Engelmann and Direct Instruction (Part 2)

In Could John Stuart Mill Have Saved Our Schools?, Siegfried Engelmann and Douglas Carnine discuss the philosophical foundations of their acclaimed Direct Instruction programme (see Part 1). They write of their serendipitous rediscovery of Mill’s work and that they

came across Mill’s work and were shocked to discover that they had independently identified all the major patterns that Mill had articulated. Theory of Instruction [1991] even had parallel principles to the methods in [Mill’s] A System of Logic [published in 1843].

— location 543 Kindle edition

What Engelmann and Carnine are attempting to do is no less than develop a scientifically reliable model of education. In their view, learners learn by constructing inferences based on the evidence or examples presented by the teacher. In other words, learners use the rules of reason and logic (consciously or unconsciously) to develop general principles from specific examples by inductive reasoning.

To me, this is a fascinating idea. Have Engelmann and Carnine hit upon the elusive essence of what learning is? Is learning genuinely a matter of constructing inferences from evidence by formal or informal logical rules?

My view is that it certainly seems a plausible idea. In the light of my own experience and thinking it has a “ring of truth”, and I suspect that I am going to find this a profoundly influential idea for the rest of my career.

Many authors and thinkers have argued that human beings construct “mental maps” or conceptual models constructed by inductive reasoning from often limited information. Anthropologist Louis Liebenberg describes an example involving the !Xõ people of the central Kalahari Desert:

While tracking down a solitary wildebeest spoor [tracks] of the previous evening !Xõ trackers pointed out evidence of trampling which indicated that the animal had slept at that spot. They explained consequently that the spoor leaving the sleeping place had been made early that morning and was therefore relatively fresh. The spoor then followed a straight course, indicating that the animal was on its way to a specific destination. After a while, one tracker started to investigate several sets of footprints in a particular area. He pointed out that these footprints all belonged to the same animal, but were made during the previous days. He explained that the particular area was the feeding ground of that particular wildebeest. Since it was, by that time, about mid-day, it could be expected that the wildebeest may be resting in the shade in the near vicinity.

— quoted by Steven Pinker in How The Mind Works p. 193

The trackers were using miniscule traces of evidence and their knowledge of the environment to make inferences about the behaviour of (currently) unseen entities. In other words, they were using inductive reasoning to put together a tentative model of what their quarry was doing or attempting to do. (And I use ‘tentative’ in the sense that the model will be adapted and corrected in the light of further evidence.)

As do we all! I would suggest that all humans use similar techniques of inference, or ‘mental modules’ in Steven Pinker’s memorable phrasing, even with vastly different subject matter. Stephen Hawking and Leonard Mlodinow even go so far as to suggest that:

we shall adopt an approach that we call model-dependent realism. It is based on the idea that our brains interpret the input from our sensory organs by making a model of the world. When such a model is successful at explaining events, we tend to attribute to it, and to the elements and concepts that constitute it, the quality of reality.

The Grand Design p.9

And where does this leave us? If Engelmann and Carnine are correct (and I believe they are} then education becomes a matter of logic. They argue that a vital criterion in designing what they call “sound instructional sequences” is that sets of examples should “generate only the intended inferences”. They note

that logical flaws in instruction could be identified analytically, through a careful examination of the teaching. If we know the specific set of examples and the inference that the learners are supposed to derive from the instruction, we can determine if serious false inferences are implied by the program.

— location 1514

And I, for one, find that a highly engaging and strangely comforting thought.

(You can read Part 3 here)

Engelmann and Direct Instruction (Part 1)

We are art’s mercenaries,
firing our thought’s arrows
at the mystery of things
— R. S. Thomas, Paving

Engelmann comes highly recommended:

In his book Visible Learning: A Synthesis of Over 800 Meta-Analyses Relating to Achievement, the researcher John Hattie evaluates the success of a range of different teaching approaches. As the subtitle suggests, he synthesised the results of hundreds of different analyses of achievement and measured the effect of different factors . . . A specific Direct Instruction programme was developed by the American educator, Siegfried Engelmann, in the 1960s. It proved incredibly successful but also incredibly controversial because it contradicted so much of what theorists like Dewey and Freire advocated. Hattie specifically endorsed Engelmann’s programme.

