Drs. Gary Morris and Paul Walter have a publication that appears in the March issue of The Physics Teacher titled, “Transition Matrices:  A Tool to Assess Student Learning and Improve Instruction.” Common multiple-choice diagnostics are often given to students at the beginning and end of a semester to assess how much learning has taken place.   Previous work by Dr. Morris provided a way of ranking the answer choices from worst to best.  This work constructs a 5 x 5 matrix for each question that provides the percentage of students that made each pre-/post-test selection possibility and makes it easy to determine whether students are not just moving to the correct answer but also if they are at least making some progress by moving to a better wrong answer.  This can provide valuable information for an instructor.  The authors constructed a tool to perform the analysis that is freely available to physics instructors.  The approach was applied to the Force Concept Inventory for first-semester introductory physics, but can be adopted and applied to other similar multiple-choice diagnostics where the wrong answers function as distractors.  The abstract is available at http://aapt.scitation.org/toc/pte/55/3?expanded=55.  A freely available version of the article is available on the arXiv at https://arxiv.org/abs/1703.01565.

Drs. Walter and Morris also published 2016 Physics Education Research Conference Proceedings titled, “Assessing Student Learning and Improving Instruction with Transition Matrices.”  The proceedings are freely available at http://www.compadre.org/per/perc/conference.cfm?Y=2016#PRP89.  One interesting finding in that work is that the likelihood of moving to the correct answer choice on the Force Concept Inventory was independent of which wrong answer choice was chosen on the pre-test.  Future work will investigate whether that holds true for larger data sets and various instructional approaches.