The hardest part in teaching science is getting a student to be able to look at nature and see mathematics. This is the bread-and-butter of any math-based science or engineering. In my opinion, it is not being taught in secondary science classes.
My position
I believe we can only teach this process, what I will call ‘formalizing experience,’ by presenting students with messy, fuzzy problems embedded in real, physical experience, and then by having them struggle through creating a mathematical formalism, a ‘model,’ to the problem. I believe teachers need to be careful in the language they use: they need to explicitly differentiate between the physical world we are describing and the mathematical models we use to describe and analyze it. Their choice of language can be disabling to their students, sending them back to scramble for the magic equation to fit the word problem.
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