How to Be Good at Mathematics
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I love this question. Most people think that either you're good at mathematics or you're not.....period....end of story. But this is such a defeatist attitude, to say the least. And worse than that, it can be a self-fulfilling prophecy. 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, before I fall asleep, scribbled on napkins in restaurants. 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!
More Hubs About Math
After reading this hub you should try my hubs about algebra, discrete math, and the irrational number pi. Or find out what's really beautiful about math.
Math Fear Poll
Are you afraid of math?
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Thank you so much,Camio.I'm so glad that I could help you. Just stick with it and don't be afraid to ask for help.
Thanks for following me. I can't wait to read some of your hubs and to get to know you better. It looks like we have some of the same taste in music.
Phew...
I could use a full-time motivational math speaker.
Or, somebody who could just do my math for me...
:D
Thanks for a neat hub nadp
:)
Thanks for your supportive comment, wyanjen. If you post your math questions I will do my best to help you. Keep up the positive attitude!
Very helpful advice. I was always poor at math so shied away from it out of laziness. A friend of mine told me to look at math as a game. There are rules to follow and when you follow them correctly, you win! That helped, and I was finally able to get an A in a math class. I didn't understand half of what I was doing, just followed the rules and stopping being intimidated.
Good for you, Dolores! Your friend was exactly right and expressed it in a really good way. I'll use that in the future!
You read my article and responded to me. That's how I found you. However, as an educator of almost 40 years, this article of yours intrigued me. I am so pleased that somebody finally spoke as you have. Think of the millions who suffer needlessly with math. Those who read your article and take it to heart will have a great tool in their arsenal as they attempt to address their nemesis.
Thank you so mu ch for your words of praise! If my article helps one person to succeed, when they never have before, I will be thrilled.
What really, really defeated me was calculus! Mathematics is a language. Paradoxically, although I work as a translator, I've never been good at languages LOL!
Hi WriteAngled. I read the fanmail (btw, thanks!)you sent this morning and was outraged to hear how that teacher of yours, so long ago, ruined any chance you might've had with mathematics! I wanted to respond but didn't quite know what format one responds to fanmail with - still getting used to how hubpages works. So I was glad to find this comment here.
You're right - mathematics is a language. I like to say that it is the language that explains the world. And paradoxically for me, I've never been good at languages either.
My previous comment that it looks like we have things in common was because you are a scientist, and science is a close relative of mathematics. At least I think the two disciplines attract people who have some things in common. Although it is certainly also true that there are also great differences inherent in people who are attracted to math, not science, and vice-versa.
The other maths-related thing that happened was when I was undergraduate. In 2nd-year biochemistry, we had to study enzyme kinetics with Prof. Gutfreund. So we went to the lectures and "duh???". Back home to check with the course book, only to find it was his and he'd been reading straight out of it. Still no wiser, a number of us fluffed the relevant questions in the exam (fortunately I passed because of everything else). Later a maths student friend, with no bioscience background at all, had a look at the paper, laughed and said "But this is easy, it's only algebra!" He proceeded to solve each question within seconds. I had been thinking of swapping to a biochemistry degree due to fascination with another lecturer's work on cell receptors. Then I found enzyme kinetics accounted for 30% of final year studies.... I stayed with cell pathology!!!
I think scientific/mathematical minds don't like to see things left sloppy and incomplete. I know I worry and worry at things until they are just right, or if I really can't, I leave it for someone more skilled to do. Also, I think we are open to being proved wrong, provided we are satisfied with the proof.
I agree with you about working on things until they are just right! Sometimes I feel like I do that to a fault - not with math, but with other things in my life. I have to force myself to realize that I may be putting an inordinate amount of time into something and that it would be okay to not work on it anymore. I mean, it may be finished, but I still see something that can be improved. I've been having some success at recognizing this, but it's amazing how hard it is to walk away.
As far as proof is concerned, I think I might have to say that I don't like to be wrong - but yes, if proof is offered that will satisfy me. What kills me is when I can prove I'm right and that is not recognized by whoever "thinks" I'm wrong. I'm very much into logic, and that is the area where this happens a lot.
By the way, I hope you don't mind that I used a reference to your comment about your discouraging teacher of 40 years ago to begin a forum - http://hubpages.com/forum/topic/36014
You might want to look at it. I hope that was okay.
