Maybe a relevant personal anecdote might help you -
My grandfather used to sit with me for an hour every morning and used to teach me maths.
He would focus on basics first. He would make sure I had the basics drilled in to me. Not just understood them, but mastered them. Then we would move on to the next topic.
It was a bit slow at first. But after a while, once the basics were done, I finished the whole year's math book in 2-3 months.
I have seen this in software engineering too. Once I am good at basics, or once they're drilled in enough, I am faster and quicker.
Drilling basics is basically like having the basics in O(1) look up with very reduced space complexity too. It reduces the amount of overhead your brain utilises. This makes your brain free to think about the actual problem you are solving. Also, I think this is what allows your brain to work in the background, even when you aren't actively thinking about the problem.
Lockdown has really shown up how my 7 year old struggles with his maths work set by school. I've gone back to basics with him and have been drilling him on simple numeracy until he can do it effortlessly using some flash cards I bought and some iPad apps (DoodleMaths, DoodleTables - can't recommend them enough).
Since then he has sailed through all of the new parts we're learning. I really expected it to be much harder than this, but it seems like not fully understanding some basic concepts and having confidence with basic numbers makes all the difference for really understanding the why of all the concepts that are build on top.
In about 6 weeks of me spending around 30 mins to an hour each weekday he has gone from refusing to look at a maths problem to being confident with it.
My grandfather used to sit with me for an hour every morning and used to teach me maths.
He would focus on basics first. He would make sure I had the basics drilled in to me. Not just understood them, but mastered them. Then we would move on to the next topic.
It was a bit slow at first. But after a while, once the basics were done, I finished the whole year's math book in 2-3 months.
I have seen this in software engineering too. Once I am good at basics, or once they're drilled in enough, I am faster and quicker.
Drilling basics is basically like having the basics in O(1) look up with very reduced space complexity too. It reduces the amount of overhead your brain utilises. This makes your brain free to think about the actual problem you are solving. Also, I think this is what allows your brain to work in the background, even when you aren't actively thinking about the problem.