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20 June 2011

Bad Graphs -- Common mistakes on data-graphing test questions part I: horrid best-fits

In the previous post, I discussed the rubric for an AP Physics question that required graphing data.  A number of folks requested that I show and discuss the most common mistakes on this type of question.  I should emphasize that while I am speaking in the context of grading the AP Physics exam, the graphing issues here are germane to experimental physics at any level.  Even in the most basic conceptual physics course, even in our professional level Research Physics course, appropriate graphing skills should be developed.

Don't let your students' graphs look like these.  You may laugh at some -- just the mere fact that you're reading this blog implies that your students would be less likely to make most of these mistakes.  But understand that every one of these mistakes is made FREQUENTLY on the AP exam. 

BAD GRAPH #1:  Non-linear axes
Aarrgh!  This is the most horrid of bad graphs, suggesting that this student has never graphed data in his life.  The only time I've seen it in my own class was the first year I taught, in the first lab I assigned to my regular 9th grade class.  That was an eye opener -- we stepped back and had a new lesson the next day.  On one hand, I used to think that AP students generally wouldn't make this mistake; however, having graded graphs on the actual exam, I'd now bet that one exam in twenty does this.

BAD GRAPH #2:  Dot-to-dot
At least this student has graphed data before.  Connecting data like this implies that we have theoretical or experimental support that the slope of the graph is or should be different in each region.  Since the slope of this particular graph is related to the fluid density, the implication is that the fluid density changes depending on what mass we float on the water.  Really?

BAD GRAPH #3:  Curve fudged to go through each data point
This is for the folks who have been told never to connect dot-to-dot, but who are still uncomfortable with the idea that data points indicate a trend -- they are not delivered unto us on stone tablets by the Almighty.  Some students do even more obvious fudging, making sure their curves go through the center of every point.  They are implying theoretical justification for a 6th order function modeling the data.  I remember the eye-opening I experienced when someone pointed out that if you make excel use a high enough order polynomial, you can produce a curve that will seem to fit ANY data set perfectly.  I counter this misconception not only by fiat (minus one million points for drawing a baloney curve), but also by insisting on an enormous amount of data in every experiment.  It's hard even for first-year students to justify fudging a fit through 20 data points.

It's not hard, folks -- when there is theoretical support for a linear graph, and/or the data look linear, just place the danged ruler down on the paper, align it approximately with the trend of the points, and draw.  When done right, a proper best-fit line takes much less time than any of the baloney above.

So that this post doesn't go on for pages, I'll stop here.  Tune in tomorrow for the "scaling issues" edition of BAD GRAPHS.

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