This got long and a little ranty sorry :/ TLDR: Take a proofs course and get perspective outside the problems you are struggling on and return with the ability to ask questions about what your actually doing and how to verify you did it right.
I am not blaming you here but this mentality "The next time around I recognize the problem and basically just solve it from memory." Raises alarm bells for me. To me this says you are not engaging critically with a problem and arguable your pervious sentence tells me why. You are going over and over a problem which is fundamentally the same which is a disengaging process of learning and reasoning.
My suggestion is to focus less on you got the problem wrong and rather diagnosis why you got it wrong. Which is a very difficult thing to do alone. If you share a problem and the mistake you got I could try and help you. In general thought for me there are 2 major types of errors I run into when doing math. Yours may vary, but mine are Arithmetic errors and not understanding the theories.
Arithmetic -- i.e i said something like 1+1=3 somewhere and everything is wrong now. This happens a surprisingly a lot but the usually go back and check all your calculations almost never finds this issue for me. (if possible) I do have a lot more success with plug your answer back into the question and calculating what your input should be. This leads to the second point
Understanding the theories (and question) - If you understand what your solution is saying you should be able to find a different question to ask about your answer to be sure its right. If you can't you don't understand what your doing well enough. I have been picking on factoring because its easy to have hard problems that can be solved in many many different ways. But if you factor something essentially you found a zero so you should be able to do 2 things. One is plug your answer in and have the whole expression equal zero after (zero is always easiest to find because math is easy when you can set things to zero.) The other though is divide the the expression by (x-a). This reduce out perfectly and was a major way I checked my errors when I took a cryptography and number theory course.
Understanding something deeply is hard because there is no easy testable why to say that you do get it. But if you can ask questions like how do I know this answer is right its a good sign you have a lot more to learn what your actually doing. My final recommendation if you are trying to learn algebra is take a break from that. Do a intro to proofs class or lesson plan if you've never done that before. Those type of courses are suppose to teach systematic approaches to math that scale beyond do you know a formula that works. They also give you more intuition into what your doing because they teach you to think about the results of what you are saying and give perspective that the "algebra 2" courses you take in high school don't bother to even think about because they are focused on doing problems for problems sake which most people have enough problems they don't need more to solve for fun they want tools to handle a more diverse set better.
Thanks for responding. I think I was just discouraged because I was doing a lot of arithmetic errors. It was unclear if the errors I was making were errors of logic or errors of arithmetic. Just like learning a new programming language: you have logical errors and syntax errors (not just ones that get thrown by the compiler, but ones that are just improper use of syntax) and sometimes it's unclear what error you're really making.
I think the bigger issue was that in high school and even college math classes was that I always felt like I was rushing or being rushed. There wasn't really time to internalize concepts or ask why.
They also give you more intuition into what your doing because they teach you to think about the results of what you are saying and give perspective that the "algebra 2" courses you take in high school don't bother to even think about because they are focused on doing problems for problems sake which most people have enough problems they don't need more to solve for fun they want tools to handle a more diverse set better.
I'll take a look at this. I did proofs in a geometry class and really liked it.
Comments
This got long and a little ranty sorry :/ TLDR: Take a proofs course and get perspective outside the problems you are struggling on and return with the ability to ask questions about what your actually doing and how to verify you did it right.
I am not blaming you here but this mentality "The next time around I recognize the problem and basically just solve it from memory." Raises alarm bells for me. To me this says you are not engaging critically with a problem and arguable your pervious sentence tells me why. You are going over and over a problem which is fundamentally the same which is a disengaging process of learning and reasoning.
My suggestion is to focus less on you got the problem wrong and rather diagnosis why you got it wrong. Which is a very difficult thing to do alone. If you share a problem and the mistake you got I could try and help you. In general thought for me there are 2 major types of errors I run into when doing math. Yours may vary, but mine are Arithmetic errors and not understanding the theories.
Arithmetic -- i.e i said something like 1+1=3 somewhere and everything is wrong now. This happens a surprisingly a lot but the usually go back and check all your calculations almost never finds this issue for me. (if possible) I do have a lot more success with plug your answer back into the question and calculating what your input should be. This leads to the second point
Understanding the theories (and question) - If you understand what your solution is saying you should be able to find a different question to ask about your answer to be sure its right. If you can't you don't understand what your doing well enough. I have been picking on factoring because its easy to have hard problems that can be solved in many many different ways. But if you factor something essentially you found a zero so you should be able to do 2 things. One is plug your answer in and have the whole expression equal zero after (zero is always easiest to find because math is easy when you can set things to zero.) The other though is divide the the expression by (x-a). This reduce out perfectly and was a major way I checked my errors when I took a cryptography and number theory course.
Understanding something deeply is hard because there is no easy testable why to say that you do get it. But if you can ask questions like how do I know this answer is right its a good sign you have a lot more to learn what your actually doing. My final recommendation if you are trying to learn algebra is take a break from that. Do a intro to proofs class or lesson plan if you've never done that before. Those type of courses are suppose to teach systematic approaches to math that scale beyond do you know a formula that works. They also give you more intuition into what your doing because they teach you to think about the results of what you are saying and give perspective that the "algebra 2" courses you take in high school don't bother to even think about because they are focused on doing problems for problems sake which most people have enough problems they don't need more to solve for fun they want tools to handle a more diverse set better.
Thanks for responding. I think I was just discouraged because I was doing a lot of arithmetic errors. It was unclear if the errors I was making were errors of logic or errors of arithmetic. Just like learning a new programming language: you have logical errors and syntax errors (not just ones that get thrown by the compiler, but ones that are just improper use of syntax) and sometimes it's unclear what error you're really making.
I think the bigger issue was that in high school and even college math classes was that I always felt like I was rushing or being rushed. There wasn't really time to internalize concepts or ask why.
I'll take a look at this. I did proofs in a geometry class and really liked it.