This also, while common sense, is unfortunately often incorrect -- at least the part about avoiding chapter 3 (a different book is a good idea).
If you didn't understand chapters 1 and 2 in a textbook, reading -- or at least skimming -- chapters 3 and 4 is usually helpful. It doesn't make sense to read them for mastery, but you'll see context where material from chapters 1 and 2 is applied, or concepts that build on them. You have to be comfortable with confusion, since most of it will go over your head. You will pick out some parts.
Once you've done that, go back to chapters 1 and 2.
Think of calculus: limits -> derivatives -> integrals.
However, you can understand a Reimann sum without derivatives or limits. It helps understand and motivate both.
This is called a whole math approach. You make successive passes with increasing depth. I've explained calculus concepts to kids under 10 with no problems, as have many others. Over time, you want to develop:
- Mechanics of integration, differentiation, and other computation
- Applications (e.g. debt versus deficit)
- Intuition
- Formalism
- And so on...
All of those support each other.
You see this in how you read research papers too. Novices read them linearly, and experts absorb them nonlinearly.
As a footnote, Vygotsky (in the original, e.g. 1978 translation) is probably the first person to discover that doing things beyond your level of ability accelerates learning. Not aiming for mastery means you're free to fail, free to try harder things, and learn faster (if more painfully).
85% of American textbooks about Vygotsky, though, always say exactly what he was trying to debunk. He pushed very hard for learning being harder and more abstract than most thought possible.
If you didn't understand chapters 1 and 2 in a textbook, reading -- or at least skimming -- chapters 3 and 4 is usually helpful. It doesn't make sense to read them for mastery, but you'll see context where material from chapters 1 and 2 is applied, or concepts that build on them. You have to be comfortable with confusion, since most of it will go over your head. You will pick out some parts.
Once you've done that, go back to chapters 1 and 2.
Think of calculus: limits -> derivatives -> integrals.
However, you can understand a Reimann sum without derivatives or limits. It helps understand and motivate both.
This is called a whole math approach. You make successive passes with increasing depth. I've explained calculus concepts to kids under 10 with no problems, as have many others. Over time, you want to develop:
- Mechanics of integration, differentiation, and other computation
- Applications (e.g. debt versus deficit)
- Intuition
- Formalism
- And so on...
All of those support each other.
You see this in how you read research papers too. Novices read them linearly, and experts absorb them nonlinearly.
As a footnote, Vygotsky (in the original, e.g. 1978 translation) is probably the first person to discover that doing things beyond your level of ability accelerates learning. Not aiming for mastery means you're free to fail, free to try harder things, and learn faster (if more painfully).
85% of American textbooks about Vygotsky, though, always say exactly what he was trying to debunk. He pushed very hard for learning being harder and more abstract than most thought possible.