For many, it is a truism that we learn from our mistakes. This leads to an approach to education which places pupils in unfamiliar territory which they have to explore for themselves. They may stumble; they may take wrong turnings, but that’s an accepted, in fact a welcomed, part of the learning process.

The intellectual territory which our pupils must explore is rugged. Many greater minds than theirs over the ages have ended up wandering down a narrow valley which turned out to be a dead end, and never getting out again. Many greater minds than theirs have fallen over cliffs as they stumbled across the terrain, without the lights to guide them, or the better paths, which later ages discovered.

It is our job as teachers to guide our pupils through this rugged terrain, as an expert guide takes uninitiated travellers over a mountain pass safely. He has the knowledge to make sure they reach the other side. He has the experience. He knows the pitfalls and the dangerous false paths that will lead to disaster.

Mistakes are not helpful for those at the beginning of the intellectual journey. Beginners need careful guidance, or they are likely to end up in all sorts of difficulties and picking up all sorts of misapprehensions. Of course, they will learn something, but it is just as likely to be the mistake as it is to be the right answer. Or maybe they will find their way over to the other side of the mountains by some miracle or slice of beginner’s luck, but they would have reached the goal more efficiently with careful guidance. And they might have done it once, but will they be able to do it again? A one-off lucky right answer is very far from secure mastery.

Direct instruction is based on this principle: the principle of getting it right. When following a direct instruction programme of study, the carefully guided, incremental path that pupils take will mean that they very rarely make mistakes, and when they do, those mistakes are quickly corrected so that they do not solidify into permanent misapprehensions.

It is also part of the principles of direct instruction that you do not begin by scaling Everest. You practice repeatedly in the foothills, then you travel to the first base camp over and over again until you know the route inside out. You need to know that route, the route which wiser and more experienced travellers mapped out, and many other similar routes to other mountain peaks before you can begin to think about planning your own mountain climbing expedition.

It’s the age-old principle of apprenticeship. You learn first by imitating the masters that have gone before you, and you need to do that for years before you can begin to work independently. Once you do begin independent work, you will not be inventing it from nothing, like the mythical Romantic genius. Your work will be based on the solid principles that have been worked out through centuries of slow, painful human progress.

Reblogged this on The Echo Chamber.

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As a general principle, what you have written here is unquestionably true — at least as I see it.

However, the devil is in the details.

I teach mathematics. One of the things my students need to know, by heart, to be able to recall instantly, is the algebraic identity, X^2 – Y^2 = (X+Y)(X-Y). They need to be able to recognize it both ways ’round, they need to be able to recognize it when ‘X’ and ‘Y’ are some other variable names, or numbers, or even complex expressions, and even when the expressions are jumbled up.

All of these ways in which this identity, in one of its forms, can turn up, need to be practiced. And they need to be practiced not just for a few days, but repeatedly, over a period of months, or the knowledge will fade away.

But what’s the best way to initially introduce the students to this identity? Is there any value in letting them mess around a bit with, say, working out (X+Y) times (X+Y), and (X-Y) times (X-Y), and getting the usual binomial expansion … and then suggesting that they be a bit experimental … hoping that they try (X+Y) times (X-Y), and seeing that the middle term cancels out.

I think that if they do this, they have a much deeper grasp of this identity, than if I just tell it to them and get them to memorize it.

But of course I have to guide them through all this, setting the right kind of thing to ‘investigate’, cutting them gently off if they start wandering down unprofitable side-roads, even helping them with the algebra if they can’t perform the multiplication.

But is this just intelligent Direct Instruction, or is it intelligent Constructivism … or what?

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Thanks for your thoughtful comments. There’s no contradiction between exploring worked examples and direct instruction. In fact, worked examples are a big part of doing worthwhile practice.

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How is it that we got away from this (direct instruction) and into the system we have now? I work in an elementary school in the U.S. see the folly of our ways on a daily basis – students with such bad handwriting that they themselves, at times, can’t read it; students being asked to write and expound on a subject when they haven’t learned and spent enough time practicing the foundational skills in order to be prepared to do such a task; students being expected to “discover” math concepts with all manner of systems which are supposed to give them greater breadth of knowledge and understanding, but in reality prove to be confusing. Thank you for this post.

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