But I do want to talk about questions that I still have about modeling after reading this definition (full disclosure, I did not read the GAIMME report): Mathematical modeling is a process that uses mathematics to represent, analyze, make predictions, or otherwise provide insight into real-world phenomena.

A question or worry about this definition is that a publisher/teacher could see the quadratics problem above and can defend it as modeling. If I understood you correctly here, when you used process, you might have implied iterative process. I know that’s something that you’ve emphasized before when talking about modeling, but the notion that this process is iterative I don’t think jumps out at me when I read this definition (again this could be further detailed in the full report–I apologize if it is). I know CCSS-M says modeling can be very simple and uses writing total cost as a product of unit price and number bought as an example. But what I guess I’d like to hear or understand better, is how can we have a definition of modeling with mathematics that respects and accurately depicts the legitimate work done by people who engage in this process (at any age/level), but that doesn’t allow for just solving simple math problems (like the “Modeling” example above) to be included.

Also, I know this speaks to your more recent post. But I’d like to take a shot at debunking why modeling needs to be connected to the real-world, though I will admit I appreciated that post, and it gave me insight to the power and advantage of using mathematics to model the real world.

That said, here is my counter-point. I was at a PD a few summers back (the presenters will remain nameless) where we analyzed a mathematical model that described the spread of zombification during a zombie apocalypse. Now I would describe what the authors of that paper did as mathematical modeling–regardless of the fact that it’s not real-world based. Similarly, I would argue that video game developers (and players) model with mathematics when they create virtual worlds (or when they try to maximize their impact on the virtual world in the case of players). I feel like the entire cycle of modeling (rather the CCSS-M model or a similar model) are iterated on extensively, and I’d have to be convinced that the work they were doing wasn’t modeling–other than simply saying it wasn’t modeling b/c it was in a virtual world. Of course removing another adjective–real-world–from the definition will only make it harder to define. That’s why it’s nice to be here on the sidelines 🙂

]]>That’s a very nice idea! I have not done that calculation, but would love to see what you come up with.

John

]]>Kind Regards

Liam Tierney

Great example for modeling. I wonder if part of the simplification in modeling lies in the assumption of treating the potato as a homogenous mass rather than heterogeneous mix of potato mass and water, both of which heat and cool at two different rates. I also wonder if the overall shape of both potatoes have to have similar shape since the heat dissipation is along the radial direction from the center and if one is elliptical and other spherical i.e. some ratio of the radii needs to taken into consideration. Now of course, one makes it a more complicated model and defeats the purpose of the lesson you were trying to convey.

Bottom line – I enjoyed reading it :- ). Excellent website. ]]>