I recently read Paul Lockhart’s incredible essay “A Mathematician’s Lament” [PDF]. Lockhart, a mathematics teacher at Saint Ann’s School in Brooklyn, wrote the piece in 2002, but it wasn’t published until last year, on Keith Devlin’s monthly column.
“A Mathematician’s Lament” begins with the nightmares of a musician and a painter, both horrified to see their art forms turned into required curricula and stripped of all soul in the process. Some choice snippets:
In their wisdom, educators soon realize that even very young children can be given this kind of musical instruction. In fact it is considered quite shameful if oneâ??s third-grader hasnâ??t completely memorized his circle of fifths. “Iâ??ll have to get my son a music tutor. He simply wonâ??t apply himself to his music homework. He says itâ??s boring. He just sits there staring out the window, humming tunes to himself and making up silly songs.”
I was surprised to find myself in a regular school classroomâ?? no easels, no tubes of paint. “Oh we donâ??t actually apply paint until high school,” I was told by the students. “In seventh grade we mostly study colors and applicators.” They showed me a worksheet. On one side were swatches of color with blank spaces next to them. They were told to write in the names. “I like painting, one of them remarked, “they tell me what to do and I do it. Itâ??s easy!”
As you might have guessed, the author proceeds to compare these reductio ad absurdum cases with the actual instructional philosophy applied to mathematics. In the process, he argues that mathematics is an art (one of “making patterns of ideas”), and he suggests that the stripping away of the context for and discovery of ideas has suffocated the joy inherent to the practice of mathematics.
Among his examples, Lockhart describes the incredible wonder of pi as “mankindâ??s struggle with the problem of measuring curves.” Which is more interesting, he asks, applying an arbitrary formula someone asked you to memorize, or understanding the story of a fascinating and powerful problem of human history? Lockhart’s impassioned conclusion: “Weâ??re killing peopleâ??s interest in circles for god’s sake!”
There are many similarly clever turns of phrase in the essay, including the ending section, a scathing “completely honest course catalog for K-12 mathematics.” But the one that follows struck me particularly:
What other subject is routinely taught without any mention of its history, philosophy, thematic development, aesthetic criteria, and current status? What other subject shuns its primary sources—beautiful works of art by some of the most creative minds in history—in favor of third-rate textbook bastardizations?
The question is rhetorical, but I found myself immediately shouting: “Computer Science!” I’ve felt this for some time, but Lockhart’s essay helps polish a particular gripe central to my critique of the way computing sees itself. Mathematics hedges between pure and applied domains, but computing fully embraces the fantasy of progress at all turns. Nowhere else is this more evident than in the conceit that the field is a “science,” and all the baggage that comes therewith. Computer science assumes that its role and purpose is the creation and refinement of new systems, which are meant not only to replace but also to destroy the past.
My Georgia Tech colleague Mark Guzdial has devoted his career to computing education. Recently, he explained that there is no such funded research in the United States. Instead, “All computing education research projects, if funded, are funded to do something else. All computing education research in the US, then, is done on-the-side, even, on-the-sly.”
There are many reasons for this state of affairs, some of the political and organizational implications of which Guzdial teases out in his post. But I think one of the greatest challenges comes from within the discipline itself: overall, computing simply doesn’t care about the development of its ideas. It fantasizes itself as a scientific or an engineering discipline, but throws the baby out with the bathwater (even the purest of sciences acknowledges that its ideas arise from the complex flows of history).
When Guzdial asks how we might bootstrap better computing education policy and practice, his question is tactical: how can we get funding agencies to allocate a portion of their budgets to the process of teaching computing as a valuable investment. This is a fine question, and an understandable one.
But what we really need is a new strategy. A wholesale shift in the way we think about computing (among other disciplines) that would underwrite a new way to do it let alone teach it. I think the frame shift we want is one that considers computing a liberal art rather than a science.
Indeed, James Duderstadt has already suggested [PDF] that engineering be newly construed as a liberal art (I’ve written about this before). And Lockhart’s gripes about mathematics should remind us that his discipline was long considered to form half of the medieval quadrivium, a fact that some institutions have not yet forgotten (consider, for example, the contextual and historical mathematics program at St. John’s College).
St. John’s offers a fascinating model, or at least a gripping pique. It is a small liberal arts college with an unusual (and extreme) focus on great books. Compare its approach to the orthodoxy that Guzdial highlights for computing education. St. John’s does what it does not because it has secured massive amounts of federal support, but because it believed in an approach and slowly built it into a tiny empire.
Mark would know better than me, but I wouldn’t be surprised if the greatest innovation in computing education will happen at liberal arts colleges rather than research universities or technical institutes, since the latter are so committed to a stale orthodoxy: funding begets research begets progress.
So, perhaps Mark is asking the wrong question. Maybe the issue is not how we can get funding so that people can do research to validate their educational methods, but how we can get people to want to exercise those methods without the funding and the validation in the first place. This exigency becomes particularly strong if validation only supports a broken orthodoxy rather than offering a path away from it.