## 2021-Udeigwe, Lawrence - Student Projects Using SIMIODE Materials to Prepare a Video Talk for High School Students

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From Dr. Lawrence C. Udeigwe, Associate Professor of Mathematics, Manhattan College, Riverdale NY USA. __lawrence.udeigwe@manhattan.edu__

This semester, I made my differential equations students (mostly sophomores, some freshmen) adopt SIMIODE materials for their final projects. Here is a link to the YouTube playlist of videos they produced in their projects https://youtube.com/playlist?list=PLXeOv9HT0vZ1yqVxivRr1u5yjwo1bJhbw .

I made my students choose among 6 different papers and work in groups of 4 or 5. I have two sections, so some of the projects are done twice.

I think they did a decent job, but next time I would give them more time and/or supervise them more closely to get things more accurate.

The course is a traditional differential equations course that is taken by mostly engineering sophomores and some freshmen. The catalogue description of the course is as follows: “This course focuses on techniques of solving first-order, second-order, and systems of first-order linear differential equations. Methods include separation of variables, variation of parameters, and the Laplace transform.”

This was my first time teaching the course since I participated in the SIMIODE workshops. This, coupled with the pandemic, made me start to think of new ways of teaching the course while making sure I cover all the required topics.

During the semester we did two projects. I introduced each project in the middle of each major topic. In particular,

- I introduced the following population project, 1-143-S-PopulationModelVariationsMATLAB, while treating first order separable equations https://www.simiode.org/resources/5889 . This Modeling Scenario was written by Bill Skerbitz, Wayzata High School, Plymouth MN USA
- I introduced the following car suspension spring/mass project 3-034-S-CarSuspensions, written by Therese Shelton, Southwestern University, Georgetown TX USA and Brian Winkel, SIMIODE, Cornwall NY USA, while working on homogeneous second order equations and characteristic equations https://www.simiode.org/resources/7869

Once I introduce a project and make the class identify the differential equation problems in the project, I leave it to them to finish and submit their individual work on the project.

A third and final project was done in group and counted for 30% of the final exam grade. The goal of the final project is to use a SIMIODE article to introduce the public to an application of differential equations. I selected 7 SIMIODE articles from which they can choose. An important punch line of the project description is: *"Your target audience is a high school student. Your job is to teach this student without intimidating him."* They had 3 weeks to get everything done.

Here is the Project Description.

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MATH 286 - Differential Equations Term Project

**Goal**

The goal of this project is to explore a phenomenon that can be explained using Differential Equations. You may choose one of the possible topics from SIMIODE. Your job is to create a comprehensible narrative, on the chosen topic, that has the following major parts:

- Introduction and Background: Origin of phenomenon; literature review on phenomenon.
- Acknowledgement of the SIMIODE article you are using as a guide.
- Mathematical Exploration: Use of Differential Equations to explore phenomenon.
- Conclusion: Possible scientific questions.
- Bibliography.

**Rules**

- You may work in a team of 4-5 people.
- Your target audience is a high school student. Your job is to teach this student without intimidation.
- Even though you may use SIMIODE treatment of the topic phenomenon as a guide, you must refrain from having your presentation look like a homework problem from a SIMIODE article.
- Any plots you use must be created by you (exceptions may be made for some figures).

**Product**

- A video recording of your presentation. This video may be up twenty minutes
- A fifty-nine second video of highlights of your presentation
- Slides of your presentation.

Note: Higher level of creativity and aesthetics will be greatly rewarded

**Tentative Grading Scheme**

- Introduction and Background – 20%
- Mathematical Exploration – 40 %
- Presentation – 20 %
- Comments – 10 %
- Creativity – 10 %

**Dates**

- 05/05/21: Videos and slides due.
- 05/09/21: Peer comments on videos due.

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I just downloaded their responses to the following questions

- How did the projects help your understanding of differential equations?
- What do you not like about the projects?
- Are there any helpful experiences you gained from working on the final project?

I have yet to analyze these responses.

I am impressed at how the students were able to synthesize the multiple facets of mathematics that they have learned. I regret not being able to hold their hands more. Next time I will definitely make them do a mid-project submission where I can fix any derailment. My favorite submission is the snail one. My least is the one on bitcoin.

I want to consider writing an article for *PRIMUS*. Over the years I had grown to hate the idea of student projects. Then I discovered that what I do not like about it is that the project audience is usually the professor and the class, making it more prone to jargon and inaccessibility. I am proposing a new approach to student projects: *Have students sell mathematics to the general public through their projects.* I think SIMIODE is a great help in doing this.

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