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Paper text:
introductory - level electricity and magnetism ( e&m ) has been investigated since the early 80 s ( see references in @xcite ) . yet , research at the upper - division level is relatively new .
recently , the university of colorado developed the colorado upper - division electrostatics ( cue ) diagnostic.@xcite one of the primary purposes of the cue is to `` serve as a comparative instrument to assess upper - division e&m courses . ''
@xcite    the cue@xcite is designed in a pre / post format .
the optional 20-minute pre - test contains 7 out of the 17 post cue questions which junior - level students might reasonably be expected to be able to solve based on their introductory course experience .
the post - test is designed to be given at the end of the first upper - division semester in a single 50-minute lecture .
the cue contains open - ended questions where students do not actually solve the given problems . instead , the instructions for the first half of the post - test are as follows :    _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ for each of the following , give a brief outline of the easiest method that you would use to solve the problem .
methods used in this class include but are not limited to : direct integration , ampere s law , superposition , gauss law , method of images , separation of variables , and multipole expansion .
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _    , with an off - center spherical cavity carved out of it .
find e ( or v ) at point p , a distance 4r from the sphere.''@xcite ]    .grading rubric for cue question 5 .
reproduced from the cue assessment grading rubric.@xcite [ cols= " < , < , < " , ]     the first thing to note is that of the relevant responses , only 3% of cu students used a potential approach ( 9% of correct answers ) , in contrast to 11% of osu students ( 33% of correct answers ) .
even more striking is the difference in the explicit use of the word `` superposition . ''
of all relevant answers ( combining a , b , c , d ) , @xmath0 of cu students explicitly used the term `` superposition , '' compared to the same percentage of osu students who did * not * use this term .
this pattern is also evident in the correct responses ( a and b only ) . of all correct answers
( combining a and b ) , @xmath1 of osu students * did not * explicitly use the term `` superposition , '' compared to 82% of cu students who * did * use this term .    in order to look more closely at the issue of
_ what _ is being superposed , we also did a comparison without considering the use of the word `` superposition '' or distinguishing between electric field and potential approaches .
these results are presented in fig .
[ fig : q5data - all ] , which groups all correct categories ( a and b ) and all incorrect or ambiguous categories ( c and d ) .
the overall results are comparable for both universities .
it was surprising to us that in both schools only @xmath2 of all students took a clearly correct ( electric or potential field ) approach to this problem ( @xmath3 of relevant responses ) .
if we look only at relevant answers , in almost @xmath4 of cases students were either unclear about what they wanted to add / superimpose or were clearly talking about adding charges .
in most e&m i courses , students begin with the electric field approach , and only after they master this concept do they move on to the potential approach . as a consequence ,
the electric field approach is an intuitive and natural way for those students to tackle problems .
this might explain why so few cu students tried to solve this problem using potentials , compared to osu students , who are introduced to potential before electric field .
this is a question we are currently exploring.@xcite    regarding the difference in explicit use of the word `` superposition '' , the cu course materials,@xcite which include lecture notes , clicker questions , tutorials , _ etc .
_ , seem to strongly emphasize the term `` superposition . ''
for example , in both the instructor and student manuals for the first tutorial , one can find the following note :    _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ a common hw and exam problem asks for the e - field caused by a charged disc .
hint : a disc is the sum of many rings . did someone say `` superposition '' ? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _    this emphasis is not similarly apparent in the paradigms materials.@xcite    additionally , as one might expect at the institution that developed the cue , one can see the impact of this test in the reformed course materials , such as clicker questions that are similar to questions on the cue , in whole or in part .
this interaction between the development of the course materials and the development of the assessment is not unexpected , but it is important to consider when extending the assessment beyond the original institution .
two of the stated goals of the cue are to `` serve as a comparative instrument to assess upper - division e&m courses '' and to help `` education researchers to learn more about specific areas where upper - level students are struggling.''@xcite using the question on the superposition principle as an example , we identify two ways in which the cue is not fulfilling these goals as well as it could using the current rubric .
the emphasis in the rubric on the terminology of `` superposition '' and lack of inclusion of a potential approach represent a potential bias toward the traditional subject order and emphasis that obscures interesting differences between approaches .
even more striking is the lack of information the current rubric provides about an important area where students seem to be struggling , independent of approach .
both osu and cu have made major reforms designed to help students understand superposition , though in different ways . yet , despite these reforms , more than 40% at each school do not recognize the need for superposition on this problem and of those that do , almost 70% do not clearly identify what they are superposing .
the categorization we propose here allows one to identify how a teaching scheme may impact responses and even more importantly , illuminates an important issue about student understanding of superposition that is obscured in the original rubric .
we suggest that a similar reexamination of the rest of the cue might provide additional examples where insight on student understanding would broaden the impact of the cue as a tool for assessing upper - division e&m courses .
the university of colorado is currently working on a multiple - choice version of the cue .
this provides an excellent opportunity for just such a re - analysis .
a recent interview with two osu undergraduates suggests that the issues raised in this paper are still of concern with the multiple - choice version of the cue .
supported in part by nsf due 1023120 .
we would like to thank steve pollock , rachel pepper and bethany wilcox for conversations about the design and grading of the cue and for sharing some of the cu test data .
while introductory electricity and magnetism ( e&m ) has been investigated for decades , research at the upper - division is relatively new . 
 the university of colorado has developed the colorado upper - division electrostatics ( cue ) diagnostic to test students understanding of the content of the first semester of an upper - division e&m course . 
 while the questions on the cue cover many learning goals in an appropriate manner , we believe the rubric for the cue is particularly aligned to the topics and methods of teaching at the university of colorado . 
 we suggest that changes to the rubric would allow for better assessment of a wider range of teaching schemes . as an example 
 , we highlight one problem from the cue involving the superposition principle . using data from both oregon state university and the university of colorado 
 , we discuss the limitations of the current rubric , compare results using a different analysis scheme , and discuss the implications for assessing students understanding .    
 address = department of physics , oregon state university , corvallis , or 97331    address = department of physics , oregon state university , corvallis , or 97331    address = department of physics , oregon state university , corvallis , or 97331