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A lot of people don't seem to understand that fluency in problem solving comes partially from memorization. Memorizing all of the theorems you need, proofs, an
by kaashif 2y ago
A lot of people don't seem to understand that fluency in problem solving comes partially from memorization.
Memorizing all of the theorems you need, proofs, and a diverse set of examples is going to make it substantially easier to approach new problems.
I've heard it from people conducting interviews, when we're discussing what we want from candidates: "I'm not looking for memorization, I'm looking for problem solving!" - if you've memorized 1000 problems, you'll be better at problem solving than if you didn't!
- magicalhippo 2y agoWhile it's true that memorization can help improve your skill, it's not a given. There are lots of folk who can remember all sorts of details but never seem to be able to figure out how to put the pieces together.
- joe_the_user 2y agoWhat do you mean by memorizing? Of course, a mathematician remembers things but no mathematician learns a field by first attain the ability to recite the theorems in a book without understanding.
- ggm 2y agoThat's almost exactly how people did the trivium, to lay the ground for what follows. I think people are trying to say memorising is critical, understanding follows, not leads.
- Jensson 2y agoUnderstanding leads to memorization, not the other way around. Chess masters can easily remember chess positions, but they didn't practice that it comes from fluency. Same with math, memorization comes by itself when you have grokked the subject well enough to make memorization trivial.
- ggm 2y agoI'm not a mathematician so if this is an axiom of the ontology of meaning in maths, I have to accept it but if we are using the words in their commonly understood meaning you're completely wrong. I have memorised the first line of "I've got a lovely bunch of coconuts" in swedish and i assure you I have no underlying understanding of Swedish. (For jor can inte far opp min kokosnutt btw)
- eszed 2y agoYeah, I doubt the "common meaning" really covers it. To extend your example: I would bet (although I know no Swedish beyond "skål!"), that the manner in which you say those words would instantly make apparent (to a Swedish speaker) that you do not speak Swedish. I think the commenters need to agree on a more-nuanced set of terms to reach agreement on this.
- kaashif 2y agoThe arrow doesn't go one way. Understanding and fluency go hand in hand. When you have all of the theorems and techniques at your fingertips, understanding actually is easier. And vice versa. But "understanding" on its own doesn't allow you to reproduce a textbook full of theorems, you have to actually study and memorize at least a bit.
- joe_the_user 2y agoThere's a reason that "trivia" comes to us from trivium. Once, in medieval times, rote memorization was a large part of the education process. This system was renowned for not producing flexible or imaginative thinkers. Medieval times produced very significant mathematicians, notably and mathematical advances actually detoured around medieval Europe, going from ancient Rome and Greece to India and the Muslim world and returning to Italy with the Renaissance. I think people are trying to say memorising is critical, understanding follows, not leads. Sure, I think those posters framing things this way are incorrect. Problem solving may be something one learns and remembers but rote memorization, as in the medieval trivium, isn't significant part of such learning.
- quantum_state 2y agoWould observe that math is something one should not learn by memorization … rather should try to get to the essence and build it up naturally while at the same time get some sense and intuition of things … so that one would become a natural …