— Daisy Christodoulo, Seven Myths About Education, location 751 Kindle edition

Later on in the book, Hattie confronts the dominance of empirically unsuccessful constructivist ideas in teacher training. He explains the effectiveness of Direct Instruction, a structured and unapologetically teacher-led method of instruction originated in 1960s America. Despite being shunned by the American education establishment, Hattie’s analysis shows that Direct Instruction has one of the largest effect sizes (0.59) for any teaching programme.

— Robert Peal, Progressively Worse, location 2689 Kindle edition

I was intrigued and wanted to find out more, so I recently read Siegfried Engelmann’s and Douglas Carnine’s book Could John Stuart Mill Have Saved Our Schools? which can be thought of as an introduction to the philosophical underpinning of Direct Instruction.

I claim no particular expertise in this field beyond that of a working teacher with a couple of decades of experience. I suppose that it is also appropriate at this point to disclose that my practice generally tends towards the traditional-didactic rather than the progressive end of the spectrum, so I am perhaps predisposed to be sympathetic to Engelmann’s ideas. Nevertheless, this blog will attempt to engage critically with his ideas and arguments.

Engelmann and Carnine open by saying that (unfortunately, in their opinion) education has historically been excluded from the domain of science. They suggest that the five principles of induction put forward by philosopher John Stuart Mill in his A System Of Logic (1843) would form a suitable basis for a scientific systematisation of effective educational practice. The efficacy of these principles when applied to education was not recognised at the time, not even by Mill himself, until Engelmann and Carnine rediscovered them in the 1970s.

I was unfamiliar with this aspect of Mill’s work, and it was a delight to be introduced to it. I was particularly struck by this bombshell from Mill:

In another of its senses, to reason is simply to infer any assertion, from assertions already admitted: and in this sense induction is as much entitled to be called reasoning as the demonstrations of geometry
— J. S. Mill, A System of Logic, location 175 Kindle edition

Philosophers have long debated the “problem of induction”. It is generally recognised that deductive reasoning (e.g. Socrates is a man; all men are mortal; therefore Socrates is mortal) is more dependable that inductive reasoning (e.g. every swan I have seen to date has been white; therefore every swan I will see in the future will be white).

However, it is a under-acknowledged truth that in our day-to-day lives (and in science generally) we rely primarily on induction and inference and, for the most part, they serve us well. What Mill is attempting to do is address the philosophical “second class status” accorded to inductive truths by formalising a set of rules that allow us to generate valid inductive inferences.

Engelmann and Carnine argue that these rules are of fundamental importance to the teacher as they allow her to construct a system of instruction that allows students to generate valid inferences and minimise false inferences:

In summary, the fabric of well designed instruction consists of details that promote specific inferences and rule out inappropriate inferences. Effective instruction is not born of grand ideas or scenarios that appeal to development or love of learning. It is constructed from the logic and tactics of science.
— S. Engelmann and D. Carnine, Could John Stuart Mill Have Saved Our Schools? location 1944 Kindle edition

One example they present is that of a constructivist approach to the teaching of prime numbers by getting students to lay out numbers of beans in rows and columns: students are invited to notice that some numbers (e.g. 7) cannot be laid out in rows of more than one bean which have equal numbers of beans. Englemann and Carnine argue that this activity does not accord with Mill’s principles because it will encourage students to generate a number of false inferences:

The false inference is that prime numbers are odd numbers. Imagine the consternation of the student who later discovers that 9 and 15 are odd, but they generate multiple rows. In contrast, 2 is even, but it is prime. A related false inference is that there is some form of predictable pattern for the occurrence of prime numbers, rather than the fact that some numbers are primes and others aren’t. Unless students had received previous instruction on what primes are, the bean counting has a potential of inducing false inferences; however, if students first learn the properties of prime numbers, the bean counting is a pointless activity. It simply provides validation that prime numbers are different from numbers that are multiples.
— location 1779 Kindle edition

I discussed this criticism with a Maths colleague who disagreed that the constructivist approach would necessarily generate false inferences — but more on that in a later post.

