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.
Comments
jeremy hunsinger
A few years ago, Matt Kirschenbaum and I discussed a similar topic. A master of arts in software, which fits with some of your ideas here.
robin2
The idea that computing is more of an art than a science has been around for a while. E.g. Don Knuth’s choice of names for “The Art of Computer Programming” and TeX; Richard Gabriel’s suggested Master of Fine Arts in Software course.
I’m not sure what the difference between arts fine and liberal would be. I’m one of those people who thinks of programmers as more artisans than artists, and so a university degree in programming makes about as much sense to me as one in blacksmithing.
Ian Bogost
@Jeremy
Right, and that’s another path that I didn’t discuss, or maybe chose not to cover in this post: the divorce of computing education from computer science. The problem (I’m way overgeneralizing) is that the humanities have stripped much of computation from computing, which isn’t the answer either.
@robin2
Sure. But Knuth had a particular sort of aesthetics in mind within the context of engineering, one that comes down to elegance and efficiency. This is not an arts that incorporates computing (back) into the context of human knowledge and ideas more broadly. I can’t speak to Gabriel, as I’m not immediately familiar with the proposal.
As for the difference between the fine and liberal arts, the latter focuses on generalization and grounding over specificity and utility. I’ve written about this before via the frame of predictable vs unpredictable usefulness.
Mark Guzdial
Ian, can we think of a field of study where innovation in curriculum and educational practice does start from the liberal arts? Larry Cuban’s “How the Scholar Trumps the Teacher” suggests that the “funding begets research begets progress” orthodoxy you describe is inherent to the American University system. Since American Universities can now own the intellectual property resulting from that progress, which can generate more funding, the cycle is only encouraged and enforced. Even schools with a liberal arts tradition are emphasizing generating more funding and intellectual property. I don’t disagree that that cycles occurs in computer science. I just suspect that it’s prevalent across American academia.
Ian Bogost
Mark, the short answer might be “any discipline in the traditional liberal arts,” but that’s probably an oversimplification. Maybe I don’t understand your question?
Your assessment of the American university is correct of course, but only (or mostly) for R1 institutions. This is why I wondered if educational innovation of the sort you work on might be so much more likely to take hold at liberal arts colleges. I don’t know if Cuban covers this, but the operation of the liberal arts college is very different from that of the research university, and at the former funding comes from tuition and (for the private ones) managed endowment funds rather than research productivity, such that external progress/innovation and pedagogy are decoupled.
robin2
Gabriel’s proposal is described at http://www.dreamsongs.org/MFASoftware.html and http://www.dreamsongs.org/PoetryOfProgramming.html
I didn’t have the content of TAOCP in mind, and perhaps a better example would have been the UNIX aesthetic (e.g. http://theody.net/elements.html). But yes, this is all confined to the programmer’s umwelt.
Gabriel is the same, really. In Patterns of Software he says that in trying to apply Christopher Alexander’s ideas about architecture to software we must remember that it is programmers that ‘inhabit’ the software in ways end users never will. You could even say that he is typical in his appreciation of elegance: he recommends programmers read modernist poetry in order to learn lessons in brevity.
Quite apart from this ‘Gentleman Hacker’ tradition there is the Seymour Papert / Alan Kaye axis, which sounds closer in spirit to what you are talking about – concerning the potential impact of computers on people other than computing professionals. For Papert, learning to program is a wonderful intellectual adventure, inherently edifying (hence the development of Logo). For Kaye, computers has to be easy to program because it is imperative that people be the masters of the medium of their age (hence the development of DynaBook and Smalltalk).
I’m not sure how things stand with this now. The impression I have is that enthusiasm for Papert’s approach to education fizzled out, whereas Kaye seems to have suffered a paradoxical success in which his ideas were hugely influential, but only to the extent that their centre could be left behind.
Ian Bogost
I’m very interested in the aesthetics of code, and I’m familiar with Knuth and others’ perspective on the matter, but the most interesting thing about code aesthetics to me is not efficiency, but constraint (e.g. JAPH and IOCCC). I use esoteric languages like Piet and Chef in my classes as one way of getting students to see this register in addition to the elegance/efficiency/brevity register.
Thanks for sharing the links to Gabriel’s proposal. I find it intriguing in many ways, and troubled in others. For one, it is deeply disconnected with the traditions of art practice and critique that normally accompany the MFA. Still, there are some Masters degrees that are moving in this direction, and I think it’s a useful one. It’s probably not related to the subject of this post, which is more about general knowledge.
As for Papert/Kay, certainly their influence remains strong. Mark Guzdial has been strongly influenced by Kay in particular. I think one thing that Papert and Kay forget is that they got to see first-hand most of the history of modern computation. Carrying that forward is difficult. Both Logo and Smalltalk were supposed to abstract while also retaining certain core principles, but they were always meant to be starting points in a larger program (one that others, like Mark, would be obliged to carry out), not the entirety of that program.
Ian Bogost
Mark Guzdial links to two other responses to the post of his I linked, one from Alfred Thompson, and another from Leigh Ann Sudol.
Mark J. Nelson
Is it really that computing is a liberal art rather than a science? Isn’t it that the sciences, mathematics, and computing are all liberal arts? Lockhart argues that case for mathematics, as you point out. And including the sciences and mathematics among the liberal arts, and teaching them that way, is a perfectly traditional way to go about it— liberal-arts colleges have offered programs in chemistry, physics, biology, astronomy, and mathematics for centuries. Science and math even make up 3 of the 7 canonical liberal arts, and 3 1/2 if you give math or computing half-ownership of logic!
