I was delighted to see that so many people not only read my last post on curriculum but offered such great comments, too. Let’s press on!
The 1930s saw an explosion of educational innovation, as my reference to Ralph Tyler in the last post reminds us. In fact, one of the most extraordinary experiments in mathematics instruction, based on Dewey’s work, was published in 1938 as an NCTM Yearbook called The Nature of Proof. The author, Harold Fawcett, taught a course in Geometry at the Ohio State Lab School that was arguably one of the greatest courses of all time. In it students developed and wrote their own theory of spatial relations all year, based on inquiry and argument (instead of using a geometry text). But the real coup de grace was the stated aim of the course: transfer one’s learning to civics and analysis of propaganda! Fawcett said, Look, geometry teachers often give lip service to the idea that geometry and math generally are supposed to advance critical thinking and problem solving more generally, so I am going to design my entire course backward from the goal of transfer of reasoning.
Another key figure of this time was Hollis Caswell who basically invented the modern idea of curriculum writing around ‘scope’ and ‘sequence’. Ironically, he stressed that sequence should best flow from student interests and development!
Much of this was at the core of my dissertation at Harvard (though I was unaware of Fawcett at the time I wrote it – which was ironic because I proposed a geometry course much like his in my thesis). My dissertation was entitled: Thoughtfulness as an Educational Aim. And a major figure in my research was, naturally, John Dewey.
A crucial and often overlooked idea in Dewey is the distinction he drew between curriculum sequence that was ‘logical’ (i.e. the ‘logic’ of the subject matter knowledge, e.g. start with axioms in geometry and march through proofs; start history in the past and march forward in time, etc.) and the sequence that was ‘psychological’ (i.e. suited the natural development of learner thought). This distinction was at the heart of Fawcett’s, Caswell’s, and Tyler’s work. It is also a key influence in UbD.
Here’s what Dewey had to say; hard to believe these words are almost 100 years old, from Democracy & Education (emphasis added). He is talking about the developmental nature of thought, whether it is the child’s first experiences or a novice adult entering a field:
The initial stage of that developing experience which is called thinking is experience. This remark may sound like a silly truism. It ought to be one; but unfortunately it is not. On the contrary, thinking is often regarded both in philosophic theory and in educational practice as something cut off from experience, and capable of being cultivated in isolation…
Speaking generally, the fundamental fallacy in methods of instruction lies in supposing that experience on the part of pupils may be assumed. What is here insisted upon is the necessity of an actual empirical situation as the initiating phase of thought. Experience is here taken as previously defined: trying to do something and having the thing perceptibly do something to one in return. The fallacy consists in supposing that we can begin with ready-made subject matter of arithmetic, or geography, or whatever, irrespective of some direct personal experience of a situation. Even the kindergarten and Montessori techniques are so anxious to get at intellectual distinctions, without “waste of time,” that they tend to ignore — or reduce — the immediate crude handling of the familiar material of experience, and to introduce pupils at once to material which expresses the intellectual distinctions which adults have made. But the first stage of contact with any new material, at whatever age of maturity, must inevitably be of the trial and error sort. An individual must actually try, in play or work, to do something with material in carrying out his own impulsive activity, and then note the interaction of his energy and that of the material employed. This is what happens when a child at first begins to build with blocks, and it is equally what happens when a scientific man in his laboratory begins to experiment with unfamiliar objects.
Hence the first approach to any subject in school, if thought is to be aroused and not words acquired, should be as unscholastic as possible. To realize what an experience, or empirical situation, means, we have to call to mind the sort of situation that presents itself outside of school; the sort of occupations that interest and engage activity in ordinary life. And careful inspection of methods which are permanently successful in formal education, whether in arithmetic or learning to read, or studying geography, or learning physics or a foreign language, will reveal that they depend for their efficiency upon the fact that they go back to the type of the situation which causes reflection out of school in ordinary life. They give the pupils something to do, not something to learn; and the doing is of such a nature as to demand thinking, or the intentional noting of connections; learning naturally results.
