Innovation in the Teaching of Mathematics for Engineers through Modeling and Technology: a Mexican Experience

Ruth Rodriguez Gallegos

Download Paper | Permalink

Conference: 2013 ASEE International Forum
Location: Atlanta, Georgia
Publication Date: June 22, 2013
Start Date: June 22, 2013
End Date: June 22, 2013
Conference Session: Reception & Poster Session
Tagged Topic: ASEE International Forum
Page Count: 16
Page Numbers: 21.33.1 - 21.33.16
DOI: 10.18260/1-2--17238
Permanent URL: https://peer.asee.org/17238
Download Count: 661

Request a correction

Paper Authors

biography

Ruth Rodriguez Gallegos Tecnológico de Monterrey

visit author page

Ruth Rodríguez is an Assistant Professor in the Mathematics Department at the Tecnológico de Monterrey, Monterrey Campus since 2007. She is a Math Education Researcher and Member of the National Researcher System and of the Mexican Committee of Educational Researchers. She was the Secretary of the Executive Committee and Member of the Network of Centers for Research in Mathematics Education (2009-2013). 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.

visit author page

Download Paper | Permalink

Abstract

Innovation in the Teaching of Mathematics for Engineers through Modeling and Technology: a Mexican ExperienceThe purpose of this paper is to share the experience of an educational practice in a privateuniversity in the Northeast of México (Tecnológico de Monterrey, Monterrey Campus) about adifferent way to teach Calculus and Differential Equations courses for future engineers based ona proposal developed by the Math faculty over 14 years. This proposal set off from the idea of re-designing the scholar mathematical discourse present in the Integral and Differential Calculuscourses for engineers. It emphasizes that Mathematics is, above all, a human activity thatanswers several problems of different nature (physical, chemical, biological, etc.), andthroughout this problem solving activity it is likely that the emergence of mathematical concepts,notions and procedures occurs.Students first learn the instrumental aspect of mathematical notions. After proper manipulation,they can theorize about the properties of the objects. This proposal considers that the emergenceof mathematical knowledge is significant from the historical and epistemological points of view,and that the teaching of mathematics to future engineers should take into account these stages.The outcomes of this proposal have been published in the form of four student textbooks –Pre-Calculus, Differential Calculus, Integral Calculus and Multivariable Calculus. The work is still inprogress; however, there has been great advance in the curriculum design for DifferentialEquations. Since 2008, innovative material (hands-on activities, laboratory practices, modelingand simulation practices, worksheets/spreadsheets) has been developed for the DE course. Itsmain axis is concerned with the modeling of biological, physical or chemical phenomena.Recent research has shown the need to change the way to teach DE, from the “traditional” way,which emphasizes analytical methods, to an integrative mode, which uses graphical andnumerical methods. This integrative mode should enable students to identify and recognize a DEin its different representations; and thus, improve the learning of DEs as mathematical objects.The student should not only learn how to use techniques to solve DEs but also learn theapplication of the DE as a tool to model several problems. This is also strengthened through theuse of specific technology and software CAS such as Maple and Mathematica; simulations, andlaboratory practices with sensors in the classroom to better model and understand thephenomenon to study: temperature, an RC circuit, or a spring-mass system. The student shouldbe capable of integrating technical knowledge (DEs) with practical skills through modeling.Different learning active environments play an important role in promoting the implementationof the course with hands-on, modeling, and simulation activities; and the development ofcommunication, problem solving and modeling skills. Since 2010, we have implemented the DEcourse in the ACE classroom following the North Carolina University SCALE-UP model.Evidence has shown that future engineers achieve better understanding of the math conceptsafter living this educational practice and further develop other skills (social, communicative,modeling and technological) along with the mathematical.

Citation
Format

Rodriguez Gallegos, R. (2013, June), Innovation in the Teaching of Mathematics for Engineers through Modeling and Technology: a Mexican Experience Paper presented at 2013 ASEE International Forum, Atlanta, Georgia. 10.18260/1-2--17238

TY  - CPAPER
AB  -              Innovation in the Teaching of Mathematics for Engineers            through Modeling and Technology: a Mexican ExperienceThe purpose of this paper is to share the experience of an educational practice in a privateuniversity in the Northeast of México (Tecnológico de Monterrey, Monterrey Campus) about adifferent way to teach Calculus and Differential Equations courses for future engineers based ona proposal developed by the Math faculty over 14 years. This proposal set off from the idea of re-designing the scholar mathematical discourse present in the Integral and Differential Calculuscourses for engineers. It emphasizes that Mathematics is, above all, a human activity thatanswers several problems of different nature (physical, chemical, biological, etc.), andthroughout this problem solving activity it is likely that the emergence of mathematical concepts,notions and procedures occurs.Students first learn the instrumental aspect of mathematical notions. After proper manipulation,they can theorize about the properties of the objects. This proposal considers that the emergenceof mathematical knowledge is significant from the historical and epistemological points of view,and that the teaching of mathematics to future engineers should take into account these stages.The outcomes of this proposal have been published in the form of four student textbooks –Pre-Calculus, Differential Calculus, Integral Calculus and Multivariable Calculus. The work is still inprogress; however, there has been great advance in the curriculum design for DifferentialEquations. Since 2008, innovative material (hands-on activities, laboratory practices, modelingand simulation practices, worksheets/spreadsheets) has been developed for the DE course. Itsmain axis is concerned with the modeling of biological, physical or chemical phenomena.Recent research has shown the need to change the way to teach DE, from the “traditional” way,which emphasizes analytical methods, to an integrative mode, which uses graphical andnumerical methods. This integrative mode should enable students to identify and recognize a DEin its different representations; and thus, improve the learning of DEs as mathematical objects.The student should not only learn how to use techniques to solve DEs but also learn theapplication of the DE as a tool to model several problems. This is also strengthened through theuse of specific technology and software CAS such as Maple and Mathematica; simulations, andlaboratory practices with sensors in the classroom to better model and understand thephenomenon to study: temperature, an RC circuit, or a spring-mass system. The student shouldbe capable of integrating technical knowledge (DEs) with practical skills through modeling.Different learning active environments play an important role in promoting the implementationof the course with hands-on, modeling, and simulation activities; and the development ofcommunication, problem solving and modeling skills. Since 2010, we have implemented the DEcourse in the ACE classroom following the North Carolina University SCALE-UP model.Evidence has shown that future engineers achieve better understanding of the math conceptsafter living this educational practice and further develop other skills (social, communicative,modeling and technological) along with the mathematical.
AU  - Ruth Rodriguez Gallegos
CY  - Atlanta, Georgia
DA  - 2013/06/22
PB  - ASEE Conferences
TI  - Innovation in the Teaching of Mathematics for Engineers through Modeling and Technology: a Mexican Experience 
UR  - https://peer.asee.org/17238
DO  - 10.18260/1-2--17238
ER  -