Identification of Common Student Errors in Solving Fundamental Mechanics Problems

Sophomore-level mechanics courses, by nature, focus on developing students’ problem solving abilities. Students are challenged with numerous typical problems in which they must interpret given information, determine what is required as an answer, set up a structured solution methodology, and execute that methodology without error. In these types of fundamental problems, there is always “one right answer”. Experience has shown that a large percentage of students do not obtain that correct answer when solving a problem on a quiz or examination. In some cases, students are unable to set up a problem correctly due to major conceptual issues. In other cases, students make more execution type errors such as using a wrong moment arm, making sign errors in equilibrium equations, and using incorrect forces or areas. Finally, in many cases students demonstrate a clear understanding of concepts but fail to obtain the correct answer due to mistakes related to mathematics (algebra, trigonometry, etc.), general carelessness (calculator entry errors or transcribing errors), or the use of proper units (conversion errors, weight/mass errors, failing to state units, etc.). For the past five years faculty in an introductory mechanics course combining elements of statics and mechanics of solids at Villanova University, and in a previous course that covered statics alone, have methodically collected data on the mistakes students make in solving these types of problems. For every quiz and exam problem, a detailed gradesheet was used that identifies every error made by every student. Over five years, this grading approach has been used on over 150 assigned quiz and examination problems and errors have been identified on over 8000 student problem submissions. Using the data collected, this paper summarizes the errors students made in solving common mechanics problems, including the topics of equivalent force systems, 2-D rigid body equilibrium, truss analysis, and centroids of composite areas. Typical problems are presented and the grading and data collection methodology is outlined in detail. The types of errors made by students are grouped for discussion into those that are major conceptual, those that are minor execution type, and those that are non-conceptual and unrelated to mechanics altogether. Conclusions are drawn and potential uses for the data in improving teaching and student learning are also discussed. Importance and Innovation in Introductory Mechanics Courses Many engineering educators believe that the first introduction to engineering mechanics, statics at most universities, is of paramount importance in a student’s journey to becoming an engineer. The course serves as the foundation for numerous other courses (mechanics of solids, materials, dynamics, fluid mechanics, structural analysis, transportation, etc.), but perhaps more importantly this course is the first introduction to developing rigorous problem solving skills. P ge 25709.2 Recent work has focused on evaluation of problem solving skills in statics courses and areas of difficulty (Newcomer and Steif , Newcomer ). Additionally, evaluations of conceptual understanding and problem solving skills have been studied and concept inventories have been developed and pre-tests and multiple choice questions analyzed to highlight typical student shortcomings (Douglas et al. , Steif and Dantzler , Steif and Hanson ). Follow up studies focused on improving problem solving performance by assessing pre-post tests and written and verbal protocols (Steif, et al. ). It was shown that problem solving could improve if students develop strategies for recognizing when and how to apply techniques. There has been significant educational effort in recent years focused on implementing new techniques to the teaching of engineering mechanics. This work has included combining traditional statics topics in a heavily design oriented backdrop (Russell , Condoor , Klosky et al. ), focusing on application to real artifacts (Seif and Dollar ), and combining statics concepts with those from mechanics of solids and machine design (Chaphalkar ). Recent efforts document successes with utilizing an inverted classroom (Papadopoulos et al.) and other innovative pedagogies. The goal of improving educational outcomes via a highly interactive classroom has been shown to be successful in formats where lectures and laboratories are combined and problem-based active learning techniques are implemented (O’Neill, et al., Gross, et al., Glynn, et al.). The innovations in topic delivery, facilitation of active and diverse learning environments, and the evaluation of problem solving skills are all positive steps to producing better engineers. Of course problem solving skills are essential to successfully navigating an engineering curriculum and becoming a good engineer. While faculty assist students in developing these skills it is essential that we not lose sight that the goal is not the skill development or concept understanding. The ultimate goal is that the engineers we are charged to educate consistently produce the correct answer. It is important to develop an assessment method that provides insights into why students do not produce the correct answer. This methodology should be able to identify deficiencies in problem solving skills as well as execution. Unfortunately this type of methodology requires rigorous assessment of real problems (divorced from the multiple-choice, easy to grade world that testing agencies and many educators prefer).