|Cardinal Newman, no doubt thinking liberally|
It is an acquired illumination, it is a habit, a personal possession, and an inward endowment. And this is the reason, why it is more correct, as well as more usual, to speak of a University as a place of education, than of instruction, though, when knowledge is concerned, instruction would at first sight have seemed the more appropriate word. We are instructed, for instance, in manual exercises, in the fine and useful arts, in trades, and in ways of business; for these are methods which have little or no effect upon the mind itself, are contained in rules committed to memory, to tradition, or to use, and bear upon an end external to themselves. But education is a higher word; it implies an action upon our mental nature, and the formation of a character...These distinctions between the purposes of the instructional and the higher purpose of education were echoed decades later by American reformer John Dewey and later still by Brazilian philosopher Paulo Freire, who called for a movement of critical or emancipationist pedagogy as opposed to what he called the "banking model of education." (Freire, however, had invested in his theories of education an essential ethos of social justice, which Newman would have rejected.)
Critics of instructional or banking education have been speaking out more often as the debate about education in America has become hopelessly linked to employment. Gary Gutting, professor of philosophy at Notre Dame, offered this rumination just last month in a New York Times column entitled "Why Do I Teach":
I’ve concluded that the goal of most college courses should not be knowledge but engaging in certain intellectual exercises. For the last few years I’ve had the privilege of teaching a seminar to first-year Honors students.... The goal of the course is simply that they have had close encounters with some great writing.Gregory Currie, philosophy professor at the University of Nottingham, complicated the value of studying literature further by casting doubt that reading gives us anything more than appreciation of aesthetic merit. He is not convinced that literature brings us greater moral sophistication, an argument with shades of Newman's view of liberal education in it. (I am more inclined to side with Martha Nussbaum, whom Currie takes on in his column.)
What’s the value of such encounters? They make students vividly aware of new possibilities for intellectual and aesthetic fulfillment—pleasure, to give its proper name. They may not enjoy every book we read, but they enjoy some of them and learn that—and how—this sort of thing (Greek philosophy, modernist literature) can be enjoyable. They may never again exploit the possibility, but it remains part of their lives, something that may start to bud again when they see a review of a new translation of Homer or a biography of T. S. Eliot, or when “Tartuffe” or “The Seagull” in playing at a local theater.
All of which is interesting stuff to fuel the imagination of humanists, but what of math and science classes? Can we parse the distinction between instruction and education there? Freire's influence brought about the radical math movement, a method which attempts to imbue issues of social justice and the mechanisms for social change into the pedagogy. In that system, mathematics becomes a tool for an ethical end—what Freire desired and what Newman rejected—but how the math gets learned is still up for debate. More recently, a progressive push in education has tried to replace the traditional style of learning math. Alice Crary and W. Stephen Wilson describe the "math wars" like so:
At stake in the math wars is the value of a “reform” strategy for teaching math that, over the past 25 years, has taken American schools by storm. Today the emphasis of most math instruction is on — to use the new lingo — numerical reasoning. This is in contrast with a more traditional focus on understanding and mastery of the most efficient mathematical algorithms.Crary and Wilson's point is that this is a false debate: that progressives make a mistake in imagining that internalizing and applying algorithms is non-creative instructional learning, and proponents of the traditional methods of teaching math (who they are more sympathetic to) must teach the reasoning behind the algorithms if students are to properly understand math. In defense of their argument, they invoke the work of philosopher Ludwig Wittgenstein, by any measure one of the great minds and human figures of the 20th century, who suggested that algorithmic thinking was more than well-oiled brain mechanics. Crary and Wilson remind us that these algorithms "are also the most elegant and powerful methods for specific operations." My sense is that their argument breaks down a bit in this parenthetical:
(Reformists sometimes try to claim as their own the idea that good math instruction shows students why, and not just that, algorithms work. This is an excellent pedagogical precept, but it is not the invention of fans of reform math. Although every decade has its bad textbooks, anyone who takes the time to look at a range of math books from the 1960s, 70s or 80s will see that it is a myth that traditional math programs routinely overlooked the importance of thoughtful pedagogy and taught by rote.)
Judging classroom pedagogy, particularly the pedagogy of math, by looking at a range of textbooks strikes me as a mistake. In my experience, math textbooks are overwhelmingly used as banks of problems to practice. It is uncommon for teachers to assign conceptual readings in math books, and even less common that students do these readings with any purpose beyond extraction of the essential formulas to solve their homework problems. Undoubtedly there have been great mathematics teachers in the older tradition, but what matters is how they presented or unpacked the concepts in class. Still, I am sympathetic to Crary and Wilson's larger point, which is a worthwhile critique of progressives:
There is a moral here for progressive education that reaches beyond the case of math. Even if we sympathize with progressivists in wanting schools to foster independence of mind, we shouldn’t assume that it is obvious how best to do this. Original thought ranges over many different domains, and it imposes divergent demands as it does so. Just as there is good reason to believe that in biology and history such thought requires significant factual knowledge, there is good reason to believe that in mathematics it requires understanding of and facility with the standard algorithms. Indeed there is also good reason to believe that when we examine further areas of discourse we will come across yet further complexities. The upshot is that it would be naïve to assume that we can somehow promote original thinking in specific areas simply by calling for subject-related creative reasoning. If we are to be good progressivists, we cannot be shy about calling for rigorous discipline and training.Here, the authors return us to Newman, whose caution against instructional learning was never to deny the foundations of "rigorous discipline and training." In Discourse VI of The Idea of a University on the subject of "Knowledge Viewed in Relation to Learning," Newman gave us this pedagogical imperative:
It is plain, first, that the communication of knowledge certainly is either a condition or the means of that sense of enlargement or enlightenment, of which at this day we hear so much in certain quarters: this cannot be denied; but next, it is equally plain, that such communication is not the whole of the process. The enlargement consists, not merely in the passive reception into the mind of a number of ideas unknown to it, but in the mind's energetic and simultaneous action upon and towards and among those new ideas, which are rushing in upon it. It is the action of a formative power, reducing to order and meaning the matter of our acquirements; it is a making the objects of our knowledge subjectively our own, or, to use a familiar word, it is a digestion of what we receive, into the substance of our previous state of thought; and without this no enlargement is said to follow. There is no enlargement, unless there be a comparison of ideas one with another, as they come before the mind, and a systematizing of them. We feel our minds to be growing and expanding then, when we not only learn, but refer what we learn to what we know already. It is not the mere addition to our knowledge that is the illumination; but the locomotion, the movement onwards, of that mental centre, to which both what we know, and what we are learning, the accumulating mass of our acquirements, gravitates.