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.

3 Men and a Donkey – Notes on hiking Le Stevenson in the Cevennes

I’ve just got back from hiking Le Stevenson with a donkey and thought I’d jot down some notes while they’re still fresh in case it helps anyone else.

What is Le Stevenson?

In September 1870, Robert Louis Stevenson was waiting for his American sweetheart to finalise her divorce and to kill time set off with a donkey to hike through the Cevennes. He later published his notes in Travels with a Donkey in the Cevennes, which brought him fame and the beginnings of his career.

Le Stevenson, aka the Chemin de Stevenson and the GR70 is a “Grand Randonee” of about 140 miles that tries to follow his route.  It isn’t wholly accurate to the route RLS took (partly because he often got lost, partly because at times a more scenic route as been edited in) but it’s a pretty good likeness and goes through the same villages he mentions.

In terms of ups and downs, as with all these sorts of walks, some days are better than others and terrain is mixed. The below is from the guide that can be found at most tourist informations and in many of the gites and hotels.

When to go/How long does it take

July and August were hot – pushing 30 degrees most days but still manageable thanks to shade and a donkey carrying our things. People in the Cevennes suggested Spring and early Autumn as the best both for temperature and colours.

Unless you’re superfit or wanting to run the whole thing, 14 days is about right for the whole thing. It is topped and tailed by a day’s walk from Le Puy en Velay to Monastier (where RLS actually started) and from St Jean du Gard (where he actually finished) to Ales. These are there simply for logistics as it’s easier to get to Le Puy and Ales than Monastier or St Jean.

We came across a number of folk chunking the walk, either because they didn’t have enough time to do the whole thing in one go or because they were with children. A lot of the villages are tiny, though, so I’d have thought Pradelles, Langogne and Florac are the best bets for chunks.


For us, donkey hire and half-board accommodation (breakfast & supper included) came in at a little over 1000 euros each for the fortnight. Below are the details of where we stayed – there were 3 of us sharing a room which was good in terms of value, possibly questionable in terms of quality of sleep.

Sandwiches could often (but not always) be bought along the route. We found it better to order packed lunches at the Gites the night before, but be ready to tire of cheese and ham baguettes if you do. There’s a butcher in La Bastide after the monastery who does an amazing deal

Distance Destination Accommodation Cost (Euros) Notes
Prologue Puy En Velay Gîte Bellevue 81 nuit et petit-déjeuner – supper in town
Day 1 19.3km Monastier  Gîte l’Estella 119
Day 2 23.6km Bouchet St Nicolas Gîte L’Arrestadou 142
Day 3 20km Pradelles Gîte Terre d’Accueil 140
Day 4 15.5km l’Herm  Gîte La Tartine de Modestine 118 In a yurt …
Day 5 19km Luc Gîte de la Huchette 137
Day 6 16.5km Notre Dame des Neiges Staying in a Trappist Monastery so“donations” are asked for rather than fees.
Day 7 17km l’Estampe Gite Le Relais de Modestine 170
Day 8 21km Station du Mont Lozère 150 euros
Day 9 14km Pont de Montvert L’Auberge des Cévennes 141
Day 10 23km Cocurès l’Hôtel La lozerette 203 More boutique hotel than gite – amazing wine list
Day 11 24km Cassagnas Relais Stevenson 159
Day 12 21.6km Lébou La Ferme de Patience 149 Our hands down favourite
Day 13 16km St Jean du Gard.

Maps, Books and GPS

Le Stevenson is very clearly marked all the way with red and white signs indicating both where to go and where not.  In general, the website for the Association Sur Le Chemin de Robert Louis Stevenson is very full and complete.

We had a range of books, maps and guides with us. Alan Castle’s book ended up being slightly annoying – lots of “the last time I was here it was better” comments – so we ditched that. The maps we had (details here) were basically a back up if the GPS failed and we didn’t use them once. A combination of the ViewRanger app and this GPS Route for Le Stevenson saw us safely along the way. The only times we went wrong were down to us chatting away and being oblivious to things, not due to unclear directions.

Backpacks, Baggage and Donkeys

Lots of people carried their own kit and quite a few used a service called La Malle Postale , which takes your bags from A to B for a small fee.