(I may be biased, having gone to a college that billed itself as a science/engineering-focused liberal arts school.)
robin2
Piet? [googles] Ooh.
The art vs science distinction should in theory be easy to draw, since it is just making vs knowing. (Then again, I’ve never read Sciences of the Artificial.)
Regarding liberal arts, I’m at a disadvantage since although I’m dimly aware of there being liberal arts colleges in America, I’ve never had any idea where they fitted in to the general scheme of things. That said, here is what Raymond Williams has to say about the word “liberal”:
[In my experience of attending an English red-brick university, you didn’t have to be terribly astute to spot the lower-middle to upper-middle class transition from computing or engineering to – say – literature or art history.]
A class distinction maps (awkwardly) onto predictable vs unpredictable usefulness – hinging on whether education is thought of as an investment which needs to provide a (dependable) return, or as a rarefied form of leisure.
Ian Bogost
Mark (N), you’re right of course. It’s not the nature of the sciences, but the approach that is the problem. Still, it’s hard to argue that the sciences themselves haven’t been swept up in the notion of research progress Mark G discusses above, although that’s perhaps less the case at Harvey Mudd.
Robin, don’t you know we don’t have class here in America? Just kidding… the issue of the liberal arts and access is a concern, one made even greater by our abysmal public secondary education. In my ideal world, liberal arts education would happen in high school, so that students could really get on with things in undergrad. Education ought to offer both predictable and unpredictable usefulness, and students shouldn’t have to choose absolutely between the two.
Jordan Magnuson
@Ian:
Thanks for this great right up. All I have to say is yes, yes, yes, yes. Yes.
Mark N.
The point that computer science (along with mathematics) ignores its primary sources in favor of third-rate textbook bastardizations, and ignores its history in favor of a myth of monotonic progress, might explain a feature that’s long puzzled me: why is computer science, of all fields, so technologically backwards when it comes to its own academic literature?
As an undergraduate, my first library-research experiences were all in my humanities classes, because of how the intro classes are taught differently. So I got used to certain technological niceties: the Philosopher’s Index electronically cross-references a large swathe of philosophy literature; and JSTOR has full-text searchable, digitized journals going back to the late 19th century.
So when I took my first computer science class that involved doing a literature review, it was a real shock to find that none of this existed. Citeseer was the closest there was to an index, and it indexed almost nothing older than 10 years. Even if I somehow found a paper from as recently as the late 1980s I wanted, in order to actually retrieve it, I had to walk to the library, request the bound volume from storage, and photocopy it. That process seemed hilariously old-fashioned in comparison.
(It probably feeds back into itself, as well.)
Annette Vee
Thanks for posting thisâ??I would very much like to see a different approach to CS education in general, too! Your colleague Mark Guzdial seems to be headed in really smart directions here, but it’s tragic what he points out: that education research isn’t valued or supported in CS.
I have been interviewing programmers for my dissertation, and interestingly, many of them have very conflicted relationships with formal CS education (caveat: the interview study is not a random, cross-section sample). Many of them have heroes like the developers of Ruby on Rails. Successful programmers seem to find a way to get emotionally involved in what they do, and syntax just doesn’t cut it. Most of them cite games for why they got into computers, outside of CS in college or high schoolâ??which means that oftentimes, it’s too late to get people really hooked if you start in college. Papert saw that, and Andrea diSessa carried out some of his ideas, too. The MIT scratch project and Carnegie Mellon’s Alice are also working on those issues of catching kids early. The liberal arts idea is a separate approach, but like the games and programming for kids approach, it also speaks to getting people more affectively involved, right? Most liberal arts disciplines begin with people very young; we all took history and literature starting in elementary school. I’d love to see that happen with programming (not computer science, exactly) as well.
David Locke
Science programs have long had BA degrees and BS degrees.
For the postmodernist, college is about getting a job. Regardless of the philosophical approach to the subject, not having a BS degree on your resume will consign you to doing something other than programming. A BA in CS would be a waste of time for most people.
If you want to be the next Tracy Kidder, great, get the BA degree. But, if you want to have a career as a programmer, get the BS degree.
Ian Bogost
David, I don’t see what the flavor of degree has to do with it; it’s the approach that matters, not the letters. For example: Georgia Tech is accredited to give BS degrees, anything we did in computing (including our Computational Media degree) would have that name.
robin2
@Mark N
I think for computing to have a myth of progress it would need to have some (inaccurate) sense of where it had been, whereas I think it is more like amnesia. I don’t think that many people would think that – with the World-Wide Web – Tim Berners-Lee improved on the ideas of Ted Nelson (or Vannevar Bush), the question just doesn’t arise.
Rapid technological change makes it difficult for traditions to build up that would make history intelligible. (The industry has economic motives for having every new product be a “disruptive technology”, another year zero.)
Whilst traditions do build up, they are relatively marginal and fragile (e.g. Lisp culture vs Unix culture vs the Windows/Java steamroller).
A big difference between computing and English Literature (say) is that there was several centuries for literary tradition to build up before it novel-reading became a university subject, making it a relatively coherent body for academia to take on. Whereas the circles of computing culture (academic computer science, the computer industry, hobbyist programmers) all came in existence more-or-less simultaneously, and all maintain relative independence.
@Annette
I don’t see that college is ‘too late’ to get interested in programming. (I’m biased: I didn’t get interested until after I left college and had a job as a programmer.)