Engelmann and Direct Instruction (Part 6)

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

I think it’s worth looking in detail at the five principles of inference proposed by Mill, and how Engelmann and Carnine adapted them for use in educational contexts.

The five principles put forward by Mill are:

  1. The Direct Method of Agreement
  2. The Method of Difference
  3. The Joint Method of Agreement and Difference
  4. The Method of Residues
  5. The Method of Concomitant Variations

In this post, I will focus on the first three.

methodofagreement

“Non-canonical” statements and inferences are highlighted with an asterisk. These are my own suppositions and, although I believe they are supported by my reading of Mill’s and Engelmann’s and Carnine’s work, I cannot claim that they have direct textual support.

To further explain the simplified “symbolic form” I have developed to highlight what I think are the salient features in the argument:

  • A= “blue”
  • a = is blue
  • b = has beak
  • c = has wings
  • d = extends above the horizon
  • e = has clouds
  • f  = has windscreen
  • g = has four wheels

Please note that the “symbolic form” is currently only a shorthand system, and any resemblance to the notation of formal symbolic logic is merely coincidental.

methodofdifference

Links to Part 5 and the other parts of the series can be found here.

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The Care And Feeding Of Ripple Tanks (Part One)

And so they’re back — ripple tanks, that is. And a Required Practical to boot!

They were a staple of Physics teaching when I started my career, but somehow they fell into an undeserved desuetude. I know many fine teachers and excellent technicians who have never used one in anger, which is a real pity, since they are a great teaching tool.

So I present here my eclectic mix of ripple tanks: what you really need to know.

The Basics: “Look at the shadows, honey, look at the shadows!”

A ripple tank is simply a container with a transparent base. The idea is to put water in the container and make waves or ripples in the water. A light source is positioned above the water so that a screen underneath the transparent tank is illuminated. The crests and troughs act as converging and diverging lenses and produce a pattern of light and dark lines on the screen which enables us to observe wave behaviour more easily.

Remember: look at the pattern of shadows on the floor or bench top, not the ripple tank itself.

If doing this as a demo, sight lines will usually be a bitch for your class. If you have an old fashioned OHP, just put the tank on top of it and project the shadow pattern on to a wall or screen. Alternatively, experiment with positioning the light source underneath the tank and projecting the pattern on to the ceiling.

“Water, Electricity, Children and Darkness: What Could Possibly Go Wrong?”

The ripple tank works best in subdued lighting conditions. Make sure that walkways are free of bags and other trip hazards. If you want students to complete other work during this time, giving them desk lamps (e.g. the ones used by biologists for microscopes) can be useful, and can actually create a nice atmosphere.

Have some towels ready to mop up any water spills.

Most ripple tanks use a low voltage (12V) bulb and vibration generator (0-3 V) to minimise any electrical hazards involved. Be vigilant when plugging in the low voltage supply to the mains and ensure that the mains cable stays dry.

Fill ‘Er Up!

Have a large plastic beaker handy to fill and drain the ripple tank in situ. Don’t try to fill a ripple tank direct from the tap and carry a filled ripple tank through a “live” classroom — unless you want to risk a Mr Bean-type episode. (But you may need to add more water if demonstrating refraction — just enough to cover the plastic or glass sheet used to change the depth.)

In general, less is more. The ripple tank will be more effective with a very shallow 2-3 mm of water rather than a “deep pan” 2-3 cm.

Use the depth of water as a “spirit level” to get the ripple tank horizontal. Adjust the tank so that the depth of water is uniform. (If this seems low tech, remember that it is likely that ancient Egyptians used a similar technique to ensure a level platform for pyramid building!)

It’s also helpful to try and eliminate surface tension by adding a tiny amount of washing up liquid. I dip the end of a thin wire in a small beaker of detergent and mix thoroughly.

And so it begins…

Before switching on the vibration generator etc., I find it helpful to show what a few simple manually-created waves look like using the tank. Using a dropping pipette to create a few random splashes can be eye catching, and then showing how to create circular and straight wavefronts by tapping rhythmically using  the corner of a ruler and then a straight edge.

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Feeling Lucky?

