What does the student understand, and what doesn’t she?

Say something intelligent in the comments, and then head over to James Cleveland’s place, for the submission is his.

  • Grant Hillebrand

    Closing the line between the two ‘9’s had me foxed for a moment, but looking at the tally data, I realised that this seems to be essentially the standard confusion between count of things (frequency) and the value of what was counted. As I science teacher, I think it is a close relative of the confusion between dependent and independent variables.

    But closing the polygon is a new level of confusion!

  • Sidebar to scanner: Might want to blot out the name in future.

    As to the understanding… wow. Uh… let’s start with the problems:
    -Doesn’t seem to understand scale. Numbers on the horizontal are not equally spaced – and yet student felt the need to add in more lines for 19 and 20! Numbers on the vertical are not equally spaced, starts big then tries to jam them in together at the top.
    -Doesn’t seem to understand histograms represent a total. Q specifically says there are 30 readings, yet the frequencies total 32. (Or possibly understands this, but didn’t check and/or wasn’t sure how to fix it based on the fact that their intervals overlapped.)
    -Doesn’t seem to understand histograms use bars, not points and lines.
    -Doesn’t seem to understand range. Jumped right into intervals by 10s, despite the lowest data at 41 and highest at 67. Should probably go with bins of size 5, or even 9 bins of size 3 or something.
    -They’ve also mixed up “tally” and “frequency”, but that’s pretty minor.

    On the other hand:
    -Understands that graphs should start at zero. Apparently to the exclusion of all else, as even the intervals started at zero, despite that being an odd temperature for April. Yay for a non-deceptive graph, but a breakpoint after the zero mark would be a good next step.
    -Understands that histograms involve frequency on the vertical axis. Regrettably, they then made the vertical scale based on the DATA, and put the frequency scale horizontally. (Did they maybe think they were doing a line graph? The lines, and the fact that “April” is mentioned makes me wonder, though they didn’t track to 30 days. Personally, I hate how line graphs force the variable onto the vertical so that time can track horizontally.)

    Where to go from here:
    -Graph breakpoints after zero, and scale. (The triangle doesn’t even look isosceles, and should – yeah, it’s not supposed to be there at all, but there’s bigger issues.)
    -Advise student to rotate head ninety degrees (to fix frequency issue – also check on understanding of line graphs), and then visualize the points as the tops of bars. Possibly connect “triangles” to the normal distribution, depending on the context of the unit.

  • I initially thought, this is clearly a white flag, indicating surrender. But then I remembered that the marshmallow challenge data is also presented “sideways”, and excel allows people to use horizontal bar charts, so I think it’s not as bad as my initial reaction. In fact, the student may have “learned ” this somewhere else.
    The student understood that 9 and 9 should be at the same level, and 14 is bigger.
    I would definitely start by putting the data into either Excel or a graphing calculator. See what the computer gives us, and then compare it to what we have. Look at labeling the charts – not a number on every line, there’s not room.
    I am pleased that the student was able to choose intervals, even if they were unsure what to do with items that appeared in both intervals.

  • The student’s frequency table reminds me of Tufts on the Challenger explosion. Well, not Tufts, but Tufts’ lesson.

  • Susan

    It seems as if the student first needs to understand what a frequency table is and how it works. For instance, not just implying that you cannot have overlapping intervals, but rather show and explain why you cannot have overlapping intervals. What might help is if the students were given a practice problem where intervals overlapped. I feel like if the problem of a frequency table was addressed then that may help them better understand how it can translate into a histogram.