Tag Archives: Education

Engelmann and Direct Instruction (Part 3)

I’m going to begin this post by pondering a deep philosophical conundrum (hopefully, you will find some method in my rambling madness as you read on): I want to discuss the meaning of meaning.

Ludwig Wittgenstein begins the Philosophical Investigations (1953), perhaps one of the greatest works of 20th Century philosophy, by quoting Saint Augustine:

When they (my elders) named some object, and accordingly moved towards something, I saw this and I grasped that the thing was called by the sound they uttered when they meant to point it out. Their intention was shewn by their bodily movements . . . I gradually learnt to understand what objects they signified; and after I had trained my mouth to form these signs, I used them to express my own desires.
Confessions (397 CE), I.8

Wittgenstein uses it to illustrate a simple model of language where words are defined ostensively i.e. by pointing. The method is, arguably, highly effective when we wish to define nouns or proper names. However, Wittgenstein contends, there are problems even here.

If I hold up (say) a pencil and point to it and say pencil out loud, what inference would an observer draw from my action and utterance?

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They might well infer that the object I was holding up was called a pencil. But is this the only inference that a reasonable observer could legitimately draw?

The answer is a most definite no! The word pencil could, as far as the observer could tell from this single instance, mean any one of the following: object made of wood; writing implement; stick sharpened at one end; piece of wood with a central core made of another material; piece of wood painted silver; object that uses graphite to make marks, thin cylindrical object, object with a circular or hexagonal cross-section . . . and many more.

The important point is that one is not enough. It will take many repeated instances of pointing at a range of different pencil-objects (and perhaps not-pencil-objects too) before we and the observer can be reasonably secure that she has correctly inferred the correct definition of pencil.

If defining even a simple noun is fraught with philosophical difficulties, what hope is there for communicating more complicated concepts?

Siegfried Engelmann suggests that philosopher John Stuart Mill provided a blueprint for instruction when he framed formal rules of inductive inference in A System of Logic (1843). Mill developed these rules to aid scientific investigation, but Engelmann argues strongly for their utility in the field of education and instruction. In particular, they show “how examples could be selected and arranged to form an example set that generates only one inference, the one the teacher intends to teach.” [Could John Stuart Mill Have Saved Our Schools? (2011) Kindle edition, location 216, emphasis added].

Engelmann identifies five principles from Mill that he believes are invaluable to the educator. These, he suggests, will tell the educator:

how to arrange examples so that they rule out inappropriate inferences, how to show the acceptable range of variation in examples, and how to induce understanding of patterns and the possible effects of one pattern on another. [loc 223, emphasis added]

Engelmann considers Mill’s Method of Agreement first. (We will look at the other four principles in later posts.)

Mill states his Method of Agreement as follows:

If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or effect) of the given phenomenon.
A System of Logic. p.263

Engelmann suggests that with a slight change in language, this can serve as a guiding technical principle that will allow the teacher to compile a set of examples that will unambiguously communicate the required concept to the learner, while minimising the risk that the learner will — Engelmann’s bête noire! — draw an incorrect inference from the example set.

Stated in more causal terms, the teacher will identify some things with the same label or submit them to the same operation. If the examples in the teaching set share only one feature, that single feature can be the only cause of why the teacher treats instances in the same way. [Loc 233]

As an example of an incorrect application of this principle, Engelmann gives the following example set commonly presented when introducing fractions: 1/2, 1/3, and 1/4.

Engelmann argues that while they are all indeed fractions, they share more than one feature and hence violate the Method of Agreement. The incorrect inferences that a student could draw from this set would be: 1) all fractions represent numbers smaller than one; 2) numerators and denominators are always single digits; and 3) all fractions have a numerator of 1.

A better example set (argues Engelmann) would be: 5/3, 1/4, 2/50, 3/5, 10/2, 1/5, 48/2 and 7/2 — although he notes that there are thousands more possible sets that are consistent with the Method of Agreement.

Engelmann comments:

Yet many educators believe that the set limited to 1/2, 1/3, and 1/4 is well conceived. Some states ranging from North Dakota to Virginia even mandate that these fractions should be taught first, even though the set is capable of inducing serious confusion. Possibly the most serious problem that students have in learning higher math is that they don’t understand that some fractions equal one or are more than one. This problem could have been avoided with early instruction that introduced a broad range of fractions. [Loc 261]

For my part, I find Engelmann’s ideas fascinating. He seems to be building a coherent philosophy of education from what I consider to be properly basic, foundational principles, rather than some of the “castles in the air” that I have encountered elsewhere.

I will continue my exploration of Engelmann’s ideas in subsequent posts. You can find Parts 1 and 2 of this series here and here.

The series continues with Part 4 here.