In summary, I am fascinated by the potential of Englemann’s and Carnine’s approach and intend to post more as I mull over its details and implications. Lord help me, but I could not help but be stirred by what could be interpreted as a call to arms:

[Our system] could certainly be improved by a concerted effort to do so. What it needs is a comprehensive critique by serious logicians and philosophers. It needs attention to its details so they can be refined or replaced to be more in accord with logic or empirical evidence.
— location 2591 Kindle edition

And perhaps more importantly, by working teachers too.

(Part Two here)

The Purpose of Education

“The value of a university education resides in the fact that it puts young people in proximity to learning. The students of Good-enough Dormitory are less than thirty yards from the Library, no more than fifty yards from the Physics Lab, and a mere ten yards from the Chemistry Lab. I think we can all be justly proud of this.”

— Robert Sheckley, Journey Beyond Tomorrow

I am simultaneously a cynic and a romantic when it comes to education.

Yes, I am the curmudgeonly staffroom cynic, always ready with an eye roll, a derisory snort and a sarcastic quip. (Or two. Or three. Or four — I mean, just read this blog!)

However, I am also a romantic: show me something that works, or even could work, and I can’t wait to try it out, for all the world like I was a naive young bright-eyed bushy-tailed NQT.

The great untold truth of teaching is that it can be a lot of fun being in the classroom. Of course, it can also be a major league pain in the arse. And the weird thing is that, even after many years experience, my expectations of whether it is going to be a good day or a bad day are often completely and utterly wrong.

A number of edu-blogger heavy hitters have been weighing in on what the point of education is. I particularly enjoyed the posts from ijstock, Daisy Christodoulou and Esse Quam Videri: they disagreed with the Education secretary’s recent assertion that the point of education is essentially to increase one’s earning power.

I agree with them, of course. But, then, what is the point of what we do?

I think it is simply this: ignorance is not bliss. It is not foolish to be wise. A person who believes (say) N sets of true things is less likely to make poor decisions than person who believes even N-1 sets of true things.

As Samuel Johnson observed to Boswell as they were being rowed to Greenwich on a summer’s day in 1703:

“Nay, Sir, it is wonderful what a difference learning makes upon people even in the common intercourse of life, which does not appear to be much connected with it.”

Boswell immediately countered that “people go through the world very well, and carry on the business of life to good advantage, without learning.”

Johnson conceded his point. “Why, Sir, that may be true in cases where learning cannot possibly be of any use; for instance, this boy rows us as well without learning, as if he could sing the song of Orpheus to the Argonauts.”

But then, unexpectedly, Johnson turned to the boy and asked him: “What would you give, my lad, to know about the Argonauts?”

“Sir,” said the boy, “I would give everything I have.”

In all my many years as a teacher, I haven’t encountered a single person who has looked back and wished that they had worked less hard in school. (The trick, of course, is to make students realise that while they’re still in school.)

I will leave the last word to the estimable Doctor Johnson:

“Sir, a desire of knowledge is the natural feeling of mankind; and every human being, whose mind is not debauched, will be willing to give all that he has to get knowledge.”

All I Really Need To Know About Teaching I Learned On My PGCE

image
Book cover

Flumine perpetuo torrens solet acrius ire.
Sed tamen hæc brevis est, illa perennis aqua
.
— Ovid, Rem. 651.

In course impetuous soon the torrent dries,
The brook a constant peaceful stream supplies.

“May you live in interesting times” is said to be an ancient Chinese curse. Sadly, I think it is evident that teachers in the UK (and elsewhere) are currently living through some very interesting times indeed.

It certainly seems that before one torrent of change has finished running its impetuous course, another torrent of radically alternative change is unloosed upon us from another direction. Heraclitus pondered whether one could step in the same river twice; teachers ponder if today’s modish ‘best practice’ will be the same as tomorrow’s ‘best practice’, because it certainly isn’t the same as yesterday’s.

And where does all this frenetic change get us? The answer, based on my two decades of experience is: nowhere.