I love mathematics! I was a very weird child. I started to read and write early. Then came the physics and mathematics. I think if more people just took a little time to look a the beauty of mathematics, there would be less phobia about it. Surely, one can ask, Why do I need integral calculus in my life? Maybe just for the beauty of it? Or maybe for its practical applications?
Thank you for this interesting hub.
Thanks again Dominique. I love what you have to say about math!
I hate math. My brother, the engineer, got all the math genes, and I got all the literature/grammar genes!
Oh, that's too bad. I guess our heredity does predispose in certain directions. But I can't help but wonder.....if you had someone who had encouraged you.......
Well, I guess that's water under the bridge!
Thanks for your comment : )
Math for me was an acquired taste. For me, I had to stand back and look at the larger concepts rather than jump right into the smaller nuances of problems. It was not until I focus first on big picture, that I actually began to enjoy math - and its a good thing because prerequisite for accetpance into any veterinary school is a full year of both physics, calculus, chemistry, and organic chemistry. Not going to get too far with those courses fearing or having amxiety about math.
In the end, math became one of my favorite disciplines because the solution was finite - you're either right or wrong. It is not like Enlgish where there is so much subjectivity involed in grading, a particular teacher necessarily jiving or not jiving with your writing style, for example. I like taking a teacher's subjective influence out of your assessment, because whether they like you or not, in math, if you're right, you're right.
Good post!
I wish I'd had a maths teacher like you! Mine told me not to bother taking the next level of qualification because I wouldn't be able to do it. Even though I got the highest grade in her class! Your students are very lucky!
Well, thanks for the vote of confidence!
Excellent, excellent, excellent! That's what we need: more math, and more competent teaching of math.
Good Math related article, enjoyed reading it.
Thank you Silver Poet. It's so nice to know that others appreciate math also. Thanks for taking the time to comment.
Good hub. As for me what was most important was the teacher. I wasn't very good at math until I got a teacher who was able to demonstrate the beauty of numbers and equations and everything else, also as a stimulus to use our mind. I even arrived at loving geometry and finding deep satisfaction at demonstrating problems. I have to say that are more than 20 years that I live on that year' study.
All your points are good so thumbs up and rated up.
Thanks, hypnodude, for the thumbs up and for taking time to comment. I think you're right - a lot does depend on the teacher. I hope that I have students that would say something similar about me. I think that some students are receptive to a particular teacher, and then some aren't. I've found the most important thing is to be myself.
Hi my name is Frank,and I am nadp's husband. I want to verify what she said about her best thinking. She gets great ideas while driving.....so she rear ends other cars,she gets ideas while falling asleep,so she doesn't fall asleep,but rather spends the next few hours on the computer,and as for napkins in restaurants,I have finished a meal and she has not started,because she solved some problem or other, and has to write it down NOW so if you really want to be good at math GOOD LUCK!!! ( but for all that, I adore her )
Yes, I have to say that my husband is very tolerant and patient with me. Actually, more than that - he encourages me to pursue all of my passions - he being one of them!
I am an MBA with major in accounting and learnt only basic math at university level. When I joined a development bank and had to work with engineers and economists, I faced problem in understanding basic terms like interpolation, extrapolation, randomness and optimization. I took interest and learnt these terms.
Later, I outsmarted many engineers by using math in solving cases of over-charging and misrepresentation in stating physical inventories in stores, land-leveling and cost-capacity factors. Also, I helped economists to forecast demand by using curvilinear regression models.
Thank you for a thought-provoking hub.
Thank you, hafeezrm, for your comments. It is good to hear that your perseverance in learning the mathematics that you needed brought you to a level of expertise that enhanced your abilities in your profession. It just shows how varied the applications of mathematics can be, and that if one sets their mind to it they can acquire the capabilities to take advantage of these applications.
I found your hub to be very interesting. I was a math major and loved Calculus, but I could never really understand why some people seemed to have such a fear of it. I think you've provided a wonderful tool for those who have put a mental block in their path, mathematics does not have to be something to fear. However, I do wonder about your statement that you don't need to understand the "why." It was only by understanding why something worked that I was able to fully comprehend and use that knowledge. Without knowing the why of how math works, it's hard to know what formula to use on a given problem. Maybe that's just me. Great hub that will benefit a lot of people!