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Playing the Game

Kings made tombs more splendid than houses of the living and counted old names in the rolls of their descent dearer than the names of sons. Childless lords sat in aged halls musing on heraldry.

— J. R. R. Tolkein, The Two Towers

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If there’s anything that makes me lose the will to live, it is being in the same room as an educational Player of Games. I’m sure everyone is reasonably familiar with the type: “I want every intervention from now until the end of term focused on improving the A*-C pass rate for left-handed Y11 students whose birthday month has an R in it.”

Yes, it might help, marginally, in some sense. On such massaging of the margins are modern educational careers and reputations built.

Personally, such considerations leave me cold. Such teachers, it seems to me, hold their statistics in higher esteem than their students. The percentage is adjudged to be the outcome, rather than merely an indicator of a number of successful outcomes.

Sometimes, when I try and express this, people look at me as if I had twelve heads. It is a nuanced and subtle difference of emphasis, admittedly, but I think it’s a valid one. As an analogy, imagine a doctor who focuses on (say) a patient’s temperature to the exclusion of all else: “Doctor, I think I’ve broken my leg.”

“H’mm, let’s have a look. Actually, your temperature is a wee bit high. Here, let me apply this cold compress to your forehead.”

“But what about my leg?”

“Well, your body temperature is back to normal now. That means that we now have the officially mandated number of ‘healthy’ patients as per Ofdoc guidelines.”

“But what about my bloody BROKEN LEG?”

“My work here is done. Next patient please!”

The other note of caution that needs to be sounded more loudly in the education world is awareness of what is known as the Halo Effect.

I learned about this in Duncan Watts’ excellent book Everything Is Obvious (When You Know The Right Answer) in which he summaries the work of Phil Rosenzweig:

Firms that are successful are consistently rated as having visionary strategies. strong leadership, and sound execution, while firms that are performing badly are described as suffering from misguided strategy, poor leadership or shoddy execution. But, as Rosenzweig shows, firms that exhibit large swings in performance over time attract equally divergent ratings, even when they have pursued exactly the same strategy, executed in the same way, under the same leadership all along. Remember that Cisco Systems went from being the poster child of the Internet era to a cautionary tale in a matter of a few years . . . Rosenzweig’s conclusion is that in all these cases, the way firms are rated has more to do with whether they are perceived as succeeding than what they are actually doing.

— Watts, p.197 [emphasis added]

In one early experiment, several teams were asked to analyse the finances of a fictitious firm. Each team was rated on their performance and then asked to evaluate their team in terms of teamwork, communication and motivation. The high scoring teams assessed themselves very highly on these metrics compared with the low scoring teams, as you might expect. However, the kick was that performance scores had been allocated at random — there was no real difference between the teams’ performance at all. The conclusion is that the appearance of superior outcomes produced an illusion of superior functionality.

Watts argues persuasively that we tend to massively underestimate the role of plain, dumb luck in achieving success. He cites the case of Bill Miller, the legendary mutual fund manager who did something no other mutual fund manager has ever achieved: he beat the S&P 500 for fifteen straight years. Watts notes that this seems a classic case of talent trumping luck. However:

. . . right after his record streak ended, Miller’s performance was bad enough to reverse a large chunk of his previous gains, dragging his ten-year average below that of the S&P. So was he a brilliant investor who simply had some bad luck, or was he instead the opposite: a relatively ordinary investor whose ultimately flawed strategy just happened to work for a long time? The problem is that judging from his investing record alone, it’s probably not possible to say. [p.201]

I trust that I do not have to draw too many lines to highlight the relevance of these points to the education world. Outcomes, in the sense of exam grades, are currently the be-all and the end-all of education. But the Halo Effect makes it clear that a simplistic reading of successful outcomes can be highly misleading.

Negating the Halo Effect is difficult, because if one cannot rely on the outcome to evaluate a process then it is no longer clear what to use. The problem, in fact, is not that there is anything wrong with evaluating processes in terms of outcomes — just that it is unreliable to evaluate them in terms of any single outcome. [p.198]

Ofsted. managers and politicians please take note: our search for a signal continues.

Approval of what is approved of
Is as false as a well-kept vow.

— Sir John Betjeman, The Arrest of Oscar Wilde At The Cadogan Hotel

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Actions and Consequences

‘I think we all owe Howard a debt of gratitude for coming up with the solution to all our difficulties,’ said one of Kirk’s [university] colleagues.

Kirk took this as his due and nodded, ignoring [the] accurate observation that all the difficulties had been created by him.

The assembled academics had all just tunnelled through the service area under the student picket lines which had been brought into being by Kirk and had surfaced in a conference room to deal with problems which had been fomented by Kirk and had finally got around to passing resolutions in conformity with the wishes of Kirk.

