Method and Matter

One complaint about current education is that it puts skills before facts. The nub of this distinction, as I see it, is the distinction between processes and results. Another way to express the complaint is to distinguish between method and matter. Here the underlying distinction is broader, since it is between processes and objects, where the latter includes results but other things as well.

Both distinctions make good sense. But the first one can be misleading because it is narrow. Clearly there is a virtue in teaching students to master a systematic processes for reaching conclusions, rather than teaching them to memorise conclusions that others have reached. But there are things that are not skills or facts, and which are also valuable.

I trust that the term “matter” has quite a lot of intuitive content. Think “subject-matter” and you are close enough. Roughly, it is the stuff that students apply their methods to. Only once the method has been fully applied will results appear – call this resulting stuff the end matter.

Here are some reasons why students should be taught matter, so defined, as well as method.

Methods are usually only applicable to certain classes of matter. Knowing these classes, and knowing how to match them up with the right methods, is an important part of the learning process. The methods of solving simultaneous equations are not much use for solving differential equations.

Is this a trivial thing, this process of using knowledge of matter to make methods work? Once we have learnt the methods for solving simultaneous and differential equations, do we really need an extra lesson to tell us how to apply them to the right sort of matter? Sort of. I guess knowledge of matter tends to be smuggled in with knowledge of method. Because of this, it would be hard to neglect matter even if we never thought about teaching it. But it is worth making the point, in case of situations (which I can’t think of right now) where the marriage between the two kinds of learning is not so tight.

End matter can also be useful as an examplar. One way to learn how to do something is to look at the end result and work backwards. This works partly because it is not always clear at the start what one wants to achieve (what does it mean to “solve this equation for x”? Showing a solution is a good way to answer this question). It works also because the end result usually contains information about its genesis (look closely at a finished building and you can get some idea of how they built).

I don’t recommend that students check the answers to every maths question before solving them. As a general method, this is close to useless. But as a method for learning how and why the right method works, it is quite useful.

Learning matter includes learning about the basic constituents of a subject, and how they differ from the basic constituents of another subject. In philosophy, questions about what is are at least as important as questions about how we know. Why not think the same of education?

One reason why not is that ontology is not very useful. If we know how to get the right results, and we know why our method works, what’s the use in learning more about the things we applied our method to? Well, perhaps there is not much use, in an instrumental sense. But if this kind of usefulness is our aim, why not forget about justification as well? The reason one would teach students why a method works (and not just how to apply it) is to enrich their understanding. This seems like a good reason to teach ontology as well.

Lastly, methods would not act at all if there were nothing to act upon. Sure, it is important for a History student to learn the general skill of writing essays. But they can’t write an essays at all without first learning something about History. Methods cannot be applied in every direction all at once from the beginning (one can’t expect a fourteen-year old to learn everything about an historical period from primary sources; some facts need to be taken on trust).

Of course, often it will be appropriate to teach matter in a methodical way. We don’t want just to tell students that maths is made up of such-and-such a collection of basic parts. We want to illuminate the process by which we came to possess this information, as for any other bit of information. But recognising that matter is worth knowing about is also an important step.