broad categories: thinking (theoria), making (poiesis), and doing (praxis). Put another way, I suppose, they are the why, the what, and the how.

In very coarse terms, and trying to link it to rhetoric,  I wonder how it matches the various posts I read on Twitter and blogs. The categories match well but I’m struggling to find indicators for good praxis posts.

Theoria posts 

There are a huge amount of posts or tweets on theoria (even more so if you include feeling in that category).

Examples might include:

  • Hack wisdom (“Teachers lose their way when they lose their why”)
  • Out-of-date management speak (“Teachers are change agents”)
  • Truisms (“Trust is important”)
  • Links to research papers & discussions of it (the odd one out in this category)
  • Many of the alpha-tweeters – they’re fascinating to read but seem to follow the same trajectory that bedevils management, becoming further and further removed from real teaching.

Poiesis posts

These are infinitely more useful in many ways but harder to sift through.

Examples might include:

  • Links to lesson plans that have been tried
  • Pictures of displays
  • Pictures of student work
  • Comments about days at school or lessons

Praxis posts

Perhaps I just haven’t found the right people to follow yet, but these for me are the rarest and hardest to find.

There are some who do this by regularly blending theoria and poiesis – Cristina and Harry are two excellent examples that spring to mind – but this category, while it’s an El Dorado of sorts, seems far harder to pin down. It’s easy to come up with examples to fit the categories above but Praxis seems far more mercurial.

The best indicator I have at the moment is both the sort of blend mentioned above and the richness of discussion. If anyone has any better ways of zeroing in (or recommendations of people to follow), I’d love to hear.

 

What Shaolin Monks Taught Me About Teaching

The best teacher training I have ever had was from a 34th Generation Shaolin  Warrior Monk, Shi Yan Jun.

Over the years, I have had in-school training such as INSETs, after-school twilight sessions, teacher observations (given and received). I have had off-site training run by battle-hardened professionals but sweetened with coffee, fancy biscuit and lecture notes. And I have followed my own CPD via conferences, Teachmeets, reading the latest literature, followed some inspirational education professionals online. Some of these have been useful (especially the last category), but a lot, however good the intention, have been poor. (For me, anyone who tells you putting up displays in a school is “sexy” needs sectioning). As the brilliant David Weston pointed out a while back, that “[doesn’t just mean] poor value for money or insufficiently effective – it’s much worse than that. A large swathe of training has no effect whatsoever on pupil outcomes.”  My time with the Shaolin monks has already had an impact.

Professional development wasn’t my reason for going to China. Instead, as John Kay might put it, the training happened obliquely. A while back I read about an inspirational headmaster who started every academic year with a challenge. He would, to take one example, play the bagpipes badly in front of the whole school, and then explain to the children that by the end of the year he would be better. At the end of the year he would show how far he had progressed. I loved the idea of publicly learning something with the children and so, in the spirit of all good learning, stole it. This year’s my 10-year old students challenged me to become a “tai chi kung fu master”. Like many teachers, I am time-rich so rather than struggle with evening classes during the working week, I decided to go to the source and visit a Shaolin monastery.

It took a month, I was forever bottom of the class and I spent a lot of the time either in pain or with “panda asthma” or both. I would also do it again in a shot. There are clearly physical and mental benefits but it has also made me a better teacher.

Teaching Take-Aways

None of what follows is ground-breaking. After all, the method the Shaolins use is centuries old. What was different for me, though, and what I had not experienced quite so vividly for far too long, was being on the receiving end of different teaching methods, day in, day out, as a struggling student. Being there, at “Level Zero“, even for a month, gave me the chance to view many things in the raw. However much I may try to read, watch and listen to edu-posts, from Ken Robinson’s Kool-Aid to testing and formative assessment, from how timetables feel to peer learning, I never see them from the point of view of a student.

I began to take notes, and was lucky enough to be able to chat to Amanda Gibson, an art teacher from Canada, to get her perspective on things. Broadly speaking, there were 8 lessons the experience held for teachers.

  1. Humour signals effort.
  2. A trellis is not a prison
  3. Small steps still need a direction
  4. Crispness beats pace
  5. Enough rope, then scissors
  6. Review, review, review
  7. Variations on a theme
  8. Value students’ free time

1. Humour signals effort. Remembering everything you have to learn is hard. It’s even harder when you’re physically exhausted, keen to do well, but a little embarrassed at how hard you’re finding it. That’s then makes you hyperaware of others doing bits quicker, or spotting how far ahead the senior students are and thinking about how far you have to go. All of our group worked hard. You could see the frustration on everyone’s faces when they made mistakes and the determination despite the aches and pains. We all, also, encouraged each other, with little bits of advice here and there, with congratulations and with humour.

