I am looking for resources for teaching math modeling to high school teachers with rusty math background. It will be a 6-week course. Some tips/directions on simple projects would be helpful. I would want to introduce coding for numerically solving systems of ODEs.
2$\begingroup$ It is not clear for me if you want to introduce systems of ODEs as a final project of the course or you want to focus the full 6 weeks on this topic. In my experience, modelling in high school is at a more basic level (for example curve fitting). Apart from the higher level Applications and Interpretations IB course, I do not know of any high school syllabus that covers differential equation systems. I am not sure either what you plan about coding. For numerically solving systems of ODEs I would recommend the use of spreadsheet or software like Geogebra to my students. $\endgroup$– Ferenc BeleznayMar 12, 2021 at 11:14
$\begingroup$ Teach them how to write scripts in Python and have them simulate a SIRS model of epidemic evolution using Runge Kutta. It's not correct for modeling covid, but it will feel topical and engage them. $\endgroup$– Dan FoxMar 27, 2021 at 18:52
The information and handbooks at SIAM Mathworks Modelling Challenge pretty helpful. One handbook introduces the reader to the modeling process and the second one introduces the reader to the communication of computation related to modeling (including ODEs via spreadsheets--you could probably generalize what they discuss to solve the logistic equation to systems). There are also have links to sample problems from previous competitions.
I would recommend checking in with the MODULE$(S^2)$ project (Mathematics Of Doing, Understanding, Learning and Educating for Secondary Schools). A few notes:
- This project is currently developing materials for Geometry, Algebra, Statistics, and Modeling. Obviously, it is the last of these that would be of interest for you. You can find links to some sample materials at the the bottom of the page I linked to above.
- The program materials are designed for use with preservice teachers, but might also work very well with the "rusty teacher" you have in mind.
- The materials are still under development, and are therefore something of a work in progress. I am not certain, but I believe the Modeling team is currently seeking partners to pilot their materials.
- Full disclosure: I am a member of the Geometry writing team, and have piloted the Algebra materials. However, I don't have any direct involvement with the Modeling group.
Another resource you might find helpful is the recently-published book The Learning and Teaching of Mathematical Modelling by Mogens Niss and Werner Blum (Routledge, 2020), part of the IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) book series.