Dealing with Maths!
Yeah, we know the feeling. That's why we are sharing these tips with you, so you will feel like we do today! Believe me, discovering this stuff was profound. In fact, lets get to it right away.
First off, the biggest problem with maths is the way it is taught - the subject itself is not half as difficult as it becomes using the normal teaching methods. If you have ever been in a maths class you probably recall, with some trepidation I imagine, the teacher writing line after line of stuff that you need to recall in that particular order. The bright ones get it and most don't quite get it. Sure we can try and recite the steps and probably pass the exams hoping never to see the accursed thing ever again for the rest of our lives. Sounds familiar? Well here are some facts that you wish you knew years ago, but which can help your kids or friends right now.
First, mathematics is a practical subject. Its something you do. This likely sounds strange to you - and if it does - you are not alone. Most people are in the same position. Now you are changing that by reading this special article.
Most mathematics that is now taught by lectures in a classroom were discovered and developed in the the real world of construction and farming and so on - and quite a large portion by trial and error. Then later, someone (or a group of persons) figured out why the thing worked and came up with a kind of short hand way of describing it. Interestingly, for the most part, the thing with maths is that it is so unforgivingly precise. Of course, in the real world that is a good thing. If you are using a method to determine how many tiles of a certain size will cover your floor, you will be able to determine how many to buy. Since this is going to cost you real money, you would want this to be precise - wouldn't you?
Second, when you figure things out yourself you usually 'know it', not just remember it. What is equally important is that when you discover the thing for yourself, even if you do not recall an exact result, you know how to figure it out. For example, if you know the price of a pound of sugar and you learned how to add, you can figure out the price of two pounds of sugar. Alternatively, you might notice that the price the cashier collected for a package of sugar is twice the amount you expected and you are certain that something is off - either the price you had was wrong or the amount of sugar in the package is wrong. Either way, you will likely figure it out really quick. Once you figure out and understand the relationship between the price and the amount of sugar, you know precisely what to expect at the cashier even before you leave home (as long as your information is correct, of course).
Third, while it is understood that learning in class is necessary for passing exams, classroom training is not necessarily geared at ensuring that you understand what you are doing and why. But then, you already know that, don't you?. Every person who is in or has been in the traditional education system has stuff they had to learn - the purpose of which they never understood. This is an unfortunate side effect of traditional classroom environment. It is geared at producing GCE or CXC passes much like the production line in a factory is designed to produce items. The ones that don't pass the quality standard are dropped from the line before they reach packaging.
Ok, so what can we do? There are a few things and you can start right now:
1. Give yourself the best information you can find on any topic. You might find that the recommended mathematics text book does not work for you. (Personally I have seen some dreadful CXC maths text books that I have difficulty with, even with topics that I know very well!) This might sound a bit odd, but it is not likely that any one text will have all you need the way you need it. So use other text books that explain it better, or use the Internet. You would be amazed at the range of choices you have to gather information and view points on any topic - including maths. Then, when you have found the explanation that is clear, express it into your own words. Once you can do this clearly and effortlessly you know you have it!
2. Try things out in a practical way. Do you think you would learn to drive properly only by reading the Road Code book? No, not even your driving instructor can do it for you. You have to sit in the driver's seat, take the controls and drive. There is no known alternative. And what fun it is when you finally have control over the thing, so you can drive effortlessly. Or, if you are not a driver, how about learning to use a computer? The same principles apply - as they do for mathematics.
3. Take a good look at your beliefs about your ability to learn. Then take a good look your beliefs about mathematics. (This applies to any subject or skill, by the way.) Here is where you'll find the biggest "gotcha" in learning the subject. I am not talking about other people's belief that it is important to learn maths, I am talking about your true beliefs. How do you do this? Its like we explained in the previous blog: just by yourself close your eyes for a moment and think about maths. What feelings come over you? What picture or pictures come to your mind? These indicate your true beliefs. Now, there might be very deep issues and beliefs in your overall belief system that are working against you even though you appreciate the need to learn maths. As you assess these you might find that it is time to change some of your beliefs by replacing them with new, better and more supportive beliefs. We will look at ways to do this later.