It struck me that I will have almost certainly at times in class misjudged students’ humour and chatter as a lack of effort and focus when it was quite the opposite. That humour is not necessarily mischief.  Often it is an indicator of how hard the students were working, or if you like the panting in between flights of stairs. Humour signals effort.

2. A trellis is not a prison. Our timetable was, on the face of it, rigid: up at 5.30, cold shower, eight hours of kung fu training a day, regimented meals to be eaten in silence, all very much like a school. Similarly, within the sessions, there was always familiar routine: qi gong, warm-up runs, stretching and then training. While I didn’t always relish the prospect, that routine boosted my readiness to learn. By doing those simple things regularly and often, when the critical part of the activity came, I was properly focused on it. Equally, while there was a basic timetable, there was flexibility within that to practise and train on what best suited me. The shifus would make sure I was all right, and I was always encouraged to ask questions, essentially so they could bespoke my experience.

A large part of me loves open space events, like unconferences, Teachmeets and the like. I’m also a big believer in the value of unstructured play, of independent, self-directed learning and am easily excited by experiments in different sorts of school structures.  While I still value those, the monastic timetable has made it clear that those little classroom routines and broad structures are not a prison were a trellis to support me. If I understood it intellectually after reading Doug Lemov and others, since coming back, I have been a believer.

3. Small steps still need a direction.  Learning the various forms, from the basics to even the most advanced, was taught by chunking. Each journey, as Lao Tzu said, starts with a single step. Forms, or series of moves, were broken down in to smaller sequences to help us learn the whole. This worked, and worked well. Whether it was Tai Chi, Wu Bu Quan or Staff Form, the shifus would take us step by step through the moves. During the longer forms, though, I often wondered how close to the end we were. (A little bit like children in a car asking “Are we there yet?”). Ignorant of the form as a whole, I had no sense of progress. For the staff form, another student, Pascal, had cunningly asked the shifu to demonstrate the moves and videoed him while doing it. He shared the end result (below) and that helped me plot my progress.

As a teacher, I sympathise completely with the shifus. It is all too easy to break the challenge down in to steps for the student and to become so focused on teaching those individual steps that one assumes the student remembers or understands the end goal. This is compounded in the UK in lessons where there is a push to focus on “progress” and showing that students are moving from A to B.

The problem with that, I discovered, is student motivation. Chunked tasks work and are hugely effective, but in and of themselves they do not add any “oomph”. What Pascal showed with his video was that an understanding of how far you have come, and how far you have to go, helps you tackle the chunked tasks with a huge amount more energy. Small steps still need a direction.

4. Crispness beats pace. For three weeks, I found it frustrating learning forms. For the most part, that was because every time I felt I’d “got” one section of the form, and demonstrated it to one of the shifus, they’d tell me I had to make another little tweak to what I was doing. While I was keen to race through and learn the whole form, they were keen on making sure everything I did was as crisp as my abilities would allow.

Slow-witted character that I am, it took me three weeks to realise this was exactly what Josh Waitzkin had outlined in his Art of Learning. I’d read this book, nodded along with it, but when the time came to apply it, or as he might say to “discover the macro by diving into the micro”, I’d ignored it all. In the end, I got it and when I did everything became both less frustrating, I felt I was learning more, and I started making more connections between what I was learning. As a teacher, I have become far more focused on taking time to make sure the micro is there. Crispness beat pace by a country mile.

5. Enough rope and then scissors.  Naturally, within each group some of us were at different levels from others. One of the principles Shi Yan Jun repeated often was that we should not teach each other new things. We could help each other try to understand what we’d been taught but teaching each other new forms ended up giving the learner bad habits. It made sense, even if it sounded a little Draconian. During practice, though, especially while I was trying to learn the staff form, I often found myself asking friends like Henry, Marcel or Nick what on earth I was meant to be doing (and vice versa). What we found was that peer-learning got us some way there, but the shifu would often have a solution that made everything easier and they often timed their interventions to perfection, letting the struggle happen but not letting our frustrations debilitate us.

In my own class, I encourage sessions of peer learning. I think it’s important for students to have a go at maths problems themselves first and I think there is value in their rephrasing ideas for themselves. Similarly, there are moments where students need to work on a task on their own. While there is not always the obvious, rapid feedback of getting your kung fu limbs in a tangle with a stick, what being on the other side has really highlighted is the value of timing one’s input as a teacher, giving students enough rope but using scissors at just the right time.

