2026 ASEE Annual Conference & Exposition

How do Students Explain Their Errors in Free Body Diagrams?

Presented at Mechanics Division (MECHS) Technical Session 1

The ability to draw a Free Body Diagram (FBD) of a mechanical system or subsystem is a core skill and essential element of a mechanics problem-solving procedure. Although much attention has been devoted to FBDs in the engineering education literature, surprisingly few studies have solicited written or verbal explanations exclusively focused on expository drawing of FBDs. Most existing studies include drawing FBDs as part of a larger problem-solving process (typically including equations of equilibrium) or focus on student explanations regarding their answers to closed-form concept questions.

As part of their teaching, the authors administer a short test on drawing FBDs of multiple body systems relatively early in the semester, requiring the use of the law of action and reaction. Conversations with students regarding their answers have led to insights that appear to be under-reported in the literature. In particular, based on discussions with students, the authors have noticed a pattern in which students draw extraneous forces (i.e., forces that are not actually present) on a FBD because they believe such forces are necessary to balance other forces that appear elsewhere, either on the given body or on a neighboring body.

To investigate the prevalence of this pattern, the authors ask this question: How do students explain their choice to draw an extraneous force on a FBD? To address this question, the authors will first provide a literature review documenting instances where such explanations have been recorded in prior research studies. Then, a study will be conducted to tabulate error types on the FBD test questions that were completed during the Fall 2025 semester. This will be followed by a mixed quantitative/qualitative survey in which students will be polled to explain the errors that they committed on their FBD tests. Some questions will be in closed form, to help classify expected error types; other questions will be open ended and will be coded for themes. Together, the authors are teaching 200 students at two different institutions, leading to the expectation of a meaningful number of participants.

The broader implications of this work are to deepen understanding about the student thought process when drawing FBDs. Do students struggle to focus on the immediate body or subsystem under study, instinctively thinking instead about how the given body or subsystem is affected by neighboring factors? Could this thought process constitute not so much an ‘error’ but a phenomenological primitive that suggests an opportunity to understand the principle of equilibrium? How might understanding these thought patterns influence the manner in which FBDs are introduced and taught?

Authors

Dr. Christopher Papadopoulos http://orcid.org/0000-0002-0259-7264 University of Puerto Rico, Mayaguez Campus [biography]

Christopher Papadopoulos, PhD, is Professor of Engineering Sciences and Materials at the University of Puerto Rico, Mayagüez (UPRM). He earned B.S. degrees in Civil Engineering and in Mathematics from Carnegie Mellon University (1993) and a Ph.D. in Theoretical and Applied Mechanics at Cornell University (1999). At UPRM he is a member of the steering committee of the Sustainability Engineering initiative, which seeks to develop new Minor, Bachelors, Masters, and professional certificate programs. In this regard he served as PI of A New Paradigm for Sustainability Engineering: A Transdisciplinary, Learner-Centered, and Diversity-Focused Approach, (de)funded by the NSF HSI program and he is a member of the Engineering for One Planet Network. He also co-chaired the 18th International Conference on Nonconventional Materials and Technologies (NOCMAT2022). Papadopoulos brings a systems thinking, transdisciplinary, circular-economic/cradle-to-cradle mindset to sustainability innovation, curricular design, and pedagogy, and personal lifestyle, actively collaborating with several faculty, students, and sustainability-focused organizations in Puerto Rico and in the US.
Dr. Jean Carlos Batista Abreu http://orcid.org/0000-0001-5380-7682 Elizabethtown College [biography]

Jean Batista Abreu earned his Ph.D. and M.S.E. at the Johns Hopkins University, M.S. at the University of Puerto Rico, and B.S.E. with Honors at the Pontificia Universidad Católica Madre y Maestra, all in Civil Engineering. Prior to joining Elizabethtown College, he served as a Visiting Assistant Professor of Mechanical and Civil Engineering at Bucknell University, and worked as a Structural Engineer at Acero Estrella.
Dr. Aidsa I. Santiago-Roman http://orcid.org/0000-0003-4136-9990 University of Puerto Rico, Mayaguez Campus [biography]

Dr. Aidsa I. Santiago-Román is a Professor and Former Chair in the Engineering Sciences and Materials (CIIM) Department at the University of Puerto Rico, Mayagüez Campus (UPRM). Dr. Santiago earned a BS and MS in Industrial Engineering from UPRM and Ph.D. in Engineering Education from Purdue University. Dr. Santiago has over 20 years of experience in academia and has been successful in obtaining funding and publishing for various research projects. She's also the founder and advisor of the first ASEE student chapter in Puerto Rico at UPRM.

Her research interests include investigating students' understanding of difficult concepts in engineering sciences, especially for underrepresented populations (Hispanic students). She has studied the effectiveness engineering concept inventories (Statics Concept Inventory - CATS and the Thermal and Transport Concept Inventory - TTCI) for diagnostic assessment and cultural differences among bilingual students. She has also contributed to the training and development of faculty in developing and evaluating various engineering curriculum and courses at UPRM, applying the outcome-based educational framework.

She has also incorporated theories on social cognitive career choices and student attrition mitigation to investigate the effectiveness of institutional interventions in increasing the retention and academic success of talented engineering students from economically disadvantaged families. She's also involved in a project that explores the relationship between the institutional policies at UPRM and faculty and graduate students' motivation to create good relationships between advisors and advisees.

Note

The full paper will be available to logged in and registered conference attendees once the conference starts on June 21, 2026, and to all visitors after the conference ends on June 24, 2026

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