How to Study Science: Integrating Spaced Repetition Review

[StudentOfScience]

Note: for easy reference, "serious" questions and such are italicized. I also should note that although the title says "science", I include many references to mathematics (I suppose one could argue that it is a science in some senses). Furthermore, in another thread that I've posted, some people were curious to know about my intent for learning these subjects. In short, I can say it's to be able to compete at the Olympiads (high school student here) in addition to learning the material to "learn the material".
Greetings, I've been thinking about this for some time now (and I'm aware that there are other threads discussing similar material); I've been wanting to know the ideal way to blend the two main components of study (learning and review, at least in my opinion) effectively using SRS - spaced repetition system - software in order to learn conceptual and problem and proof based subjects (such as the mathematics). Namely, I am wanting to study a wide array of subjects, so having an effective study system is desirable. (I'm not sure what I'll major yet; my Biology base is stronger than my chemistry and physics, and I'm just starting to seriously get into theoretical math. Hey, I may like more than one discipline and may double or triple major; it's just too early to know.) I should also state that SRS, while has the potential to be very useful - may not be ideal for everything. What I am asking you all, the friendly and insightful PF users, is how efficient and useful is this prospective study system?
Learning

For math and physics, I suspect learning would consist of active reading and a large amount of problems. In reading, one could try proving each theorem and noting where difficulties arise or where there are noteworthy points/tricks/etc. Timely, but from suggestions I've seen, it may be useful. In regards to problems, I would think a problem that is noteworthy or emphasizes an important point should be done. However, knowing which problems to do or omit isn't always easy. For instance, it seems just about almost every problem in Morin's Mechanics falls under the "noteworthy" category. This leads me to this question: how do you pick out your practice problems, especially if most of the problems are very challenging? Also, since I am not a seasoned proof-writer, am I allowed to post my proofs on PF to be dismantled (so that I could see what I did wrong)?
I find this quote from https://www.supermemo.com/english/ol/ks.htm#Intelligence interesting. " In other words, apart from solving particular problem instances as a form of repetition, I see no reasonable alternative to pure memorization of derivation steps as the best means of boosting the student’s problem solving capability (i.e. intelligence in the first of the mentioned interpretations). The general rule then is: whenever possible and sensible, memorize the derivation steps of a particular solution to a general problem." I don't know if this will help me reach my goal of being able to prove or disprove a claim based on a collection of hypothesis (in a subject that I've studied sufficiently) without having to rote-memorize theorems and their proofs. What are your thoughts?
Now onto subjects that still have problems but their role is not as significant as it is in mathematics and physics (I think): chemistry and biology. Rote-memorizing is also advised against; understanding is the important part. I have found that I am not very good at taking notes; I go overboard on the details and my notes essentially become a slightly rewritten version of the chapter with my questions. And I do this for specific reasons. I think that the details are important as well as building the conceptual foundation where the details in which the details fit. But I am too OCD about leaving out the details that my efficiency is bogged down. It may be that I'm not good with active note-taking in these subjects as they may require me to filter through the information.
This leads me to an array of questions: how exactly do I learn chemistry and biology, then? How should I handle the details? In regards to Organic Chemistry, I find post #6 from https://www.physicsforums.com/threads/how-do-you-study-organic-chemistry.636283/ intriguing. What is the right way to study organic (when I get there)? What about choosing my problems? Would it be effective to use SRS software, and would it encourage rote-memorization (which is not recommended, unless it's something like anatomy)? I appreciate your answers.
Review