Napoleon’s generals not only had to be loyal, brave and skilled in arms (obviously enough), but the Emperor also demanded of them a more nebulously indefinable quality. When others in his entourage would laud the skills of a particular soldier, Napoleon would ask the pointed question: “Yes, but is he lucky?”

It seems to me that being lucky is the quality that, these days at least, is the one most valued in teachers by those in power above them. The old adage about success having many fathers but failure being an orphan was never truer than in today’s educational world. Examination results, or “outcomes”, are the bit-coin currency of choice in the go-getting world of “performance management” and “high stakes accountability”.

Forgive me, but I am awearied of all that talk. More and more I feel something akin to Duke Ellington’s response to long-winded analyses of the magic of jazz as being “talk that stinks up the room”.

In my career, I have faced Triumph and Disaster in terms of results. Although Kipling advised us to treat “those two impostors just the same”, the truth is that we don’t. Few human beings can. Our perceived Triumphs make us arrogant, the Disasters make us hostile and defensive.

And yet, I think I begin to see a pattern. 

My triumphs occurred when I just got on with the business of teaching: turning up, teaching solid straightforward lessons, setting and marking regular homework. I remember one (internal) observer asking a student about their past paper practice question booklet, returned with a simple percentage grade (in red pen), “And how often are you set homework like this?” and the student answering matter-of-factly: “Every week”. I was so proud. That said, the observer still gave me a “3 (requires improvement)”, citing “lack of pace”, “no plenary” and “no feedback” (when they actually meant no written WWW/EBI comments). But I carried on regardless. And that year’s results were amongst my best ever.

My Disasters seem to occur when I am scrabbling manically to follow what is currently lauded as best practice. In other words, trying to copy what other schools do — or perhaps, more accurately, what other schools say that they do — badly.

Coincidence? Possibly.

So, am I a lucky teacher, in the Napoleonic sense? Sometimes, when I have the good sense to follow my experience and instincts, rather than fads and fashions.

So what about you, when faced with the russian roulette lottery of exam results (you do know it is just a lottery, right?): Are you feeling lucky, punk?

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It’s Not All Relative: Five Things That Einstein Never Said

We have all done it, haven’t we? Each and every one of us has, at some point, appropriated (or misappropriated) a quotation from a great thinker or writer to lend a spurious profundity to our own footling little thoughts.

While it may be well-nigh irresistible to wrap ourselves in the borrowed robes of literary or scientific genius, the temptation is fraught with dangers. To spare both our own blushes and those of our unsuspecting audience, it’s a good idea to check whether the Great Person actually said what they are reputed to have said.

For one reason and another, the life, career and reputation of Albert Einstein makes him an especially tempting target for spurious attributions.

This is my eclectic list of five things that Einstein did NOT say, and yet seem to be quoted and requoted again and again, especially in an educational context.

It is a melancholy truth that these particular memes will most likely be circulating on the internet until the last router rusts away to nothingness. However, on the principle that it better to light a candle than complain about the dark, I present this list (although, given their preternatural persistence, a flamethrower might be more appropriate).

Watch out, any one of them may well be coming to a CPD near you sometime soon…

Nein-stein No. 1

Everyone is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid.

This, according to Quote Investigator [QI 1], was first attributed to Einstein as recently as 2004. The original allegory about animals attending a school and being judged against inflexible criteria, can be traced back to physicist Amos E. Dolbear who published it under a pseudonym in 1898.


Nein-stein No. 2

Everything is energy and that’s all there is to it. Match the frequency of the reality you want and you cannot help but get that reality. It can be no other way. This is not philosophy. This is physics.

Philosophy this gem certainly isn’t. Sadly, it bears no relation to any recognisable form of Physics either. (“Pass the bag labeled ‘New Age Quantum Claptrap’ please, Alice.”)

The original form of this quotation was penned by special effects artist Darryl Anka in 1998 — forty years after Einstein had shuffled off this mortal coil (or, at least, had become significantly less ordered).

Incidentally, Anka never attempted to attribute this thought to Einstein. In fact, he claimed that it had been obtained via “trans-dimensional channelling” from an extraterrestrial entity named “Bashar”. [QI 2]


Nein-stein No. 3

Two things inspire me to awe: the starry heavens and the moral universe within.

