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.


“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.


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

Part 1    Part 2     Part 3     Part 4    Part 5

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.

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?