# A Common Source of Student Mistakes

by Justin Skycak on

Many students who pattern-match will tend to prefer solutions requiring fewer and simpler operations, especially if those solutions yield ballpark-reasonable results.

Cross-posted from here.

## General Framing

Many students who pattern-match (as opposed to reasoning from first principles) will tend to prefer solutions requiring fewer and simpler operations, especially if those solutions are

• "directionally correct" in the sense that they make a quantity increase or decrease as expected, and
• "order-of-magnitude correct" in the sense that the final result is on a sensible order of magnitude compared to expectations.

It’s essentially the result of applying Occam’s razor in the case when common sense has granted you some significant but imperfect level of predictive ability. (This might also be characterized as the principle of least effort.)

## Examples of Predicted Mistakes

Here are some examples of mistakes that would be predicted by this framing in the context of percents.

If the price is $\$500$after a$20\%$discount, then what was the original price? Well, the original price was obviously higher, and the simplest way to get a sensibly higher number using the quantities given in the problem is to just add$20\%$of$\$500$ to the original price.

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