Arithmetic for a Slave

In their 1920 book How to Measure, Guy Wilson and Kremer Hoke describe what they call “the newer psychology in arithmetic.” They say (the bold parts are my emphasis):

The arithmetic of a generation ago was based upon a belief in formal discipline. The purpose was to develop general powers. While arithmetic is doubtless as useful as any other subject in developing general ability, it is now realized that responses are specific and that ability gained in one line contributes to success in another line only in so far as the two lines have elements in common. There is no such thing as general ability in a subject. There are, in fact, as many separate abilities in even a single subject as there are different specific responses. Arithmetic has been developed rapidly in line with this newer psychology and we have come to realize that each separate response in the useful tool materials of arithmetic must be mastered, and in turn must be tested if the diagnosis of the pupil’s ability is to be complete.

Now , let me say that these measures and tests of which Wilson and Hoke speak (they list 19 available tests on the following pages) are in some cases very valuable, especially when every single school age child is compelled to be in the classroom, willy or nilly. I do not mean, in this post, to question the value of their tests and the diagnoses their tests enabled. What I mean to challenge is the psychology behind the tests.

“There is,” they say, “no such thing as a general ability in a subject.” This statement asserts the fundamental premise of the progressive educator and renounces the fundamental psychology of the Christian and classical tradition. And where did this new psychology come from?

Oh, look! Here’s a big surprise: Teacher’s College, Columbia University. Whoodathunkit? And the theorist: Edward L. Thorndike, a behavioral psychologist who formulated laws of learning that, Diane Ravitch tells us in Left Back, A Century of Failed School Reforms, “were based on the observed connection between stimulus and response.” After all, the last thing the progressive educators wanted was to think about “metaphysical or traditional sources of authority,” when they could make themselves the authorities.

Ravitch’s description is exceptionally clear, as is all her writing, so let me share an extended quote with you:

Thorndike and his colleague Robert S. Woodworth conducted several experimnets to determine whether training one mental function would improve any other mental function. In one instance, subjects were asked to estimate teh length of various lines or estimate weights. In another, subjects were instructed to select certain letter combinations (e.g. the letters e and s) or words  or geometic figures. They also tested the influence of memorizing “on the general ability to memorize.” From their various experiments, the authors found that “the amount of improvement gotten by training in an allied function is small.” They concluded that, “It is misleading to speak of sense discrimination, attention, memory, observation, accuracy, quickness, etc., as multitudinous separate individual functions are referred to by any one of these words. These functions have little in common. There is no reason to suppose that any general change occurs corresponding to the words ‘improvement of the attention,’ or ‘of the power of observation,’ or ‘of accuracy.'” The alleged benefits of mental discipline, they held were “mythological, not real entities.” Rather than seeing the mind as a collection of separate functions (or “faculties”), they maintained that “the mind is, on the contrary, on its dynamic side a machine for making particular reactions to particular situations.” (Page 64 in Ravitch)

The effect of this research?

The Thorndike-Woodworth studies had a dramatic effect among pedagogical professors, who greeted them as proof  that the theory of mental discipline had been decisively ‘exploded.’ Parents and other members of the public continued to talk about ‘training the mind,’ but educationists believed that this had been revealed as a myth.

The issue of transfer of training became crucial to the viability of the academic curriculum, and the implications for the schools were mind-boggling. Some educational psychologists, citing Thorndike and Woodworth, insisted that nothing learned in one situation could be applied to any other, so that all training must be specific to the task at hand. Seen in this light, nothing taught in the school had any value or utility except to satisfy college admission requirements or to prepare those who planned to teach the same subject in the future or those who might have an occupational purpose for learning subjects such as algebra, chemistry, history, or German.

But we’re just getting warmed up:

Pedagogues quickly realized that Thorndike’s experiments had undermined the rationale for the traditional curriculum and that it was up to them to create a new education, one that would train the students for the real world of work.

Did you just feel the earth move? Did you just hear the shackles click? Ravitch continues:

Thorndike confidently asserted that scientific research had made obsolete the once-customary claims about “training of the reason, of the powers of observation, comparison and synthesis” or “training the faculties of perception and generalization” or “disciplining the senses.”… Now pedagogical science would decide which youngsters should study Latin, geometry, English, bookkeeping, cooking, sewing, or woodworking, and which subjects should be removed from the curriculum.

OK, fine, so what does this have to do with testing? I turn again to Ravitch:

Thorndike had faith in the scientific value of measurement, and he developed intelligence tests, aptitude tests, and every other kind of mental test. Only such faith, detached from any cultural values, could make possible the assumption that studies such as Latin and geometry had been decisively invalidated by laboratory experiments in which students memorized nonsense syllables or underlined meaningless letter combinations.

Because I believe that most of my readers will see the prima facie folly of Thorndike’s approach I won’t spend a great deal of time on the refutation (that isn’t really my point anyway, which I’ll come to shortly). But let me include Ravitch’s reference to Pedro Orata, who exposed Thorndike’s theories in his doctoral dissertation. This highlights some crucial points:

Orata… contended that Thorndike’s experiments had been profoundly misleading; that the efforts to replicate them had been inconclusive; that they tested only “mechanical habits,” which were of little value; and that Thorndike’s theory supported an apprenticeship system, not a democratic system of education. Orata pointed out that psychologists who had trained students to understand “meanings, concepts, and principles or generalizations” had demonstrated considerable transfer of training. When students understood what they were learning, why they were learning, and why it had implications ouside the classroom, they were likely to transfer what they had learned to new situations. Transfer of training occurs, Orata pointed out, when teachers make it a goal of instruction.

Thorndike’s experiments had been focused too narrowly on habit formation and drill, Orata complained, excluding any role for logical thinking and concept formation. His emphasis on the specialized nature of mental functions had made no provision for “disinterested study, for the acquisition of knowledge for its own sake,” or for gauging the ways in which studies of literature, science, and the arts taught importnat intangibles such as open-mindedness and appreciation of other cultures.

No, when you don’t value knowledge apart from its utility, I don’t suppose you would make provision for “knowledge for its own sake.” And yet, to this day, curricula still base their pedagogy on Thorndike’s careless, disrespectful quasi-science, probably because it gave power to people who develop abstract and rather arbitrary measures of students’ development. 

Freedom is rooted in the notion of ideas. The man who cannot see the truth of principles cannot make up his own mind. The man who cannot transfer learning from one domain to another cannot function on his own. Thorndike developed the psychological underpinnings of an education for slaves.  Wilson and Hoke affirmed the application of this slave’s training to measuring arithmetic.


2 Responses

  1. “A Mathematician’s Lament” is a funny, powerful, provocative condemnation of current K-12 slave math. In it, Paul Lockhart claims that math, the art of discovering beautiful patterns in shapes and numbers, not only is not taught in most contemporary schools, but the natural desire for it is completely killed.

    Even better news: Lockhart is coming out with a book showing how he thinks it should be done! Keep an eye out for it.

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