That the situation should be of such a nature as to arouse thinking means of course that it should suggest something to do which is not either routine or capricious — something, in other words, presenting what is new (and hence uncertain or problematic) and yet sufficiently connected with existing habits to call out an effective response. An effective response means one which accomplishes a perceptible result, in distinction from a purely haphazard activity, where the consequences cannot be mentally connected with what is done. The most significant question which can be asked, accordingly, about any situation or experience proposed to induce learning is what quality of problem it involves.
At first thought, it might seem as if usual school methods measured well up to the standard here set. The giving of problems, the putting of questions, the assigning of tasks, the magnifying of difficulties, is a large part of school work. But it is indispensable to discriminate between genuine and simulated or mock problems. The following questions may aid in making such discrimination. (a) Is there anything but a problem? Does the question naturally suggest itself within some situation or personal experience? Or is it an aloof thing, a problem only for the purposes of conveying instruction in some school topic? Is it the sort of trying that would arouse observation and engage experimentation outside of school? (b) Is it the pupil’s own problem, or is it the teacher’s or textbook’s problem, made a problem for the pupil only because he cannot get the required mark or be promoted or win the teacher’s approval, unless he deals with it?
No one has ever explained why children are so full of questions outside of the school ( so that they pester grown-up persons if they get any encouragement), and the conspicuous absence of display of curiosity about the subject matter of school lessons. Reflection on this striking contrast will throw light upon the question of how far customary school conditions supply a context of experience in which problems naturally suggest themselves. No amount of improvement in the personal technique of the instructor will wholly remedy this state of things. There must be more actual material, more stuff, more appliances, and more opportunities for doing things, before the gap can be overcome…
.. Logical order is the proper form of knowledge as perfected. For it means that the statement of subject matter is of a nature to exhibit to one who understands it the premises from which it follows and the conclusions to which it points. As from a few bones the competent zoologist reconstructs an animal; so from the form of a statement in mathematics or physics the specialist in the subject can form an idea of the system of truths in which it has its place.
To the non-expert, however, this perfected form is a stumbling block. … its connections with the material of everyday life are hidden. To the layman the bones are a mere curiosity. Until he had mastered the principles of zoology, his efforts to make anything out of them would be random and blind. From the standpoint of the learner scientific form is an ideal to be achieved, not a starting point from which to set out. It is, nevertheless, a frequent practice to start in instruction with the rudiments somewhat simplified. The necessary consequence is an isolation of [the subject] from significant experience. The pupil learns symbols without the key to their meaning. He acquires a technical body of information without ability to trace its connections with the objects and operations with which he is familiar — often he acquires simply a peculiar vocabulary.
There is a strong temptation to assume that presenting subject matter in its perfected form provides a royal road to learning. What more natural than to suppose that the immature can be saved time and energy, and be protected from needless error by commencing where competent inquirers have left off? The outcome is written large in the history of education. Pupils begin their study… with texts in which the subject is organized into topics according to the order of the specialist. Technical concepts, with their definitions, are introduced at the outset. Laws are introduced at a very early stage, with at best a few indications of the way in which they were arrived at...
The chronological method which begins with the experience of the learner and develops from that the proper modes of scientific treatment is often called the “psychological” method in distinction from the logical method of the expert or specialist. The apparent loss of time involved is more than made up for by the superior understanding and vital interest secured. What the pupil learns he at least understands.
But there is no magic attached to material stated in technically correct scientific form. When learned in this condition it remains a body of inert information. Moreover its form of statement removes it further from fruitful contact with everyday experiences than does the mode of statement proper to literature.
Atoms, molecules, chemical formulae, the mathematical propositions in the study of physics — all these have primarily an intellectual value and only indirectly an empirical value. They represent instruments for the carrying on of science. As in the case of other tools, their significance can be learned only by use. We cannot procure understanding of their meaning by pointing to things, but only by pointing to their work when they are employed as part of the technique of knowledge.
No one would have a knowledge of a machine who could enumerate all the materials entering into its structure, but only he who knew their uses and could tell why they are employed as they are. In like fashion one has a knowledge of mathematical conceptions only when he sees the problems in which they function and their specific utility in dealing with these problems. “Knowing” the definitions, rules, formulae, etc., is like knowing the names of parts of a machine without knowing what they do.