— Clive James, review of 1981 TV adaptation of Malcolm Bradbury’s The History Man, from Glued to the Box, 1983

I am sure all teachers have been in that student disciplinary meeting that suddenly goes all Kafkaesque in a manner reminiscent of the academic conference described by Clive James above: what begins as a formal gathering to address the many difficulties created by the student, challenge the obfuscations and untruths put in place by the student, and alleviate the problems fomented by the student; suddenly and inexplicably, often at SLT’s behest, turns to passing resolutions in conformity with the wishes of the student. For example, Kayleigh gets to come off Red Report and SLT will have a serious chat with her teachers about their “questionable attitudes towards her” because, after all, “Kayleigh wants to do well“.

I started thinking about actions and consequences in response to the Quirky Teacher’s provocative post Is Hardship Really So Bad?

TQT argues that perhaps people today are too insulated from genuine hardship. While I think he has a point, I would argue (as in the example above) that, although Kayleigh may well have hardships enough in her life, what the education system as it stands is insulating her from are the long-term, serious consequences of her actions — until it’s too late.

It seems to me that there is, or can be, a widespread acceptance of misfortune and hardship — although perhaps it can often be characterised as sullen rather than stoic. What is different from the world I remember being raised in, is the precipitate rush to don the holy mantle of victimhood; as if the fact that that other individuals or institutions were involved in creating the unfortunate situation absolves the “victim” of all responsibility whatsoever.

At times, of course, the victim is truly the victim and, in all fairness, no portion of blame can be attached to her.

That given, what I am attempting to highlight is an unfortunate trend in modern culture that seems to hold that if one has been sinned against, then by definition, one cannot have sinned: in other words, victimhood = sainthood.

This is, I think, the mindset behind the demands that students cannot be “allowed” to fail and that it is entirely the responsibility of the teacher to make sure that every student not only passes, but achieves their over-inflated “aspirational” (dread word!) target grade.

I disagree: of course, the teacher has a responsibility to ensure that every student in her care is as well prepared as possible. But the student is also responsible for her own preparation and I am concerned that the balance of responsibility has shifted too far towards the teacher (and, to be fair, towards the school and SLT — which is why the pressures are passed down the line management structure).

It has been said that a pennyworth of example is worth a pound of preaching. I cannot help but feel that having more students (and parents) being aware that failure is an option and that success is not a birthright would result in a healthier educational culture.

You must reap what you sow. There is no reward, there is no punishment, but there are consequences, and these consequences are the invisible and implacable police of nature. They cannot be avoided. They cannot be bribed. No power can awe them, and there is not gold enough in the world to make them pause.

— Robert Green Ingersoll, Ingersoll Again Answer His Critics IV, 1891

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Education And The English Language

Or: Tristram Hunt: Must Try Harder

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“When there is a gap between one’s real and one’s declared aims, one turns as it were instinctively to long words and exhausted idioms, like a cuttlefish squirting out ink.”
— George Orwell, Politics and the English Language, 1946

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“Ladies and Gentleman, my argument today is very simple: we must transform. And we must trust. Because a powerful convergence of social, economic and technological forces are creating huge challenges for our future prosperity that education can no longer ignore. We find ourselves at a unique and incredibly fragile moment in our economic history. With technology and globalisation combining to ferment a ‘third’ industrial revolution. Creating a digitally enhanced brave new world filled both with enormous challenges and opportunities.”
— Tristram Hunt, Speech to ASCL Conference 20/3/15

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“This mixture of vagueness and sheer incompetence is the most marked characteristic of modern English prose, and especially of any kind of political writing. As soon as certain topics are raised, the concrete melts into the abstract and no one seems able to think of turns of speech that are not hackneyed: prose consists less and less of words chosen for the sake of their meaning, and more of phrases tacked together like the sections of a prefabricated hen-house.”
— Orwell 1946
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“[This] means education must also serve as a strategy for national economic renewal; that our country’s future prosperity depends on unlocking our education system’s hidden potential. It is that force which I would suggest drives our system’s ‘high stakes’ nature. And it is not an inconsiderable concern.”
— Hunt 2015
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“Phrases like a not unjustifiable assumption, leaves much to be desired, would serve no good purpose, a consideration which we should do well to bear in mind, are a continuous temptation . . .  [and], like cavalry horses answering the bugle, group themselves automatically into the familiar dreary pattern. This invasion of one’s mind by ready-made phrases (lay the foundations, achieve a radical transformation) can only be prevented if one is constantly on guard against them, and every such phrase anaesthetizes a portion of one’s brain.”
— Orwell 1946
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“[Y]ou have the democratic promise of Sir Timothy Berners-Lee’s “this is for everyone” vision. Where enterprise, creativity and idea becomes the true currency of opportunity. As opposed to class, identity, power, wealth or status . . . For this truly is the wonderful thing about the digital revolution. It democratises power. It stimulates innovation. Weakens bureaucratic control. And provides new platform for articulating an alternative.”
— Hunt 2015
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“The inflated style is itself a kind of euphemism. A mass of Latin words falls upon the facts like soft snow, blurring the outlines and covering up all the details . . . Political language – and with variations this is true of all political parties, from Conservatives to Anarchists – is designed to make lies sound truthful and murder respectable, and to give an appearance of solidity to pure wind. One cannot change this all in a moment, but one can at least change one’s own habits, and from time to time one can even, if one jeers loudly enough, send some worn-out and useless phrase – some jackboot, Achilles’ heel, hotbed, melting pot, acid test, veritable inferno or other lump of verbal refuse – into the dustbin where it belongs.”
— Orwell 1946