Sadly, this doleful and melancholy truth does not seem to be widely accepted. The purveyors of the many varieties of educational ‘magic beans’ continue to loudly hawk their wares, all too many of which rely more on cant, humbug and the partiality (and sometimes naked partisanship) of friends in high places rather than any demonstrable or proven effectiveness.

Too much of students’ and teachers’ precious, precious time is wasted attempting to implement the latest muddle-headed initiative, or at least minimise the harm it will do. Careerists — teachers, politicians and inspectors alike — pay fulsome public lip service to ideas that they then go on to cheerfully deride in private. (Mea culpa! on that one BTW.)

So what are the eternal verities of teaching? I’m not sure if I can provide an exhaustive or definitive list, but here are a few of what I consider to be, if not eternal undying truths, then reasonably sound advice. And, yes, I do think I learned many of them on my PGCE course.

1. Avoid whole class detentions or sanctions: they are almost always unfair and an admission of weakness rather than a demonstration of strength.
2. Avoid shouting or raising your voice: it might work the first time, but each iteration of this behaviour diminishes its effectiveness.
3. Set suitable work. Although it won’t magically resolve all behaviour issues all by itself (contrary to what some misguided mentors think), it does help.
4. Watch what you say, especially any offhand negative or sarcastic comments, even if meant in jest. Although it may not always seem like it, most students genuinely care what their teacher thinks of them.

These, to my mind, begin to exemplify the “constant peaceful stream” that makes the genuine difference in teaching, rather that over-hyped “Year Zero” and “world-turned-upside-down” models so beloved of politicians and careerists at all levels.

I am not against change; it’s just that a lot — an awful lot! — of the changes that I have been asked to carry out over the years have proven to be transient and temporary, and within a matter of days, weeks or months we go back to the old ways. Show me a better way and I will gladly do it, but I have grown both wary and weary of the change-for-change’s-sake that is all too often foisted on us as a profession.

Genuine, useful change? Only time will tell.

Opinionum commenta delet dies, naturæ judicia confirmat.   
–CICERO, vi. Att. 1.  

Time obliterates the fictions of opinion, and confirms the decisions of nature.

Secular Pantheon? Oh noes!

I read Joe Kirby’s excellent blog regularly and find myself nodding happily in agreement with many of the points that he makes. However, his recent post Secular Pantheon: what can schools learn from religions? (following suggestions made by Alain de Botton) made me spit out my muesli in frustration. Richie Gale has also written a thoughtful response to Joe’s post, but was in broad agreement with its theme that schools could learn some useful lessons from religion.

I am not.

My main problem is with the claims made by Alain de Botton:

Probably the most boring question you can ask about religion is whether or not the whole thing is ‘true’. Unfortunately, recent public discussions on religion have focused obsessively on precisely this issue, with a hardcore group of fanatical believers pitting themselves against an equally small band of fanatical atheists. [ HuffPo 3/2/12]

While de Botton pats himself on the back for being so much more nuanced and accommodating than the “fanatical atheists” he decries, he is actually neither. I believe Jason Rosenhouse puts it nicely:

When someone says the truth or falsity of religions are their least interesting aspects, you can be sure you are reading the work of someone who thinks they are false. If there were a strong argument to be made on behalf of the truth claims of Christianity or Islam, say, that would not be boring at all. That would actually be a momentous contribution to humanity’s understanding of the world. [EvolutionBlog 8/3/12]

To me, de Botton’s world weary pose is comparable to that of an adult pressured by her children into presiding over a funeral service for a hamster.

I think it is more actually more respectful of religion to take their truth claims seriously enough to debate rather than sideline them with a twinkly eyed “Well, really, whether they’re true or not isn’t the point, is it?”

Joe approvingly highlights this sentence from de Botton:

We need institutions to foster and protect those emotions to which we are sincerely inclined but which, without a supporting structure and a system of active reminders, we will be too undisciplined to make time for.

Well, on the plus side, here de Botton at least talks about emotions rather than the empirically unverifiable spirit or soul. Emotions are undoubtedly important, and I’ll even accept the concepts of soul and spirit when used metaphorically.

