Teaching and Training – 1

I’ve been thinking recently about the difference between teaching and training.

Some of you may be familiar with my occasional idea that there’s not really any such thing as “teaching” in the sense teachers are supposed to do: there are merely environments (and states and habits of mind) that are more or less conducive to learning.  But leaving that question in abeyance for the nonce…

There definitely is such a thing as training, and since that seems to be what many teachers do for much of their time, it might be worth thinking about when we want the one thing (teaching) and when we want the other (training).  Let’s accept a provisional definition that “training” is the repetition and internalization of an essentially algorithmic process.  The algorithm need not be explicit: one can train to do basketball lay-ups effectively, for instance, without having anything other than a good feedback process (though the training is facilitated by a good model and coach).

As most really good athletes know, it’s the automatic and internalized responses that are the hallmark of success.  If you’re going to have to think about how to hold your racket, where to start your swing, how much follow-through you need, and so on, you’re rarely going to hit a fine shot in a fierce tennis match.  Anything that can be internalized, should be in order either to free your mind to think strategy (maybe tactics) or to blank out “in the zone” where your body works at its best, free from the distraction of conscious thought.

Such training is eminently feasible in many academic areas.  Students used to spend a great deal of time learning to spell words.  Some still spend a large amount of time learning how to “solve” many kinds of problems in math courses.  It is not necessary, and perhaps arguably undesirable for the purpose at hand, to learn how languages evolve and how the history of a word may, in a language like English or French, be revealed in its spelling.  It may be counterproductive if you’re trying to get people to prepare for the math part of the SAT, for instance, to learn how to think mathematically.  Learning how to do as many kinds of problems that are likely to show up is, perhaps, a better strategy to train for the test.

It is arguable, however, the extent to which learning to score well on a math SAT test is tied to mathematical thinking.  And it is certainly not clear to me why “good schools” push all students to take math all the way through basic calculus without teaching a fair number of them much of the beauty or joy of creativity in mathematics.  It is quite possible for a student to leave even a good school without knowing how “a mathematical approach to reasoning” is applied to other than “math problems.”  It is almost likely in some places that a student may learn many interesting facts about biology, for instance, without learning how to come up with a hypothesis about something she doesn’t know, then design and carry out an experiment to test the hypothesis.

Interestingly, and perhaps it’s because most of us start talking and even reading well before we do much with numbers other than counting (and maybe grouping), English courses tend to do a better job at teaching students how to write and support their conclusions with evidence than math courses (perhaps outside of geometry?).

While every three-year-old I’ve known has an insatiable curiosity about the natural world, somehow high-school science courses tend to teach “facts” and “formulas” and “how to solve problems” as their main goals. Maybe English/Language Arts courses have a head start on other disciplines; maybe there is also a cumulative effect of more hours of ELA instruction in the younger grades.  And my experience is biased toward what used to be called middle-class households where parents (or other caregivers) read more to their children, ask them more questions, and just generally interact more with them verbally than families from lower economic groups are sometimes able to do.