Caline, our brilliant companion

We hired a donkey (Caline not Modestine) from Canelle Labaume of Arts and Nature and it was all a lot easier than we initially feared. Essentially the set-up is this:

  • You get an initial training in how to groom the donkey and the do’s and don’ts before you start, how to put on a harness and bags etc.
  • Grooming involves: picking stones out of the donkey’s hooves, brushing her, adding ligament to any nicks and grazes she may have picked up, and pasting on some anti-fly juice.
  • Grooming needs to be done morning and night, before and after the walk. We were told that a lot of families didn’t do this and the donkeys end up either injured or truculent.
  • Donkeys are meant to be fed in the morning and in the evening and given a drink. In practice, we found it impossible to effectively stop Caline from munching what she wanted along the route but it never stopped us for long and was often a welcome breather.
  • Each place we stayed had a field nearby to put Caline in. Donkeys sleep out and usually the food is the foliage and grass in the field. Some gites provide proper food though. Most of the gites owners knew far more about donkeys than any of us ever would so we took their advice.
  • The maximum load for the donkey is 40 kg. We had about 30kg and this had to be balanced evenly in side-sacks. Inners for rucksacks are perfect for putting in these. Plastic bags also work but you might find your clothes end up smelling of turps and donkey for a while after the trip.
  • Caline was far surer footed on many of the paths than we were so while we panicked at first that she wouldn’t be able to make things she was always fine.

Water & Last Words

One final note is water. Ironically, given you are traipsing around Europe’s largest watershed, there is no guarantee of regular water. Many of the villages you pass through are virtually empty and you are in a National Park for a lot of it.  Unlike the Via Francigena or some other Caminos, there are no pilgrim taps. It’s well worth taking more than you think you’ll need. Your donkey can always carry it.

There’s probably a lot I’ve missed out, but the main thing that surprised us was how easy the donkey was and what a good companion she was compared to Modestine. It’s hard work but a great fortnight.

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.


Life Lessons from Bergson

My dogears from Michael Foley’s excellent “Life Lessons from Bergson”


“Time” is now the most-used noun in English, whereas many primitive peoples, for instance the Amondawa tribe of the Amazon and the Australian Aborigines do not have a word for it. (p.24)


The corollary of predictability as comfort is randomness as threat … We would almost rather accept gross injustice than randomness. At least with injustice there is someone to blame. And good fortune is just as rarely recognized. For bad luck, we blame others and for good luck, we take the credit ourselves. (p.32)

Habit & Old Fogyism

Could the young but realize how soon they will become mere walking bundles of habits, they would give more heed to their conduct while in the plastic state. (p. 40, from William James’ Psychology: The Briefer Course)

Old Fogyism begins at a younger age than we think. I am almost afraid to say so but I believe that in the majority of human beings it begins at about twenty-five. (p.40, from William James’ Talks to Teachers)


It is the function of comedy to repress any separatist tendency, to convert rigidity into plasticity, the readapt the individual to the whole (p. 43, from Bergson’s Le Rire)


How can the eyes be asked to see more than they see? Our attention may enhance precision, clarify and intensify; but it cannot bring out what was not there in the first place. That is the objection – in my opinion, refuted by experience. In fact for hundreds of years there have been people whose function was precisely to see and make us see what we do not naturally perceive. These are the artists. (p. 49, from Bergson’s La Pensee et le mouvant)

Character and Attention

According to James, our experience of life is nothing other than what we have chosen to pay attention to, and the choice is decisive because experience is character. (p64)

Ripples, Systems and Effects

If everything is connected to everything else then every action propagates its effects for ever, and if feedback loops are the method of propagation then every action also modifies the character of the actor. Many of these nano-modifications are below the level of perception but they eventually add up to a cumulative change that is all too perceptible. One day you may wake up and realize you have become a shithead – or, more likely, your partner wakes up and informs you of this in a loud, outraged tone, en route to the door. (p.75)

[Photo: Edinburgh University]

Mohini The White Tiger and Learned Helplessness

I’ve been watching a lot of TED talks recently (part of a NY’s resolution), and have been struck by the number that say something along the lines of “school is broken” and “how do we make children like school?”.

There’s a sad story about a tiger called Mohini that Tara Brach tells as follows.

Mohini was a regal white tiger who lived for many years at the Washington D.C. National Zoo. For most of those years her home was in the old lion house—a typical twelve-by-twelve-foot cage with iron bars and a cement floor. Mohini spent her days pacing restlessly back and forth in her cramped quarters. Eventually, biologists and staff worked together to create a natural habitat for her. Covering several acres, it had hills, trees, a pond and a variety of vegetation. With excitement and anticipation they released Mohini into her new and expansive environment. But it was too late. The tiger immediately sought refuge in a corner of the compound, where she lived for the remainder of her life. Mohini paced and paced in that corner until an area twelve by twelve feet was worn bare of grass.

This could be read in different ways, I suppose.

In one, the cage might represent school, and Mohini’s retreat might equate to that adult refrain that students have lost the “ability to think for themselves”, have an overreliance on spoonfeeding, or even have had their creativity killed and the like. In this, like in many of those TED talks, it’s the cage that’s the problem.

In another, though, it is not the cage that is the problem but the adults. The cage might represent what a student thinks they know and like, and the habitat a world of unfamiliar but more rewarding opportunity. The sad part for me is not that Mohini retreated, but that the staff do not appear to have kept on trying to bring Mohini out.

[Picture: Smithsonian Institution]