Integration enhances learning across the curriculum
William Cluett, Chemical Engineering & Applied Chemistry, University of Toronto
In 2009, I participated in the creation and delivery of a new half-course for first year Engineering Science[1] students at the University of Toronto called Engineering Mathematics and Computation, ESC103F. This course grew out of a quarter-course called Matrix and Vector Algebra, MAT190F that was part of the Engineering Science Foundation curriculum (Years 1 and 2) introduced in 2005-06.
After the 2008-09 school year, it was decided to remove all quarter-courses in Years 1 and 2 including MAT190F but the algebra material taught in MAT190F was deemed important and hence was retained in ESC103F, while adding a computational component. As Chair of the Division of Engineering Science at the time, I inserted myself as the instructor for both sections of this course as a way to get to know the entire first year class and to provide timely advice and encouragement to help students make a successful transition from their various high school experiences to the rigors of Engineering Science.
One other advantage of being Chair was that I had good knowledge of the first year curriculum. With this knowledge, I set about to find ways to connect ESC103F with other courses the students were taking in the fall semester as a way to break down the silos between courses. These efforts to integrate material across courses are greatly appreciated by students and help them to make meaningful connections themselves as they move through the program.
My efforts over the years have led to the following "points of integration" in the 2015 fall offering of ESC103F:
- In CSC180F[2]: Students implemented Gaussian elimination in Python in Lab #7.
- In ESC103F: Students formulated the Warren truss problem found in their CIV102F[3] problem set #5 as a system of linear equations in the form AX=B as a classroom exercise.
- In ESC103F: Students simulated in Lab 2 using MATLAB® the dynamic behaviour of a two storey structure under dynamic loads such as earthquakes and wind forces.
- In ESC103F: Students saw in class how the least squares problem is formulated in their PHY180F[4] gravity lab to help them solve for an estimate of the acceleration of gravity.
- In ESC103F: Students learned how to carry out numerical integration using MATLAB to complement the analytical approach based on the Fundamental Theorem of Calculus studied in MAT194F[5].
- In ESC103F: Students learned how to numerically solve initial value problems using MATLAB to complement the analytical approaches studied in MAT194F for solving such differential equations.
Feedback from students regarding this integration was positive. Here are some excerpts from the 2015 course evaluation:
- Prof Cluett did an excellent job at explaining course material as well as relating it to other courses and engineering in general. This was supplemented by the extensive blackboard posts that gave a deeper understanding into some of the concepts. This was a great introductory course for engineering science.
- I loved the integration of other courses within the course, especially the CIV102 incorporation.
- The instructor did a good job of integrating the course material to other courses and practical applications.
- Very intellectual prof who perfectly knows our program inside out, and let us interleave between different courses using contents learned on this course.
- The connections made to other courses were useful, as they emphasized the value of the content of the course with respect to an overall engineering education and significantly increased my interest in the topics covered.
- The professor did a great job of explaining how the concepts learned in this course are applicable to diverse fields in both science and engineering.
- Concepts were well-explained and it is interesting to see how my other courses all come together in this course.
[1] Engineering Science at U of T is an enriched program that provides excellent preparation for postgraduate studies in engineering and science as well as for other professional degree programs such as business, law and medicine. Graduates of the program are also well qualified to immediately embark on professional engineering-related careers.
[2] CSC180F: Introduction to Computer Programming
[3] CIV102F: Structures and Materials – An Introduction to Engineering Design
[4] PHY180F: Classical Mechanics
[5] MAT194F: Calculus I