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Weasel Words in Education Part 5: Rigour

A crack team of DfE boffins test the proposed new system for the management and oversight of the United Kingdom’s increasingly fissiparous school system.

Rigour, n.

1. The quality of being extremely thorough and careful.

2. severity or strictness.

3. (when pluralized) harsh and demanding conditions

In education (as in other walks of life) the word rigour is usually meant in sense (1) when applied to one’s own thinking or the thinking of one’s friends or allies: “I am being rigorous. However, you, sir, are merely pedantic.”

These days, sense (2) seems to require the insertion of a prefix, as in “The moderation of our controlled assessments was over-rigorous.”

Rigour is therefore a good thing, right?

However, in my opinion it seems to be used more and more as a talisman rather than as a genuine description.

Mr Gove told the Commons: “The new specifications are more challenging, more ambitious and more rigorous. That means more extended writing in subjects like English and history, more testing of advanced problem-solving skills in mathematics and science.”

The Independent, July 2013

I am not sure if Michael Gove* is using the word in sense (1) or sense (2) here. If he meant it in sense (2) then it is a rhetorical flourish to emphasise the idea that GCSEs will be more challenging. If he meant it in sense (1) then the promise of “extended writing [and] more testing” doesn’t tell me how the new exams will be more thorough and careful. This is not saying that the examination system does not need to be more thorough and careful, merely that “extended writing [and] more testing” won’t necessarily make it so.

Let me emphasise that I am not opposed to rigour. I like rigour and being rigorous, at least in sense (1). I would perhaps favour the words consistent and fair rather than use rigour in sense (2) in an educational context, but that’s a personal preference.

In short, I wish people would be more rigorous in their use of the word rigorous. You shouldn’t just use it because you think it sounds good. A is rigorous while B is not should mean more than I like A and dislike B.

And as a final thought, I strongly suspect that many of the people who are most keen to bemoan the lack of rigour in education would have to step out of the kitchen when push came to shove, as in this little vignette:

[I listened] to magazine columnist Fred Barnes . . . whine on and on about the sorry state of American education, blaming the teachers and their evil union for why students are doing so poorly. “These kids don’t even know what The Iliad and The Odyssey are!” he bellowed, as the other panellists nodded in admiration at Fred’s noble lament.

The next morning I called Fred Barnes at his Washington office. “Fred,” I said, “tell me what The Iliad and The Odyssey are.”

He started hemming and hawing. “Well, they’re … uh … you know … uh … okay, fine, you got me—I don’t know what they’re about. Happy now?”

No, not really. You’re one of the top TV pundits in America, seen every week on your own show and plenty of others. You gladly hawk your “wisdom” to hundreds of thousands of unsuspecting citizens, gleefully scorning others for their ignorance.

— Michael Moore, Stupid White Men (2001), p.58

 

* His successor Nicky Morgan look set to continue Gove’s use of the term.

Postscript: For the those (including myself) who are classically undereducated: The Iliad is an ancient Greek epic poem by Homer about the Trojan War. The Odyssey is another epic poem by Homer recounting the ten-year journey home from the Trojan War made by Odysseus, the king of Ithaca.

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Assessing Without Levels: the Lewis Carroll Perspective

An alternative look at assessment without levels…

As part of our reforms to the national curriculum , the current system of ‘levels’ used to report children’s attainment and progress will be removed.  It will not be replaced.

DfE, 2013

 

Bellman Map

 

He had bought a large map representing the sea,
Without the least vestige of land:
And the crew were much pleased when they found it to be
A map they could all understand.

 

“What’s the good of Mercator’s North Poles and Equators,
Tropics, Zones, and Meridian Lines?”
So the Bellman would cry: and the crew would reply
“They are merely conventional signs!

 

“Other maps are such shapes, with their islands and capes!
But we’ve got our brave Captain to thank:
(So the crew would protest) “that he’s bought us the best–
A perfect and absolute blank!”

 

— Lewis Carroll, The Hunting of the Snark

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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.

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