But I would argue that emotional lives are far healthier when they are based on truth rather than falsehood. It may well be emotionally satisfying to conclude that you have not succeeded because the world is against you and always has been, but it is far healthier to have an emotional reaction based on the most accurate and honest assessment of the state of the world that you are able to produce, rather than retreat into any form of fantasy.

The plea for a “supporting structure and system” to address our chronic indiscipline is a simply a plea to return to the world of the child, to have someone or something in authority over oneself. Being an adult is hard work. Taking responsibility for oneself is hard. I am sure that shaking off that burden is an attractive thought for all of us, on occasion.

Perhaps de Botton is right, and most religious believers retreat into the comfort of their religious structure and system without worrying too much about its truth or falsity. However, I think that the majority of religious believers follow their religion because they genuinely (for good or bad reasons) believe it to be true.

They are not organizing their lives and defining their identities around religion because they find the rituals quaint and enjoy socializing at the receptions after services. They are doing it because they believe what their religion tells them about the world. [EvolutionBlog 8/3/12. Emphasis added.]

And therein, I think, lies the problem.

The Twelve Physics Pracs of Gove (Part Two)

A true-devoted pilgrim is not weary
To measure kingdoms with his feeble steps

–William Shakespeare, The Two Gentlemen of Verona

 

A picture [of reality]  . . .  is laid against reality like a measure  . . .   Only the end-points of the graduating lines actually touch the object that is to be measured  . . .   These correlations are, as it were, the feelers of the picture’s elements, with which the picture touches reality.

–Ludwig Wittgenstein, Tractatus-Logico-Philosophicus 2.141-2.1515

 

What they say of disc jockeys is also true of teachers: that someone, somewhere will remember some of your words forever; or, at least, for the duration of their lifetime. The downside is, of course, that you never know which of your words are going to be remembered. The wittily-crafted, near-Wildean aphorism pregnant with socratic wisdom — probably not. The unintentionally hilarious malapropism that makes you sound like a complete plonker — almost certainly.

To this day, I still remember Dr Prys’ sharp and appropriate response to a flippant comment (possibly from the callow 6th form me) about whether the scientific constants listed in the data book were truly trustworthy: “Look,” he said, “people have dedicated their whole lives to measuring just one of these numbers to one extra decimal place!” True devoted pilgrims indeed, mapping out the Universe step by tiny step, measurement by measurement.

I have written before on what I consider to be the huge importance of practical work in Physics education. Without hands-on experience of the hard work involved in the process of precise measurement, I do not believe that students can fully appreciate the magnificent achievement of the scientific enterprise: in essence, measurement is how scientific theories “touch” reality.

I am encouraged that parts of this view seem to be shared by the writers of the Subject Content guidance. (All hail our Govean apparatchik overlords!)

Of course, this has to be balanced with the acknowledgement that (as I understand it at least) teacher-assessed practical work will no longer count towards a student’s final exam grade. Many are concerned that this is actually a downgrading of the importance of practicals in Science and thus a backward step.

Sadly, they may turn out to be right: “We have to have this equipment for the practical/controlled assessment!” will no longer be a password for unlocking extra funding from recalcitrant SLTs (and from the exam budget too — double win!)

And, undoubtedly, some “teach-to-the-test” schools will quietly mothball their lab equipment (except for the showy stuff — like the telescope that no-one knows how to use — that they bring out for prospective pupil tours).

That would be sad, and although the DfE have, to be fair, nailed their pro-practical colours to the mast, we all know that the dreaded Law of Unintended Consequences may have the last laugh.

I would say it all depends on how the new A levels are actually put together. I will be attending some “launch events” in the near future. I will blog on whether I think we can expect an Apollo 11 or an Apollo 13 at that time.

In the meantime, I will be setting practicals galore as usual, as I’m old-fashioned enough to think that they give a lovely baroque feel to a scheme of work…

Look at me, I design coastlines, I got an award for Norway. Where’s the sense in that? None that I’ve been able to make out. I’ve been doing fiords all my life, for a fleeting moment they become fashionable and I get a major award. In this replacement Earth we’re building they’ve given me Africa to do, and of course, I’m doing it will all fjords again, because I happen to like them. And I’m old fashioned enough to think that they give a lovely baroque feel to a continent. And they tell me it’s not equatorial enough…
–Slartibartfast, from The Hitch-Hikers Guide to the Galaxy by Douglas Adams

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The Twelve Physics Pracs of Gove (Part One)

It’s not often that a DfE publication makes me feel like Kent Brockman, the newsreader from The Simpsons.