6. Review, review, review.  Each shifu started the session with a recap of what had been learned in the previous session. Often, this was as simple as doing the form as far as we knew how to. The benefits were two-fold: for the shifus, it provided a very obvious “how are they each getting on” assessment. For us, as students, it also helped. It highlighted areas we didn’t know. Less obviously, perhaps, it gave us a chance to ask questions about what we had not understood.

That last bit was a Damascus moment for me. As a student, it takes time to understand what you don’t understand. As a teacher, I have probably been guilty of moving on too quickly. The simple review allows the students time to have processed what they learned (or didn’t) in the previous session. It was this focus on review at the start of the lesson that was perhaps the biggest take-away of the trip, and one that I think both Amanda and I found the most obvious, despite our different subjects. Since China, “review, review, review” is at the top of all my planning.

7. Variations on a theme.  There were four shifus who taught me and they all had different styles. If I had to characterise them broadly, there was kindness, strictness, energy and enthusiasm. Depending on how I felt I was doing, any one of those might work or not. Some students clearly preferred others, depending on levels, characteristics and approach. What did happen, though, was that the variety of styles, when combined with their unison of purpose, honed our skills. (Xie xie, shifus!)

If jury service taught me anything it was this: that you could disagree with the individual voices but agree with their collective effect. This same dynamic seems to work with teaching styles. Students will always chime with some teachers and not with others. Similarly, given the range of different styles in a staffroom, it is easy to feel “I should be more like X or Y”. But that is not standardising on the right thing (Dave Gray has some interesting things to say on this). Seeing the effect of the different characters of shifus has made me think that the variety is all to the good as long as we are variations on the same theme.

8. Value students’ free time. I was worried before I went that the other Westerners would be six-packed, testosterone heavy “alpha” types who were keen to prove their standing. Nothing could have been further from the truth. The gentle, cheerful support everyone gave each other was astonishing. And what was nurtured in time away from the monastery came back ten-fold during practice.

From a teacher’s point of view, the effect is simple. Give the students time to be together outside of lessons and that will only benefit them as they try to learn. In more jargony terms, unstructured play clearly works. In less jargony terms, let people know that you are aware that there is more to life than school, and school seems a more sensible place to spend your time.

Be rubbish and you will learn

As above, none of this is new, or even close to being groundbreaking. What worked for me, as CPD, was the perspective. Rather than sitting in a hall, or a classroom or a seminar, and rather than imagining what it was like to be a student, I went up a mountain and did something I found hard. I learned a little bit of kung fu, but I learned a lot more about how to teach and more importantly how better to empathise with my students. If you want a different type of CPD, but one that stays with you, I would recommend doing something where you are the student, where you are underconfident and where you start at Level Zero.

Early Steps in Blended Learning

I think a penny has finally dropped. I’ve been mulling over blended learning for a while but have never quite summoned up the energy. I’ve also been thinking about ways I can apply the DRY (Don’t Repeat Yourself) principle to my teaching, so I can spend more time doing the fun parts of teaching.

Slower than most, I suspect, but I have had my mini-Damascus moment. One of the more repetitive parts of my work is explaining worked problems from the necessary evil that is practice papers. By recording myself working through these I could, in theory, only have to explain a working out once and point students to the video.

One of my classes is a scholarship maths set so I’m trialling the process with them. My first bash is this: answers to the Mathematics Paper B from the Eton King’s Scholarship 2014.

In terms of the mechanics, I’ve bought an IPEVO Point 2 View Camera so I could scribble down my workings out. It’s a little fiddly but seemed to be the cheapest option short of buying a tablet.
In terms of sound, that’s recorded directly to my Macbook and the video files are unedited from the IPEVO bundled software. Levels are a little low, but that may just be me mumbling self-consciously.

Do let me know if you see mistakes, better solutions or have questions about the explanations. Equally, any tips as to how to improve the actual video gratefully received!

The Master and His Emissary

I keep on thinking about the below.

