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Closing the Gap Between Physics and Calculus: Use of Models in an Integrated Course

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2015 ASEE Annual Conference & Exposition


Seattle, Washington

Publication Date

June 14, 2015

Start Date

June 14, 2015

End Date

June 17, 2015





Conference Session

Engineering Physics & Physics Division Technical Session 2

Tagged Division

Engineering Physics & Physics

Tagged Topic


Page Count


Page Numbers

26.353.1 - 26.353.14



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Paper Authors


Angeles Dominguez Tecnologico de Monterrey & Universidad Andrés Bello Orcid 16x16

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Angeles Dominguez is a Professor of the Department of Mathematics within the School of Engineering at the Tecnologico de Monterrey, Monterrey, Mexico, and she is currently at the University Andres Bello at Santiago, Chile, for a sabbatical period collaborating with the School of Engineering. She holds a bachelor degree in Physics Engineering from Tecnologico de Monterrey and a doctoral degree in Mathematics Education from Syracuse University, New York. Professor Dominguez is a member of the Researchers’ National System in Mexico (SNI) and currently she is the President of Red de Investigación e Innovación en Educación del Noreste de México (REDIIEN). Angeles has been a visiting researcher at Syracuse University, at the University of Texas at Austin. She teaches undergraduate courses in Mathematics and graduate courses in Education. Professor Dominguez is a thesis advisor on the master and doctoral programs on education at the Tecnologico de Monterrey. Her main research areas are: a) models and modeling, b) use of technology to improve learning and c) evaluation. In addition, Professor Dominguez is the coordinator of the conTIgo T3 Latin America group that focuses on an effective and efficient use of the Texas Instrument technology in the mathematics and science classroom.

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Jorge Eugenio de la Garza Becerra Tecnologico de Monterrey (ITESM)

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Jorge de la Garza is a Lecturer of the Physics Department within the School of Engineering at the Tecnologico de Monterrey, Monterrey, Mexico. He holds a bachelor degree in Physics Engineering and a doctoral degree in Education both from Tecnologico de Monterrey. Dr. de la Garza has been recognized by the government as a member of the Researchers’ National System in Mexico (SNI). He also actively participates in the different initiatives of the University mainly those related to interdisciplinary approach of teaching and learning, looking to close the gap between how knowledge is created and how students learn. His main research areas are a) models and modeling, b) learning environments and c) problem solving.

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Closing the gap between physics and calculus: Teaching innovations in an integrated courseThis study builds into bridging the gap between mathematics and physics by teaching anintegrated first-year college course of calculus and physics using Modeling Instruction andmodels and modeling perspective. This innovation involves redesigning the course content,combining teaching strategies, reshaping the classroom setting, and the use of technology.In this study 37 first-year engineering students were enrolled in the integrated physics andcalculus course. The research questions are: What elements of the physical and mathematicalmodels do students use in solving a complex real problem? How do students’ performancescompare in the final exam of this course to students in non-integrated physics and calculuscourses? To answer the first question, students worked collaboratively on a project that involvedthe analysis of an extreme bungee jump. Students’ performance in this project revealed: a)students’ integration of physical and mathematical models, b) robustness of students’ models andc) different representation used the solution. To answer the second research question, this studycompares students’ performance on the final exam as well as the results of concept inventorytests, for physics and for mathematics.As conclusions we can state that the more robust models the students’ constructed, the morehelpful they are in their problem solving. It was observed that students constructed physicalmodels that lead them to mathematical models that required numerical methods. The solving ofthe numerical methods using technology is part of the natural integration of physics, math andtechnology. Also, based on the final exam grades, students responded as well as students’enrolled in non-integrated courses indicating that the redesigned curriculum satisfies the contentrequirements of the physics and calculus courses. The faculty involved in this project stronglybelieves that the design of well-structured activities and the effective use of technology elicit theconnection between physics and mathematics.

Dominguez, A., & de la Garza Becerra, J. E. (2015, June), Closing the Gap Between Physics and Calculus: Use of Models in an Integrated Course Paper presented at 2015 ASEE Annual Conference & Exposition, Seattle, Washington. 10.18260/p.23692

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