I love this question. Most of you think that either you're good at mathematics or you're not. If you think you aren't good at mathematics (or anything else for that matter), if you've always been told that you're not good at mathematics, if even your parents say that THEY were not good at mathematics, well then what chance do you have? The answer is, none. But I believe that all of this is a fallacy. There are several key elements necessary to be good at mathematics, and these are available to anyone who desires them.
1. You must be interested in mathematics. You must want to be good. If you find that after a while you start to see the beauty in mathematics this is all the better.
2. What many people don't realize is that mathematics does not come easily to anyone - not even to mathematicians. If it did, they would lose their interest in a heartbeat. My absolute favorite quote of all time comes from Albert Einstein - "Do not worry about your difficulties in Mathematics. I can assure you mine are still greater." Anyone who pursues mathematics reaches a point where it becomes difficult. But as they say about physical exercise - "No pain, no gain." The important thing to realize is that just because you don't understand a mathematical concept at first, or don't know how to solve a problem this doesn't mean you are not good at it. Imagine if Einstein had thrown up his hands and said "Oh, I'm just not good at this!" when he ran into his first difficulty!
3. Don't get hung up on thinking that every step you take as you are learning has to make sense to you; that you have to understand what it means, why you are doing it, where it will lead. I picture myself back in high school, loving my math and not caring in the least if I didn't know "why." And sometimes, I even felt like saying "Don't bother me with WHY - just let me do it." I've found that lots of other mathematicians and math teachers say the same thing. But the cool part is that as your knowledge deepens and broadens you probably will find that "why?" begins to become clearer. Sometimes you have to have a larger perspective to be able to step back and see how it all fits together. This comes with time. And don't worry - there'll always be a new "why?" on the horizon.
4. Don't equate being quick with math to being better at math. Slow doesn't mean "not good." I remember my moment of epiphany when I was in graduate school. I was so intimidated by other students in the class who shouted out the answer right away when the professor posed a problem. I couldn't do that. But then I realized that just because I was not as quick as some didn't mean I was not as good as they were. I needed time, and quiet to concentrate. I got an A in the course - some of those "quick" students probably didn't. Being quicker certainly did not make them better.
5. Don't be afraid to "get your hands dirty". Imagine that your car isn't running. You lift up the hood and stand there staring into the engine trying to figure out what's wrong, and wondering how to fix it. Standing and looking will never get it fixed. You have to get in there and check things out, try different things, get your hands dirty - until you find and then fix the problem. Well math is the same way. If someone who is "good at math" sees a problem they are not familiar with it would be very rare that they would see the whole solution laid out in their mind before they even start step one. But they are not afraid to start - anything that seems like it might lead somewhere. Then take the next step, and the next step in a similar manner. And if they find that it is not leading anywhere, well then they crumple up the page and start over again trying something different.
6. Step away for a while from a problem that is perplexing you. I do some of my best thinking while I'm driving or before I fall asleep.You never know when the light bulb will suddenly turn on and illuminate the way.
So go ahead; try it. Expect some frustration, and great gratification once you've solved the problem. Revel in the gratification for a bit, and then challenge yourself to begin the process again with a new problem. And try to relax about it and maybe even enjoy it!
1. You must be interested in mathematics. You must want to be good. If you find that after a while you start to see the beauty in mathematics this is all the better.
2. What many people don't realize is that mathematics does not come easily to anyone - not even to mathematicians. If it did, they would lose their interest in a heartbeat. My absolute favorite quote of all time comes from Albert Einstein - "Do not worry about your difficulties in Mathematics. I can assure you mine are still greater." Anyone who pursues mathematics reaches a point where it becomes difficult. But as they say about physical exercise - "No pain, no gain." The important thing to realize is that just because you don't understand a mathematical concept at first, or don't know how to solve a problem this doesn't mean you are not good at it. Imagine if Einstein had thrown up his hands and said "Oh, I'm just not good at this!" when he ran into his first difficulty!
3. Don't get hung up on thinking that every step you take as you are learning has to make sense to you; that you have to understand what it means, why you are doing it, where it will lead. I picture myself back in high school, loving my math and not caring in the least if I didn't know "why." And sometimes, I even felt like saying "Don't bother me with WHY - just let me do it." I've found that lots of other mathematicians and math teachers say the same thing. But the cool part is that as your knowledge deepens and broadens you probably will find that "why?" begins to become clearer. Sometimes you have to have a larger perspective to be able to step back and see how it all fits together. This comes with time. And don't worry - there'll always be a new "why?" on the horizon.
4. Don't equate being quick with math to being better at math. Slow doesn't mean "not good." I remember my moment of epiphany when I was in graduate school. I was so intimidated by other students in the class who shouted out the answer right away when the professor posed a problem. I couldn't do that. But then I realized that just because I was not as quick as some didn't mean I was not as good as they were. I needed time, and quiet to concentrate. I got an A in the course - some of those "quick" students probably didn't. Being quicker certainly did not make them better.
5. Don't be afraid to "get your hands dirty". Imagine that your car isn't running. You lift up the hood and stand there staring into the engine trying to figure out what's wrong, and wondering how to fix it. Standing and looking will never get it fixed. You have to get in there and check things out, try different things, get your hands dirty - until you find and then fix the problem. Well math is the same way. If someone who is "good at math" sees a problem they are not familiar with it would be very rare that they would see the whole solution laid out in their mind before they even start step one. But they are not afraid to start - anything that seems like it might lead somewhere. Then take the next step, and the next step in a similar manner. And if they find that it is not leading anywhere, well then they crumple up the page and start over again trying something different.
6. Step away for a while from a problem that is perplexing you. I do some of my best thinking while I'm driving or before I fall asleep.You never know when the light bulb will suddenly turn on and illuminate the way.
So go ahead; try it. Expect some frustration, and great gratification once you've solved the problem. Revel in the gratification for a bit, and then challenge yourself to begin the process again with a new problem. And try to relax about it and maybe even enjoy it!
Makkah Time
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