There was once a wise spiritual master, who was the ruler of a small but prosperous domain, and who was known for his selfless devotion to his people. As his people flourished and grew in number, the bounds of this small domain spread; and with it the need to trust implicitly the emissaries he sent to ensure the safety of its ever more distant parts. It was not just that it was impossible for him personally to order all that needed to be dealt with: as he wisely saw, he needed to keep his distance from, and remain ignorant of, such concerns. And so he nurtured and trained carefully his emissaries, in order that they could be trusted. Eventually, however, his cleverest and most ambitious vizier, the one he most trusted to do his work, began to see himself as the master, and used his position to advance his own wealth and influence. He saw his master’s temperance and forbearance as weakness, not wisdom, and on his missions on the master’s behalf, adopted his mantle as his own – the emissary became contemptuous of his master. And so it came about that the master was usurped, the people were duped, the domain became a tyranny; and eventually it collapsed in ruins.

This version is quoted from Iain McGilchrist. While he uses the story to highlight some relationships in the brain, I’m trying to work out whether the story holds true if the master is liberalism.

Navigating Education

I almost never go back to the things I highlight on my Kindle.

So a mini-holiday project was to stop me being quite such a knowledge tourist. I’ve built a little tool to make it easier to export, browse and actually think about my Kindle highlights.At the moment it’s set up to randomly send me a highlight by email every day and am kind of enjoying that.

Today’s quote was from Wade Davis’s wonderful book, “The Wayfinders: Why Ancient Wisdom Matters in Today’s World”.

And it made me think about how we use feedback as teachers, the quantitative and the qualitative, and balancing a focus on the particular with a focus on the whole.

Expert navigators like Mau, sitting alone in the darkness of the hull of a canoe, can sense and distinguish as many as five distinct swells moving through the vessel at any given time. Local wave action is chaotic and disruptive. But the distant swells are consistent, deep and resonant pulses that move across the ocean from one star house to another, 180 degrees away, and thus can be used as yet another means of orienting the vessel in time and space. Should the canoe shift course in the middle of the night, the navigator will know, simply from the change of the pitch and roll of the waves. Even more remarkable is the navigator’s ability to pull islands out of the sea. The truly great navigators such as Mau can identify the presence of distant atolls of islands beyond the visible horizon simply by watching the reverberation of waves across the hull of the canoe, knowing full well that every island group in the Pacific has its own refractive pattern that can be read with the same ease with which a forensic scientist would read a fingerprint.

All of this is extraordinary, each one of these individual skills and intuitions a sign of a certain brilliance. But as we isolate, deconstruct, even celebrate these specific intellectual and observational gifts, we run the risk of missing the entire point, for the genius of Polynesian navigation lies not in the particular but in the whole, the manner in which all of these points of information come together in the mind of the wayfinder. It is one thing, for example, to measure the speed of the Hokule’a with a simple calculation: the time a bit of foam or flotsam, or perhaps a mere bubble, takes to pass the known length separating the crossbeams of the canoe. Three seconds and the speed will be 8.5 knots; fifteen seconds and the vessel slogs at a mere 1.5 knots. But it is quite another to make such calculations continually, day and night, while also taking the measure of stars breaking the horizon, winds shifting both in speed and direction, swells moving through the canoe, clouds and waves. The science and art of navigation is holistic. The navigator must process an endless flow of data, intuitions and insights derived from observation and the dynamic rhythms and interactions of wind, waves, clouds, stars, sun, moon, the flight of birds, a bed of kelp, the glow of phosphorescence on a shallow reef — in short, the constantly changing world of weather and the sea.

What is even more astonishing is that the entire science of wayfinding is based on dead reckoning. You only know where you are by knowing precisely where you have been and how you got to where you are. One’s position at any one time is determined solely on the basis of distance and direction travelled since leaving the last known point. “You don’t look up at the stars and know where you are,” Nainoa told me, “you need to know where you have come from by memorizing from where you sailed.”

There’s a rich metaphor in there somewhere.

[If you want some more snippets, the rest of the highlights I made from the book are here: The Wayfinders – Wade Davis. The image is from Elizabeth Lindsey’s National Geographic series]

 

Delivery mechanisms for values

Two interesting things I’ve seen recently have got me thinking.

The first was Mark Slouka’s comment that

The humanities, done right, are the crucible within which our evolving notions of what it means to be fully human are put to the test; they teach us, incrementally, endlessly, not what to do but how to be…. They are thus, inescapably, political. Why? Because they complicate our vision, pull our most cherished notions out by the roots, flay our pieties. Because they grow uncertainty. Because they expand the reach of our understanding (and therefore our compassion), even as they force us to draw and redraw the borders of tolerance. Because out of all this work of self-building might emerge an individual capable of humility in the face of complexity; an individual formed through questioning and therefore unlikely to cede that right; an individual resistant to coercion, to manipulation and demagoguery in all their forms. The humanities, in short, are a superb delivery mechanism for what we might call democratic values. There is no better that I am aware of.  This, I would submit, is value-and cheap at the price.

