Between the textbook, the instructor, reference books, and your mind, there is a bridge: your notebook. For most people, taking notes is necessary before a complete knowledge system for a subject has been formed. By taking notes and reviewing them repeatedly, you can memorize key concepts and problem-solving techniques. By writing down your insights on certain topics in one or two sentences and constantly revising them, you can correct your understanding. By recording problem-solving techniques in your notebook after finishing a problem and reflecting on them often, you can gain a deeper understanding of fundamental concepts and principles.
Classroom and Your Notebook If you have already formed a complete, clear, and accurate knowledge system for a subject, you may not need to take notes in class. For example, a professional with great expertise and interest in mathematics never takes math notes. Their method of learning mathematics is to solve problems, the fundamental reason being that they have long formed a complete and precise system of mathematical knowledge and problem-solving techniques in their mind. Each new problem they master expands this mental system. If you have fundamentally grasped the core philosophy and methods of a subject, your ability to reason and derive will be very strong, and you can also choose not to take notes during lectures. For example, a researcher with profound insight into physics never takes physics notes. Their method of learning physics is to repeatedly study classic textbooks. The fundamental reason is that they have already mastered the essence and core principles of physics. With each read of a textbook, their understanding of the fundamental principles of physics deepens.
What to Put in Your Notes
Key points: Write down important formulas, theorems, and core concepts that you often forget.
Summary of Key Insights: In one or two sentences, summarize the key points of concepts, theorems, or laws from textbooks and reference materials. After solving a problem, use a few words or a sentence to summarize the essence of the solution technique.
Frameworks and Outlines: Record the overarching, structural elements from syllabi and textbook tables of contents. Review and memorize them frequently to form a complete overall framework for the subject.
Learning Insights: Jot down your insights on learning methods and problem-solving techniques as you go.
Supplementary Knowledge: Record knowledge you discover while doing problems that is not in your textbook but is relevant to your learning goals. This is particularly important in fields like language and chemistry. For instance, while doing a language comprehension or error correction exercise, you might find some typical, commonly tested distinctions between words. Or from a chemistry “substance deduction” problem, you might learn about the specific chemical properties or reaction phenomena of certain substances. This content may be in your textbook, but it might not be comprehensive or presented from the same angle.
Problem-Solving Techniques: Write down techniques you’ve developed or learned from instructors and reference books. For problems that took a long time to solve, write down the techniques and steps in more detail.
Multiple Solutions, Single Problem / Single Solution, Multiple Problems: Record particularly clever and representative problems in your notebook. Review them frequently. When you encounter similar problems, compare them and look for connections—this is “single solution, multiple problems.” If you learn new techniques, try to apply them to old problems—this is “multiple solutions, single problem.”
Mistakes: Record problems you’ve gotten wrong more than once to use as a reference for similar problems in the future.
Misconceptions: Note down knowledge points where your understanding is skewed, such as a complex grammar rule or a physics law. Use a few simple sentences to capture your misconception. Later, when you encounter similar topics in textbooks or reference materials, think about them deeply and correct your previous errors.
Breakthrough Ideas or Insights: Sometimes, especially during deep contemplation, you may have a sudden breakthrough or an idea. Generally, the more advanced you become in your field, the more these insights will come. Write these down immediately, as they are very valuable.
Constantly Enriching and Correcting Your Notes Accumulating a lot of knowledge can cause confusion, and reading too many reference books can sometimes be overwhelming. For example, a software engineer named Zhang Ming, early in his career, enjoyed reading many technical documents. As a result, different documents on the same type of problem or knowledge point often had different explanations, which often confused him. Later, he began to note down confusing problems and knowledge points in a notebook. When he read other reference materials and encountered a detailed explanation of a similar problem or knowledge point, he would compare and analyze them, choose what he found to be the most reasonable explanation, and record it. Through this process of repeated correction, his understanding became more accurate. You can write down typical mistakes, incorrect understandings, or unclear knowledge points in the simplest terms. Review them frequently, and through consulting textbooks, reference books, or asking experts, correct your old misunderstandings. This way, your knowledge system will become more complete, and your understanding of each point will become more precise. For example, an experienced English editor has a dedicated notebook. Whenever he encounters a nuanced word distinction, a grammatical rule, an error correction problem, or a writing technique in his work, he records it in this notebook. He reviews it often, removing what he has fully mastered and highlighting what remains unclear for future analysis. He never delves too deeply into overly obscure or complex issues to avoid getting overwhelmed. Gradually, the number of confusing language points diminishes, and his grammar and word choice errors in writing become fewer.
The Notebook as a Basis for Your Mental Knowledge System You must form a knowledge system in your mind, and your notebook serves as the basis for that system. A textual knowledge system in your notebook can be easily reviewed and reinforced in your mind. Combine your notes with textbooks and reference materials to continuously supplement, categorize, and link your knowledge points with a certain thread, forming a unified knowledge system. Then, record this system in your notebook. Once a knowledge system is formed, you should supplement it with new knowledge as you acquire it. When you simplify your knowledge system, you should also record the updated version in your notebook. From one perspective, if reference books supplement textbooks and instructors, then your notebook, containing your insights, summarized techniques, and knowledge system, supplements your instructors and reference books.