4. Reduce the subject to the simplest terms that work for you. For example, take a topic like reading a book. For you the simplest terms may be:
a. Take up the book and open to the page at which you need to start
b. Read.
c. If you are not at the end of the book and have to stop, take a note of the page
that is, if the book is written in a language you understand. If it is not you will find that the steps may be a lot more detailed - to include a translation dictionary and other learning aids.
The same is true of any subject. Your previous experience and skills will determine how simple or detailed the terms need to be. Once you have mastered this you will find that you are much more effective at doing any subject - no matter how difficult you might have thought it to be.
5. Take a look at the questions you ask yourself and the answers you come up with. You will find that your experience will tend to match that. For example, if you believe that other people have learned the subject that you are trying to master and that you can too, you would ask yourself "how did they do it?" You will find that you begin to see how, and will even find yourself in situations where you can learn from such person either directly or indirectly. Opportunities that were not visible before pop up, sometimes completely unexpectedly. If you believe that the subject is difficult and nobody could possibly make sense of such crap, you will find more an more people and situations to support that too. It has to do with the way our minds work - and believe me - your mind is extraordinarily powerful - but you have to direct it. If your direction to your mind (through your real belief system) is: maths is difficult lets see how we can avoid this thing, your mind will come up with ways to do this. You already know that, don't you? If, as in the example before, your direction is: we can do this, lets find a way - rest assured that your mind will go the extra mile to find the way. In both cases, you will get the results you directed your mind to look for.
Try this. When you feel challenged, frustrated or even angry at not being able to master a subject, stop. Just stop and note how you feel. Don't fight with yourself for feeling that way, just take note. Then see whether there are other factors in your physical environment that is contributing to this. Are you hungry or thirsty, for example. Are you uncomfortable or are there distractions like noise or heat or any other number of things that support the negative feelings. So far as you can, fix those. Then, when you are more comfortable, think of something pleasant. Stay with it until you feel better and no longer have the negative feelings. Then go back to the subject.
If the material you are using is not clear enough for you, try other material. If you still have difficulty even with other material there is a good chance that the problem is not the subject. This is a good time to talk with someone who can help. It is easier to get help if you have put in an honest effort and can explain what difficulty you are having. If you cannot do either of these at the time but you can take a complete break and get back to the subject some other time, that can sometimes work too as you will likely have developed a clearer picture of the problem you are having.
Now, when you get back to the subject, remind yourself that someone else has mastered this thing and so can you, its just a matter of understanding. And it really is! In fact, it has to be easier for you because you don't have to go through the trial and error - you just have to learn the solution part.
You see, its not the subject that's the problem, its your mindset which controls what you believe and how you go about learning and solving problems.
Another important part of paying attention to the questions you ask yourself as you deal with matters you have to learn and decisions you have to take is that asking certain questions automatically answers others and creates a different mind set. When you ask how a thing can be done, you automatically answer the question of whether or not it can be done. Did you get that? It is summed up in an old saying: always the beautiful answer to.... the more perfect question.
So now there are two remaining issues. One is the matter of fixing your belief system and the other is examples of learning mathematics as a practical subject. The matter of beliefs will be dealt with last as we will be linking to some more proficient sources on that subject. So that will be dealt with second. Right now, lets look at maths.
Practical maths
Take the geometric constant known as pi. If you are from the old school you know this as 22/7 and if you are from the new schools you know it as 3.1416, which is what you get, to four places of decimal, if you divide 22 by 7. Alternatively, if you convert the decimal 3.1416 to an improper ( top heavy) fraction you get 22/7, with some effort I might add.
The really big question is, what is it? How did they come up with this thing? I have asked this question of students of practically every age and the answer has been the same, "Don't know". I have asked a number of maths teachers and, believe it or not, the answer has been the same although they generally go around a lot more corners to say it.
So what is it really? We'll 'discover' it practically, like so many of my students have. You will need a ruler, some string or thread, a lean sheet of letter sized paper, a pencil and something to draw a circle with. If you have a geometry set it would have all you need except the paper and the string or thread.