Reviewing will keep you (hopefully) from forgetting what you have learned, which would be unfortunate, especially if the subject is difficult. The idea of using the SRS is so that I have a review schedule which will help counter the "forgetting curve". This may even help me to build an intuition in more theoretical subjects since I will be repeatedly exposed to the subject matter. (Using intuition rather than logic, though, may be advised against. Intuition based on logic from review may not hurt. I am not sure though).
I think that an SRS system, like Anki, could even be used with reviewing mathematics. However, a different approach, rather than just reviewing concepts like in Biology, would reference problem sets and individual steps in a proof so that you will be familiar with a, say, clever trick used (and hopefully you'll be able to use it later in a different proof). I am not saying to memorize all the theorems and proofs word-by-word; I am suggesting that this type of review might keep you fresh with the material, and, after the methods of that course (like ODE or anlaysis - I'm just throwing out examples) should become "ingrained". With this, you might* be able to prove something on your own by knowing a collection of hypothesis/implied hypothesis without memorizing a theorem verbatim. Feedback on this review of math (and probably physics as well) is appreciated!
As an example for the previous paragraph, consider this quote from https://www.scotthyoung.com/blog/2014/11/07/srs-for-concepts/:

"Anthony • 2 years ago

I agree with what has been written in this article. However, there is a way to use SRS that I believe eliminates most of these problems. Instead of using its flashcards to pose questions directly, the flashcards may be used to give instructions. In this way, its spacing algorithm may be used while retaining the flexibility of practice associated with non-SRS review. For example, one may give instructions to review a particular problem-set; in this case, the problems selected for review of the relevant concepts might be new.

To increase the usefulness of spaced practice when focusing on questions that have been solved before, one could use a big-picture focus and explain the concepts involved in solving the problem while solving the problem, as if giving a tutorial."
For chemistry and biology, reviewing with SRS may be good. It may encourage the rote-memorization path though, which is what I want to avoid (unless if it is a subject like anatomy. Seriously, is it possible to study anatomy at an in-depth level without rote-memorizing?). I could possibly do something similar with math and physics; referring to a specific problem may be useful, but how would I review concepts? Maybe I could employ an informal "teach it to someone else". What do you all think?
Overall, SRS seems to promise a "counter" to the forgetting curve as well as increasing logic-based intuition one has on a subject. It may even help while learning a subject such as biology, and if a program like Anki is used, it may also be used to review. However, other subjects such as math are probably better learned by trying to prove what you can and solving a multitude of problems. Obviously, I am not very knowledgeable in many of these subjects; I'm indebted to your feedback. And, thank you for taking the time to read this very, er, wordy post.
*I am not at this point yet; I am speculating. For all I know, this may just be ineffective and is a fancy way of saying to rote-memorize, which is a no-no in many subjects such as mathematics. This highlights the importance of your feedback

 

[StudentOfScience]

Bump.

 

[Mark44]

Your post is quite long, which might have caused many readers to ignore it.

My area of expertise is mathematics, so I will comment on the parts of your post where you discuss this discipline.

Note: for easy reference, "serious" questions and such are italicized. I also should note that although the title says "science", I include many references to mathematics (I suppose one could argue that it is a science in some senses). Furthermore, in another thread that I've posted, some people were curious to know about my intent for learning these subjects. In short, I can say it's to be able to compete at the Olympiads (high school student here) in addition to learning the material to "learn the material".
Greetings, I've been thinking about this for some time now (and I'm aware that there are other threads discussing similar material); I've been wanting to know the ideal way to blend the two main components of study (learning and review, at least in my opinion) effectively using SRS - spaced repetition system - software in order to learn conceptual and problem and proof based subjects (such as the mathematics). Namely, I am wanting to study a wide array of subjects, so having an effective study system is desirable. (I'm not sure what I'll major yet; my Biology base is stronger than my chemistry and physics, and I'm just starting to seriously get into theoretical math. Hey, I may like more than one discipline and may double or triple major; it's just too early to know.) I should also state that SRS, while has the potential to be very useful - may not be ideal for everything. What I am asking you all, the friendly and insightful PF users, is how efficient and useful is this prospective study system?
Learning

For math and physics, I suspect learning would consist of active reading and a large amount of problems.

Bingo.

In reading, one could try proving each theorem and noting where difficulties arise or where there are noteworthy points/tricks/etc.

I don't know that this will be an effective use of time, particularly in areas at or below calculus, and depending on how rigorous the textbook is. In many textbooks, the expectation is that the student will merely use the theorem to work problems; the theorems themselves are often considerably more sophisticated than the problems the theorems are meant to be applied to.

