Monthly Archives: May 2015

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)

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Filed under Direct Instruction, Education, Philosophy, Siegfried Engelmann

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)

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Filed under Direct Instruction, Education, Philosophy, Siegfried Engelmann, Society