A beautiful quote, but Einstein? Naaaah. From Immanuel Kant’s Critique of Practical Reason (1788), actually. Highbrow enough for ya? [Ref 1]


Nein-stein No. 4

The definition of insanity is doing the same thing over and over and expecting different results.

Not Einstein. Not Benjamin Franklin. Not Rita Mae Brown either. The earliest instance tracked down by Wikiquote was from a Narcotics Anonymous publication from 1981.


Nein-stein No. 5

Two things are infinite: the universe and human stupidity. Actually, I’m not sure about the universe.

Einstein may or may not have said this, but the only evidence we have is from the works of therapist Frederick S. Perls, who credited the quote to a “great astronomer” in a book published in 1947. In later works, Perls specifically named Einstein as the originator of the quote which was said during a personal meeting with Perls. However, Perls did present different versions of the statement over the years. [QI 3]

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Engelmann and Direct Instruction (Part 5)

‘Sunlight’s a thing that needs a window
Before it enter a dark room.
Windows don’t happen.’

— R. S. Thomas, “Poetry For Supper”

For this post, I have decided to dispense with the abstract logic-chopping of some of the earlier posts in this series. (Although, I confess, I am quite partial to a nice bit of abstruse ratiocination now and again — in moderation, of course.)

Instead, I want to focus on what a teaching sequence using the principles outlined by Engelmann would actually look like in practice.

 
Some Basics

Firstly, the designer must have an expert-level understanding of the content to be taught.

[If] we are to understand how to communicate a particular bit of knowledge (such as knowledge of the color red, or knowledge about the operation of square root), we must understand the essential features of the particular concept that we are attempting to convey. [1]

The analysis of the knowledge system assumes that the designer will be able to create efficiency in what is to be taught if the designer understands the technically relevant details of the content that is to be taught. [2]

Secondly, a Direct Instruction sequence should be efficient; that is to say, it will aim to produce significant.results with the minimum effort.

The efficiency results from teaching only the skills and strategies that are necessary, and from designing strategies that apply to large segments of what is to be taught, rather than small segments. [2]
The goal is simply to teach as little as possible to provide thorough coverage of the content.[3]

Thirdly, there is no single “royal road” for Direct Instruction: two designers may map out entirely different routes while still being consistent with the guiding principles of D.I.:

[T]his efficiency does not imply general strategies for teaching something like beginning reading, critical analysis, or pre-algebra. As also noted, there is no single right way to achieve this efficiency; however, there are ways that are more efficient than others. [3]

 

Order and Efficiency

The guiding principles for ensuring efficiency are as follows:

[A]rrange the order of introduction of things to be taught for a particular topic or operation so that the more generalizable parts are taught first, and the exceptions or details that have limited application are introduced later. [3]

[However each] exception must be taught because if it is ignored, the learner may not learn it. [4]

The most efficient arrangement is to teach something and then [practice and review it] at a high rate.. . . Once taught, the operation should be used regularly. [5]

When a teaching sequence is developed using these principles, it may look very different from more familiar teaching sequences. For example, in a sequence for teaching basic fractions developed by Engelmann, the terms “top number” and “bottom number” rather than “numerator” and “denominator” were used.

The rationale for not using the “technical terms” is that they do not facilitate the instruction in any way, and they logically complicate the teaching by introducing a discrimination that is irrelevant to understanding fractions. [6]

Carnine and Engelmann argue that this allows learners to focus on what the numbers do rather than on what they are called. They are very insistent, however, that the correct technical terms will be taught — but not necessarily at the beginning as in a standard course.

This has led to some teaching sequences that are significantly different from the ones that most teachers are familiar with. Carnine and Engelmann comment that:

The point is that something may look quite simple but requires significant care in teaching, while something else (like the fraction relationship) may appear to be quite abstract but is quite easy to teach. The difficulty of what is taught is judged by the performance of students who are learning the material. [7]

Since D.I. courses seek to group together irregularities that are irregular in similar ways, Carnine and Engelmann say that this

. . . results in efficiency, but it may create a set of examples that are traditionally not grouped together. [8]

 

Thinking Into Doing

A maths teacher friend challenges a student who is intimidated by some difficult new learning with the question “Tell me what’s the most difficult thing that you’ve ever learned how to do?”