Draw a circle on the sheet of paper. Draw it to a reasonable size, say four or five inches across. Now draw a line across the centre of the circle as accurately as you possibly can. This line, of course, is the diameter of the circle you drew. Use the ruler to measure the diameter and write down this measurement. Now stretch part of the string or thread to exactly match the circle. This would be the circumference of your circle - the distance around it and a string is a simple way to get an accurate measurement of the circumference. Do it carefully and write down this measurement. Now make a few more circles of different sizes and do the same exercise for each one. Now, divide the measurement you have for the circumference of your first circle by the measurement you have for its diameter. Do the same for each circle. What do you notice? Did you notice that the figure always comes out just a fraction more than 3 every single time? In fact, if your figures and measurements were 100% accurate you would get 3.14, give or take.
You have just discovered pi, the ratio or the fixed relationship between the diameter of a circle and its circumference. The relationship remains regardless of the size of the circle! Once you know this you can figure out the two key measurements of any circle if you have one of these measurements. The circumference will always be just over three times the diameter (or pi times the diameter) and therefore the diameter will always be just a fraction less than one third the circumference. That's all there is to it! Now, if you play around with the circle and read more on the subject of circles a whole new world will open up for you. But don't just take my word for it, give it a try.
Now, as promised, here are some links on the subject of beliefs, and in particular, eliminating limiting beliefs:
http://abundancejournal.com/2007/how-to-get-rid-of-your-limiting-beliefs/
http://thinksimplenow.com/happiness/6-steps-to-eliminate-limited-beliefs/
http://www.law-of-attraction-lifestyle.com/eliminate-limiting-beliefs.html
If you do a search for "eliminate limiting beliefs" on the Internet there will be nor shortage of links to look at. Take a look and see what makes sense to you, what resonates with you. Then start fixing your belief system so that it supports your progress rather than hinder it.
So, until next time, keep in touch.
2GNEC: Secrets to faster, more effective ways to learn? Oh yes, definitely! And some of them are so simple and effective you'll wish someone had told you this stuff years ago! That was exactly my feeling as I learned and that's why I am sharing then with you - for free !
A simple technique, correctly applied, massive results. Like I said, your mileage will vary, but, done right, you will get similar results if this is the problem you (or your child or friend) is having. Of course, If you are near us, we can help. Better still, if you become a 2GN student you have access to all this and much more.
So call us at (876) 488-2771 or email us at info.2gnec@gmail.com
Yeah, we know the feeling. That's why we are sharing these tips with you, so you will feel like we do today! Believe me, discovering this stuff was profound. In fact, lets get to it right away.
First off, the biggest problem with maths is the way it is taught - the subject itself is not half as difficult as it becomes using the normal teaching methods. If you have ever been in a maths class you probably recall, with some trepidation I imagine, the teacher writing line after line of stuff that you need to recall in that particular order. The bright ones get it and most don't quite get it. Sure we can try and recite the steps and probably pass the exams hoping never to see the accursed thing ever again for the rest of our lives. Sounds familiar? Well here are some facts that you wish you knew years ago, but which can help your kids or friends right now.
First, mathematics is a practical subject. Its something you do. This likely sounds strange to you - and if it does - you are not alone. Most people are in the same position. Now you are changing that by reading this special article.
Most mathematics that is now taught by lectures in a classroom were discovered and developed in the the real world of construction and farming and so on - and quite a large portion by trial and error. Then later, someone (or a group of persons) figured out why the thing worked and came up with a kind of short hand way of describing it. Interestingly, for the most part, the thing with maths is that it is so unforgivingly precise. Of course, in the real world that is a good thing. If you are using a method to determine how many tiles of a certain size will cover your floor, you will be able to determine how many to buy. Since this is going to cost you real money, you would want this to be precise - wouldn't you?
Second, when you figure things out yourself you usually 'know it', not just remember it. What is equally important is that when you discover the thing for yourself, even if you do not recall an exact result, you know how to figure it out. For example, if you know the price of a pound of sugar and you learned how to add, you can figure out the price of two pounds of sugar. Alternatively, you might notice that the price the cashier collected for a package of sugar is twice the amount you expected and you are certain that something is off - either the price you had was wrong or the amount of sugar in the package is wrong. Either way, you will likely figure it out really quick. Once you figure out and understand the relationship between the price and the amount of sugar, you know precisely what to expect at the cashier even before you leave home (as long as your information is correct, of course).
