How to Study:-The following notes give some hints about how to do better at school studies in general, and at maths in particular.
1. SUCCESS BREEDS SUCCESS.
Finding that you can do something well is one of the best incentives to wanting to do even better.
2. A USEFUL TIP
Try to understand and master something beyond your normal, expected level. E.g.in maths, finding out how to solve quadratic or other equations in algebra when they don't come into your syllabus until the following year. This will make you feel good, a step ahead of others, and encourage you to work harder.
3. GET YOUR PRIORITIES RIGHT
Master the process first. You can analyse why it works later. This is especially true for a subject like Calculus. Most textbooks on this begin with the theory of how calculus was developed and talk about 'small increments shrinking to zero', which can be pretty confusing and off-putting to a beginner. Its also completely unnecessary at the initial stages of the subject. The mechanics of differentiation and integration isn't all that hard. All the why's and wherefor's can come later.
4. BUILD UP THE MUSCLE OF YOUR MIND
When you buy a new laptop, or a battery for your car, you are told to charge it and discharge it deliberately several times in order to build up the plates of the cells. This is called a 'conditioning process' and results in a strong battery ready to give many years of service. Athletes also know the importance of doing exercises to build up muscular strength. The same principle applies in preparing the brain. Exercise the brain with a variety of mental challenges to build up its strength and you'll find you'll be able to think more powerfully about anything on which you later focus your attention. And remember, these mental challenges can be fun activities or puzzles, such as Sudoku, or Chess, or Crosswords, as well as mental arithmetic, all of which strengthen the'muscle of the mind'.
5. MAKE SENSIBLE USE OF THE INTERNET
The internet is a most wonderful resource. Its like having the world's best library and encyclopedia at your fingertips, and all for free. Of course your computer can be used for light-hearted pleasures, contacting friends via social networking sites, finding good music to enjoy, playing games, etc., but always remember it can also be a most powerful aid to learning and finding out things. Just doing a search in Google or Youtube can often yield the answer to just about any query you have.
6. DIVIDE UP LARGE PROJECTS
When faced with a large-scale written project, such as an essay or a report, begin by drawing up a draft plan with sub-divisions, then deal with each sub-section in turn. By breaking the project up in this way and doing one stage at a time it will seem easier. As an analogy, think of how in cricket a batsman compiles a high score by steadily accumulating runs, or the stages necessary in preparing a meal, or even how those climbing Everest have to use camps at various stages. They can't just rush for the summit in one go. So learn to pace yourself and take things bit by bit, in stages.
[By way of analogy, imagine how hard life would be if you had to understand the workings of an internal combustion engine or synchromesh geaarbox before being able to have driving lessons!]
7. REPETITION
Although you may think you understand some new topic or mathematical process after just one brief explanation, the information learnt is unlikely to stick until you've practised using it in solving a variety of problems. By repeating a process you learn to establish it firmly in the mind. So aim to test yourself with about twenty problems of each kind until you've 'programmed' your thought processes correctly.
[Once again, a good analogy is the way a pianist has to practice playing scales or may play through a piece many times before being able to perform it from memory. Likewise with an actor learning his lines. Repetition is the key in all these.]
N.B. In many instances you can invent your own problems to test out your understanding of a topic, provided that you have someone around to help check your answers. Otherwise, use a standard textbook or an internet site offering free online test papers with answers. E.g. go to http://www.thatquiz.org or type 'free online maths tests' into Google.
8. EXPLAIN TO OTHERS
There is no better way thoroughly to learn a new topic , once you think you've mastered it, than by trying to explain it to someone else. So try to get a parent or friend to be your 'pupil' while you attempt to explain what you've just learnt. You may be surprised what gaps in your understanding this process can reveal!
[Note: Please see my other blogs (e.g. Cool Calculus; Algebra for All, etc.),for help with specific topics in maths. You can also contact me via email at dr.pythagoras@gmail.com]
1. SUCCESS BREEDS SUCCESS.
Finding that you can do something well is one of the best incentives to wanting to do even better.
2. A USEFUL TIP
Try to understand and master something beyond your normal, expected level. E.g.in maths, finding out how to solve quadratic or other equations in algebra when they don't come into your syllabus until the following year. This will make you feel good, a step ahead of others, and encourage you to work harder.
3. GET YOUR PRIORITIES RIGHT
Master the process first. You can analyse why it works later. This is especially true for a subject like Calculus. Most textbooks on this begin with the theory of how calculus was developed and talk about 'small increments shrinking to zero', which can be pretty confusing and off-putting to a beginner. Its also completely unnecessary at the initial stages of the subject. The mechanics of differentiation and integration isn't all that hard. All the why's and wherefor's can come later.
4. BUILD UP THE MUSCLE OF YOUR MIND
When you buy a new laptop, or a battery for your car, you are told to charge it and discharge it deliberately several times in order to build up the plates of the cells. This is called a 'conditioning process' and results in a strong battery ready to give many years of service. Athletes also know the importance of doing exercises to build up muscular strength. The same principle applies in preparing the brain. Exercise the brain with a variety of mental challenges to build up its strength and you'll find you'll be able to think more powerfully about anything on which you later focus your attention. And remember, these mental challenges can be fun activities or puzzles, such as Sudoku, or Chess, or Crosswords, as well as mental arithmetic, all of which strengthen the'muscle of the mind'.
5. MAKE SENSIBLE USE OF THE INTERNET
The internet is a most wonderful resource. Its like having the world's best library and encyclopedia at your fingertips, and all for free. Of course your computer can be used for light-hearted pleasures, contacting friends via social networking sites, finding good music to enjoy, playing games, etc., but always remember it can also be a most powerful aid to learning and finding out things. Just doing a search in Google or Youtube can often yield the answer to just about any query you have.
6. DIVIDE UP LARGE PROJECTS
When faced with a large-scale written project, such as an essay or a report, begin by drawing up a draft plan with sub-divisions, then deal with each sub-section in turn. By breaking the project up in this way and doing one stage at a time it will seem easier. As an analogy, think of how in cricket a batsman compiles a high score by steadily accumulating runs, or the stages necessary in preparing a meal, or even how those climbing Everest have to use camps at various stages. They can't just rush for the summit in one go. So learn to pace yourself and take things bit by bit, in stages.
[By way of analogy, imagine how hard life would be if you had to understand the workings of an internal combustion engine or synchromesh geaarbox before being able to have driving lessons!]
7. REPETITION
Although you may think you understand some new topic or mathematical process after just one brief explanation, the information learnt is unlikely to stick until you've practised using it in solving a variety of problems. By repeating a process you learn to establish it firmly in the mind. So aim to test yourself with about twenty problems of each kind until you've 'programmed' your thought processes correctly.
[Once again, a good analogy is the way a pianist has to practice playing scales or may play through a piece many times before being able to perform it from memory. Likewise with an actor learning his lines. Repetition is the key in all these.]
N.B. In many instances you can invent your own problems to test out your understanding of a topic, provided that you have someone around to help check your answers. Otherwise, use a standard textbook or an internet site offering free online test papers with answers. E.g. go to http://www.thatquiz.org or type 'free online maths tests' into Google.
8. EXPLAIN TO OTHERS
There is no better way thoroughly to learn a new topic , once you think you've mastered it, than by trying to explain it to someone else. So try to get a parent or friend to be your 'pupil' while you attempt to explain what you've just learnt. You may be surprised what gaps in your understanding this process can reveal!
[Note: Please see my other blogs (e.g. Cool Calculus; Algebra for All, etc.),for help with specific topics in maths. You can also contact me via email at dr.pythagoras@gmail.com]
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