Comment by londons_explore | Hacker News Reader

Comment by londons_explore | Hacker News Reader

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londons_explore

It's because most exams and curriculums in the UK are so strictly defined that all questions are almost guaranteed to follow one of a small set of structures.

And schools have figured out that rather than teaching the subject from first principles, it's easier to get students to get high grades by teaching them each of the structures. Eg. "Whenever there is a question about differentiating x^7, just put 7x^6 as the answer." They then get the students to try a few examples (x^3 becomes 3x^2, x^77 becomes 77x^76, etc), and thats the way every science-y subject is taught.

I often think it leads to students who do well in exams, but can't solve many real world problems.

It could be solved by having a part of every exam paper be never-seen-before applied problems. For example, for differentiation, one might ask "A road's height in meters as a function of the horizontal distance along the road in kilometers is defined as sin(x)cos(x)tan(x). At what points are the steepest uphills? Would you describe the slope of the road as 'very hilly', and why?"

I think the problem is they want calculus in the curriculum and it is too late to be able to put it in context. There are some great uses for calculus that are accessible to many high school students. In particular, with physics you usually learn about capacitors and nuclear decay. Both of these cases are basically solving the differential equation y' = ky but:

- the physics course can’t depend on the concurrent maths course because you are allowed to take physics without taking maths, so you just learn weird equations full of exponential a instead of the ODE

- I think the maths course doesn’t even teach differential equations. They are in FP1 (from a separate ‘further maths’ course) but definitely not in AS (penultimate year of school) maths. Possibly a few turn up in A2 (final year) but then they can’t have any good examples from physics because not everyone doing maths will be able to depend on knowledge about what a capacitor is or how nuclear decay works. But I guess population models might work.

- there can be some better stuff in the further maths course (e.g. I think they might even have the ‘exponentiate a matrix’ solution to systems of first order linear ODEs)

I recall in my highschool the math and physics (both were mandatory) teachers explicitly coordinated so that the derivatives and other relations were taught right before they got applied in physics. There are much simpler examples than capacitors and nuclear decay, you can explain all aspects of physics (starting with basic mechanics, position/speed/acceleration) simpler if you can rely on calculus.

I've seen pretty bright seeming UK university applicants able to do whatever you ask them but then completely shit the bed when you ask them to differentiate e^y with respect to y rather than e^x with respect to x.

Even worse, I've seen a lot of people that where convinced the derivative of f(x)=e^7 is e^7

That would trick me too... Exam questions never ask 'trick' questions like that where the answer is zero/infinity/undefined.

I genuinely don't know whether the trick of that question is swapping the `e^x` with `e^y`, so just renaming a variable – or is `y` a function?

You're differentiating the function f(y) = e^y with respect to y

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