Timely, but from suggestions I've seen, it may be useful. In regards to problems, I would think a problem that is noteworthy or emphasizes an important point should be done. However, knowing which problems to do or omit isn't always easy. For instance, it seems just about almost every problem in Morin's Mechanics falls under the "noteworthy" category. This leads me to this question: how do you pick out your practice problems, especially if most of the problems are very challenging? Also, since I am not a seasoned proof-writer, am I allowed to post my proofs on PF to be dismantled (so that I could see what I did wrong)?

Yes. You can post them in one of the sections under "Homework and Coursework Questions." There are two sections for Physics, and two more for math.

I find this quote from https://www.supermemo.com/english/ol/ks.htm#Intelligence interesting. " In other words, apart from solving particular problem instances as a form of repetition, I see no reasonable alternative to pure memorization of derivation steps as the best means of boosting the student’s problem solving capability (i.e. intelligence in the first of the mentioned interpretations). The general rule then is: whenever possible and sensible, memorize the derivation steps of a particular solution to a general problem." I don't know if this will help me reach my goal of being able to prove or disprove a claim based on a collection of hypothesis (in a subject that I've studied sufficiently) without having to rote-memorize theorems and their proofs. What are your thoughts?

It's useful to have a collection of problem-solving techniques on hand, so I guess this means that you should have a good idea of the steps involved. I don't think that it's necessarily a good idea to rote-memorize the proofs of a bunch of theorems.

Now onto subjects that still have problems but their role is not as significant as it is in mathematics and physics (I think): chemistry and biology. Rote-memorizing is also advised against; understanding is the important part. I have found that I am not very good at taking notes; I go overboard on the details and my notes essentially become a slightly rewritten version of the chapter with my questions. And I do this for specific reasons. I think that the details are important as well as building the conceptual foundation where the details in which the details fit. But I am too OCD about leaving out the details that my efficiency is bogged down. It may be that I'm not good with active note-taking in these subjects as they may require me to filter through the information.
This leads me to an array of questions: how exactly do I learn chemistry and biology, then? How should I handle the details? In regards to Organic Chemistry, I find post #6 from https://www.physicsforums.com/threads/how-do-you-study-organic-chemistry.636283/ intriguing. What is the right way to study organic (when I get there)? What about choosing my problems? Would it be effective to use SRS software, and would it encourage rote-memorization (which is not recommended, unless it's something like anatomy)? I appreciate your answers.
Review

Reviewing will keep you (hopefully) from forgetting what you have learned, which would be unfortunate, especially if the subject is difficult. The idea of using the SRS is so that I have a review schedule which will help counter the "forgetting curve". This may even help me to build an intuition in more theoretical subjects since I will be repeatedly exposed to the subject matter. (Using intuition rather than logic, though, may be advised against. Intuition based on logic from review may not hurt. I am not sure though).
I think that an SRS system, like Anki, could even be used with reviewing mathematics. However, a different approach, rather than just reviewing concepts like in Biology, would reference problem sets and individual steps in a proof so that you will be familiar with a, say, clever trick used (and hopefully you'll be able to use it later in a different proof). I am not saying to memorize all the theorems and proofs word-by-word; I am suggesting that this type of review might keep you fresh with the material, and, after the methods of that course (like ODE or anlaysis - I'm just throwing out examples) should become "ingrained". With this, you might* be able to prove something on your own by knowing a collection of hypothesis/implied hypothesis without memorizing a theorem verbatim. Feedback on this review of math (and probably physics as well) is appreciated!

This is basically what I said earlier -- that it's important to have a number of techniques on hand, but not necessarily the verbatim proofs.

As an example for the previous paragraph, consider this quote from https://www.scotthyoung.com/blog/2014/11/07/srs-for-concepts/:

"Anthony • 2 years ago

I agree with what has been written in this article. However, there is a way to use SRS that I believe eliminates most of these problems. Instead of using its flashcards to pose questions directly, the flashcards may be used to give instructions. In this way, its spacing algorithm may be used while retaining the flexibility of practice associated with non-SRS review. For example, one may give instructions to review a particular problem-set; in this case, the problems selected for review of the relevant concepts might be new.

