When you read the concepts on your own, you can proactively organize the concepts and control your pace, but when you listen to a lecture, you become passive because you listen to the lecture at the instructor's pace.
Moreover, speaking while listening is difficult because it interferes with listening.
In times like these, it's okay to pause the lecture for a moment, summarize the lecture content verbally, write it down in a notebook, or explain it to someone next to you.

--- p.20

Rather than simply memorizing formulas and accepting concepts, it is necessary to wonder why they hold true.
The act of asking and thinking about the question “Why?” is more than twice as effective in helping you remember a concept.

--- p.24

To avoid forgetting what you have studied, you need to repeat and review it several times before going to bed.
If you review what you studied every day, your brain will store what you studied every time you sleep.
In particular, if you keep pulling out certain information from your head, you will eventually reach a stage where it will come to mind naturally.

--- p.27

Mathematics is a subject that requires a focus on building strong brain networks through repetitive and consistent practice and memorization, which leads to a deeper understanding.
Therefore, in-depth learning that allows you to fully master the concepts step by step is more important than quick learning.
Through these exercises, various mathematically related networks become firmly established in the brain, giving you the ability to study more mathematics and become better at it.

--- p.38

Just watching someone else let go doesn't strengthen your brain connections.
You must actively solve all problems or study on your own initiative.

--- p.41

Students who do not learn to accurately understand concepts and principles and understand why things work the way they do in elementary school end up studying that way in middle and high school and end up not being good at math.
Therefore, in order to overcome it, we need to understand and study the 'why' from now on, and we need to be able to derive all the formulas one by one.

--- p.63

Simply finding a school or teacher who provides good explanations and is willing to answer questions will only serve as a much-needed oxygen supply for students who are weak in math.
What's the point of failing in high school? I hope I can learn how to overcome it on my own and improve my learning ability by studying step by step.

--- p.65

The most important reason why problems are not solved is because the concepts are not sufficiently stored in long-term memory.
Review the concepts relevant to the problem and listen to the lecture on the concepts again to organize the concepts.
It is better to explain the concept by writing it down on a worksheet.

--- pp.67~68

If you are aiming for the top level, I recommend solving advanced problems using only basic concepts rather than solving problems using advanced concepts.
In particular, the college entrance exam, the CSAT, presents unstructured questions (unfamiliar questions that you have never seen before), so studying and mastering advanced concepts is not very helpful.

--- p.78

Students who are bad at math mainly study 'what'.
In other words, there is a high possibility that you will only memorize and study what the formula is, what the theorem is, and what the definition is.
However, mathematics should be studied not about 'what' but about 'why' and 'how'.
In other words, you can be good at math only if you know why it is established and how it is derived.

--- p.83

Most students solve problems without thinking, make mistakes, and correct them without even understanding the concept.
That's why I'm bad at math.
If you organize your wrong answers while forgetting the concept, you will not be able to solve the problem accurately, and your correct answer rate will inevitably become uneven.

--- p.84

Most problems you can't solve in the textbook are because you've forgotten the concepts, so it's important to look up and review the concepts related to the problem rather than thinking about them for a long time.
I recommend reviewing the concepts naturally in this way while solving the problems, and learning the concepts along with the problems.

--- p.88

Opening a concept book and looking at the contents and explaining them is not well stored in the mind.
After familiarizing yourself with the contents of the concept book, you should explain it while recalling it in your head so that you can understand and memorize the concept well.
The advantage of explaining is that it helps me memorize, but it's also effective in helping me figure out what I didn't quite understand.

--- p.91

If you get stuck while solving a problem, always go back to the concept.
Getting stuck while solving a problem means you've missed a concept.
Reread the concepts and check if there are any concepts you don't understand.
Then try to solve the problem again.

--- pp.94~95

Many students misunderstand that the act of listening to an explanation or looking at an explanation and then writing down the solution in a notebook when they come across a problem they don't know is "correcting their mistakes."
But this is just a simple summary.
Doing this will not solve similar types of problems.
The true solution to wrong answers is to solve the problem repeatedly enough and internalize the solution to the problem.

--- p.98