How are formulas created?

I saw this question on Reddit: "How are formulas created?"  (Turns out Reddit has a lot of people asking math questions!) The answer provided by commenters is "mathematical modeling" -- done in science courses! This answer makes me sad! Mathematicians make plenty of models, too! When you think about it, though, how many high schoolers get to see that? In fact, how many sophomores in college have ever seen math at work making models?

Well, here are a few examples if you're interested!

  • Stefan's equation for sea ice thickness: these two posts talk about modeling sea ice thickness with a differential equation but don't ask you to use data to create a model
  • Modeling tides on the California coast, with more here: these two posts give worksheets on creating your own model of the tidal patterns at Point Reyes Seashore using actual NOAA data
  • Lynx! for cute fuzzy animals with sharp teeth! These two posts have students develop their own trig model for lynx populations, see how bad that model is, and then use a logarithm composed with the trig function to get a model that better fits the sharp population peaks.

Sometimes I feel like teachers who make room for this material are swimming upstream since so many of our high school math curricula don't provide the time for experimental, living mathematics... but every now and then I meet someone who really makes it work. And maybe with modeling as one of the high school Common Core standards there will be some official space for this in high school classes! It is so sad that students can go through 12 years of school and never really see mathematical model-making at work.

Feel trapped by boring fake word problems in your math textbook? Get intros to real-life issues in the natural world and see math at work.
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