...only to purge it from brain as soon as that exam was passed. If i dont use knowledge, then my brain purges it to makes room for something more useful.
A theory to this is that it isn't a "purge" as such, but the way your brain works is that when you learn and reinforce, the signal paths in your brain that exercise that knowledge strengthen. As you stop using that knowledge, those same signal paths weaken and become much harder to recall or use that knowledge.
Just like a muscle - it strengthens with use and weakens otherwise, which makes it more difficult to use effectively.
Sometimes learning maths - like learning many things - is more than just numerical knowledge or mathematical process. It's about creating mathematical "sense" and aptitude in the same way that running laps of a circuit builds fitness and stamina.
That is part of the issue. rote learning formulas is meaningless without knowing the the principles behind it.
While interest and compound interest can be derived without knowing calculus, it is much simpler and intuitive to derive using calculus.
We might have to agree to disagree on this one. I think it's far simpler to derive and understand compound interest without (or rather, pre-) calculus. That's a reason why we can teach compound interest far earlier than we can teach calculus (
formal calculus; not counting concepts like average rates of change).
Understanding formulae won't be enforced unless it is tested. It's fascinating, mathematically satisfying and does give great insight if you are adept at maths; for those who are struggling, it does the opposite of helping them. Which is probably why most textbooks have dispensed showing proofs of formulae now.
Besides, it's one thing to be able to use a formula. It's another if you can rearrange it (
without memorising all possible rearrangements).
For example, why is the area of a circle 𝛑r?
The easy way to understand this is to cut the circle into infinitesimally small "pizza" pieces and stack them opposite side to side to form a rectangle and knowing the axiom that C=𝛑d
...and that might involve calculus-like concepts (infinitesimally small slices), but overall the development and understanding does not fundamentally require calculus.
To actually derive the area of a circle via proper calculus is quite advanced.
That is true but that assumes that superficial knowledge is all that is required.
The problem arises when a deeper understanding is required.
I run into this issue both with maths and digital technologies.
People presume that we won't really need to learn coding at all fairly soon; much less HTML and CSS to know how to write web pages. It is true that there are a lot more tools out there which can help one create a website without so much as knowing a shred of HTML or CSS (let alone JS) - and decent ones at that, even with merchant facilities - and many tools out there to help with coding, ringing in the "vibe coders". But knowing what goes on under the bonnet is still incredibly valuable and I think will take a long while before that goes away.
Luckily, as a digital technologies teacher, I don't get swathes of parents writing complaints in about how useless it is to teach kids coding because of powerful AI.
Maxim for the modern era: just because a child has a computer and appears to be able to use it
doesn't mean they know how to use it properly. My school is BYOD, so you'd think my students know how to use their own computer? Ask them to create a folder in a folder, download a document, move it to a folder, rename it to something else, create a .zip archive from a folder, find a file in their folder system...... yeah, pretty much all of them failed. Of course, nearly all my students use Macs.
