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Building Bridges Between Mathematics and Engineering: Identifying Modeling Practices Through Differential Equations and Simulation

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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

Mathematics Division Technical Session 3

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Page Count


Page Numbers

26.302.1 - 26.302.20



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Paper Authors


Ruth Rodríguez-Gallegos Tecnologico de Monterrey (ITESM)

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Ruth Rodríguez-Gallegos is a Research Professor in the National Graduate School of Humanities and Social Sciences at the Tecnológico de Monterrey since August 2014. Ruth Rodríguez-Gallegos had worked as an Associated Professor in the Mathematics Department in the same institute, Monterrey Campus since 2007 until 2014. She is a Math Education Researcher and Member of the National Researcher System and of the Mexican Committee of Educational Researchers. She is the President of the Executive Committee and Member of the Network of Centers for Research in Mathematics Education (2014-2016). Since 2009, she has coordinated the faculty academy of differential equations in the Mathematics Department (ITESM Campus Monterrey). She is a thesis advisor and professor in the graduate programs of Education and Educational Technology and in the PhD program in Education at ITESM’s Virtual University School of Education Her interests are the teaching and learning of mathematics for future engineers through modeling and technological applications and the construction of a bridge between the discipline of mathematics education and the community of engineering education.

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Rafael Ernesto Bourguet-Diaz Tecnologico de Monterrey (ITESM)

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BSIE minor in electronics (1983), MSEE (1994), and PhD AI (2003). Assistant Professor at Tecnologico de Monterrey, Department of Industrial and Systems Engineering. Research interest on: (a) knowledge re-utilization in corporate using System Dynamics and Systems methodologies, and (b) on hybrid environments for learning and teaching Mathematics and Systems Thinking.

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Building bridges between mathematics and engineering: identifyingmodeling practices through Differential Equations and SimulationThis paper aims to show the results of an innovative design of a DifferentialEquations course through modeling and computer simulation. This course wasfirst implemented in a private university in the northeast of Mexico in 2010. Sincethen, it has been upgraded every school term. This course aims at helpingstudents better understand the application of this mathematical object in differentareas, especially those of a physical and/or social nature. The study presented isanalyzed from a mixed research paradigm (qualitative and quantitative).This paper is divided in three parts. First, it will consider the qualitative approachthat leads students to identify key aspects of modeling, aspects that are of highinterest for future engineers. The qualitative approach includes interviews withexperts of different engineering fields, observations in specialization coursessuch as Electric Circuits; Control Theory, Mass Balance, and Dynamics Systems;analysis of textbooks, technologies and languages used; and academicdiscussions with experts.The second part will deal with the discussion and the collaborative design ofmodeling activities done by engineers and DE teachers. These have led tointroduce a series of activities that ask the students to model the reality aroundthem or the reality they suppose will eventually become a part of their everydaylives at the workplace. This should be done taking into account two things: thekey ideas of the DE mathematical aspect, and above all, the modeling practicesof the 21st century engineer.Finally, in the third part, it has been considered to show the results of aquestionnaire developed within a qualitative/quantitative paradigm frame. Thisquestionnaire has been administered over a period of one year to engineeringstudents enrolled in DE courses. This seeks to validate the contribution of thisapproach to teaching DE courses through modeling and simulating from theengineering point of view. The results are evidence of the positive contribution ofthis course design in regards to the student’s perception on how useful theseactivities are in his understanding of the basic content and above all the use ofthis knowledge in his future professional life.  

Rodríguez-Gallegos, R., & Bourguet-Diaz, R. E. (2015, June), Building Bridges Between Mathematics and Engineering: Identifying Modeling Practices Through Differential Equations and Simulation Paper presented at 2015 ASEE Annual Conference & Exposition, Seattle, Washington. 10.18260/p.23641

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