The Myth of Curriculum (Part 3)
Planting the tree of knowledge
This is the third post in a three-part series. Part 1 can be found here. Part 2 can be found here.
Education is not the filling of a pail, but the lighting of a fire. -Plutarch
Here’s where we stand: On the one hand, complex skills are too fluid and undistillable to really be taught; they must be acquired through firsthand experience.
On the other hand, an expert guide is helpful—if not critical—in acquiring any complex skill. The challenge is that the guide must simultaneously impart categories to organize new knowledge and promote familiarity in or with that body of knowledge. I refer to this chicken-and-egg as the vertical and horizontal axes of instruction.
With this context in mind, I think we’re finally ready to tackle the practical question at the heart of this series: What should a good curriculum actually look like?
My humble opinion: A good curriculum is a vertical structure masquerading as a horizontal one.
The Ladder to Nowhere
Let me be clear about what I’m not claiming: that every curriculum needs to good. (By “good,” I mean something like “designed to promote long-term mastery of a complex skill.”)
For purely instrumental learning—say, to pass an exam; to get up-to-speed on HR policies; to understand how to operate a new appliance—a utilitarian approach is perfectly appropriate. You don’t need a guru to iteratively, lovingly reveal to you the inner workings of your microwave; you just need your pizza bites not to be frozen.
What I’m claiming is that if the goal is to instill long-term success in some complex area, there are dangers to an overly structured curriculum.
We’ve all encountered this kind of instruction before—in long, dry textbooks, or mandatory corporate trainings. The material is impeccably ordered (each segment or chapter includes a summary of key points; perhaps there is a little progress bar marching along the bottom of the screen). Certainly there is a time and place for this kind of signposting in any good class, but in excess it’s formulaic and boring.
Moreover, in their presentation of finite lessons, these vertical structures risk reducing to a checklist that which, in reality, is actually a process of recursive improvement. (How many students have completed their schooling with the false impression that they know the scientific method or how to write an essay—as if science or writing were subjects that one could ever definitively “know”?) As investor-essayist Paul Graham describes:
Knowledge expands fractally, and from a distance its edges look smooth, but once you learn enough to get close to one, they turn out to be full of gaps…The big prize is to discover a new fractal bud. You notice a crack in the surface of knowledge, pry it open, and there's a whole world inside.
Or to return to a previous metaphor: Expertise is a menu, not a map; that menu must be continuously refined and updated in order to stay relevant.
So a good curriculum, I think, doesn’t ignore the vertical axis of instruction, but it doesn’t lead with it. It leads instead with curiosity and hands-on practice—the horizontal axis—and only later, more tactfully, reveals its grand design. This strategy is important for precisely the two reasons I covered in Parts 1 and 2 of this series:
While an explicit framework is often helpful, it is also inherently false; true understanding defies verbal expression.
For the novice, learning is mostly horizontal whether we like it or not. At the start, instructors are better off working with this “ant’s eye-view”—not forcing students to gaze at a canvas that has yet to make any sense.
The Tree-shaped Curriculum
It might seem that skilled practitioners always need a good mental model of what it is they’re doing. Maybe this is true at the highest levels of performance, but in general, people can surprisingly far through a combination of instinct and imitation, all without really understanding. As philosopher Daniel Dennett describes:
We tend to think of comprehension as being the source and guarantor of our competence. That’s why we’re down on rote learning and things like that. But rote learning is actually very powerful. And even for human beings, very often, competence precedes comprehension. If you want to really understand mathematics, you better have a flawless fluency with numbers, with counting, with addition and subtraction, multiplication and so forth. The competence comes first; comprehension is a later add on.
In this light, the goal of a good curriculum is not necessarily to impart explicit comprehension; it’s to train intuition and give students the desire to continue learning. While these may not produce much measurable impact at the end of a semester, they are the essential ingredients for deep mastery—which of course can’t be acquired in a single semester anyway.
In my current class, for example, two of students’ homework assignments are to conduct experiments with the way they read and write. (This could entail, among other things, varying the duration, location, or time of day when they work.) The purpose of this exercise is not for students to identify their optimal mode of productivity—which, of course, is a decades-long pursuit. Rather, it’s simply to stress that they can design and alter their work environment along many different parameters: to suggest a wider menu of options.
If I had to describe this approach in conceptual terms, I would say that the ideal curriculum shape is a tree.
By “tree,” I don’t mean a vertical taxonomy like the one below, with discrete branches and independent paths:
I mean something more like this—a sprawling, organic structure, whose leaves rub up against those on abutting branches, and whose root network is as extensive as the part you can see above the ground:
There is a logic to this structure, and if you wanted you could even create a simplified model of the above image in the mode of the first diagram. But that model would be only a loose guide to the shape of the tree—an abstraction that fails to capture the texture of its bark, the true shape of its branches etc. These subtle details are the horizontal axis of instruction.
As students move through material, they won’t perceive the vertical structure right away. But gradually, as the curriculum progresses, it will start to emerge organically and implicitly. This is far more enjoyable than having an outline handed to them. More importantly, it’s a more motivating and realistic template for future learning: Because knowledge was built from the middle-out rather than top-down, there is a sense that it could branch out infinitely in any direction—as indeed it could.1
Again, this is not to say that instructors should never zoom out to point out a larger vertical structure—just that the primary experience of learning should be of moving through the material. It’s sort of like one of those Prezi presentations (do people still use Prezi?): As a viewer, you’re aware that slides are part of a larger picture, and every once in a while the presenter may zoom out to show that picture. But most of the time you’re just flowing around within and between slides, and these slides may have multiple interdependent relationships.
Ultimately, in my own classes, I don’t want students to leave with a total sense of closure. I don’t want them to feel they’ve reached the top of a ladder. Instead, I want them to perceive some structure in the end—trunk, limbs, branches, leaves; but, more importantly, I want them to sense how these concepts can grow and bend and cross-pollinate with one another. And I want them to build this understanding on their own, as much as they can.
Coda: The Myth of Curriculum in Three Sentences
Complex skills are undistillable and therefore can’t really be taught.
They can, however, be learned—that is, with a basic framework and opportunities for students to work with or through material.
With this in mind, curriculum design is strangely simple: Pick a branch, any branch, and point them towards the sun.
In practice, I think the tree-shaped curriculum is not so different from the better-known “spiral curriculum,” whose key principles are as follows:
Cyclical: Students should return to the same topic several times throughout their school career.
Increasing Depth: Each time a student returns to the topic it should be learned at a deeper level and explore more complexity.
Prior Knowledge: A student’s prior knowledge should be utilized when a topic is returned to so that they build from their foundations rather than starting anew.
Personally, I find a tree to be a more evocative and accurate analogy for this approach than a spiral because it branches outward in multiple directions.