Look at what a lot of things there are to learn — pure science, the only purity there is. You can learn astronomy in a lifetime, natural history in three, literature in six. And then after you have exhausted a milliard lifetimes in biology and medicine and theocriticism and geography and history and economics, why, you can start to make a cart wheel out of appropriate wood, or spend fifty years learning to begin to learn to beat your opponent at fencing. After that you can start again on mathematics, until it is time to learn to plough.

—

Merlin, in T. H. White’sThe Sword in the Stone(1938), XXI.

I should say a little bit about this attempt to formulate an educational version of the infamous Iron Triangle of project management. I like interdisciplinary work; it’s where I spent most of my research career, and the first course I ever designed was an attempt to introduce some techniques of mathematical modelling through their applications in geoscience. However, as the years have gone by and I’ve been exposed not just to the failures of my own attempts in this direction but to the gallons of well-meaning tosh poured out in commendation of interdisciplinary education, I’ve become a reluctant sceptic. This is an attempt to explain why.

Most of the calls for “education fit for the twenty-first century” and similar slogans seem to want three things at once. Education should be flexible, so that learners have freedom to choose as many options and as many routes through the material as possible; it should not be regimented by prescribed curricula or — horror of horrors — prescribed assessments. Education should be deep, so that learners don’t merely learn disconnected facts but learn a way of thinking about a subject that equips them to assimilate new information and to apply underlying principles to new problems. And education should be interdisciplinary, equipping learners to make connections across “artificial” subject barriers and to apply their knowledge to complex problems such as climate change which cross the territories of many disciplines. I can’t honestly argue with any of these aspirations, and in the long run it may be possible for some learners to fulfil them all. But in the context of the finite time and finite resources available in a school, college, or university education, I fear it’s necessary to pick no more than two.

Suppose we want the education we provide to be both deep and interdisciplinary. Depth will require that learners understand the structure of each discipline: without that intellectual structure, a subject is not a discipline but a vaguely thematic scrapbook. Interdisciplinarity, meanwhile, will require that learners do this for more than one discipline, and also learn how to connect ideas between their disciplines. It’s clear that learning a single subject systematically places constraints on what one can learn when; if this now has to be synchronised with a second subject the constraints clearly become stronger; and with every further subject that’s added the more complex becomes the task of designing a meaningful syllabus. As the interdisciplinarity goes up, the choice necessarily diminishes.

The popular way to square this circle seems to be to quietly sacrifice depth and to provide an education that is avowedly flexible and interdisciplinary. So, for example, maths is taught in an “interdisciplinary” context by following the requirements of another subject — engineering, biology, economics — and when a mathematical idea is required the relevant piece of maths is called like a subroutine by the application. The result is that each individual piece of maths is disconnected from the others, and frequently that the machinery available to explain why a method works is unavailable. The learner does not acquire an interdisciplinary education, because the maths taught is without discipline; at best she acquires that parody known as “maths for X”, and at worst a collection of ritual observances that serve only to make mathematics more alien and inaccessible than it was to start with. In an extreme case, the flexibility of the education is such that the learner’s principal subject is also dismembered, and she ends up, in the words of the old jibe, illiterate in two languages.

Finally, suppose that we want the education we provide to be deep and flexible. This is hard enough to achieve for a highly structured subject like mathematics, but there are some options. Certain content — basic set theory, calculus, linear algebra — must remain at the roots, but beyond this there are opportunities for the learner to select and pursue one branch rather than another, following the internal logic of each subdiscipline. This seems, in fact, to be the most reliable route to genuine interdisciplinarity: once one has served one’s time in mathematics, one can go back and start over with another discipline, doing one’s best to learn it from the bottom up and calling the mathematical subroutines as they’re required — not now from the Big Book of Mathematical Incantations, but from a genuine understanding of their meaning. But heaven help the learner who tries to take a short cut: who reaches out from his branch of the mathematical tree to clutch at a swaying branch in a different tree, not realising that to cross the gap he has a laborious climb down and out along another limb, and who inevitably misses his hold and plummets to the forest floor.

Next time you hear or read the call for the mythical twenty-first-century education that will bring together the three sides of the triangle, ask which one we’re supposed to begin with, and go no further until you have a sensible answer.

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