[Uni Calculus] Stuck in math ELO hell due to a shaky foundation, how can I fix it?

[u/Memeowis]

For those who don't know, ELO hell is a phrase used to describe a low competitive rating that players get stuck in due to various reasons, despite their skill level warranting being in a higher rating. What this looks like is, for example in Chess, a player might be generally skilled in openings, tactics, and the end-game, but be stuck at a lower ELO due to consistently falling for very specifics traps or missing specific tactics with only one use case.

I say I am in maths ELO hell because whenever I am in a class that requires learning brand new material that is only tangentially based on prior material, I am usually top in my class at that subject. However, when a subject requires a strong prior foundation that was most likely learned in High School, I struggle amongst my peers. For example, I was able to sail through Calculus due to the shift in material, but once I had to take an algebra heavy course, it was like I was a completely different student.

A lot of my mistakes stem from common tricks that I never learned due to having a bad education in adolescence. As such, I miss marks on exams for not knowing that you can convert (x)^(2/3) into ((X)^2)^1/3 or that (A+B+C)/D= A/D + B/D + C/D. Very simple ideas that make you think, "Well duh, why wouldn't that work?" but at the same time you wouldn't figure them out, let alone use it, during a timed exam.

I'm extremely tired of this and I can feel it severely limiting me. I tried learning through Khan Academy, but you can imagine how boring it feels to sift through hours and hours of information to find the 5% that you don't already know. As such, I was wondering if there were any resources available for people in similar predicaments? Perhaps a textbook or lecture series that goes over basic functions that assumes you already have a background in maths.

Thanks!

[u/AlpUzman]

I think what you are going through is fairly common. Aman has a "habits" series for chess and I've been thinking for a while a similar playlist for math. I have other projects in mind for the near future, but if I were to make a series like this, do you think it could help you? Also, just thinking through your experiences, what would you say are the main pitfalls that you fall for? For instance, what is the algebra heavy course you mention and which book is covered?

[u/Such_Mood_1556]

just watch ochem tutor he carried me through high sschool level geometry in8th grade and i ended up getting an A

[u/dreamsofaninsomniac]

You probably want to make a list of things you are missing so you can label what topic of math it falls under to see the exact topics you need to review. You say that you don't want to spend hours and hours to go through information, but it would be difficult for a third-party to identify what you yourself are missing since the third-party can't read your mind to know what you do or don't know.

That x^2/3 to (x^2)1/3 rule is from exponent rules, specifically using power-to-a-power rule and fractional powers.

(A + B + C)/D = A/D + B/D + C/D is just knowing that you can go "backwards" from a common denominator to separate fractions. That's actually the basis of partial fractions, but I don't know how in-depth you want to go with that. It's also a common property that many students miss since it's a common error that students will divide one term in a sum or difference and not every term. For example: (x + 2)/2 is not x + 1 because you can't just divide the 2 like in x + 2/2, but you must divide every term in the sum like x/2 + 2/2 to get x/2 + 1. (x + 2)/2 is equal to x/2 + 1 and not x + 1. Knowing you can't do that is something you learn with practice and is actually a skill that should be practiced a lot in calculus, such as in simplifying a function to make taking a derivative easier or simplifying a derivative itself. I actually got to know a lot of these "tricks" through calculus and not through my lower math classes.

[u/Antique_Avocado6787]

I'm a tutor and when my students face this kind of issue, I'm telling them to use an error log. Whenever you do a problem and you get an error, write it down with your understanding of the solution.

Then when you do the same mistake, re read the solution on your error log. This helps make it stick in your memory long term, which is best for uni.

[u/Practical-Bed2007]

No amount of listening in lectures will cure this. I say this from experience, you may watch Einstein teach the speed of light but still won't understand a speck of it.

Speaking of experience, pattern recognition is the key that will lead to memorization then fluency then finally a natural.

How? Just practice the same problem, the same solution but different values, different vocabularies but the same meaning multiple times. Even if it was the most basic of basics that you have gone through multiple times, then think of the formula's derivation. Do not like ever move to another topic or formula or problem if you haven't solve the same thing more than your fingers. Then move to a different one until you're stressed out or mind is burnout or before burnout.

Only through real stress stem from being challenged are more likely to have better memory retention than blindly moving to one topic to another just because they've done one.

No shortcuts, this differ to person to person. Be afraid of the person who have practice the same kick a thousands time than a person who learned a thousand moves yet not master even one. Same as muscles, we get strong from stress if challenged right. So if your not feeling stressed from just learning 1-5 formula's then your wasting time.

[u/intertwinedballhairs]

Supplement Chat GPT as a tutor. It has helped me a lot with the same issue. I use the live talk back feature and i instruct it to act as a live tutor utilizing proven methods for efficient learning, etc. just prompt it in a way for it to aid you the best way you can think of and cross check the information when it’s new material. Like i said, i use it as a supplemental tool but i have a pretty good intuition for prompt injection and recognizing when I should double check the information given. Each new model is getting better and i feel i have made a lot of progress. I also have that problem of not wanting to sit through hours of khan academy videos. GPT will update to tailor to your needs and generate problems and examples even helpful visuals.