Thanks so much for your interest, Lamme. I am pleased to think that my writing will help those who've had problems with math. I know what you are saying as far as understanding "why". I think there is maybe not such a clear boundary between when knowing "why" is not critical and when it does become necessary, in order to go further.Certainly for applications that level of understanding is necessary. But there are some personalities that need to see the full picture of where something is going before they can take even the first step, and I think that in the beginning stages of learning this can be an impediment.
You comment about needing to know which formula to use on a given problem is well taken. That, of course is necessary. I often tell my students that I remember struggling through statistics until I realized that when I was studying for a test I not only had to study how to do a certain procedure, but that I also had to study how I would know when to use a procedure. Once I realized that, I did much better. I think this is what you were referring to.
Again, I really appreciate your thoughtful comments.
Great hub. A great hub + A nice person = 2 thumbs up, a good rating and a follow! Keep it coming.
Thanks so much Darryl! I appreciate your kind words.
Hi! I think being good at mathematics is a gift...
There is some thing called-- mathematical brain -- that is an inborn gift which makes great mathematicians like Newtons and Einsteins -- Thanks
Hello ss sneh. Thanks for reading and commenting. I do agree with you that a mathematical brain is a gift - a talent like artistic talent. And without that I don't think you can become a mathematical genius like Newton and Einstein. But still, I think that there are things people can do to be better at math than they are.
again, thanks so much. I appreciate your interest.
I am trying to turn my career life around, never managed to get more than 50% in high school had an army brother in law who instilled fear of math into me when i was a kid, I am 31 now and i still have that fear, I have discovered that one thing that has been bothering me and keeping me back is this fear, I have decided to fight it any good books or any suggestions I will be more than happy to listen.
Deciding to fight the fear is the first step. As far as recommending books, I have one that is good. It's called Mastering Mathematics - How to be a Great Math Student, by Richard Manning Smith. The book that I have is pretty old so I'm not sure if it's still around but of you google it you should find something. Now that you have a real reason to conquer math I bet you'll find it not as scary as you did back then! Good luck!
With all due respect, I have to disagree that math is a learn-able aptitude. In order to do well in the higher mathematics, you must have an exceptional visuospatial capacity.
I'm not sure what you mean by "visuospatial" capacity. I agree that not everyone can do well in higher mathematics - everyone has their ceiling. But my point is that a lot of people have the capacity to be better at math than they think, at any. level,
Thank you for your suggestion, I have just completed a 6 hour Cognitive Test and have found that a part of the brain that is responsible for Math is my case underdeveloped which means that I have what they call a learning disability, my IQ is average and parts of the brain that are responsible for understanding and comprehension are in my case extremely well developed so what I am lacking is a math brain. For everyone who reads this I would like to share that I am a normal 31 year old male, with a full time job working in the accounting as an A/P person, I have a wife and two gorgeous boys. I live without any problems other than the fact that I am not satisfied with what I have achieved with my life so far, I am learning that there is a lot of help for people with learning disabilities and I am going to make sure that my kids have this test done so that we know if there are areas of weakness we can target and strengthen. I am going to look up this book and hopefully find a good tutor as I am planning to attend University this fall, so keep your fingers crossed for me I will let you know how it goes.
Marko
Hi Marko - I really admire your perseverance - with that I'm sure that you'll go far. I will definitely keep my fingers crossed - and please, do let me know how University goes for you.
hii nadp ? anyway i have a test tommrow and im not really good at remembering maths and maths its self so i was wounering if u can give me tips on how i can get full marks there mostly on about percenages and time tables and working out and stuff wich im not good at myself soo plese hellpppp ME im only in year 6 and im not taht smart but i know if i try i can do it
Hello mee. I guess the best tips I can give you are in my hubs - this one and the one about studying. Just don't give up and work really hard. Good luck!
Thanks for this hub which give some confidence guide to those people who lack in mathematics.
Why im hard to solve math algebra and our topics?
And thank you for your comment, TopUniverse. If it really helps people that's the best thanks I can get!
Nadp, this is a great hub, half the battle is remaining open minded towards the subject. The other half would be the emphasis on reconstructing our compulsory education system that enables young minds to grasp the concepts with relative ease.
Thank you so much, Opticlllusions, for your comment! I'm
glad you enjoyed the hub. I'm not sure what you mean about reconstructing our education system. Not that I don't agree there are plenty of changes that need to be made - I don't know what you think should be done. I'd be interested to hear.
