Just this morning I gave my (third year) students a set of x-y data. During the previous lecture (which was on ultrafiltration) we derived a mathematical model that predicted
where a and b constants.
Their challenge was to use the data to evaluate a and b. Only a small minority of the 30 or so students came up with a solution. Why did such a simple data analysis problem challenge them so much?
My theory is this: the students I teach are learning on a multidisciplinary programme and they do not get immersed in mathematical and computational reasoning to the extent that I would like them to.
Consequently, they do not have the basic rules of mathematics, the grammar of the mathematical language, ‘at the ready’, waiting to be called upon when they have to solve engineering problems. They are not ‘triggered’ to make the leaps that an engineer or a mathematician might make.
So in the above instance they don’t make the first logical step, the step that anyone who is fluent in the language of mathematics would make, i.e., they don’t simply write
Some, but not all, will then be able to extract a and b from the slope and the intercept of a plot of y versus lnx.
This tells me two things: (i) remembering the rules of mathematics is important because having immediate recall is usually the thing that drives mathematical problem-solving and (ii) multidisciplinary programmes are hard to deliver.