The submitter of this mistake reports that the student is a “high flyer.”
- What is this student’s confusion?
- Why made this mistake so tempting? After all, if a student just doesn’t understand “slope” there are a million things that they could do wrong. Why this one?
Thanks to Jeff de Varona for the submission. Go check out his blog and follow him on twitter.
4 replies on “Slippery Slope”
Ya, that question is a bit unatural – I don’t like it. The x-values in the table are going “backwards” (decreasing), so looking at the y-values you tend to think there is negative slope. The kid probably noticed the decreasing y-values and had negative slope in their head from the start. I would not be concerned about this mistake.
I would hesitate to pass it off as an unnatural question because the learner made the same mistake on the first problem which was not “backwards” (a bit difficult to see).
Interesting. Didn’t notice that the first question was incorrect as well. Now I am not so sure that the student isn’t using a method that requires the points or the table to be “in order” but doesn’t realize they must be “in order”.
For question #1 were the points given in the order (20,17) followed by (-16, 7)? I am guessing they were, in which case it is a similar issue. In any event, the student wrote 17 – 7, and was probably thinking of the y-value decreasing from 17 to 7 so negative slope.
I am not surprised that this is a stronger student. This sort of error comes from not blindly following a formula, but actually thinking about what would make sense (though the thinking is faulty). I suspect only a short conversation is needed for this student to realize why their method is useful, but not quite correct.
I don’t think that there’s anything wrong with the question. That’s an unnaturalness that the student should be able to handle.