A Comparison of Student Misconceptions in Rotational and Rectilinear Motion

The Test of Understanding Graphics in Kinematics (TUG-K) has been modified to produce a Test of Understanding Graphics in Rotational Kinematics (TUG-R) to probe student understanding of rotational kinematics. The seven objectives of the TUG-K were modified with three questions to explore each objective resulting in a 21 question TUG-R which closely parallels the original. For many questions the modification was a simple substitution of the equivalent rotational quantity for its linear counterpart in the question stem, answers and graph-axis labels. For the remainder of the questions the modification was straightforward. For instance, references to objects moving in a straight line were replaced by references to objects spinning about a fixed axis. The TUG-R was administered to 198 students at a small, liberal arts college in New England. The use of a calculator was permitted and students were offered as much time as they wanted to complete the examination. No inducement or reward was offered to students to take the examination and it was not counted toward their grade in the class. In order to make a more direct comparison to the results of the TUG-K, the data were narrowed to consider only 93 students where the TUG-R was administered post-instruction in both linear and rotational kinematics. This group includes student instruction in a traditional, lecture-based format as well as active engagement classrooms. Approximately 80% of the students were enrolled in an algebra-based course, the remainder in a calculus-based course. Post-instruction student responses on the TUG-K and TUG-R were compared. A 2 tailed z-test was performed to assess whether or not differences in sample size can account for the differences in results between the TUG-R and TUG-K which are reported. An objective by objective, question by question analysis of the results suggests the three basic types of misconceptions noted following post-instruction analysis of the TUG-K, namely graph type confusion, slope calculation and slope vs. area confusion, continue to be exhibited at some level by students taking the TUG-R. However, significant differences were noted, with TUG-R students performing better on every question in two of the seven objectives on 8 of the 21 questions and equally well on 9 of the remaining 13. Further work will be conducted to verify that these observations and conclusions remain consistent as the testing sample is expanded across a broader spectrum of students of different levels, using different instructional techniques and at a larger cross section of institutions. Introduction Over the past few decades, the field of physics education has matured and grown. A reasonably comprehensive description of the state of the field can be found elsewhere 1 . The process of identifying misconceptions, creating curricula to address those misconceptions and then evaluating the efficacy of instruction has been applied to many areas of physics 2 , perhaps nowhere more successfully than mechanics. In that arena, many well-validated and established instruments exist, including the Mechanics Baseline Test 3 , Test of Understanding Graphics in Kinematics (TUG-K) 4 and the Force Concept Inventory 5 to name but a few. Physics educators have created a wide variety P ge 2.34.2 of research-based, pedagogically appropriate approaches and curricula including Peer Instruction 6 , Workshop Physics 7 , Real-time Physics 8 and Studio Physics 9 . But, what about circular mechanics? Arnold Aron’s observes 10 , “The kinematics of circular motion in a plane is usually glossed over very quickly because of the obvious parallelism to rectilinear motion. For students who have genuinely mastered the concepts and relations of rectilinear kinematics, this is appropriate since unnecessary repetition would waste their time.” This philosophical approach has pervasively infiltrated introductory textbooks. Whole chapters are devoted individually to the topics of velocity, acceleration, etc. while all of rotational kinematics and sometimes even dynamics are crushed into the space of a single chapter or perhaps two 11 . Remarkably little work has been done in creating instruments of evaluation 12,13 and research-based curriculum exploring rotational mechanics. Without additional evidence, it would seem a valid conjecture that any student difficulties which exist concerning rectilinear motion would continue to be carried forward, further compounded by the inherent two-dimensionality of rotation about a stationary axis adding layers of complexity to an already murky understanding of that rectilinear motion.