How you can learn not learn but at least can understand it?
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Answer:
So, how can you get to the point where you understand something well?
At the end of each class, spend 30 seconds (or more if you can) replaying in your mind what took place in this class. What was most important, or significant, or interesting? Write these thoughts down at the end of your notes for the day, even if they duplicate some of what you already wrote in your notes. Reflection is an important part of summarizing.
When doing homework, read the text closely, deliberately, and slowly.
Check for understanding at the end of every sentence fragment, and if in doubt, re-read and think about it until you are certain you understand exactly what the author intended to say (the same as my recommendation for how to start word problems). Only then should you proceed to the next sentence.
After reaching the end of a paragraph or section, reflect on what has been described and ask (“quiz”) yourself the most important questions for understanding:
– What?
What was just described (in my own words)?
What concepts is it connected to or based upon?
– Why?
Why am I being asked to learn this?
Why is this idea being brought up at this point?
– How?
How does this relate to what we learned earlier?
How do I know it’s true?
How does this work in the world I live in?
When you reach an example in the text, do not read through it – do it yourself by covering up the solution until you have solved it. If you get stuck and have tried every approach you can think of, use the author’s work to “cheat” and figure out the step you were stuck on… but don’t look beyond that! Only uncover as much of the solution as you need to get yourself un-stuck. Solving a problem yourself helps develop a stronger understanding – reading through someone else’s solution is seldom as effective.
After working on something completely different for a while, and perhaps again a day later, quiz yourself on what you just learned. What was presented? Why is it relevant? What else is it connected to? What major and minor points were made? What kinds of problems does it help solve? Then find a few such problems and solve them.
Remember that “thinking you understand the ideas” or the formula is often a very different thing from being able to solve a problem… you must both understand the ideas and be able to solve problems based on them before you are ready to take a test.
If you find yourself seeking to memorize all possible problem types and their solution patterns, you are not trying to understand the concepts. Stop memorizing, and focus on describing the problem visually as well as verbally. Sketch (or “doodle”) the situation if possible, and annotate the sketch with key facts from the problem. Write a list of needed variables with a brief description of each. Then describe the problem using mathematics notation. Coming up with a complete (solvable) mathematical description of a problem is often the most challenging part… from there the solution process is often less challenging.
Teach and explain the topic to someone else… either in person or by writing out what you would say. When you stumble across things that are hard for you to explain, you have discovered an area you do not understand well (yet). Writing, then editing, an explanation of the topic until you are happy with it is a great way to improve your understanding of the topic.
If you can find the time and the patience to approach homework and studying in this manner, quizzes and tests should be much easier to prepare for, and your grades should rise as well. Why? Because you are:
spending more time on the subject
giving yourself time to identify and reinforce connections between ideas before you are tested on them
practicing recalling new material by answering questions you ask yourself (quizzing)
reducing pre-test stress by avoiding the need to “cram” for a test
increasing your self-confidence by mastering material soon after it is presented, then confirming your mastery to yourself over the next few classes
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