# Learning of new concepts being impeded by an error in previous work

Note: I'm framing this question in terms of tutoring math since that's what I tutor most, though it applies to a wide range of subject matters.

I do a decent amount of tutoring, and this is one phenomenon I see popping up constantly, and I occasionally catch myself doing the same thing, though less often since I've become aware of it

What happens is a student learns a new concept/formula/algorithm in class and then does practice or assignment questions. They will then come up to me and ask me to check their work because the answer they are getting doesn't make sense, or doesn't line up with a known answer. Sometimes, they will even have spent hours double or triple checking their work on this new formula.

I will look over their work and confirm its correctness. I have learned to ask "Can I see the work you did to get to this point?" They then show me this work, and most of the time, there is a simple arithmetic error or oversight (and if its a misunderstanding of previous material, then its a whole other issue).

What has happened is that the assignment question involves multiple steps, the student makes a simple error in an early step, and assumes the error to be in the later steps involving the newly taught equations, and wastes hours looking for an error there.

My related questions are:

• Does this phenomenon have a name, and if so what is it?
• What are the psychological processes behind this, i.e. why does the student not double check all of the work?
• Is there any way to mitigate this behaviour besides simply being aware of it?
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Sometimes this happens to me in programming as well. I'm going to guess that this has to do with overconfidence leading to not thoroughly examining the more simple areas, but I'm interested to see what the answers are! –  Josh Gitlin Feb 28 '13 at 13:04
@JoshGitlin As a programmer as well, I can say, I certainly fall victim there too. Overconfidence is an interesting idea, and on the other side of the coin it could also be underconfidence in the new material. –  DPenner Mar 1 '13 at 17:36

There is a difference between being wrong and knowing you're wrong.

I like to think of this with the analogy of Wiley the Coyote from looney toons. He would usually try to catch the runner, and run off the cliff, but keep running for a while, and only fall when he realizes that he ran off a cliff.

The point in which your student is doing the assignments based on incorrect previous calculations is that point between coyote running off the cliff and realizing he has done so.

I'm not sure of the terminology about this phenomena, but here's my theory on why people tend to do this: Most of the students nowadays are conditioned to feel right about everything because knowing, that you are wrong feels bad, they feel like there is something wrong with them (rather then just being wrong), while the alternative, of being wrong and not knowing about it that feels exactly as being right.

This conditioning is introduced in our educational system very early and often results in not taking chances that could result in them being wrong, or (more related) in not even considering the possibility that they might be wrong at some point (when most of the time they are).

I think that the only way of fixing this is deconditioning ourselves (or your students) in this case, that being wrong is something bad. Instead, indicating being wrong as a sign of progress. I think Einstein said:

A person who never made a mistake never tried anything new.


Encouraging your students questioning even things that might be established as truth by others is the key in my opinion.

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I like that advice at the end; its certainly something I'm going to try out more. But, I'm not entirely convinced that is that they're conditioned to feel right about everything. In this scenario, they are usually well aware that they are wrong, but it is an incorrect assumption of where they went wrong that causes problems. –  DPenner Mar 1 '13 at 17:44