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Enhancing Student Meaning-Making of Threshold Concepts via Computation: The Case of Mohr’s Circle

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2017 ASEE Annual Conference & Exposition


Columbus, Ohio

Publication Date

June 24, 2017

Start Date

June 24, 2017

End Date

June 28, 2017

Conference Session

Mechanics, Music, Meaning, and Mohr

Tagged Division

Civil Engineering

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Paper Authors


Hayden William Fennell Purdue Polytechnic Institute Orcid 16x16

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Hayden Fennell is a Ph.D. student in the department of Computer and Information Technology at Purdue University. He holds an M.S.E. degree in Materials Science and Engineering from Johns Hopkins University and a B.S. in Mechanical Engineering from the University of South Carolina.

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Genisson Silva Coutinho Instituto Federal de Educação, Ciência e Tecnologia da Bahia

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Genisson Silva Coutinho is a Ph.D. student at the School of Engineering Education at Purdue University. He is a CAPES grantee and also professor in the Department of Mechanical and Materials Technology at the Instituto Federal de Educação, Ciência e Tecnologia da Bahia. He is a mechanical engineer and holds a Bachelor's degree in law and a Master's degree in mechanical engineering. He has been teaching at different levels, from the first year of technical high school to the final year of mechatronic engineering course, since 1995. He also has considerable experience in the design and implementation of mechatronic and production engineering courses. His non-academic career is centered on product development and manufacturing processes.

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Alejandra J. Magana Purdue University, West Lafayette Orcid 16x16

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Alejandra Magana is an Associate Professor in the Department of Computer and Information Technology and an affiliated faculty at the School of Engineering Education at Purdue University. She holds a B.E. in Information Systems, a M.S. in Technology, both from Tec de Monterrey; and a M.S. in Educational Technology and a Ph.D. in Engineering Education from Purdue University. Her research is focused on identifying how model-based cognition in STEM can be better supported by means of expert technological and computing tools such as cyber-physical systems,visualizations and modeling and simulation tools.

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David Restrepo Purdue University


Pablo D. Zavattieri Purdue University

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Dr. Pablo Zavattieri is an Associate Professor of Civil Engineering and University Faculty Scholar at Purdue University. Zavattieri received his BS/MS degrees in Nuclear Engineering from the Balseiro Institute, in Argentina and PhD in Aeronautics and Astronautics Engineering. From 2001 to 2009, he worked at the General Motors Research and Development Center as a staff researcher, where he led research activities in the general areas of computational mechanics, smart and biomimetic materials. His current research lies at the interface between mechanics and materials engineering. His engineering and scientific curiosity has focused on the fundamental aspects of how Nature uses elegant and efficient ways to make remarkable and more sustainable materials. He has contributed to the area of biomimetic materials by investigating the structure-function relationship of naturally-occurring high-performance materials at multiple length-scales, combining state-of-the-art computational techniques and experiments to characterize the properties.

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Stress, strain, and the relationship between the two are foundational concepts within mechanics of materials. However, because these phenomena are complex and are often not directly observable, students often have trouble internalizing the concepts in consistently applicable ways (Brown & Montfort, 2013). Mohr’s circle diagrams are often used as an important tool for visually representing the relationship between stresses and strains within a material. Indeed, Mohr’s Circle has been identified as a “threshold concept” in engineering: a critical concept that integrates multiple important modes of thinking within a discipline (Meyer & Land, 2003; Quinlan et al., 2012). However, because these threshold concepts are often complex and difficult to learn, they require careful teaching approaches to ensure that students are able to combine ideas and navigate the complexity effectively. Computational tools are sometimes employed to help teach or illustrate the Mohr’s circle technique through computer simulation, but these simulations often use a “configuring approach” to computational thinking, in which students alter input parameters of the system and the program outputs the resulting diagram (Carbonell, Romero, Martínez, & Flórez, 2013; Lee, Ryu, & Park, 2014; Osueke & Onokwai, 2015). This study presents a method for simultaneously teaching Mohr’s circle diagram concepts and computational literacy through a “programming approach” in which students are asked to construct, operate, and interpret results from a computational simulation. The research question is: How can we effectively scaffold students’ computational thinking to make meaning of Mohr’s Circle diagrams following a “programming approach?”

This study pulls from data collected from students in an undergraduate mechanics of materials course at large, Midwestern university. Specific participants include 15 students who chose to participate in an optional assignment to determine the durability of support columns under various loads at a hypothetical sports stadium. The participating students used MATLAB to construct a computational model that would calculate and construct Mohr’s Circle diagrams for given inputs. The students then used this model to analyze hypothetical strain gauge data provided in the assignment to determine whether or not individual support columns in a section of seating were at risk of failure. Projects were then graded using a rubric that considered both the computational and disciplinary elements of the assignment to identify how effectively students engaged in the overall process.

Initial results show that students who scored lower on the project tended to struggle more in the results and discussion sections, possibly indicating difficulty in making connections between the computational, mathematical, and physical models. Interestingly, lower performing students also tended to struggle in the abstract/summary section, further suggesting that these students may have struggled to make meaningful connections between the various representations of the system.

This study is relevant because computational literacy and modeling and simulation skills have been identified as important qualities of engineers in the modern workplace (American Society for Engineering Education, 2013). However, finding ways to effectively incorporate the teaching of these skills into existing engineering curriculum is an ongoing challenge. This study provides a framework for future research on implementing computational literacy oriented learning experiences in civil, mechanical, and materials engineering coursework.

Fennell, H. W., & Coutinho, G. S., & Magana, A. J., & Restrepo, D., & Zavattieri, P. D. (2017, June), Enhancing Student Meaning-Making of Threshold Concepts via Computation: The Case of Mohr’s Circle Paper presented at 2017 ASEE Annual Conference & Exposition, Columbus, Ohio. 10.18260/1-2--28279

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