Putting Mathematics in Context: An Integrative Approach Using Matlab

Micah Stickel

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Conference: 2011 ASEE Annual Conference & Exposition
Location: Vancouver, BC
Publication Date: June 26, 2011
Start Date: June 26, 2011
End Date: June 29, 2011
ISSN: 2153-5965
Conference Session: Computers and Software in Teaching Mathmatics
Tagged Division: Mathematics
Page Count: 20
Page Numbers: 22.1205.1 - 22.1205.20
DOI: 10.18260/1-2--18843
Permanent URL: https://peer.asee.org/18843
Download Count: 418

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Micah Stickel University of Toronto

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Micah Stickel is a lecturer in Electrical and Computer Engineering Department at the University of Toronto. He first came to the department when he started as an undergraduate student in 1993. Since that time, he has completed the B.A.Sc. (1997), M.A.Sc. (1999), and Ph.D. degrees (2006). He has been involved in a number of research projects, including the use of spiral antennas for Radio Frequency Identification (RFID) systems, the design of high-fidelity directional couplers for digital circuits, and the application of micromachining techniques in the fabrication of bandpass filters for broadband wireless systems. He has also worked as a post-doctoral researcher in the developing field of three-dimensional metamaterials. He is interested in advancing the art of engineering education through the appropriate use of technology both in and outside of the classroom. As well, he has recently become more involved in the department's efforts to highlight the many engineering applications of electricity and magnetism to high school students.

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Abstract

Putting Mathematics in Context: An Integrative Approach Using MatlabThe teaching of foundational engineering mathematics courses can be quite challenging due theabstract nature of the subject matter for freshman and sophomore students. Often it is difficultfor the students to see how the material is relevant to their future engineering work, and as aresult many students do not become as fully engaged with the course as the instructor may hopefor. One method which has been proven to be effective for increasing student engagement is toplace these abstract concepts in a practical context. This way the students can experience theusefulness of these concepts and can relate it to the other subjects which they are learning at thesame time.Recently, we have added a new component to a second-year Advanced Engineering Mathematicscourse, which is part of our electrical and computer engineering (ECE) curriculum. This coursecovers the main topics of ordinary differential equations, Laplace transforms, and complexanalysis, so it has a rich variety of applicability to the other parts of the ECE curriculum. Thisnew component has been designed to give the students direct experience with the application ofthese mathematical concepts to engineering problems. These problems are drawn from theirother concurrent courses and courses which they will take in future terms. This enables thestudents to see how these concepts are an integral part of the rest of their program.In order to enhance both their theoretical and practical engagement with the material we havecreated a set of application homework exercises and a set of Matlab-based modules. Thehomework exercises expose the student to a more advanced application of the material within aguided-inquiry framework. While the Matlab modules introduce the students to the practicalside of engineering problem solving through modeling and numeric computation. Since this isthe first exposure that our students have to any computational software, these modules alsoprovide an introduction on how to use Matlab. These modules are self-study exercises, but thestudents are supported by custom-made video tutorials. These tutorials contain a review of theessential concepts in each module, as well as examples of how to use Matlab to solve thesuggested application problems. To assess the main outcomes of these modules, two onlinequizzes have been delivered through the course management software. These quizzes provideindividualized questions and exercises which enhance the quality of the assessment and give thestudents the incentive to complete the modules on their own. In this paper we will describe andassess the effectiveness of this new component in terms of improving student engagement withthe material. The assessment will be based on student survey data and statistical analysis of thisdata in comparison with their relative performance on these modules and the course as a whole.

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Stickel, M. (2011, June), Putting Mathematics in Context: An Integrative Approach Using Matlab Paper presented at 2011 ASEE Annual Conference & Exposition, Vancouver, BC. 10.18260/1-2--18843

TY - CPAPER
AB - Putting Mathematics in Context: An Integrative Approach Using MatlabThe teaching of foundational engineering mathematics courses can be quite challenging due theabstract nature of the subject matter for freshman and sophomore students. Often it is difficultfor the students to see how the material is relevant to their future engineering work, and as aresult many students do not become as fully engaged with the course as the instructor may hopefor. One method which has been proven to be effective for increasing student engagement is toplace these abstract concepts in a practical context. This way the students can experience theusefulness of these concepts and can relate it to the other subjects which they are learning at thesame time.Recently, we have added a new component to a second-year Advanced Engineering Mathematicscourse, which is part of our electrical and computer engineering (ECE) curriculum. This coursecovers the main topics of ordinary differential equations, Laplace transforms, and complexanalysis, so it has a rich variety of applicability to the other parts of the ECE curriculum. Thisnew component has been designed to give the students direct experience with the application ofthese mathematical concepts to engineering problems. These problems are drawn from theirother concurrent courses and courses which they will take in future terms. This enables thestudents to see how these concepts are an integral part of the rest of their program.In order to enhance both their theoretical and practical engagement with the material we havecreated a set of application homework exercises and a set of Matlab-based modules. Thehomework exercises expose the student to a more advanced application of the material within aguided-inquiry framework. While the Matlab modules introduce the students to the practicalside of engineering problem solving through modeling and numeric computation. Since this isthe first exposure that our students have to any computational software, these modules alsoprovide an introduction on how to use Matlab. These modules are self-study exercises, but thestudents are supported by custom-made video tutorials. These tutorials contain a review of theessential concepts in each module, as well as examples of how to use Matlab to solve thesuggested application problems. To assess the main outcomes of these modules, two onlinequizzes have been delivered through the course management software. These quizzes provideindividualized questions and exercises which enhance the quality of the assessment and give thestudents the incentive to complete the modules on their own. In this paper we will describe andassess the effectiveness of this new component in terms of improving student engagement withthe material. The assessment will be based on student survey data and statistical analysis of thisdata in comparison with their relative performance on these modules and the course as a whole.
AU - Micah Stickel
CY - Vancouver, BC
DA - 2011/06/26
PB - ASEE Conferences
TI - Putting Mathematics in Context: An Integrative Approach Using Matlab
UR - https://peer.asee.org/18843
DO - 10.18260/1-2--18843
ER -