In my friend’s opinion, the most difficult thing that most people have learned is how to walk. He then goes on to assure the worried student that the same techniques that allowed her to learn to gad about on two feet from an early age will serve her well in maths (e.g. not giving up after the first fall, not minding looking a bit silly at times, learning from your mistakes, and so on).

I think it’s a nice analogy that can help students, and I’ve shamelessly lifted this tactic from him. However, as Carnine and Engelmann point out, learning a physical operation such as walking has one major advantage over learning all cognitive operations. The advantage is that the physical environment usually provides immediate, continuous and unambiguous feedback on physical operations.

The physical environment, when viewed as an active agent, either prevents the learner from continuing or provides some unpleasant consequences for the inappropriate action.. . . [However the] physical environment does not provide feedback when the learner is engaged in cognitive operations. . . . To build adequate communications, we design operations or routines that do what the physical operations do. The test of a routine’s adequacy is this: Can any observed outcome be totally explained in terms of the overt behaviours the learner produces? If the answer is “Yes,” the cognitive routine is designed so that adequate feedback is possible. To design the routine in this way, however, we must convert thinking into doing. [9]

Thinking Into Doing

An example of Thinking Into Doing? From Theory of Instruction (1982) location 1273

The aim of Direct Instruction is to provide a measure of immediate, continuous and immediate feedback for cognitive operations that is analogous to that provided by the physical environment for physical operations.
Another One In The Eye For Traditional Differentiation?

Direct Instruction stimulus material is meant to be carefully designed so as to be logically unambiguous. It should generate one — and only one — inference for all learners. This means that as long as students respond correctly to the material, we can assume that both high and low performers have learned the same inference:

The major difference between higher and lower performers is the rate at which they learn the material, not the way they formulate inferences. This difference does not support designing one sequence for higher performers and another for lower performers, but rather providing more repetition and practice for the lower performers. [10]

I don’t know about you, but to me this sounds absolutely great. If I may borrow a phrase from my fellow blogger, The Quirky Teacher: who’s with me?

 

Links

To access the previous blogposts in this series, click on the links:

Part 1    Part 2     Part 3     Part 4

 

References

[1] Carnine, D. and Engelmann, S., Theory of Instruction: Principles and Applications (1982), Kindle location 299

[2] Carnine, D. and Engelmann, S., Could John Stuart Mill Have Saved Our Schools? (2011), Kindle location 610

[3] 2011 loc 640

[4] 2011 loc 678

[5] 2011 loc 671

[6] 2011 loc 648

[7] 2011 loc 671

[8] 2011 loc 685

[9] 1982 loc 1319-1348

[10] 2011 loc 719

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Engelmann and Direct Instruction (Part 4)

Much is due to those who first broke the way to knowledge, and left only to their successors the task of smoothing it.

— Samuel Johnson, A Journey To The Western Isles Of Scotland (1775)

In 1982 Siegfried Engelmann and Douglas Carnine published their Theory of Instruction. This was some 300 years after Newton started the scientific revolution by publishing his Principia; and some 70 years after Russell and Whitehead in the Principia Mathematica attempted to show that the entirety of mathematics could be derived from the laws of logic (famously taking 300 pages to prove that 1+1=2).

In short, Engelmann and Carnine were attempting to start an educational scientific revolution. They wanted to replace the traditional liberal arts foundation of educational theory with a rigorously logical scientific foundation. Their Theory of Instruction is quite simply nothing less than an attempt to write a Principia Pedagogica.

Towards a 'Principia Pedagogica'?

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? Kindle edition, location 1944

In the opening section of the T.O.I., Carnine and Engelmann argue that human beings learn primarily, and in fact literally, from the power of example.

[Learners have the] capacity to learn any quality that is exemplified through examples (from the quality of redness to the quality of inconsistency) . . . This mechanism . . . is capable of learning qualities as subtle as the unique tone of a particular violin or qualities that involve the correlation of events (such as the relationship of events on the sun to weather on the earth).

— S. Engelmann and D. Carnine, Theory of Instruction: Principles and Applications, Kindle edition, locations 365-383

To this end, they propose a simplified (or minimalist, if you will) two step mechanism of how human beings learn:

The first step of the proposed learning mechanism is the presentation of a range of examples. For instance, to explain the concept of “red” an instructor would present examples of red objects; to explain the concept of “conservation of volume”, she would present instances of (say) a fixed volume of liquid being poured into containers of varying shapes.