Third, while it is understood that learning in class is necessary for passing exams, classroom training is not necessarily geared at ensuring that you understand what you are doing and why. But then, you already know that, don't you?. Every person who is in or has been in the traditional education system has stuff they had to learn - the purpose of which they never understood. This is an unfortunate side effect of traditional classroom environment. It is geared at producing GCE or CXC passes much like the production line in a factory is designed to produce items. The ones that don't pass the quality standard are dropped from the line before they reach packaging.
Ok, so what can we do? There are a few things and you can start right now:
1. Give yourself the best information you can find on any topic. You might find that the recommended mathematics text book does not work for you. (Personally I have seen some dreadful CXC maths text books that I have difficulty with, even with topics that I know very well!) This might sound a bit odd, but it is not likely that any one text will have all you need the way you need it. So use other text books that explain it better, or use the Internet. You would be amazed at the range of choices you have to gather information and view points on any topic - including maths. Then, when you have found the explanation that is clear, express it into your own words. Once you can do this clearly and effortlessly you know you have it!
2. Try things out in a practical way. Do you think you would learn to drive properly only by reading the Road Code book? No, not even your driving instructor can do it for you. You have to sit in the driver's seat, take the controls and drive. There is no known alternative. And what fun it is when you finally have control over the thing, so you can drive effortlessly. Or, if you are not a driver, how about learning to use a computer? The same principles apply - as they do for mathematics.
3. Take a good look at your beliefs about your ability to learn. Then take a good look your beliefs about mathematics. (This applies to any subject or skill, by the way.) Here is where you'll find the biggest "gotcha" in learning the subject. I am not talking about other people's belief that it is important to learn maths, I am talking about your true beliefs. How do you do this? Its like we explained in the previous blog: just by yourself close your eyes for a moment and think about maths. What feelings come over you? What picture or pictures come to your mind? These indicate your true beliefs. Now, there might be very deep issues and beliefs in your overall belief system that are working against you even though you appreciate the need to learn maths. As you assess these you might find that it is time to change some of your beliefs by replacing them with new, better and more supportive beliefs. We will look at ways to do this later.
4. Reduce the subject to the simplest terms that work for you. For example, take a topic like reading a book. For you the simplest terms may be:
a. Take up the book and open to the page at which you need to start
b. Read.
c. If you are not at the end of the book and have to stop, take a note of the page
that is, if the book is written in a language you understand. If it is not you will find that the steps may be a lot more detailed - to include a translation dictionary and other learning aids.
The same is true of any subject. Your previous experience and skills will determine how simple or detailed the terms need to be. Once you have mastered this you will find that you are much more effective at doing any subject - no matter how difficult you might have thought it to be.
5. Take a look at the questions you ask yourself and the answers you come up with. You will find that your experience will tend to match that. For example, if you believe that other people have learned the subject that you are trying to master and that you can too, you would ask yourself "how did they do it?" You will find that you begin to see how, and will even find yourself in situations where you can learn from such person either directly or indirectly. Opportunities that were not visible before pop up, sometimes completely unexpectedly. If you believe that the subject is difficult and nobody could possibly make sense of such crap, you will find more an more people and situations to support that too. It has to do with the way our minds work - and believe me - your mind is extraordinarily powerful - but you have to direct it. If your direction to your mind (through your real belief system) is: maths is difficult lets see how we can avoid this thing, your mind will come up with ways to do this. You already know that, don't you? If, as in the example before, your direction is: we can do this, lets find a way - rest assured that your mind will go the extra mile to find the way. In both cases, you will get the results you directed your mind to look for.
Try this. When you feel challenged, frustrated or even angry at not being able to master a subject, stop. Just stop and note how you feel. Don't fight with yourself for feeling that way, just take note. Then see whether there are other factors in your physical environment that is contributing to this. Are you hungry or thirsty, for example. Are you uncomfortable or are there distractions like noise or heat or any other number of things that support the negative feelings. So far as you can, fix those. Then, when you are more comfortable, think of something pleasant. Stay with it until you feel better and no longer have the negative feelings. Then go back to the subject.
If the material you are using is not clear enough for you, try other material. If you still have difficulty even with other material there is a good chance that the problem is not the subject. This is a good time to talk with someone who can help. It is easier to get help if you have put in an honest effort and can explain what difficulty you are having. If you cannot do either of these at the time but you can take a complete break and get back to the subject some other time, that can sometimes work too as you will likely have developed a clearer picture of the problem you are having.
