Hitting upper level classes and I can barely remember anything

[knightknave]

Hello guys,

I was wondering if you all, who are more experienced than I, could perhaps offer a bit of advice about something I'm struggling with. I'm starting to feel very, very stupid.

I'm a third year math/finance major who's struggling with upper level courses. For some reason my entire degree has been a blur to me. I feel like I could have learned as much by watching youtube videos of people doing implicit differentiation.

While taking Calc 3 I realized I forgot the bulk of the finer details I learned in Calc 1 and 2 and therefore had to restudy it to get the details back. Similarly, while doing LA 2 I forgot the bulk of the more complicated stuff in LA 1 (eigenvalues/bases/subspaces/spectral theorem etc.) and had to restudy it. Intro. to analysis was not so bad as the bulk of it was self contained. This is starting to burn me in upper year as classes are much faster paced and profs rightfully assume we can recall all of our previously learned material.

In general, I find I can remember the general concepts and what the words mean, but in terms of actual details I come up blank. For example, one of my math profs the other day asked me to prove the chain rule and I couldn't despite doing it 5 times about 6 months earlier! My mind drew and absolute blank.

I'm not a poor student- I've gotten an A or A- in every math class I've taken thus far. For some reason though, none of it sticks. I generally do the majority of the practice problems and do attend every lecture so its not from a lack of effort.

Has this ever happened to anyone? Is it normal?

 

[chiro]

Hey knightknave and welcome to the forums.

Just so you know this happens to me as well.

It really depends on the course and what the focus is though.

If its a computational course where you plug in stuff, I usually forget all of the actual specifics of the formulas although I do remember what it all means.

The key thing I've found is to try and reduce everything down to comprehension in its minimal form. In every course there are only a handful of important concepts of which everything is derived from and if you do that then you will at least know a lot of the steps you need to derive what you need to derive.

I'm not saying the calculations are not important, but in my view they are secondary because its a lot easier to relearn a calculation than to relearn in your terms what the concepts are (sometimes you will have to phrase in your own understanding what you think the concepts are compared to what the other students or even your professor thinks the concepts are, so just remember that).

What do you try and remember and how do you think about math?

It's not really important as I said to know all the specifics, but it is important again in my view to know what the real focus is and why. If you know that, then the rest will come naturally even if you have to relearn how to do the calculation almost from scratch.

Also if you are worried that you can't remember a tonne of formulas or tables or whatever, then I wouldn't really be concerned about that because that's not what math is about: it's not about remembering formulas like you did in high school but rather something different.

 

[knightknave]

Thanks for the reply.

I'm glad to hear I'm not the only one who gets hit with this phenomena.

Generally, I try to learn the underlying concepts of the class I'm studying and then I try to link it together with what I've learned throughout the course to get sort of a "big picture" overview. Other times I'll get a theorem and try to figure out what it is useful for and remember it via. its use. However, I still find I cannot internalize the definitions to the point where I can actively recall them- just vague images of them.

Usually I have to severely concentrate for a prolonged period of time to remember something that I've done from first or second year- unless it was something purely rote like taking a derivative or integration parts. I wouldn't be able to do the harder questions (require more familiarity with the material) in linear algebra or analysis to save my life.

 

[homeomorphic]

Retention. Interesting issue. My views on the subject have evolved over time quite a bit.

If I had gotten serious about remembering what I learned back in high school, I wonder where I would be now. My old standard back then was that I would remember things enough to answer a question if I was quizzed on it. If the question triggered my memory to answer it, that was enough.

Of course, it goes without saying that we may not be aware of everything we gained from a certain class. I may not remember everything from my high school English class and have not made any effort to retain any knowledge about the books and plays that we read, but I honed my vocabulary and writing skills. So, part of it is the skills that you pick up. The second time you learn something, you probably can learn it at least twice as fast as you did the first time.

Another thing is that maybe a lot of what we learn in courses, you could think as support material for the main ideas, and that we should not be bothered so much if we forget it.

Finally, you could take the attitude that school is kind of like wine-tasting. You just try each wine and at the end, you can decide which ones you want to get more of. So, I may take a chemistry class and decide I don't like it. So, I don't have to make an effort to remember the contents of the course (although, personally, I would like to retain the basics of subjects so fundamental to the way the world works). You might not keep buying the wine, but maybe you can remember what it tastes like. And similarly, you might not remember the details of the class, but you remember the general flavor.

