Too Much of A Good Thing

Greg Ashman:

If more guidance makes minimally guided approaches more effective then why not use a fully guided approach? Won’t that be still more effective? It is an argument that plays out again in the book and one that offers little comfort to proponents of open-ended problem solving in high school maths classes.

But, Jordan Ellenberg:

The difference between the two pictures is the difference between linearity and nonlinearity, one of the central distinctions in mathematics…Mitchell’s reasoning is an example of false linearity—he’s assuming, without coming right out and saying so, that the course of prosperity is described by the line segment in the first picture, in which case Sweden stripping down its social infrastructure means we should do the same.

But as long as you believe there’s such a thing as too much welfare state and such a thing as too little, you know the linear picture is wrong. Some principle more complicated than “More government bad, less government good” is in effect. The generals who consulted Abraham Wald faced the same kind of situation: too little armor meant planes got shot down, too much meant the planes couldn’t fly. It’s not a question of whether adding more armor is good or bad; it could be either, depending on how heavily armored the planes are to start with. If there’s an optimal answer, it’s somewhere in the middle, and deviating from it in either direction is bad news.

Also, John Sweller:

That is not to say that there are no disadvantages to the use of worked examples. A lack of training with genuine problem-solving tasks may have negative effects on learners’ motivation. A heavy use of worked examples can provide learners with stereotyped solution patterns that may inhibit the generation of new, creative solutions to problems.

Greg’s argument is, “If a bit is good, isn’t a lot better?” But this sort of falsely linear thinking isn’t compelling, no matter what you think about direct instruction.



3 thoughts on “Too Much of A Good Thing

  1. It is not the case that my argument is based upon a ‘false linearity’. There is plenty of evidence that fully guided approaches are highly effective. What’s needed is some evidence that inquiry or problem solving approaches offer anything that fully guided instruction does not offer. Otherwise, the fact that adding more guidance into these methods makes them more effective can be attributed to this additional guidance making these methods more like fully guided instruction.


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