For common multiple-choice assessments, we can investigate progress in student understanding by creating simple transition matrices that identify the percentage of students who select each possible pre-/post-test answer combination on each question of a diagnostic exam such as the Force Concept Inventory. In order to create a transition matrix, we first rank answer choices from worst to best using item response curves. This allows us to determine changes in understanding of concepts and misconceptions even when students do not get the correct answer on the post-test. Our work outlines the utility of transition matrices and the availability of a new tool for adoption by high school and college level physics teachers who use a common assessment. We then construct transition probabilities matrices and find that students who chose an incorrect answer to a question on the pre-test are equally likely to choose the correct answer on the post-test regardless of which wrong answer she or he selected on the pre-test.