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What are some of the best ways to study?

What methods do you employ to understand and study math? How do you decode the text? What are the best ways to learn math?

  • When you study math, what kinds of skills and methods do you use? And what do you do? This question is not about what subjects to study, but about how to learn and understand a certain material or topic. And this is not about what resources are available out there. This is about what happens or what you make happen when you try to learn something new in math.

  • Answer:

    I'll try to give you an idea what I'm looking for. (My examples are not good ones. They are quite vague, but hope that this will get you some ideas.) (1) When I read a text about a new stuff, it seems I search for the previous knowledges that are similar to what's on the text. When I try to find something to go on or make further connections, more often than not, I try to find some visual interpretations that can be used in that context. (2) Some say that they try to come up with a specific image from the first page without going on further. It could take them hours and hours doing this. So, when they get to the second page, they already have quite a lot to make connections or changes to. Three or four pages in, they are more likely to have quite a comprehensive idea or intuition of the topic. It takes me a long time to go through the first few pages, but not as much. I try to read the text comparing with what I already know and find something that's not like my previous knowledge. Then I try to come up with a new image or idea which can appropriately represent the topic. If I fail to do so, I mark it down in my mind and go on to the next. When I finish reading the topic, I come back and try to complete the puzzles with all the bits and pieces that didn't add up previously.

Matt Park at Quora Visit the source

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I think that there are two notions that are stopping a lot of people: 1. That you should know how to solve math problem based on 1-2 examples. Otherwise you are just dumb. 2. That formulas solve problems. I feel like these false ideas are created in school where you are expected to keep up with the class. Teacher shows you the formula 2 different examples and you are on your own. There is no foundation established, no deep learning occurs. Only surface-level skimming through. That's why individual tutoring is a multi-billion dollar business in US. In reality, solving is impossible without foundation for anybody. You need to create a foundation and then practice to gain practical understanding (being able to lead, not just follow the solution). To create the foundation: Analyze and understand 5-6 examples (or as many as you need to grasp the concept). It is not about skimming through, I'm talking deep understanding. Know where each number, each line came from. Know why the formulas were used and what allow for their use. This is a intense process, but after you finish this, nothing can stop you. To gain practical understanding: Solve 5-6 problems (semi-hard). You can even try to solve the problems you have just analyzed. If you get stuck, go back to the solutions and reread the part you got stuck on. And books are created the same way. You have 2-3 examples. 1-2 solutions. And then examples to solve. Unfortunately, they are altered to match the surface-level school style. So you don't get solutions, only answers. You don't get 5-6 deep examples. Instead, you have 2-3 very basic problems. Also, I believe that the important thing in math is line-awareness. Instead of focusing on the whole problem, ask yourself: What happened between line 1 and 2? What happened between line 2 and 3? And so on. This narrows your focus down and you can break down the problem and accurately identify the parts you don't understand. Hope that helps, Amadeus

Amadeus Ciok

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