I’d like to remind them that as a trusted TV personality, I can be helpful in rounding up others to toil in their underground sugar caves.
Kent Brockman: “I, for one, welcome our new insect overlords.”

This feeling stems from reading the “Use of apparatus and techniques – physics” section from the DfE’s April 2014 Subject Content for AS and A level Biology, Chemistry, Physics and Psychology publication (p.23).

I had the rather novel feeling that it’s actually a sound list: and I, for one, welcome this intervention from our Govean-apparatchik overlords.

Why do I welcome this? Well, I feel that all too often we lose sight of the fact that, at its heart, Physics is, and must remain, a practical subject, the foundation of so much of the modern world.

Miroslav Holub’s poem “A Brief Reflection on Accuracy” paints a haunting and disturbing picture of what could be described as an entirely postmodernist, deconstructed and relativist (rather than relativistic) universe:

A certain soldier

    had to fire a cannon at six o’clock sharp every evening.

    Being a soldier he did so. When his accuracy was

    investigated he explained:

I go by

    the absolutely accurate chronometer in the window

    of the clockmaker down in the city.

   [ . . . ]

Oh, said the clockmaker,

    this is one of the most accurate instruments ever. Just imagine,

    for many years now a cannon has been fired at six o’clock sharp.

    And every day I look at this chronometer

    and always it shows exactly six.

[ . . . ]

So much for accuracy.
And fish move in the water, and from the skies
comes a rushing of wings while

Chronometers tick and cannons boom.

Without the grounding supplied by the art and science of measurement, I believe that we would all inhabit a castle-in-the-air universe as outlined above by Holub (whose experiences as an immunological research scientist are said to have influenced much of his poetry).


Is Holub’s nightmarish scenario even a remote possibility? Would we ever be in a world where “chronometers tick and cannons boom” but no-one actually checks the actual time by, say, looking out of the window to see if it’s daylight or not?

As with most nightmares, it’s probably closer than you think: “The sleep of reason brings forth monsters” as Goya suggested, and the steps that produce the monsters are often small, seemingly-harmless compromises of apparently little consequence.

One of my Y13 students, who has been attending a number of interviews for Physics courses, reports that some university departments have told him that “We spend a lot of the first year teaching students how to write formal laboratory reports as we find many of them have not learned how to do this during their A level courses.

Whaaa-aat? I nearly fell off my lab stool when Sam* told me this. In my opinion, that is unconscionable. “Oh, yeah,” Sam went on, “some of the students there said things like ‘Oh, our A level course content makes it unsuitable for practical teaching’.”


Opinions like that, if they genuinely reflect the views of the schoolteachers involved, are steps on the road to bringing forth monsters. Of course, it may not seem like a big deal to either the students or the teachers who are probably following what they see as a reasonable path of little resistance. But it is a big deal, it really is.

“And what did you say, Sam?” I asked.

“I said that we do a formal write up with a full analysis of experimental uncertainties every lesson.”

“Do we, Sam? Every lesson? Really?”
“Yeah, well,” said Sam with a smile, “I lied about that, didn’t I?”

“Exaggerated, Sam. I think you mean exaggerated.”

“Whatever you say, sir,” said Sam.

More on the 12 pracs of Gove in a later post..

* not his real name

What About the Wombles?

# Underground, overground, wombling free # The Wombles of Wimbledon Common are we.

Teachers know that every school is the same, and yet every school is different.

Every school is the same in the sense that they are set up to do ostensibly the same job: most of them have classrooms, teachers, desks, timetables and other things of that ilk. Every school is different in the sense that the culture, expectations and unwritten rules of each and every school is absolutely, completely, insanely and utterly unique.

Even the language, cant and argot of each school is unique. Even for the staff.

