[omnicognate]

I had a similar view as a kid, driven mostly by the fact that I wasn't very good at memorisation. I found that I could get by in maths without it, eg. deriving the quadratic formula by completing the square rather than memorising it. I didn't value memory much as a tool in maths.

After having studied maths and physics at university and worked as a programmer in a mathematical field for 20 years (and studied much more maths in my spare time), I now see my poor recall as the limiting factor in my abilities in maths. The main reason I don't think I could ever have been a professional mathematician is that I would have reached (and have reached in my own learning as an amateur) a ceiling.

I have maths books that are beloved to me, that I have read multiple times (actively, working with pen and paper as one should) and which I will enjoy again in future. But the concepts in those books do not remain in my mind. I don't reach a point where the structure of basic linear algebra, say, is baked in.

I am good at the problem solving, but maths is an edifice, one people have been building onto for millenia. I explore that edifice, and keep returning to my favourite bits of it, but the portion of that structure that is resident in my mind is, and I think always will be, small. It's a window, and as more comes into it, more slides out. Everybody must have such a window, but I know others have much larger windows than me. And that's fine - I'm a programmer, not a mathematician. But I think it's something I would have benefitted from understanding earlier in my life. Perhaps I would have set about "learning to learn" differently. Rote memorisation and active curation of memories already formed could have benefitted me greatly.

[Hayarotle]

> I had a similar view as a kid, driven mostly by the fact that I wasn't very good at memorisation. I found that I could get by in maths without it, eg. deriving the quadratic formula by completing the square rather than memorising it. I didn't value memory much as a tool in maths.

Isn't the structure of the school curriculum also at fault here? If concepts like the quadratic formula being presented without context on why you will need to memorize them, and you're able to succeed without doing it, it's clear why you might choose not to memorize it. That wouldn't be the case if they presented you with challenging, applied problems where having the quadratic formula memorized really is actually necessary.

The curriculum seems to be structured under the assumption that the students will memorize the facts for the sake of memorizing (as most students do) in order to get good grades, and only later apply them on more advanced classes. If you're able to derive the results fast enough, and as such you see no point in memorizing them, then that assumption is broken, and the curriculum won't work the way it is expected to. Those students would need to take initiative themselves to adapt their learning style to the way books and classes are structured, as it's not obvious for them that such memorization is necessary.

[BeFlatXIII]

From my personal experience, I find that schools often fail to prepare their top students because the exercises meant to teach you how to work hard for real this time are still passable with a last-minute cram session by the fastest students. By the time the assignments are actually too long to be crammed, it's often well past the safety of K–12 education.

[tartoran]

I’ve had a similar intuition and approach as a kid though in school I had to memorize definitions and formulae, I never fully commited them to memory, instead choosing to derive them on the spot thinking I was practicing a different muscle, understanding. The bad part was building a bad habit of avoiding rote memorization at all costs whict lead to similar limitations later on. Only later on did I understand that it’s all about building good habits that yield great returns over time.

[BeetleB]

> After having studied maths and physics at university and worked as a programmer in a mathematical field for 20 years (and studied much more maths in my spare time), I now see my poor recall as the limiting factor in my abilities in maths.

Same story here. Undergrad engineering math curriculum came easy to me, and it stuck as it was our bread and butter (calculus + diff eq). Once I got to grad level courses, the frequency with which we would utilize the material elsewhere dropped dramatically, and the net effect of that was I could never recall the topics until I needed them.

The next problem was even more significant: If I took even higher level courses, they relied on knowledge of the material I took in one of those prior courses that had not been burnt into memory, and may have taken 2+ years prior. The only reason I did poorly was because I had not memorized enough of the prior material.

On my own, I studied/reviewed the undergrad statistics course 3 times over many years and it never stuck. Finally, in 2018 I used spaced repetition to memorize much of the material, and over 3 years later I can still read material that utilizes those statistics and understand what I'm reading.

Memorizing is useful for things you don't use often.