The second was Lee Bryant’s fascinating talk about instiutions as delivery mechanisms for our values.

  • Humanities are a great delivery model for democratic values
  • Institutions act as delivery models for our values

Given that, doesn’t it make sense to keep the humanities in schools and for organisations to actively encourage that? If institutions are actively looking to act as stewards for values, then should they be trying to encourage the humanities in education as well as STEM and the like?

The Dynamo and the Social

Thought this was an interesting piece at Slate based on Paul David’s paper. There are some obvious parallels with personal or mobile computing and education and the difficulties we have with using it well.

“Electric light bulbs were available by 1879, and there were generating stations in New York and London by 1881. Yet a thoughtful observer in 1900 would have found little evidence that the “electricity revolution” was making business more efficient.

Steam-powered manufacturing had linked an entire production line to a single huge steam engine. As a result, factories were stacked on many floors around the central engine, with drive belts all running at the same speed. The flow of work around the factory was governed by the need to put certain machines close to the steam engine, rather than the logic of moving the product from one machine to the next. When electric dynamos were first introduced, the steam engine would be ripped out and the dynamo would replace it. Productivity barely improved.

Eventually, businesses figured out that factories could be completely redesigned on a single floor. Production lines were arranged to enable the smooth flow of materials around the factory. Most importantly, each worker could have his or her own little electric motor, starting it or stopping it at will. The improvements weren’t just architectural but social: Once the technology allowed workers to make more decisions, they needed more training and different contracts to encourage them to take responsibility.

Last year’s OECD report was one of many to suggest that it might, just might, be a little more complicated than putting more computers in classrooms. I do wonder whether, at some level, the school as an organisation will have to undergo a similar redesign to make the most of our new dynamos.

Simple Current Affairs Game for Children

The following seems to be going down well with my class. They are both enjoying it and seem to be learning more about current affairs at the same time.

What it is

Once a week when the children (who are 10 or 11 years old) come into class for morning registration, I’ll have something like this up on the whiteboard.

Screen Shot 2014-09-13 at 14.15.11

The game is simple. They need to do three things:

  1. spot the mistakes on the site
  2. say what the correction should be and
  3. explain what the story is about.

So, for example, with the above they’d need to

  1. spot that it shouldn’t be Holly and Drew, (or Amelia, or Nora, or Armand);
  2. suggest something close to businesses and
  3. explain that it has to do with the Scottish vote for independence and businesses saying they will move south if Scotland breaks away from the Union.

So far, the children are in loose teams but (and I’m pleased about this) they’re more interested in the stories behind the news than points. So far the feedback has been good, from children and parents. Continue reading Simple Current Affairs Game for Children

Toffler, The Trivium & The Holy Trinity

I’ve been having an interesting conversation on Twitter with Martin Robinson and Carl Gombrich (a big thank you to both).

Two things had been bouncing around recently: Toffler’s ubiquitous “Learn, unlearn, relearn” and the Trivium, in no small part thanks to Martin’s excellent Trivium 21C. I wondered, slightly loosely, whether they were connected, along the lines of this diagram.

Rather vague wondering
Rather vague wondering

Carl did not see any obvious connection and (sensibly, I think) warned against numerology/seeing patterns in 3 and the like and, broadly, I think I’m coming to the conclusion that he’s right in that the two are not interchangeable (as I’d initially thought). That said, I do think there is a connection. If nothing else, they are sibling concepts in that both are born of the idea that knowledge is fluid and changing.

There are two differences that Carl’s doubt and Martin’s questions highlighted for me. First, the Trivium is not quite so overtly pro-“change for its own sake”. While the unlearning phase seems fairly wholesale under Toffler, the Trivium’s dialectic is more even-handed. Critique doesn’t have to shatter one’s beliefs or force you to reject what you have learned; it can strengthen them too. Second, for my money, the Trivium deals with the social aspect of learning in a more sophisticated, group-oriented way. Toffler’s “learn, unlearn, relearn” works on an individual level (as it did for Carl’s drumming), but the rhetoric phase of the Trivium works at both individual and social (whatever you think you’ve learned, you can’t have learned it until you’ve persuaded someone else of it).

Anyway, enjoyed the tweets. Especially discussing the holy trinity of Xavi, Messi and Iniesta on a Sunday morning. Seem to remember Maradona talking about Messi playing with Jesus, which sort of begs a question …