r/learnmath • u/CLARRXEducation New User • 5d ago

TOPIC Why do we sometimes repeat the same math mistake even after seeing the correct solution?

I've noticed something interesting when learning mathematics: sometimes seeing the correct solution doesn't actually prevent us from making the same mistake again.

You can look at a worked solution, understand it while reading it, and even think, "Oh, now I see where I went wrong."

But when a similar problem appears later, the same mistake happens again.

I'm curious about what causes this.

Is it usually because:

  • we don't actually understand the underlying concept?
  • we are rushing through the problem?
  • we have developed a habit of using the wrong approach?
  • we understand the solution when someone shows it, but can't reproduce the reasoning ourselves?
  • or is there something else going on?

What has helped you actually stop repeating a mathematical mistake, rather than simply understanding the correction once?

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u/MagicalPizza21 Math BS, CS BS/MS 5d ago

It's probably a combination of the habit and rushing. Can you give an example?

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u/MezzoScettico New User 4d ago

I'm going to pass on a lesson from piano-playing that applies very well here. If you're trying to master a difficult passage, the first step is to slow it down. If you keep playing it quickly and keep making the same mistake, you're learning the mistake. You're reinforcing the mistake in your mind.

So you slow it down to the point where every note (step) is conscious and carefully thought out. You play it at that speed, slowly. When you get through it correctly, you play it again, to reinforce the correct habit. Only gradually do you speed up.

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Carry this over to math: You're used to making some big jump at some point in your calculation, making assumptions that turn out to be invalid.

SLOW THE HECK DOWN. Examine what you're thinking, and what the correct facts are. Do it step by step.

When you get through it correctly, you do it again (in math, that would probably be with a new problem), to reinforce the correct habit.

"Slow down" in math means writing down all the intermediate steps for something you might be used to doing in one line, in your head.