To increase the usefulness of spaced practice when focusing on questions that have been solved before, one could use a big-picture focus and explain the concepts involved in solving the problem while solving the problem, as if giving a tutorial."
For chemistry and biology, reviewing with SRS may be good. It may encourage the rote-memorization path though, which is what I want to avoid (unless if it is a subject like anatomy. Seriously, is it possible to study anatomy at an in-depth level without rote-memorizing?). I could possibly do something similar with math and physics; referring to a specific problem may be useful, but how would I review concepts? Maybe I could employ an informal "teach it to someone else". What do you all think?
Overall, SRS seems to promise a "counter" to the forgetting curve as well as increasing logic-based intuition one has on a subject. It may even help while learning a subject such as biology, and if a program like Anki is used, it may also be used to review. However, other subjects such as math are probably better learned by trying to prove what you can and solving a multitude of problems.

I agree. I don't see much advantage in a software solution here.

Obviously, I am not very knowledgeable in many of these subjects; I'm indebted to your feedback. And, thank you for taking the time to read this very, er, wordy post.
*I am not at this point yet; I am speculating. For all I know, this may just be ineffective and is a fancy way of saying to rote-memorize, which is a no-no in many subjects such as mathematics. This highlights the importance of your feedback

 

[StudentOfScience]

I don't know that this will be an effective use of time, particularly in areas at or below calculus, and depending on how rigorous the textbook is. In many textbooks, the expectation is that the student will merely use the theorem to work problems; the theorems themselves are often considerably more sophisticated than the problems the theorems are meant to be applied to.

Yes, I am self-studying multivariable calc with linear algebra using Hubbard and Hubbard. It probably isn't the MOST rigorous, but I intend to make a second pass on these subjects more rigorously (e.g., using Kunze Hoffman for Linear Algebra). Given this information, do you think this type of active reading (of course with problems) is effective? Or would just understanding (but not attempting to prove the theorem & its proof) the theorem and proof followed by problems be more effective?

Also, I remember you saying

It's useful to have a collection of problem-solving techniques on hand, so I guess this means that you should have a good idea of the steps involved. I don't think that it's necessarily a good idea to rote-memorize the proofs of a bunch of theorems.

I see where you are coming from and can relate; for example, it'll probably be a long time before I forget some earlier math concepts since I've practiced them a lot and used them in later courses that built upon the earlier ones. However, I would think that this is probably (not sure though) harder to achieve with more abstract mathematics. Do you suggest any effective ways to review math and how often I should review them?

Thank you so much for your response!

 

[StudentOfScience]

Bump. So far, I've got an idea for math and physics learning (but not exactly sure for review). For more conceptual subjects like biology and chemistry, how do you all suggest I review and learn? Would SRS (spaced repetition system) review be helpful?

Thank you all.

 

[Drakkith]

Bump. So far, I've got an idea for math and physics learning (but not exactly sure for review). For more conceptual subjects like biology and chemistry, how do you all suggest I review and learn? Would SRS (spaced repetition system) review be helpful?

Thank you all.

I don't think there's really any way for us to know what would work for you. Repetition is good for memorizing things and to cement certain skills, but how much repetition you should use versus something else is difficult to say. Pictures, charts, mnemonics, or other ways of making it easier for your brain to "connect the dots" are also helpful.

Honestly my best advice is to not to worry too much about trying to find the perfect method and just do something. In other words, pick a couple of methods and just keep doing them. If you find that one method just doesn't work for you, then don't do that one.

Also, please don't bump threads more than once. Per the rules:

Bumping
Do not "bump" one of your threads to the top of a forum's thread list by posting a basically empty message to it, until at least 24 hours have passed since the latest post in the thread; and then do it only once per thread.

 

[StudentOfScience]

Thank you so much for the advice, and I'm sorry about the infarction of the rules; thanks for letting me know ;).