In one of my previous schools, the staff codeword for a “bottom set” student was “womble”. Although some might view such terms as demeaning to the students, I believe that the Head of Science who originated it actually used it with genuine affection and humour (try saying it with a Scottish accent through a thick beard for best effect), and I`d like to think that we used it in a like manner too. (I think that it’s certainly less judgemental than “muppet”, although I’m not sure why.)

Teaching a class of wombles is a skill in itself. There are times when you feel like the best teacher in the world: wow, you say to yourself, nearly everyone got that idea — I am a teaching genius!

And then next lesson comes around. Remember what we covered last lesson? you begin with a confident smile, willing and eager to move on. Cue: thirty blank looks and slightly-furrowed brows and you can see the thought “Huh? We were here last lesson…? We did something last lesson…?” forming in their brains. And you realise that you are still at square one. Or, possibly, square zero.

Not that I am suggesting that we should give up. I am game to try and keep trying and keep on trying.

The point I want to make is simply that so much of educational discourse ignores the both the existence and the needs of the wombles.

Part of the problem is that education in the UK is still very narrowly focused on academic achievement: if you don’t get into Oxbridge then you’re a failure. Oh, and it’s your fault. And your teachers, of course.

I cannot shake the feeling that what are we going to do about the wombles? is a question that is not asked often enough. We concentrate on the A*-C grades (and anyone who can be cajoled or armtwisted into getting a C), and are seemingly content to allow those getting below those grades to think of themselves as failures.

Not too long ago, I set up a talk by an Oxbridge admissions tutor for a group of very mixed ability inner city kids. My oh-so-well-meaning aim was very “growth mindset”: you can achieve anything you want if you work hard. The tutor was genuine, funny and charming and so were the undergrads from inner city backgrounds that she brought along. But my little Dweckian-soiree achieved the exact opposite of what I wanted. Hearing that a few GCSE grade Bs won’t necessarily completely scupper your chances of entry to an elite Oxbridge college isn’t what you want to hear when even a grade D seems a distant unattainable dream. My students feedback was that the event merely confirmed what they thought: this isn’t for me.

Now just because I have filed someone in the “womble” drawer doesn’t mean that they will be unsuccessful. One of the more encouraging — and yet humbling — recurring events in a teacher’s life is meeting past students who have moved on. Some of them will be parents, craftsmen, artists, pilots, business owners, chefs, firefighters and police officers. And as they chat amiably with you about schooldays past, their passing references to their life and career begin to make you feel like the womble.

And very often, they have warm memories of you not because of anything that you did, but because you had a sense of humour and were kind on occasions, and above all else, you tried.

And then you realise that, actually, those were the reasons why you liked some of them more than many of the lazy, tiresome, arrogant jerks in the top set: the wombles were often funny, kind and frequently tried hard.

After all, the truth is that each and every one of us is a womble to someone else.

Salieri : I will speak for you, Father. I speak for all mediocrities in the world. I am their champion. I am their patron saint. Mediocrities everywhere… I absolve you… I absolve you… I absolve you… I absolve you… I absolve you all!

Amadeus (1984) by Peter Shaffer

The Metaphor of Progress

Whatever anybody says, time is most definitely not money.

Time is space.

Let me explain: the language we use to describe and reason about time uses space and (more exactly) movement as a metaphor.

We may picture ourselves journeying through time, where we are physically moving toward the future; perhaps like a passenger on board a train: “We’ll soon reach the end of the month”, or “It’ll be a long time before I reach retirement age.”

train 1

Alternatively, we may picture ourselves as standing still and time moving past us; perhaps like a person standing on a platform watching a train go by: “Christmas will soon be here”, or “The examination season will soon be upon us.”

Original image from http://pippagoldenberg.wordpress.com/2011/05/23/special-relativity/

Why do we make these analogies? It is not just to co-opt words but to co-opt their inferential machinery. Some deductions that apply to motion and space also apply nicely to possession, circumstances and time. That allows the deductive machinery for space to be borrowed for reasoning about other subjects. […] The mind couches abstract concepts in concrete terms.

— Steven Pinker, How The Mind Works, p.353 [emphasis mine]

I don’t want to suggest that time is only a metaphor, but rather that our ordinary, everyday ways of thinking about time are, in the main, part of the time-is-space bundle of metaphors.

