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fubarobfusco comments on Why do people commit mathematical mistakes? What are the mechanisms behind them? - Less Wrong
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Comments (37)
"Sloppiness" just means "tendency to make errors that you later notice", doesn't it?
This doesn't seem to actually be an explanation, just a relabeling.
As someone who's often struggled with this, I'd disagree. "I listened to the lecture but I just can't understand how this works" is a different category of math mistake than "I added 36 and 9 and got 43." (I made this mistake on a test recently). I think math mistakes in schools break down to two categories:
Not understanding the concepts (or understanding them as magic, and blindly applying rules even where they don't fit).
Making stupid arithmetic mistakes (which seems to come from going too quickly or being tired or distracted).
More like not bothering to actively think about how to optimize reliability of problem-solving, as opposed to thinking about how to solve the problem. "Try harder" or "be more careful" is advice of very limited power, while there are many creative ways of ensuring reliability of results (for any given problem) that are much more powerful.
"Be more careful" is meta-advice, most people don't actually start trying to be careful until they recognize the need. Worse, and I don't understand why, but they often need to be reminded of it again in different situations, that is the need to be careful or to pay close attention seems to be context dependent.
+1 for admitting a mistake.
No, sloppiness (or carelessness, if you prefer) is a particular category of mistakes resulting in not paying enough attention to what you are doing while you are doing it. Either because you are distracted or are rushing to get done.
The latter is particularly common with homework that you are not interested in doing in the first place, the worst thing about it is that like many behaviors it can become habitual, and you start doing it even when the result is important to you.