How to study and learn math (or anything, really)

Professors Warren Esty and Norah Esty

 

            Learning takes effort, time, and concentration. 

 

The Basics

 

Attend class. Most serious students attend every class.

Do the homework. Good students take the commitment seriously. "Practice makes perfect." Not doing a homework on time is a warning signal that you are getting behind.

 

 

Beyond the Basics (Important things you might not know are in blue)

 

• Put in the time. We expect to teach you so much that you need to study, on average, two hours outside of class for every hour of class, minimum. Mathematics is just like anything else. If you want to get good at anything, you have to put in the time working, learning, and continually practicing.  Think of it like a sport. You don't get good at basketball by watching basketball. Beginners must practice a lot to get good, and even the best players continue to practice regularly for many hours a week. Research studies show that the thing that differentiates experts from amateurs is not how much they enjoy practicing (they don't; no one likes it), but how willing they are to do it anyway.
  
• Review right away.  When you get information sometimes your brain puts it into long-term memory, but mostly it just forgets it.  There are two things you can do to tell your brain that you want something to go into long-term memory.  First, repeat the information many times to yourself with intent to remember it. Second, review it shortly after you learn it  (after 5-20 minutes, or as soon as possible). Research shows that immediate review (right after studying something) increases long-term memory very dramatically compared to the same amount of review a day or more later. So if you have a class in the morning, try reviewing your notes immediately afterward, or as soon as you have free time. It will help you remember things.
• Don't multitask while studying.  Multitasking works for getting simple tasks done, but you can not learn something if your mind is doing several things at once. In order to learn you need to give the material your full attention, and that means ignoring everything else for a block of time. Organize your life so that you do not expect to be electronically interrupted while working. (Don�t text or use Facebook or respond to e-mail when you are studying.) If you cannot commit to doing this, then don't be surprised when you are unable to learn deeply. Learning takes not only effort and time, but also intense concentration.
• Work without notes.  Try doing assignments without looking at the book, notes, or solution manual.  If there is a problem you don�t remember how to do, of course you look in your text or notes to find out how, but with the serious intent to remember how. Doing without remembering is not learning. If you always do your homework or study with your book and notes open next to you, you will be left with a false feeling of how much you know.
  
• Don't say "I knew that." To learn, you must do the work yourself. Many students watch in class, nod, and think "I would have done that." Many copy the solutions manual or a friend's work and think "I see how it's done. I can do that." These thoughts are often wrong. Don't kid yourself. The proof of your ability to do it is in your doing it by remembering how.
• Get enough sleep.  Research has shown that learning has a passive component. While you are asleep tonight your brain will categorize and file things you "learned" today. At night it makes connections so that you can recall things later. However, you will remember far less tomorrow if you get only five hours of sleep. Get enough sleep.

 

Serious Students

To learn math more efficiently you must learn to read math. You learn to read by reading.

 

                     Read your text. Read with two goals:

1) to learn the current material

            2) to practice reading in order to learn to read more fluently. The ideas of mathematics are best expressed in written symbols (not aloud in English). By learning to read you learn how mathematics really works.

                    Think of the book as a well-designed lecture you can follow at your own pace.

 

           If you find reading your text difficult, you can blame the text, or take responsibility and recognize that you are dangerously weak at an important skill � mathematics reading comprehension.  The harder you find reading math, the more you need to work at it. Don't kid yourself. No one else will take time to teach you to read math � you�ve got to do it yourself.

 

          Figure it out! If something in the text does not make sense right away, take the time to figure it out. Read it again with your brain in gear. Study the text's example again. Go over it, carefully, until it makes sense.

   Asking your instructor to explain something is sometimes necessary, but not as often as students seem to think. If you read the text and work on an example with the intent to figure it out, you probably can. Then your learning will be better and longer lasting than if you ask someone else to do it. Plus, in the process, you will be learning how to learn! You will find you are getting better and better at understanding what you read. The effort pays dividends, not just for today's lesson, but for all future reading. Believe it!

 

          Reflect. Do not walk out of class and immediately put on your earphones and join the world of entertainment. Right after class is the very best time to review the material, even if only in your mind as you walk across campus, and move it to long-term memory.

 

 

            "Deferred gratification" is a reward to be received later. It takes serious effort to develop skills for which employers pay well. (Many older students return to college after learning that the hard way.) Put that effort in now. Learn to appreciate your developing skills. Enjoy your education. Enjoy the process, and you will do well.