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## 17 June 2011

### Graphs in laboratory -- a rubric

The 2010 AP Physics B exam, question 2, provides a typical lab-based question involving graphical analysis of data.  Students were asked to graph a small set of volume-vs.-mass data on the axes provided; the density of the oil used in the experiment was then determined by the inverse of the graph's slope.

It's instructive to look at the portion of the rubric (look at pages 5 and 6) relating just to the graph.  Graphical analysis is an important skill, one evaluated in our classes and tested on the AP exam.  But an equally necessary skill is that of creating and presenting a graph in the first place.  You might think that merely making a graph is child's play compared to understanding the graph's meaning, but even strong students don't usually do a good job presenting graphs until they've practiced many times.

Part of the students' issue is that they perceive the graph creation process as drudgerous busy work.  "I've got the data my teacher told me to take right here in a table.  Why do I need to bother making this graph?  I'll do it because my teacher is making me, but it's stupid."  And they make the graph as quickly and sloppily as they can.

Well, the creation and presentation of a graph was worth 4 of 15 points on AP Physics B 2010 #2.  Maybe significant credit -- or loss of credit -- can convince students to make graphs properly.  It's instructive to look at how those points were awarded.  We can see and communicate to our classes the elements of a graph that college professors, the AP exam, and we as high school physics teachers are looking for.

Point #1:  axes.  Were the axes of the graph labeled properly, with units?  On this particular problem, the axes were pre-labeled, but the units had to be included.  On a lab in class, I ask the students to use the axes to communicate in words the quantity measured, along with its units.

Point #2:  scale.  The scale must be linear (i.e. the space between gridlines must always represent the same value); the scale should allow the plotted points to take up most of the grid.  On 2010 B2, the standard for credit was that the scale must allow the data to take up more than 1/4 of the grid area.  I'm more stringent in my class, requiring the use of more than 1/2 the grid area.

Point #3:  plot The points must be plotted correctly and visibly, such that the measurements could be correctly extracted from the graph.  Earning this point is usually a matter of attention to detail, but part of experimental physics is attention to detail.

Point #4:  best-fit.  A best-fit line must be straight, meaning drawn with a straight-edge.  It must never deliberately connect point-to-point.  It must not be forced through the origin.  (That's the most common mistake here.)  It should reasonably represent the trend in the data.

However you grade your students' graphs, in lab and on tests, the elements in this rubric can provide a guideline for what's important.  Train your students to check each of these elements before turning in a graph.  Perhaps even make them redo a graph that is substantially missing one of these elements.

Point is, a scientist would never dream of presenting for publication a graph that doesn't meet each of these four standards.  Your students shouldn't, either.

GCJ

1. Really good point, you can also set part of your lab rubric based off of experiment questions dealing with the following

Draw a diagram of the experimental setup (2005 question 4, 2006 question 2)

Showing explicitly how the equations are used to determine the experimental value (a lot of the experiment questions deal with this)

2. There is something very wrong with Point 4.

If the model you are fitting is m = c v, with only one free variable c, then the line should be forced through 0. Fitting m = a v + b is incorrect, as that is not the model being fitted. Just because that is the best straight line for the data does not make it the correct model to fit!

The underlying question determines what sort of curve to fit. If you are just trying to determine the density (and not questioning whether mass is directly proportional to volume), then only fits that go through 0 should be accepted.

Also, it is actually extremely common as a scientist to use log scales or other non-linear scales rather than linear scales (though for this particular problem, linear scales are the most appropriate).

3. The original question is from the 2010 AP Physics B exam. I can't post it here because the College Board's lawyers would hunt me down. But the original question begins by deriving the formula relating displaced volume and mass... which gives a function with a nonzero y-intercept. That's why the best fit should not be forced through the origin here.

As for log scales, you're right that scientists commonly use them. However, since I've never seen such a graph on either AP exam, I don't bother teaching their use except occasionally to my research course.

GCJ
GCJ