Now, when you get back to the subject, remind yourself that someone else has mastered this thing and so can you, its just a matter of understanding. And it really is! In fact, it has to be easier for you because you don't have to go through the trial and error - you just have to learn the solution part.
You see, its not the subject that's the problem, its your mindset which controls what you believe and how you go about learning and solving problems.
Another important part of paying attention to the questions you ask yourself as you deal with matters you have to learn and decisions you have to take is that asking certain questions automatically answers others and creates a different mind set. When you ask how a thing can be done, you automatically answer the question of whether or not it can be done. Did you get that? It is summed up in an old saying: always the beautiful answer to.... the more perfect question.
So now there are two remaining issues. One is the matter of fixing your belief system and the other is examples of learning mathematics as a practical subject. The matter of beliefs will be dealt with last as we will be linking to some more proficient sources on that subject. So that will be dealt with second. Right now, lets look at maths.
Practical maths
Take the geometric constant known as pi. If you are from the old school you know this as 22/7 and if you are from the new schools you know it as 3.1416, which is what you get, to four places of decimal, if you divide 22 by 7. Alternatively, if you convert the decimal 3.1416 to an improper ( top heavy) fraction you get 22/7, with some effort I might add.
The really big question is, what is it? How did they come up with this thing? I have asked this question of students of practically every age and the answer has been the same, "Don't know". I have asked a number of maths teachers and, believe it or not, the answer has been the same although they generally go around a lot more corners to say it.
So what is it really? We'll 'discover' it practically, like so many of my students have. You will need a ruler, some string or thread, a lean sheet of letter sized paper, a pencil and something to draw a circle with. If you have a geometry set it would have all you need except the paper and the string or thread.
Draw a circle on the sheet of paper. Draw it to a reasonable size, say four or five inches across. Now draw a line across the centre of the circle as accurately as you possibly can. This line, of course, is the diameter of the circle you drew. Use the ruler to measure the diameter and write down this measurement. Now stretch part of the string or thread to exactly match the circle. This would be the circumference of your circle - the distance around it and a string is a simple way to get an accurate measurement of the circumference. Do it carefully and write down this measurement. Now make a few more circles of different sizes and do the same exercise for each one. Now, divide the measurement you have for the circumference of your first circle by the measurement you have for its diameter. Do the same for each circle. What do you notice? Did you notice that the figure always comes out just a fraction more than 3 every single time? In fact, if your figures and measurements were 100% accurate you would get 3.14, give or take.
You have just discovered pi, the ratio or the fixed relationship between the diameter of a circle and its circumference. The relationship remains regardless of the size of the circle! Once you know this you can figure out the two key measurements of any circle if you have one of these measurements. The circumference will always be just over three times the diameter (or pi times the diameter) and therefore the diameter will always be just a fraction less than one third the circumference. That's all there is to it! Now, if you play around with the circle and read more on the subject of circles a whole new world will open up for you. But don't just take my word for it, give it a try.
Now, as promised, here are some links on the subject of beliefs, and in particular, eliminating limiting beliefs:
http://abundancejournal.com/2007/how-to-get-rid-of-your-limiting-beliefs/
http://thinksimplenow.com/happiness/6-steps-to-eliminate-limited-beliefs/
http://www.law-of-attraction-lifestyle.com/eliminate-limiting-beliefs.html
If you do a search for "eliminate limiting beliefs" on the Internet there will be nor shortage of links to look at. Take a look and see what makes sense to you, what resonates with you. Then start fixing your belief system so that it supports your progress rather than hinder it.
So, until next time, keep in touch.
2GNEC: Secrets to faster, more effective ways to learn? Oh yes, definitely! And some of them are so simple and effective you'll wish someone had told you this stuff years ago! That was exactly my feeling as I learned and that's why I am sharing then with you - for free !
A simple technique, correctly applied, massive results. Like I said, your mileage will vary, but, done right, you will get similar results if this is the problem you (or your child or friend) is having. Of course, If you are near us, we can help. Better still, if you become a 2GN student you have access to all this and much more.
So call us at (876) 488-2771 or email us at info.2gnec@gmail.com
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