The second step of the learning mechanism is when the learner mentally constructs a valid generalisation, or mental rule about the qualities or features common to the examples presented. Carnine and Engelmann argue that human beings naturally and immediately attempt to generalise or form such rules when presented with any new information.

Table

From: T.O.I, Kindle loc 399

They do not attempt to argue that the whole of human behaviour can be reduced to this simple two step mechanism, but merely that by accepting this simple model, one “can account for nearly all observed cognitive behaviour” (T.O.I. Kindle loc 375)

Note that the first step is about what is to be learned, and the second step is about how it is learned.

In Carnine and Engelmann’s view, the first step is the responsibility of the instructor. The planning should focus on a rigorous logical analysis of the concept that is to be taught, and should not include any consideration of the likely behavioural response of the learner (e.g. whether she will find it “fun”).

The only factor that limits the learner . . . is the acuity of the sensory mechanism that receives information about [the concept]. (T.O.I. Kindle loc 380-1)

The second step is within the purview of the learner. However, this is also the point at which the instructor would use behavioural analysis to ascertain

. . . the extent to which the learner does or does not possess the mechanisms necessary to respond to the . . . presentation of the concept. [Then one should design] instruction for the unsuccessful learner that will modify the learner’s capacity to respond to the . . . presentation. This instruction is not based on a logical analysis of the communication, but on a behaviour analysis of the learner. (T.O.I. Kindle loc 348-352)

Teachers will, of course, be aware that this is not how we do things in our current educational system, especially as far as the standard techniques of differentiation are concerned.

Are Carnine and Engelmann correct? I’m not sure, but I find their ideas fascinating. Looking at them through the lens of my experience, I would go so far as to say that, intuitively at least, they appear to have the copper-bottomed “ring of truth” (as Richard Ingrams used to say) about them. At the very least, they are deserving of further study and attention.

Part 1 of this series can be found here.

 

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The Joy of a Cheese Sandwich

O tempora, o mores!

What times! What customs!

— Cicero

We are all orthorexics now.

Or so it would seem, at least to me. Orthorexia is the obsession with eating foods that the individual considers ‘healthy’. When I started teaching, a typical teacher’s packed lunch consisted of a sandwich, an apple and a packet of crisps. This was such a common combination that I remember one wag saying that such unthinking adherence to culinary group-think would even have brought joy to the heart of Josef Stalin.

But now — oh my goodness me! What times! What customs! What a huge selection of weird and wonderful Tupperware!

And the food! Growing up in North Wales in the 70s, I’m sure that the majority of food being ingested in our staff room would not have been available in most supermarkets. Perhaps not even in Llandudno ASDA where my parents, cosmopolitan souls that they were, would venture every now and again to buy exotic packets of VESTA dried foods.

But enough of Vesta packets (my favourite was the Beef Risotto, especially eaten as a sandwich), what kind of modern foods am I talking about? Examples would be Black Lentil and Aubergine Stew (“Because black lentils are so much more nutritionally dense than your everyday red lentils, darling!”), Kale and Lemon with Giant Couscous Salad or Smoked Mackerel Pilaf.

Oh lordy, it’s enough to make a chap self-conscious about his cheese sandwich, apple and packet of crisps. Except . . . the way I look at it is: food is food. The human organism is evolved to ingest any old random crap that either can’t or doesn’t run away fast enough and turn it into, well, human-stuff: snot, phlegm, fingernails parings, earwax and so on. A human being can survive for a surprisingly long time on “empty” calories, provided that a few trace nutrients are also present (“Scurvy, anyone?”).

What I do find strange about the now almost universal orthorexic mindset is the attribution of near magical properties to food-stuffs, especially the less familiar and exotic ones.The power of a secretary of state of education seems as nothing compared to that of Jamie Oliver.

That said, there is cause for concern in the amount of processed sugar consumed by youngsters and well, everyone else actually. But I cannot help but feel that there is a strong element of public performance, and perhaps even “nutritional virtue signalling”, in the eating patterns of many adults today.

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