And this, of course, is fine. We live our lives relying almost exclusively on inference, induction and guesswork (rather than logical analysis, deduction and rational consideration) and — usually — it’s great! These short-cuts and rules of thumb often lead us to the correct answers more quickly than other pathways. But not always.

Sometimes our machinery of inference gets things wrong. For example, who could have predicted the strange composite entity known as spacetime that is used in relativistic physics and the many counter-intuitive (but experimentally verified) predictions that stem from it?

So, if time is space, what is progress?

Pinker (pp.357-8) summarises the work of Lakoff and Johnson which suggests (amongst other things) that “virtue is up“:

He is high-minded.
She is an upstanding citizen.
That was a low trick.

It seems to me that, currently, in the world of education in general, progress buys into both the progress-is-up and progress-is-forward bundle of metaphors.

These test scores are disappointing: we need to move this class forward to show progress.
She has made excellent progress and is working at a higher level.

And my point? That although the word progress sounds real and concrete, it’s actually not. It is just a metaphor.

When we say that students are “making progress” what are we actually saying? Are they gaining higher test scores? Are they copying stuff neatly off the board? Are they writing coherent, original paragraphs in their exercise books? Are they working on a higher textbook page number than last week? Are they able to solve more difficult problems? Do they collaborate with each other to solve problems? Are they more often in brain-state X rather than brain-state Y?

I am not sure. If I say (and I have said it before and will probably continue to say it again, both verbally and in writing): “Student A has made progress. She is working at a higher level than she was last term.” —  is there actually any useful information in that first sentence other than the implication than I like what Student A has done?

Again let me reiterate that I, myself, am not sure about this. But since the idea of progress is central to much of appraisal and performance management in education, I would like to feel we are not building on sand. Is there a way of nailing this idea of progress, other than “I knows it when I sees it”? (For some reason, I hear this said in a Yorkshire accent.)

When inspectors ask to see evidence of students making progress in a lesson, are they actually only asking to see “some stuff that I like”?

Let me emphasise that I am not averse to metaphor, especially professionally useful metaphors, but I am not sure if progress is one of those.

My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them — as steps — to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) He  must transcend these propositions, and then he will see the world aright.

— Ludwig Wittgenstein, Tractatus Logico-Philosophicus, 6.54

Is it time to throw away the simple ladder idea of progress? Just asking…

The only way is up, baby
For you and me, baby
The only way is up
For you and me

— Yazz and the Plastic Population

The Gift of Screws

Essential oils are wrung:
The attar from the rose
Is not expressed by suns alone,
It is the gift of screws.

— Emily Dickinson, Time and Eternity XXV

It’s a memorable image that Dickinson presents: that the delightful, fragrant oil of attar does not spontaneously waft or pour from a rose, but rather it must be wrung from the petals using the force of a screw press.

Screw Press

In other words, this beautiful, natural, organic fragrance is the gift of screws.

What prompted me to recall these lines? Firstly, Leonard James’ recent excellent blogpost “Kayleigh Wants To Do Well“:

So ‘Kayleigh wants to do well’? Show me a child who doesn’t want to do well! If one accepts that the overwhelming majority of children want to do well then the vapidity of the questioning becomes clear. Extracting a meaningful dialogue from an underachieving child begins with putting their desire to achieve to one side and focusing on whether the child wants to put in the effort required to make it happen. Like many an adult who wants be thinner but doesn’t want to lay off the cake, Kayleigh wants a string of good grades without making the sacrifices required to achieve them.

This resonates with my own experience with some students: “Oh. so you do want to do well? Then do the bloody work then!” (Sorry, I’m going through that time of year that I refer to as “Coursework Hell” at the moment, so I might be on a tiny little bit of a short fuse.)

Secondly, let’s not forget that learning, proper learning mind you, is bloody hard work (and I make no apology for quoting this line yet again, since it so neatly crystallises and encapsulates what I think is the single most important lesson of my two decades in teaching) :

Learning happens when people have to think hard.

Professor Robert Coe

Learning, real learning, is also the gift of screws.