> Math should be motivated by science and modeling, otherwise it's just an exercise in diddling numbers.
I like a lot of what you said, but I do disagree with that point. Immediate application of mathematical concepts may be gratifying, but making it the _only_ motivating factor behind maths can result in students who conflate the underlying machinery with its application [1].
Taking a pure maths course in undergrad with related subject matter prior to one of my Controls classes made the class substantially easier to understand. Learning the abstract concepts beforehand let me see the common applications more quickly than others.
I think the biggest difference is that when I learned some Calculus through Physics, it was a little more difficult to go from a concrete basis to a more general one. My understanding ended up being based on analogies to other concepts until I went back and covered the theory again.
[1] This is all my own opinion, I'm not an educator so the most I can do is pull from my own pedagogical experience :)
I like a lot of what you said, but I do disagree with that point. Immediate application of mathematical concepts may be gratifying, but making it the _only_ motivating factor behind maths can result in students who conflate the underlying machinery with its application [1].
Taking a pure maths course in undergrad with related subject matter prior to one of my Controls classes made the class substantially easier to understand. Learning the abstract concepts beforehand let me see the common applications more quickly than others.
I think the biggest difference is that when I learned some Calculus through Physics, it was a little more difficult to go from a concrete basis to a more general one. My understanding ended up being based on analogies to other concepts until I went back and covered the theory again.
[1] This is all my own opinion, I'm not an educator so the most I can do is pull from my own pedagogical experience :)