Mapping science onto the world
For mathematicians, mathematics is an essence unto itself. Engineers are a little more pragmatic. For them, mathematics is the language that describes the science they map onto the world.
Engineering undergraduates enter their programs with a strong background in both math and science. While some fly through the very demanding four years of study, others have moments (or entire terms) where their trusty friend mathematics abandons them, suddenly seeming aloof, foreign and unwieldy.
“It’s not their fault,” said George Vatistas (Mechanical and Industrial Engineering) emphatically. “Certainly a number will struggle and leave the program, but most should succeed.” He and the Faculty of Engineering and Computer Science (ENCS) believe that the way mathematics has been taught in engineering (in general, not just at Concordia) has not sufficiently bridged the gap to applied science theory, so they’re doing something about it.
EMAT 213 is the first in a series of common math courses taken by undergraduate students in the faculty. It is prerequisite for many of the classes which follow, and thus a key to future success. That success requires not just understanding the math on an abstract level (strangely, not a problem for most engineering students) but understanding what the numbers, equations and operations mean in the real world.
In order to build and solidify that understanding for students, EMAT 213 has been completely dissected and reassembled. It’s part of the overall strategic plan in ENCS which Vatistas helped formulate during his tenure as an associate dean. One of the goals, he explained, is to move towards excellence in teaching across the faculty by revamping both the materials and methods used in the classroom.
“The abstract side of math is very beneficial. However, engineers must be able to synthesize and produce products for the benefit of society. So, why would we talk to engineering students about mathematics in a purely theoretical sense?” Vatistas asked. “We expect them to apply it; the course should reflect that.”
“These are smart kids,” he added. “We (and their textbooks) were making great logical leaps, and we expected them to come along for the ride. Instead, we were undermining their self-esteem.” As far as Vatistas is concerned, that’s not what undergraduate education is about.
“In engineering education, our first approach in dealing with a concept should be to prove its validity either experimentally or using logic. [We must] convince the students that what we have developed is realistic by measuring it against reality. [And we must] persuade them that it is of value by means of examples from relevant applications.”
What is relevant obviously varies from program to program, so the course focuses on examples which are applicable across a broad range of systems. “Systems may not necessarily resemble each other physically,” Vatistas explained, “but they are considered analogous if, and only if, they can be described by the same set of equations.” So the mass-spring-damper system that is often used in mechanical engineering is analagous to a resistance-inductance-capacitance system in electrical engineering and to models for heat flow through wall systems in building engineering. Each system is an excellent teaching tool for EMAT 213.
“Applying the math to models. which students will see over and over again throughout their studies, helps them understand how the equations describe the systems and the changes which occur within them,” said Vatistas. While the changes to EMAT 213 are new, they are producing promising outcomes.