In A level and university mathematics, do you need to know WHY you do what you do?

Im in GCSE right now and I realise that I dont know why I do what I do. I just follow a set of rules, for example I know that the quadratic formula is-b ± √b^2-4ac / 2a but i dont know why we divide it by 2a or why its -b and not +b at the start. Is this how a level and university is?

(edited 5 years ago)

Reply 1

Muttley79

Original post by Azimbrook1

I cover this at GCSE - it comes from completing the square on a general quadratic equation. You don't have to learn the proof at GCSE but I think it's helpful to know why it can be used and why it works.

Reply 2

pearl_rose

No I think at A Level you are shown how the quadratic formula was formulated if I remember correctly. And I think there are several proof questions that deal with why you do what you do...

Reply 3

poohat

High school mathematics is taught very, very badly. As you say, it tends to just be a case of being shown various formula and told to memorise/use them. Students rarely have any real idea where they come from or why they are true, since this isnt taught. Its a shocking failure of curriculum design. So your lack of understanding isnt your fault, and almost all other students will have the same experience.

In university mathematics things are completely different, and the emphasis is on learning and understanding _why_ things are true, and being able to derive and prove them.

(edited 5 years ago)

Reply 4

poohat

This is incorrect, at least for a maths degree. Everything should be fully derived and explained (at least in the pure courses).

For an engineering degree, a lot of details will be skipped over (as you say) but enough concepts are taught to get a general understanding.