Be that as it may, the way most people go about learning in school does seem pretty inefficient. Sometime towards the end of high school or the beginning of my undergrad, this started to dawn on me. At first, I started to review more. It was no longer enough to just be able to answer a question when prompted. I would try to recall things without any note-cards, books, or anything else to prompt my memory.

One day, the thought struck me that maybe I could remember everything. Yes, you read that right. Everything.

In some ways, it's not so far-fetched as it may seem at first glance. I dismissed this thought at first, but it was such an interesting possibility that I continued to mull it over. After all, I thought, there are some things you just don't forget. Like, really basic things. I mean, you don't forget what a window is, all of the sudden. What is it about really basic things that causes them not to be forgotten? The second reason why this idea is less far-fetched than it seems is that everyone temporarily does it for tests if they are a good student. They remember everything just fine up until the final. It's only afterwards that the memory disasters begin.

What I ended up trying was just summarizing everything I learned in each class up to that point in my mind every day. So, actually, I came very close to remembering damn near everything in some classes. I still remember a very large portion of my undergraduate electromagnetics class to this day, something like 9 years later. Ditto with complex analysis. I haven't even thought about those subjects that much, and I did get rusty eventually on some things, but I reviewed the arguments so well in my mind back when I learned them that a great deal of it did stick.

However, when I got to grad school, I found the amount of material being thrown at me overwhelming and unmanagable. It became clear that I could no longer even come close to remembering everything. So, really, you have to be selective about what you try to remember. After you take a class, you have to look at it and ask what's the most important thing to take from the class. And focus on at least that one thing. A central thread, maybe. And you can keep thinking about it and reviewing if possible, so as not to forget it. Also, remember how to derive things, rather than remembering the things themselves can free up some mental resources. A related aid to retention is to try to get the feeling that you could invent the subject yourself. This is one reason why motivation is so important and why I am appalled by the lack of motivation present in many textbooks.

Another shortcoming of traditional ways of learning is that different subjects are kept too separate from each other. This is not helpful for retention (and other purposes). You remember ideas that are well-connected better than ones that have no relation to anything else that you know. For lack of a better expression, you want to try to make a complete graph. Connect all the vertices. Avoid the "bunch of random topics" approach. Try to build one big cohesive thing in your mind where every subject is related to every other subject.

Finally, one reason why I am so adamant about the importance of visual thinking and intuition is that they aid retention. When things are done by ugly, meaningless computations or brute formal manipulations, no can remember anything. Visualization and a deep understanding of concepts makes things memorable.

 

[chiro]

One sort of rule I have is that if you are able to take a problem and then flesh out a rough sketch of how you want to solve a problem, then that is a good indication that you understand the material.

This is the thing that needs to be done before any specifics are incorporated to solve a problem. Once you have done the first thing then you can look up any specifics and implement them as necessary.

Also the above is not the best definition because we all have a different idea of what a 'rough sketch' is and what exactly it includes especially in terms of specifics.

Again, with respect to my thinking, if you can explain the rough sketch in a simple manner to someone and they understand it, then its a good indication that you have something. It's obviously better to explain to someone with enough familiarity to comprehend what you are saying, but the point is that if you get this far, then you'll have enough comprehension to get into the nitty gritty details.

Also with regard to first year, I found a lot of this stuff is more or less just a set of tools to use when you have to use them. In other words, a lot of this stuff did not really contribute to actually solving problems, but more or less are the tools you need to go from the broad to the more specific solution. Manipulating symbols on a page in many contexts to me at least is not really problem solving, but more or less like using a screwdriver or a hammer when you are building a table or a house.

 

[genericusrnme]

Two methods work for me;
1) Study the subject for 9+ hours a day, work with it, solve problems and try to apply it to stuff.
2) Revise or recite everything you learned the next day without looking at notes

The second one I ripped straight out of one of those learn a language packages that I bought when I went to work in Greece for a period. It works surprisingly well.

 

[20Tauri]

That happens to me. Only a year after I took linear algebra I had a frightening moment when I realized that not only had I lost all the theoretical stuff, but I couldn't multiply matrices or take dot products (I looked those two things up, because that was a little inexcusable, haha). I can't remember, like, anything from calc except the most basic derivatives and integrals. It's awful. You use it or lose it, which is why the physics students I know are better at calculus than the math students who get pushed into proofs and then suddenly have to remember everything for real analysis.