Your hub is awesome. You had the courage to say out loud what math teachers (like myself) have been insisting (for ever, or so it seems). Young folk have no trouble understanding the need to work and practice in disciplines like dancing, singing or sports. Yet no one wants to believe that math simply requires work too
Excellent tips.....in fact maths has become an important part at every education level....even quality medical colleges are testing their new comers about their maths skills....so no great escape. Thanks.
nuce hub my dear friend, best of luck. Wana know more about Logical Statements and Truth Table.... visit my hub
Thank you for such fantastic and reassuring advice. I'll be coming back here to re-read this when I start studying maths and chemistry later on this year.
This is actually a very good article.
When I was at school, I saved up for months to buy a scientific calculator. Proudly, I showed my maths teacher and he said, "Boy, you wasted your money. You will never use any of these functions (waving his hand over the trig, eng, and stats buttons).
Luckily I took the attitude, "Right, we will see about that." but it could so easily have gone the wrong way. He was serious about demotivating me that's for sure. To this day, I don't know why.
Anyway - I could do with a sanity-check on some of my mathematical hubs, so if anyone would like to take a peek and provide constructive criticism that would be great.
nadp, more people need to read your hub - especially maths teachers. Most just don't 'get it'. I spoke with my Son's math teacher one day and he was telling me how he teaches that all the angles of a triangle *always* add up to 180 degrees. I don't know why, but I said, "Really? I thought that was a special case." He didn't get it, but the kids would get it if you did some experiments on every surface except a flat one, then introduced that special case... :-) You see, in most cases there is no mystery and intrigue taught in in maths classes. It's all clinical, dry and boring. Maths would be better off being approached from a historical perspective to show the pain and struggle and misguided routes, and the joy of a breakthrough.
thanks very much i am so glad!the world has become easier for me as my world is was and will stay maths.but i wanna know how to score a hundred in maths.
thanks
jj
While these are fantastic points, I find one problem: I cannot get my heart to love it. I never liked the "language" of math, much less physics. I've always been the historian. :/
Well my question isn't like this.. It's pretty weird. I do like math and after all my hard work, I end up getting bad results. And that's only with Math. Why not the other subjects? Honestly, I almost score full marks in the other subjects, Like straight A's ! But Math :( I don't really know why! Help me!
I think that good at mathematics can be only people that have heart and soul in this great science. For me, term "good" means that you can easily understand! But love can be mutual, which means if you are not sure that you love math, you may love it after you "meet" with her.
Hi, my name is mariam and im not good at maths and i really need help, I also read your artical and it was fab! thanks you really incouraged me, and you helped me to belive that maths isnt just plain numbers its a gift everyone would love, and that you should practice. And my mother used to tell me that:"mistakes always lead to perfect". ant thats true! email me at: mariamtanveer16@gmail.com. hope u reply thanks!!
Thanks very much for a wonderful inspirational advices of yours.. My teacher said "it's not too late", and we only have approx. 11 school weeks to go before me and my classmates do our final exams to enter colleges. After reading your article, I feel not losing hope. :) Thanks a million!
i met some inspirational math people within waldorf education where they teach it as a beautiful extention of the natural world with lots of geometry etc... i am a plodder myself and can get there with lots of time and patience but truly my brain seems to struggle with claiming the numbers ... i need to write it all down or they float away. acutally i have a point... a question... now i am homeschooling my child who seems like me. she hasnt really owned the numbers fully which i guess is time and practice but i am trying to find the really logical paterns to anchor her. any suggestions of sites that might help us?
hello mam i really appreciate your nice nice work.
just 11 hubs in the past 2 years speaks for itself that you only concentrate on writing good stuff ..
and the way you keep on interacting with the other hubbers through your reply to the commenters shows that you are really passionate about what you write...
here is a link to a good mathematical article...
please if after reading this article you feel that you should include a link to the article in your hub please do so..
here is the article
my maths is so poor i never get good marks and i'm starting to doubt myself...i reali want to pass my maths but i don't know how to practice/study please help me!
I want to kwn hw to slove math wel wel
i want to be good in math ..lol
camlo 2 years ago
Next year I'll be starting a three year course, and Maths is involved ... in a big way.
I was never good at it, and am dreading it.
Apart from practicing before hand, I'll be keeping your words here in mind. I'm sure they'll help.
Thanks for an inspiring Hub!
All the best, Camlo