ambiguity is deeply writ

AMBIGUITY IS WRITTEN DEEPLY INTO KNOWLEDGE STRUCTURES

What puzzles me most about Direct Instruction is that it is good practice but poor theory. Part of what I mean follows.

Zig Engelmann starts with the great idea that instruction should be tidied up and made very clear but then takes that too far into the claim that in general instruction can be made unambiguous, “I didn't realise how radical the single interpretation principle was ...” (Teaching Needy Kids in our Backward System, p. 3)

We can strive for clearer instruction, that is a worthy goal, but it is not possible to achieve unambiguous instruction.

For example, when teaching the subtraction sixty two minus fifty seven (62 – 57), the DI teacher asks the students “Can we subtract 7 from 2” and the students are taught to say “No”. They then go onto rearrange 62 into 50 + 12 so as to be able solve the problem. This is good teaching, but there are other ways to solve it as well. Two take seven equals -5. Sixty take fifty equals 10. Ten – five = 5.

My aim here is not to improve DI by making it more complicated. DI works, in part, because it simplifies things. I don't deny that. But the complexity and multiple pathways are written deep into the knowledge domain of mathematics. The claim of unambiguous instruction fails. We can subtract 7 from 2. The answer is not "No". Many more examples of such oversights in DI scripts can be cited.

This is not against DI as such (which in certain contexts works better than anything else in my experience) but against the over simplified arguments often presented by advocates of DI. The idea that data provides the ultimate scientific certainty is mistaken because it is impossible to separate out data from concepts developed internally in the mind. Ambiguity is written into educational theory as well as practice.

These observations are presented here as a stepping stone towards developing a better theory of why DI often works than the unsatisfactory theory (uncritical acceptance of JS Mill's Logic) developed by Zig Engelmann and Doug Carnine.

I speculate further that this seems to tie into a critique of JS Mill, initiated by John Dewey and further developed by Hilary Putnam. JS Mill thought that a perfected science of individual psychology would be able to deliver social laws to solve social problems. This reminds me of the Zig Engelmann cult, which promotes him as the one true educational visionary amongst a sea of deceivers:

"Like Copernicus, who proofs were rejected by the church for 300 years, Engelmann remains a scorned revolutionary, anathema or simply unknown to most people in the field"
- Barbash, p. 8

I can't go along with the way that Piaget, Bruner and Dewey are rubbished in this cult war. I think they have all made valuable contributions to educational theory. Some positives, some negatives, some ambiguities. There is not one true way.

These thoughts were crystallised in thinking about these comments from Hilary Putnam about empiricism:

“Empiricism … thinks that the general form of scientific data, indeed of all empirical data, can be known a priori – even if it doesn't say so in so many words! From Locke, Berkeley, and Hume down to Ernst Mach, empiricists held that all empirical data consists of “sensations”, conceived of as an unconceptualised given against which putative knowledge claims can be checked. Against this view William James had already insisted that while all perceptual experience has both conceptual and non conceptual aspects, the attempt to divide any experience which is a recognition of something into parts is futile: “Sensations and apperceptive idea fuse here so intimately [in a 'presented and recognised material object'] that you can no more tell where one begins and the other ends, than you can tell, in those cunning circular panoramas that have lately been exhibited, where the real foreground and the painted canvas join together” (quoted in Dewey's Ethics, p. 273). Dewey continued the line of thought that James had begun, insists that by creating new observation concepts we “institute” new data. Modern physics (and of course not only physics) has richly born him out. A scientist may speak of observing a proton colliding with a nucleus, or of observing a virus with the aid of an electron microscope, or of observing genes or black holes, and so forth. Neither the form of possible explanation nor the form of possible data can be fixed in advance, once and for all...

Among the classic empiricist thinkers, the most famous ones to call before John Dewey did for the application of scientific research to the problems of society were Mill and Comte. But Comte reverted to meritocracy. He visualised handling social problems over to savants, social scientific intellectuals, a move which falls under Dewey's criticism of the idea of a 'benevolent despot'.

It might seem that this same criticism cannot be voiced against Mill, who, as much as Dewey was to do, valued active participation in all aspects of the democratic process. But as far as the application of social scientific knowledge to social problems is concerned, what Mill called for was the development of a perfected science of individual psychology, from which he thought … we would be able to derive social laws (via the hoped for reduction of sociology to psychology) which could then be applied to particular social problems. This entire program, as most would concede today, is a misguided fantasy
- Ethics without Ontology, pp. 98-100

Further reading will be required to get the bottom of this: Barbash, Shepard. Clear Teaching: With Direct Instruction, Siegrried Engelmann Discovered a Better Way of Teaching (2012)
Dewey Logic
Dewey Ethics
Dewey The Quest for Certainty
Engelmann, Zig. Teaching Needy Kids in our Backward System: 42 Years of Trying (2007)
Engelmann, Zig and Carnine, Douglas. Could John Stuart Mill have saved our schools? (2011)
Jame, William. Radical Empiricism?
Mill JS A System of Logic
Putnam, Hilary. Ethics without Ontology
Quine Two Dogmas of Empiricism