1. Hard work trumps natural talent.
As in most everything, the people who are most successful in math are the ones who work the hardest–not those with “natural talent.” In school, those who work hard get better grades in math than the “smart” students who just coast. Most aspects of mathematics can only be learned by hard practice. This holds true whether you want to develop your problem solving abilities or your computational skills. No one thinks they can run a marathon by using only their natural talent, but there are lots of people with no talent for running who have worked hard and have successfully completed many marathons.
2. Keep an open mind.
In math almost everything you learn is useful, even if you can’t see it right away. All the formulas, theorems, ideas, proofs, and problems you study in high school and college are connected to lots of real world applications, even if you don’t see them now. And more importantly, even if you think you’ll never use the specific things you are studying, they help develop your mind and make it easier for you to solve other problems later–the problems you really care about. It’s like boxing: training programs for boxers often involve lots of jumping rope. A boxer might complain “When am I ever going to use this? I am never going to jump rope in a match.” But jumping rope makes them better boxers, even though the boxers never actually jump rope while fighting. The math you are learning is much more useful than jumping rope; but even if you never use it in your daily life yet, it makes you smarter. That is the most important reason to study it.
3. Find the reasons–don’t just memorize.
Mathematics is not just a long list of random formulas that someone invented out of nowhere. Math works because it is true–there is a reason for every step, every rule, and every part of every formula. Don’t just memorize the formulas and the rules. Find out where they came from, why they work, and what they mean. It may sound like more work to do this, but if you try it, you will quickly find that understanding the reasons and the meaning actually makes everything easier.
4. Never give up.
Math is hard. Anyone who says otherwise is lying. But you can do it anyway. If you want to be good at anything, you have to stick with it, even when you feel like quitting. You gain the most when you finally figure out a problem after a long struggle. That’s how you get smarter. But you’ll get nowhere if you give up whenever a problem is confusing or when you can’t solve it right away.
Athletes know that working, fighting, against something that is hard makes you stronger. The same goes for your brain–getting the right answer quickly won’t make you smarter, but fighting with a hard problem for a long time will.
5. Learn to read the textbook.
Math books are not like other books–they pack a lot of information into a small space. One page might take you an hour to really understand well. That is not because the books are poorly written–it is because it takes time to absorb the information, and you have to think carefully about every line. You even have to think a lot about the pictures.
Most people who try to read math books get frustrated and give up–they expect the math book to be as easy to read as their favorite novel. But if you slow down and really think about what is happening in each step, you will find that your book is like a personal tutor. Most books have lots of examples and explain things in several different ways. Most of them are written by someone who has been teaching for a long time and knows how to help you with the confusing parts. Once you get the hang of reading them, they can make learning math a lot easier.
The one thing a book can’t do is answer questions. The great secret is read the book before you go to class. Then you can ask the teacher about all the things that didn’t make sense in the book. Most people only try to read the book after class, when they didn’t understand some part of what the teacher was saying. But then if you have a question, you’re stuck–you can’t ask your questions because the teacher is gone.
6. Talk to your teacher.
Professors and teachers want to help you. Get to know them. Go to them for help–they love to talk to students who want to learn. Go to them to get help finding the right classes, to get help with homework (even for a class they are not teaching), and just to discuss life. They can help you with your math, and they can help you avoid the mistakes they made when they were students.
7. Look for the beauty.
Math is extremely useful, but it is also beautiful. It connects lots of different ideas into one. It explains important things that cannot be understood in any other way. When you finally get it, it is exciting to see how things fit together, why things work, how it all makes sense. Enjoy the experience of opening your mind.