I had the opportunity to help with this years IMA/MathCEP mathematical modeling camp a few weeks ago and wanted to share my thoughts on it. Daniel Schulthies organized the camp and followed the SIAM modeling guide fairly closely. We picked modeling topics which were local, current, and which there was enough data about. We did a cursory search to make sure there seemed like enough public data available, but students had to find the data on their own.
We used the following projects:
- What is the best location for a new MLS stadium in the twin cities (list of possible locations provided)?
- How soon could Minnesota convert to 100% renewable energy sources?
- What is the best light rail expansion route (list of possible routes provided)?
- Find a good location for Wayzata to build a new middle school.
- Following the poor air quality in early July due to Canadian wild fires, can you create a predictive model for air quality based on various observable events such as traffic, weather, wildfires, pollen, etc…?
Its was fascinating to see the wildly different models that different groups of students came up with, and it is always inspiring to see how excited these students are about math. I’m pleased that all groups got good results. Most of the models they used were simple, rank linear functions, graph models, and correlations. The tools they used for that were equally simple: google drive, docs, sheets, and slides. We provided goolgle drive folders to all the groups, and most of the students did all their work there. Early on, we had to force students to move their work from paper/blackboard into a spreadsheet. Once they moved into a spreadsheet, their models got significantly better, because they could refine their model and update data without doing significant computation. Interesting from a teaching perspective were which projects seemed to give interesting models. Itseemed to me like the most open-ended questions let students create more interesting models and had a larger variety of answers. Both “renewable energy” and “Wayzata middle schools” saw students use very different models to arrive at remarkably similar answers.
Having everyone in drive folders was great. We could see who was editing their spreadsheet at 1:15AM. Amusingly, it wasn’t just the students working late: I’m guilty too, one morning Daniel pointed out to me that my presentation had time stamps of 11:45pm one night and 7:00am that morning. The best story of the camp came during the presentations, when we called a group to present, only to discover they wern’t in the room. When we looked at the drive log, we saw that they were editing their presentation from the hallway.
If there was a flaw in this year’s camp it was the air quality problem problem. We asked for suggestions for topics from the returning students and they proposed air quality. They actually got interesting results, but it was a hard enough problem that they also left the problem discouraged. For next year’s camp, we are thinking models from this year’s students. See if they can build off an existing model to make it better. I’d also like to see a wider variety of models in next years camp. I suspect that is our own fault, some of the prompts were too similar and didn’t lend themselves to different models. Next year it would nice to have prompts which push students towards a greater variety of models. One thing which I think would help with that is having a variety of case studies to give the students. I gave a 15 minute presentation on moose and wolves on Isle Royale. I think would be neat to collect favorite mathematical models to include in classes and future modeling camps. Anyone have suggestions for models to use?
I was finally struck by how tricky it was to communicate to students what a mathematical model IS and what it DOES. Having to communicate that to students made me thing that mathematical models are not taught enough. I kept having flashbacks to casual conversations and industry work where the MO is “We must make a model that takes EVERYTHING into account”. I come away from the camp even more convinced that this is the wrong view, we don’t want everything – we just want to explain interesting behavior. I’ll close with a quote I was reminded of the yesterday at a conference:
“In anything at all, perfection is finally attained not when there is no longer anything to add, but when there is no longer anything to take away.” –Antoine de Saint-Exupery