e=mc2andallthat

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)