System, O My Darling

Following on from this little thing about method and matter, here is a little thing about system. A fine thing, system, and worth talking about. From one direction, it looks like the value of system is unique to matter: system is all about taking objects and arranging them neatly. But it is important to method as well. Methods are not just processes, but systematic processes. And the best part about teaching matter is ontology, the part where students learn how a subject is made up of a system of parts. System is not a bangle on the wrist of learning, but the fibre in her cloth, the leather in her shoes. Praise her!

Anyway, system makes things easier to remember, for the same reason that it is easier to remember Pascal’s triangle than phone numbers. But it also confers understanding. Indeed, arguably the pursuit of understanding just is the attempt to bring more system to our awareness of the world.

I guess some disciplines are more amenable than others to a systematic approach to teaching. Mathematics, that powerhouse of systematicity, should surely be taught so as to bring its neatness to the fore. Currently students are taught two different ways of solving simultaneous equations (substitution and elimination) when really they are the same thing. Subtraction is analogous to division, but you would not know it from text books. A lot school-level of algebra is based on a handful of basic rules (associative, distributive, commutative etc.), but this tends to get lost. Rediscover this, and school maths would look more like University maths. And maths in general would at once become easier and more interesting.

One senses that English might not work so well under a systematic tutor. Is there really a method for writing a poem? And would we want one? But still there are parts of that subject that make more sense when put in an ordered way. Like any other subject, it contains concepts and statements that can be illuminated by their interrelations. A simile is not something completely different from a metaphor, and pedagogy usually reflects this. A symbol is not completely different from a metaphor either, nor from an epitome or an image. And the following words all mean much the same thing: trait, characteristic, feature, quality, attribute. Pedagogy should reflect these things too.

A plausible objection to all this system is that it makes everything too rigid. It would be to deny the variety of mathematics, the way in which there are often many different paths to the right answer. And it would suck all the creativity out of the study of literature.

But there is no need for system to suppress the profuseness of mathematics. For most students the choice is usually between using a consistent and transparent method, and using either the wrong method or no method at all. And for those students who can see a variety of right methods, there is value in showing them how these are connected (eg. how geometric and algebraic methods are analogous to one-another). There is value, too, in showing them how some methods are better than others, in the sense of being more elegant or simple, or using less extraneous information (as in the case of simultaneous equations, mentioned above).

It is also wrong to conflate system with over-authoritative teaching, at least in mathematics. The fact that different aspects of any subject are richly interlinked would surely make it easier for the teacher to take a passive, guiding role in the learning process. They can point out connections and leave the student to follow them up, extrapolating from prior knowledge. How might you extend this formula to the 3D case? How might you solve a system of three equations rather than 2? Look for other ways in which negation is analogous to division. All of these are good exercises, and they rely for their success on the system that is just sitting there in all mathematics, waiting for teachers to grab it.

Almost certainly, an over-emphasis on system would indeed suck the creativity of literature. I expect it is easy to do it badly. But this is no reason not to use the system in the parts of the subject where it does exist. And it is still worth pursuing a kind of systematicity in more unruly parts of the subject. We want students to draw comparisons between different texts, to set characters alongside one another and see what we find, to look for repeated images. All of this is a move towards a more organised view of a novel or poem or whatever. (It’s just that we look along different lines in the English case: we look for similarities in respect of personality, manner, mood, instead of shape or angle).

It’s all very well going on about how system is the greatest thing since Dewey. It’s another thing to give some examples of how it could be achieved in practice. Given the right proportions of time, energy and brown bread, I will try to do this in some later posts.