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Success story in the making, make that made already . . .

As Director of SIMIODE I fully intended to keep a quality running blog of ideas and stories related (somewhat at times) to our goal at SIMIODE which is to support faculty who wish to use modeling to motivate and teach differential equations. I have not made an entry since August 2018. So much for keeping up!

However, recently I received this story from Eric Stachura of Kennesaw State University and I want to share it with you. Eric was a participant in our NSF Funded Workshop: MINDE- Model INstructors in Differential Equations, held in Summer 2018 at Manhattan College, Riverdale NY USA.  Incidentally, you can look up details about our forthcoming Summer 2019 workshops and apply if you believe one of these are appropriate for you. 

We put up front this detail. In addition to engaging in modeling in his differential equations course, using SIMIODE ideas, and participating in a SIMIODE MINDE workshop, Eric along with fellow MINDE workshop colleague, Robert Krueger, Concordia University, Saint Paul MN USA, have authored a Modeling Scenario of their own, 6-024-DronePackageDelivery.

Here is Eric’s story which he submitted to us for another purpose, but which I use now to kick start my return to blogging in SIMIODE on a wonderful note. Thank you, Eric.

How I got involved with SIMIODE

Eric Stachura, Department of Mathematics, Kennesaw State University,

In the Fall semester 2017 at Haverford College, I was beginning to prepare to teach a course in differential equations in Spring 2018 for the very first time. I was thinking back to when I took the course, and I remember how dry some of the material was (the irony here, is that my research area is partial differential equations!). My goal in preparing for this course was to keep the material exciting, and teach it from a non-standard way (whatever that may mean). To this end a colleague recommended the SIMIODE website and I started browsing through it. Having assigned writing projects in the past for students, I thought perhaps I can use one of these scenarios as a group project for students.

This is what I did! I had the students complete two writing assignments based on Modeling Scenario 1-003-College Savings (which entailed students constructing a model to save for a child’s college education), as well as Modeling Scenario 6-023-Drone Heading Home, where students solved a differential equation model for the trajectory of a drone. Personally, I am a big fan of writing assignments in mathematics courses (this is largely due to the math faculty at Haverford—thanks all!), as I believe this adds another layer of understanding for the students. Additionally, I have noticed at the lower levels that students frequently have difficulty articulating and explaining mathematics, so this aims to address that issue in particular.

These projects in class were a big hit, and in fact were many students’ favorite part of the course! The next time I teach differential equations (likely Fall 2019) I will again have students complete writing projects with SIMIODE materials, but perhaps with different problems this time around.

In preparing for the Spring 2018 course on differential equations, I was two years post Ph.D. employed as a Visiting Assistant Professor at Haverford College. I was very open to new teaching methods, and once I found SIMIODE and all the materials within, I knew I had a fantastic resource to use in future courses. I am even considering adapting some of these materials to the calculus level, since I frequently have applied/modeling problems in my calculus courses as well. Indeed, I developed worksheet materials for modeling when I taught calculus I in graduate school.

To be honest, when I was first exposed to SIMIODE materials, I was slightly reluctant about using them, and for me the Spring 2018 differential equations course was somehow a test for me. Having seen how wonderfully the problems were received, though, and then having attended the MINDE- Model INstructors in Differential Equations, NSF workshop in Summer 2018, I am completely convinced by the value of this community. My goal is to stay involved as much as I can, develop new scenarios for the community and to use in my own courses (especially on partial differential equations—my expertise!), and continue to use modeling in my courses. As I mentioned above, I frequently include modeling type problems in my calculus courses (with significant scaffolding), so this is perhaps one direction I will go in the future: develop modeling problems specifically meant to be implemented at the calculus level.

Recently I was selected to be a MAA Project NExT Fellow. In the coming years as part of this fellowship, my plan is to discuss my previous experience with modeling in my differential equations course, but I also hope to learn a lot from others who have been doing such things for longer than me. In this way I can use modeling scenarios even more effectively, perhaps to introduce a concept, reinforce old material, etc. The point is, I have just started my journey into modeling in differential equations. As a new Assistant Professor at Kennesaw State University, my department is completely behind my initiative in this regard. I hope to build a community of differential equations instructors at KSU who are also interested in applied/modeling techniques in their courses.

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