How To Study & Revise

MATHEMATICS - SUGGESTIONS FOR STUDY AND REVISION

Don`t skip lessons! You may think that you can afford to work on your own, or miss a few lessons, but this is highly unlikely.

Get yourself a notebook or a folder. It should be your constant companion throughout your studies. Notes in this book or folder must be neat and in ink. In addition to this you should have a small jotter. You should take your jotter to all your lessons. In it you should jot down all the rough notes you can. In it you can do all the rough classwork set. But keep it apart from your folder. Your jotter will contain many notes unworthy of your folder - but the more important notes in your jotter should be transferred into the pages of your folder as soon as possible. Your folder is your own vital document. You write it in your own way to suit your own studies it is a product of your personality. And after you have finished it, you read it through many times until you know it back to front. You must read through your notes again and again and again and again and again and again and again. Then read it through again. Read it until the very last moment before the exam. By then you should be able to visualise every single page.

In class, you don`t always have to take notes - but you do have to take note! Never take notes just for the sake of taking notes. Don`t merely be a living piece of carbon paper! Think about your notes in the way that seems most important to you. If the teacher writes important notes on the board and tells you to copy them down, you should do so. Note-taking is valuable because it is an active way of studying it helps you to keep your mind on your work and it prevents you from day-dreaming. But don`t copy down every word a teacher utters. Only take notes of items which will probably be of use to you in an exam. The idea of note-taking is to get down important facts - not to carry out a difficult dictation test.

Process (i.e. re-write and re-arrange) your notes, as soon as possible after the lesson, preferably within hours. Merely reading them through is almost useless by comparison. Look at formulae and try to see what the different bits mean in a general way. Try to improve on the notes by writing your own, re-ordering arguments and expressing them in a way that suits you better. If you are not writing, then you are probably not working sensibly or as efficiently and effectively as you could. Eventually you will find that much of the original notes consist of redundant material once you have understood what you are doing, and that it can be thrown away. You will probably find this disintegrating at first, but don`t worry the subject becomes worse before it becomes better.

Remember that you do not go to class just to get basic facts and figures - you can get these from your text books. You go to watch your teacher`s expert mind at work! He should transmit his own particular way of looking at things, his own enthusiasm, his own way of tackling problems, his own personality. Try to emulate him - or better!

Don`t merely follow your teacher through the course. If possible, keep ahead of him . Go to the library and get ahead of his lessons try to do the next exercise in the textbook Be one up on your pals, and never, never one behind. It makes classwork simple, sends your confidence soaring, and saves you months of work. Your bit of extra effort will mean that you take everything, including the exam, in your stride. But once you fall behind your teacher and your classmates - even if it`s only one day behind - you can easily be puzz1ed in your work, embarrassed in your class, overpowered by last-minute exam cramming and defeated in the exam. So, as early as possible, get into the habit of keeping ahead. It`s certain to bring success.

Commit some proofs to memory. Find out why your memory fails you : have you forgotten what it is you`re trying to prove, or what the key point is that you are trying to reach? Always try to locate the key points in a proof much of the rest will be found by routine algebra (a vital area in Maths).

Keep revising definitions, formulae, theorems, and the really fundamental results. That is, write them out with the book closed - don`t just look at them. Write them out several times until you really know them.

Do the problems you are set, but don`t use them as a bridge to theory. If you have special difficulty with one, write it out again and again until you really understand it. There must be a reason why you thought it specially hard. Never be afraid to ask your teacher anything you don`t understand. One problem fully understood is worth several half understood.

Every so often try to recreate a large section of material via definitions and theorems and try to see how far you`ve got sort out what parts are fundamental, which show genuinely new techniques, and which items are merely tricks or short cuts. What kind of problems could you now solve, given enough free time? Imagine you were in the process of inventing the topic yourself, or were going to teach it. Would you be satisfied with your work could you convince your friends where might it go wrong where might it go next do the worked examples you have really illustrate anything?

For revision you should try to reduce the amount of notes to an absolute minimum. Definitions and theorems should (where possible) be reduced to clear statements and contain enough keys to enable a proper proof to be reconstructed. Make up tables of paradigmatic examples, of the simplest type which illustrate the concepts of the topic. For example, you should have concrete examples of several proofs polynomials which factorise over reals and those which do not graphs of simple equations and those of more complex equations examples of odd and even functions and those which are neither lists of derivatives and integrals examples of particles on slopes or moving under gravity, etc. The list is almost endless.

Always study past exam papers. You need especially to get to know the type of questions set, the sort of wording used, how to answer an exam question, and what sort of answers examiners look for. Interpreting a question is part of being able to answer it properly.

How to Succeed in Maths Step 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.

Step 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.

Step 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.

Step 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.

Step 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.

Step 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.

Step 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.

This resource was uploaded by: Raj

Other articles by this author

• 10 tips for tackling a Maths exam
• How To Do Well In Mathematics