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25 Nov 2020
From Ayşe Şahin, Professor and Chair, Department of Mathematics and Statistics, Wright State University, Dayton OH USA (with permission).
What are your thoughts on these issues?
Why did I start to use modeling?
My research area is in dynamical systems, so I tend to approach the topic with the philosophy "if you can solve it, who cares to talk about it anymore". I do teach techniques of course, but I like to make sure the course is balanced in : why we worry about differential equations (modeling, making them realize that modeling the rate of change is much easier than trying to model the function itself, not to digress but that's actually a cool thing about the feral cat project, too bad it's off limits now: some of them modeled the first scenario, and the second scenario, then tried to adjust the function to fit the third one, without worrying about how the rate of change of the population changed. Got themselves in all sorts of trouble.) So, I introduce themes: why do we care? What does it mean to solve? Solving: sometimes analytically, sometimes not possible – then numerical, qualitative analysis, geometric tools. And I try to balance the amount of energy spent in each theme. When applying techniques I focus on the structure of the equation and the structure of the solutions hoping they will develop some intuition as to what a solution should look like given a particular type of equation and forcing function, for example.
I tend to be very generous with my grades, in that there is always a possibility to improve your grade. I give them extensive feedback on what progress they made and where they fell short. Even though we were remote this semester I was hugely successful (I think!) in training them to articulate what they do not understand. I gave difficult take home exams, for instance, and the grades were based not on the final answer, but their approach/reflection. For students who took a pass at a problem and wrote an explanation of how they know it is wrong, but they don't know how to address the issues, I graded according to the pass they took. If what they didn't know how to address was something that we had covered extensively (they could go to my videos, the book, their old homework and it was right there spelled out) well that's a C or D depending on their reflection. If what they struggled with is deeper, some new territory, then that is an A or B. The fact that I have students who were able to do that is how I measure the success! I don't think it happened before, and I think it's because my assessments were always "sit in a room and show me everything you know" vs "here are some problems that can be tackled with the tools you spent time learning, take a pass, use whatever you want, just don't google or talk to anyone else but me". The SIMIODE materials are interesting and deep, and many of them that I have looked at have multiple entry points so everyone can get started. It is hard to write good problems, as you know. I value a treasure trove when I find one!
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