Abstract

Teaching is a very rewarding experience for me, and I intend to approach it in a manner that maximizes the engagement of my students, and the cohesiveness of the concepts being taught. I believe, based on my past experiences, that concepts should be approached as a cycle of questions, considerations, and realizations, producing a satisfying path of close-knit challenging realizations for the student. This leads the students to develop good mental habits of understanding a concept and then wondering what the next step is. This leads to an inquisitive mindset, well-suited for continued learning and for contributing to engineering and science.

My Teaching Approach

As an engineer and scientist, I feel that approaching teaching as a functional, and ``living'' process is vital to success. Engineering and science, in any form, cannot be taught by rote repetition or routine. Engineering and science are the recognition that there is not a single solution to all problems within a topic, and so students of engineering and science must learn to approach each new problem with their eyes open, looking for new avenues to success. This means they need the means to look beyond their previous experience, and find new methods when circumstances demand. Therefore, my intention is to promote the development of the mental tools and habits for learning, and to maximize student engagement.

When teaching, concepts need to be introduced to emphasize the underlying logical structure and purpose. If a concept appears disconnected from previous discussions, or if a logical jump between case simplifications is too large, students will become lost and disengaged. In teaching, there are few things more damaging than this to a student's progression. Therefore, when progressing the lesson from the most simplified case into more complex or generalized derivations, my goal will be to emphasize exactly why the added complexity or change in logic is necessary to the new cases. Each time the class reaches the end of a particular case or condition, it will be important to raise the question “but what if the key circumstance, or the assumption that allowed this case, had been different?” By asking that question, and providing example cases that invalidate the previously presented solution method, I will be presenting the topic to my students in a satisfying cycle of “questioning, consideration, then realization,” repeating with the next logical expansion of the concept.

By relating progression back to previous steps, I intend to cement the topic as a well-connected and grounded framework, promoting conceptual learning for the students. Assignments will be in part practice of the lecture material, but then will extend beyond into cases the students must solve themselves. The students will be told in advance that the structure of the assignment is intended to challenge them with the next logical step, leading them to apply the underlying logic of the topic, rather than repeating a routine from the lecture. Similarly, by including in-lecture challenges where I present a purposely incorrect solution and then challenge the students to identify the flawed assumption and correct the work, I can teach them to act as engineers upon their own knowledge. By this method, I intend to promote not just the learning of engineering concepts, but also the learning of how to learn when presented with unfamiliar terrain.

To maximize engagement, a variety in the presentation of new information is needed. Something as simple as performing a practice problem by having the class make and justify every step and decision in the solution, can be effective. Vital to this is a classroom atmosphere that allows for small failures without embarrassment. In these “cooperative solution” exercises, I would start by telling the students that there will likely be mistakes and not to worry, because the point is experiencing the corrections and the reasoning behind them. Experiencing something that is incorrect and then understanding why it is incorrect is just as valuable as being guided through correct solutions; however the former provides the opportunity for curiosity, and thus keep students interested and ready for more.

Example: Teaching opportunity with a co-op student

During my PhD I was entrusted to hire, supervise, and mentor three first-year engineering co-op students who worked as my research assistants. These were very satisfying experiences, and one in particular provided an exceptional teaching opportunity. Our lab was in need of a piece of custom equipment that needed to be designed and machined and my co-op student, who I will call “Bill,” was interested in being involved in this work. However, we realized he had not yet taken his first year Static Mechanics course, and so he did not have the necessary knowledge to participate. Seeing his interest, I felt that it was important to use this as a teaching opportunity, and assigned him the project. Similar to many undergraduate design projects, his task was 1) to learn not only the static mechanics theory necessary, but also to learn how to identify design requirements while making engineering design decisions and materials selections, 2) to learn how to check his decisions through iterations, and how to apply multiple safety factors to adjust the design as it evolved, and 3) how to then machine and assemble the components into the working device, and perform further design iterations to accommodate the design elements necessary to perform the machining.

I had Bill work semi-independently from me, setting goals for him each day based on my existing knowledge of the topic. We would meet regularly, for me to teach the new design and static mechanics concepts he would need, or to present loosely related examples from the text book, or to clarify areas of the topic he was grappling with. I would have him present his progress to date every second day, asking him to justify his decisions and often using leading questions to guide him into recognizing any errors he made or areas requiring greater attention. By maintaining an environment of “little puzzles” to solve in the short term, I was able to teach Bill the foundational concepts necessary in a highly practical way. I also used this time to teach Bill the basic hands-on and conceptual knowledge needed for machining the parts, which he was highly engaged with. This culminated in Bill fabricating his design, and assembling the equipment. Bill has now gone on to excel in his undergraduate studies at the University of Waterloo, and is currently involved with an entrepreneurial start-up company, based around mechanical design. The equipment he designed has performed flawlessly, and has become a workhorse in our lab's research stream.

Final Thoughts

Watching Bill learn throughout his design project also taught me important lessons about being a mentor. I could see which of my approaches encouraged him, and I could also see when my under- or over-teaching caused him to disengage or to expect the answer to simply be given to him. This reinforces my earlier statement: engineering and science are the recognition that there is not a single solution to all problems, and that includes teaching. As a teacher, I must be just as engaged with my class as I hope that they will be, and I must respond to them and encourage their responsiveness. I must perform honest review of my own work throughout the term, by reviewing the students' performance in assignments, midterms, and in-class. Areas where understanding of the topic is weak need to be addressed, and the original means by which they were taught must be reviewed or reconsidered, while maintaining the challenge to students that will lead them to achieve the levels of excellence expected for representatives of our institution.