I disagree. I have to learn by committing to muscle memory. I always say I'm a slow learner, but a fast thinker.
Yes, I can read/hear a concept and understand it in abstract and visualize it pretty easily, but it will leave my brain just as easily as it entered. Just the way my memory works.
Solved problems speeds up that muscle memory learning process significantly as opposed to going line by line and attempting to generate your own problems/solutions. In addition, you can solve a problem correctly, but not have the correct prose, solution manuals can help there as well.
Edit: Honestly the biggest thing about solving problems is that it gives a sense of progression and a dopamine-reward loop that most people just don't get from reading one line at a time. That being said, good problems and good solutions can be time consuming to generate, so it makes total sense to me that the PhD-level textbooks don't follow that format.
> Solved problems speeds up that muscle memory learning process significantly as opposed to going line by line
completely agree. I would recommend checking out mathacademy.com. I've been using it the last two months to raise my skill levels in math and its been a great investment of my time. It gives you a short lesson on the topic and then just gives you problem sets to burn though. what I like about it is that you don't think about your learning objectives. I just log in every day and do the problem sets and lessons until I feel like I did enough for the day. repeat everyday and you'll just naturally find yourself improving.
It’s been great for me. As of today I crossed 324 days of using it straight. I wrote about my experience here: https://gmays.com/math
And yes, I’m a total fanboy. I’ve also known the founder for over a decade and he’s been working on it for most of that time. Math Academy came out of him helping his son learn math even before that.
I haven’t found anything close to teaching math than this. It’s legit.
Been using it for 3 months now. When I started, I took their placement test. its been 20 years since I had to do any difficult math so I pretty much bombed haha. It recommended their foundations 1 which is for adults returning to math after a long time.
in terms of difficulty, I found the problems to be somewhat easy. you see a set of modules on the right and your progress on the left. you click on a module to start and it gives you a written tutorial on how to solve a problem. Then you go though several of them. If you complete it with less than 3 wrong, it gives you the xp and youc an continue on another module.
if you do get 4 wrong, it stops the module and you go with the next one. usually a day or so later, it throws the lesson at you again. I've had this happen twice. usually its a sign I've been on the platform for too long for the day and my brain just can't process math anymore. Over time, it introduces more lessons and harder topics along with periodic review modules to test stuff I haven't looked at in awhile.
I'm a few days away from completing course 1 and its been a much needed review of a lot of topics I remember from algebra 2 back in highschool. One of my biggest weaknesses back then was factoring polynomials and I think mathacademy explains the process 1000x better than any of my highschool teachers did. on certain topics like factoring, i'd say I'm much stronger now than when I was in highschool.
The key is to make time for it. I view it like going to the gym. every day I set aside an hour minimum and just crank through them till I either get tired or have some other obligation I have to take care of.
Is it worth it? so far Id say its probably one of the best roi activities I've partaken in. it really does automate the process of learning math. I love that the feedback is rapid so the time between I attempt the problem and can learn from my mistakes have let me progress much faster than I could have in a classroom. you just have to make sure use it consistently. have a notebook and a calulator next to you so there's no distractions and just crank thoguh problems.
TLDR: its worth the $50 every month. As long as you're consitent with it, You WILL learn math with this program.
Yes, I can read/hear a concept and understand it in abstract and visualize it pretty easily, but it will leave my brain just as easily as it entered. Just the way my memory works.
Solved problems speeds up that muscle memory learning process significantly as opposed to going line by line and attempting to generate your own problems/solutions. In addition, you can solve a problem correctly, but not have the correct prose, solution manuals can help there as well.
Edit: Honestly the biggest thing about solving problems is that it gives a sense of progression and a dopamine-reward loop that most people just don't get from reading one line at a time. That being said, good problems and good solutions can be time consuming to generate, so it makes total sense to me that the PhD-level textbooks don't follow that format.