How do you teach students to use simple scales for graphs?

From a physics teacher message board:

This topic recently came up on a Facebook group: Some students when plotting graphs will choose an axis scale that uses every line-division, but in turn makes the scale difficult to use and read when plotting points and calculating slopes, etc.

I agreed with most responses that say the student deserves full credit. But I also agree that the scaling makes the graph difficult to use when plotting points and calculating slopes. I always tell my students to select a scale that uses at least 50% of each axis AND is easy to use for plotting points and reading values. However, I have struggled to teaching students HOW to do this. I would appreciate any help or suggestions of exercises or teaching strategies that can reliably help students choose good scales that are easy to use and that work for a variety of graph paper types.

These recommended scaling instructions are exactly what I give my students.  Using 50% of the available grid space on each axis earns full credit for every AP physics rubric I've ever seen.  As for getting students to actually use simple and appropriate scales... as with so much of physics teaching, I think we have to let students mess up, then explain the better approach when the context for that advice is exactly right.

It doesn't matter what I say before we start a lab - no one is listening then.  Nor is anyone listening when we have finished an experiment and are ready to move on.  Just as when teaching Newton's Third Law, there's no One Weird Trick for perfect comprehension.  Rather, the best you can do is fight a year-long war of attrition.  Each time just one more student gets the idea of scaling experimental graphs, rejoice; then hope another student comes on board next week.  

I usually have the conversation about scaling at two key moments in the course of an experiment.  And I design the general approach to full-on graphical analysis laboratory exercises so these two moments are likely to happen.

(1) Data collection: All data is required to go on a graph as it is collected, though it's fine to first take one or two data points for the purpose of estimating the overall scale.  And yes, I have to holler and cajole and (figuratively) poke students until they actually follow this requirement.  But as I'm moving from group to group checking their graphs, I'll often see a graph as you describe - with each line-division representing 3.67 m/s, or 0.13 N, or something similarly silly.  Such a group is generally behind others, perhaps a bit frustrated, possibly arguing with one another.  That means they're ready to listen.  

"Hey, can you tell me what x and y axis values this dot (I point at the graph randomly) represents?  Yeah, it's tough to figure out, isn't it.  But what if you rescaled so that instead of the graph going up exactly to 0.82 N at the top, the top line were 1.0 N, or 1.2 N, or 1.25 N or something like that that's easy to deal with?  Take a look here (where I do a simple rescale on a draft piece of paper, and graph a data point easily)."  Generally at least someone in the group says "oh!" and does the rescale.  

"But Greg, only that one student understood - the other group members will make the same mistake again."  Yup, very likely.  My responses are, (1) see above about the war of attrition; and, 

(2) Analysis:  I only ask for one experimental graph per group.  If the fastest grapher (or the only person in the group who is any good at all at graphing) makes this initial graph, that's fine.  But the next part of the experiment generally requires students to linearize their graph, and then to use the slope of a best-fit line to determine an unknown quantity.  And for the linearization and analysis, each student must make their own graph individually.  They all take pictures of their group's data table, but then they graph the data by themselves.  Collaboration according to the five-foot rule is acceptable, which explicitly means students can't just copy other students' work.  They can talk, they can look, but they have to *do* the scaling and the plotting by themselves.

Students come and show me each step in their analysis, including the linearized graph.  When someone shows me a graph with inefficient scaling, the time is right to have a conversation.  Usually, if the scale is awkward, the data isn't quite plotted correctly; and even if the data is technically correct, they can't answer the "what x and y values does this dot represent?" question quickly.  Either way, I explain how an easy-to-read scale avoids these issues, I suggest a simpler scale... and I ask the student to redo the graph.

Here's where my approach differs significantly from what you're probably seeing on Facebook.  You're right that on an AP exam, a graph done correctly but with suboptimal scaling will earn full credit.  Thing is, my laboratory is emphatically NOT an AP exam.  It's a studio, a place for practice, collaboration, and learning.  The point of plotting data points isn't to earn points.  

Generally, a student sighs, goes back and replots their graph, and finds the new graph much easier.  Aha!  I can rejoice over this student's progress.  Sometimes they got help from a friend to do the rescale.  That's fine, too - because they have to physically create the graph by themselves, they also see for themselves the elegance and utility of a simple scale.  

Very occasionally, a student might try to argue that they don't need to rescale.  I say only very occasionally, because I'm not taking off points, I'm not docking a grade, I'm just asking the student to redo the graph, the same way an art teacher might ask their student to mount their painting to a more attractive frame before the big art show.  The only thing this student has lost is some time.  So such a student generally gets a sympathetic smile from me along with a firm, "I'm sorry you have to regraph, I know it's a pain in the butt, but it's gotta be done."  

(And if a student were to become hostile, the problem is beyond one of whether the graph is acceptable or not.  Passive-aggressive or actual-aggressive argument-for-the-sake-of-argument is unacceptable in the classroom, whether we're talking about scaling graphs, using free body diagrams correctly, or starting a justification with a fact of physics.  Culture building from day one of the class means that generally students listen rather than lawyer up.) 

This student who feels like they have "wasted" their time with a badly-scaled graph usually doesn't make that mistake again!  Lost time matters to students in a way that grades do not.  I cannot recall having this conversation about proper graph scaling in the analysis section of a lab twice in a year with the same student.   

Because my students have been graphing large data sets by hand all year, when the AP exam asks them to graph 5 or 6 data points, they practically laugh at the simplicity.  The large amount of in-class time spent on experimental graphs pays off in that moment.