The submitter of this mistake reports that the student is a “high flyer.”

  1. What is this student’s confusion?
  2. 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.

  • mr bombastic

    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).

      • mr bombastic

        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.