[HN Gopher] Spaced Repetition for Mathematics
___________________________________________________________________
Spaced Repetition for Mathematics
Author : mkl
Score : 16 points
Date : 2022-08-08 20:40 UTC (2 hours ago)
(HTM) web link (cronokirby.com)
(TXT) w3m dump (cronokirby.com)
| ksd482 wrote:
| The "mochi cards" link leads to Anki. But I think this is the one
| the author is talking about: https://mochi.cards/
| e_joules wrote:
| Intuitively I do not think this would work. Well, I mean it
| depends on what you are doing. For graduate oral exams it might
| be a good way to prepare.
|
| But if you want to get dexterity in some field, i.e. being able
| to actual solve problems, I think it would not work so well. I
| think there is a difference in how the brain stores and recalls
| information in this case. If you learn a definition by heart or
| learn a proof technique by heart, you would be able to recall it
| perfectly when asked directly for it. However, I suspect that
| when you would be actually solving a problem and you would need
| to recall this information your brain would not be able to make
| the connection.
|
| That is why in mathematics one is usually required to solve a lot
| of problems and why studying the theory by heart does not help
| much. When you do a lot of textbook problems you brain starts
| making connections between the chucks of proof techniques and the
| chunks of definitions and the chunks of whatever features your
| textbook problems have. Those connections are the most important
| part of learning mathematics and you would not get them by simply
| learning facts.
|
| Basically, to say it in another way, you would learn the theory,
| but you would not learn the problem solving associated with this
| theory.
|
| Source: I studied mathematics, the wrong way for many years.
|
| EDIT: The most bitter experience I had studying mathematics. It
| was the first year of my graduate studies and I took an undergrad
| class in Graph Theory as my introduction to discrete mathematics.
| Since I was now a graduate student I decided to approach the
| class in the graduate student way. That means I focused really
| hard on learning the theory and learned all the proofs and all
| the proof techniques that we went through. And that was very fun
| because the proofs in Graph Theory tend to be very elegant. And I
| fell in love with the field. And then came the exam and I was
| feeling really good about all of this, because for maybe the
| first time in my life I had learned 105% of the theory required
| for the exam. That was the worst grade I got in my whole
| mathematics studying career. The problems on the exam were much
| simpler than any example or theorem encountered during class, but
| I just could not make the connections between the proof
| techniques that I had memorized and what I was looking at on my
| exam paper. I retook the exam three years later (it had no
| influence on my grade at this point), with very little
| preparation, but the preparation was 100% in solving exam type
| problems. I could maybe recall 60% of the theory and proof
| techniques. I got top grade.
| yCombLinks wrote:
| I think it's a good tool for quick access to many useful tools
| in a toolkit. Yes, you need to know how to apply the tools, but
| quickly being able to manipulate a problem into several other
| forms makes lots of problems much easier.
| spekcular wrote:
| I agree with the claim that problem solving is essential to
| learning mathematics. And I have had the exact same experience
| where I did well on math exams by ignoring most of the theory
| and proofs of main results, and focusing solely on examples and
| problem solving.
|
| However, I think straight-up memorizing definitions and theorem
| statements is really useful for problem-solving/exam prep, just
| so they're at your fingertips. There's no way you're passing a
| real analysis exam if you can't regurgitate the epsilon-delta
| definition of a limit in your sleep.
|
| What seems to occur (at least for me) is that you naturally
| memorize all of these things in a somewhat inefficient fashion
| by doing problems. If the concept gets used in enough problems,
| it slowly burrows its way into your memory - and this is a very
| durable kind of memory, as you point out. But I do think for
| things like graduate school qualifying exams you can "juice"
| the process by explicitly memorizing core material.
|
| Probably it's not as useful for doing research, though.
| bitlax wrote:
| "In order to be successful as a mathematician, you must commit to
| memory all definitions and statements of theorems, for these are
| the tools by which you can construct valid mathematical
| arguments. Of course, memorization is not always fun, but
| sometimes it is just simply required." -Steven Roman, Abstract
| Algebra: A Comprehensive Introduction, Volume 1: Linear Algebra
| rahimnathwani wrote:
| In the 'conditions for theorems' section, I wonder whether it
| would be easier (and just as effective) to put the whole theorem
| (including conditions) in at once, and then use cloze deletion to
| get tested on different parts.
___________________________________________________________________
(page generated 2022-08-08 23:00 UTC)