[[[[[[Harv wrote; >THEY made a silly error due to thoughtlessness at the time.
Sorry Harv, but I disagree. Eileen]]]]]
Sorry Eileen, but no one can disagree on experiences I have experienced. The story I related did, indeed, happen and the student did, indeed, admit to being thoughtless at the time.
[[[[[[[Even if students admit to making a "silly error" a teacher who is truly using student responses to assess students understanding would use this information as diagnostic to determine what mis-understanding the student has that would allow this type of error. This is obviously a student who does not understand the "concept" of division when it is stated in that way.]]]]]]
Or is this obviously just a kid who made a silly error as mentioned earlier? Math can be a bit confusing at times and an average student can very easily write that 2/8=4 when simply in a thoughtless state of mind at the time. It is not clear at all that this student does not understand the concept. High school students quite often find themselves in thoughtless states of mind and will quite often give an incorrect answer to a problem that they really know how to do. So...it may not be a misunderstanding at all, the cause of which the teacher must diagnostically assess, which created the error.
[[[[[More assessment would need to be done to see if the student understands division in other circumstances, to determine if it needs to be addressed.]]]]]
And I naturally do this when I feel the student has made the error due to a clear misunderstanding of the concept. However, I rarely do this extra assessment when, as in the cases I cited, the student admits it was just a silly error and clearly understands he/she was just being thoughtless at the time.
[[[Moving on at the point where a student is having this misunderstanding and attributing it to laziness or lack of motivation is a common response for teachers that are unaware of what they are seeing.]]]]
Again...I would only move on after the student has admitted they had been lazy or thoughtless and, in reality, know the concept. Sometimes kids (and adults) are in a "please don't fish the scare away" mode.
[[[[[Bottom line, it is inconceivable to me that students who 'could' do accurate computation would 'refuse' to do so for any reason. ]]]]]]
Who said they REFUSED doing an accurate computation??? My post clearly states that these students merely thoughtlessly erred in performing a computation (they even admitted their carelessness at the time!) I, too, doubt that a student would ever refuse to do something that they could do....but that's not what is at issue in this little mole hill that seems to be rapidly turning into a mountain for some reason.