Stop Making Stupid Mistakes: Improve Your Math Skills with These Tips!

[Teegvin]

I just came home from a local math league, and I completely let my team down by making a mistake on what is quite possibly the easiest problem I've ever seen, even in junior high (we're in high school): Find the sum of all multiples of 9 less than 50.

I thought, for some reason, that 54<50.

Anybody have any advice for people like me?

 

[radou]

It happens. Exercise and learn how to concentrate.

 

[verty]

Get used to making a plan before you proceed. If you separate the process into a planning phase and an execution phase, it'll allow you to concentrate on avoiding silly execution mistakes.

 

[tim_lou]

meh, how about 6*4=32. I remembered I made that mistake on AMC 12

 

[ranger]

Anybody have any advice for people like me?

Yea. Think before you act

Dont sweat it. These kind of things will happen to everyone at some point in their life.

 

[robphy]

"measure twice, cut once"

 

[brouser]

I added 3 to 18 and got 22 in a final at Berkeley 25 yrs ago -I'm still pissed. Happens - passed the course, got a job.

 

[theperthvan]

I once did 2.5 + 2.5 = 4.5 a few years ago.

 

[a_lawson_2k]

It happened to me all the time; just write down the information from the problem once onto the paper, then double-check it and let it sink in. I find that helps cut down on the mistakes.

 

[dontdisturbmycircles]

Take your time. Ensure that you understand the problem and always make sure your answer is reasonable!

 

[complexPHILOSOPHY]

I often times make extremely silly mistakes when working with integers. Elementary arithmatic is the bane of my existence. :P

 

[Ki Man]

I went down a full letter grade on my last math quiz because it said to list the angles from least to greatest and i had the right answer but i put it in greatest to least

 

[moose]

Check each problem you do several times and the problem may go away on its own. About two years ago, I was making a ton of silly mistakes like that on tests in math. I started checking each part of each question once or twice to ensure it was correct. On top of that, I wasn't trying to think ahead of what my hand was writing too often... I haven't made such a mistake in a really long time now.

 

[ssivark007]

hey, i once factored 8... = 4... x 4... (... represents some variables) & spent the last 1/2 hor of my exam trying to find the mistake. i found it 5 mins from the end, but it was 2 late 2 correct anything.
again,quite often i tend 2 make mistaes in copying down terms/numbers in questions and end up wasting a LOT of time on such questions...
the list goes on ...abt how i took limits of ((e^x +1)/x) instead of ((e^x -1))
...
this is frustrating...
but then u got to b determined 2 do better next time.i guess there's not much we can do abt this. but i guess practice might help.
all da best...hope u find a soln...tell me if u do

 

[Crosson]

Work on problems that are less trivial, so that the competition is based on skill rather than robot-like perfection.

They should call it arithmetic-league.

 

[Teegvin]

Check each problem you do several times and the problem may go away on its own. About two years ago, I was making a ton of silly mistakes like that on tests in math. I started checking each part of each question once or twice to ensure it was correct. On top of that, I wasn't trying to think ahead of what my hand was writing too often... I haven't made such a mistake in a really long time now.

This is good advice. Thank you

Work on problems that are less trivial, so that the competition is based on skill rather than robot-like perfection.

They should call it arithmetic-league.

The other problems were less trivial. That was the easiest problem there, and the most likely person to be doing would be someone in grade 10.

 

[acm]

Either pump out hundreds of past papers (Make sure your so comfortable with the work you don't get nurves) or make sure you come to the exam fresh (ie Not Tired) and use your time effectively. There is no sure fire method to stop all stupid mistakes, but you can help yourself spot your errors by being on top of your game.

 

[apples]

Work on trying to increase your attention span.
If you're like me who switches channels quickly, read an article and then realize you didn't understand because you were thinking about something else, then there's a problem with your attention. Try reading novels. Try to focus on what you're doing. Try keeping everything else out of your mind, don't day dream, don't think about other stuff, and focus on what you're doing. try to calm yourself before doing something and remain calm.
That'll make you more focused.

 

[Sojourner01]

Write out in words precisely what it is you're doing as you do it. One line of writing, one line of working. Justify even the most basic mathematics. It feels tedious but actually doesn't take long and gives you a good feeling that you've done things thoroughly and neatly. It's also easier to mark :)

 

[Moonbear]

Unfortunately, the timed format of something like a math-league forces one to try to rush through answers, especially on the apparently easier questions, rather than taking time to check and double check. Rushing through your work lends itself to mistakes. Experience of making those mistakes is what eventually teaches you to go back through your work and check for trivial errors like that, and to know where to look for such trivial errors (the bane of my existence back in my undergrad days seemed to be adding 3+3=9, or multiplying 3*3=6 ...lose points for that a few times and you start skimming your answers for the simple addition and multiplication mistakes, just like you proofread essays for missing punctuation before turning it in).

 

[Sojourner01]

Perhaps, but I'd much prefer to answer as many questions as possible perfectly and not have time for the last one, than rush all of them and make a hash of each. I cannot imagine that a little extra wording would be a great drain on time - at least, not the way I do it.

 

[verty]

Experience of making those mistakes is what eventually teaches you to go back through your work and check for trivial errors like that, and to know where to look for such trivial errors

I find that I am useless at looking for errors, perhaps it's a knack that some people have. For me, prevention is so much better.

 

[complexPHILOSOPHY]

I find that I am useless at looking for errors, perhaps it's a knack that some people have. For me, prevention is so much better.

I make a lot of errors but I have an extremely good error, detection rate when I pass over problems. The method that I implement is one in which you immediately go over the problem for errors, identify them and then move on to the next one. After I complete the next problem, if I have time, I will go back over the previous problem to scan for more errors. If I don't have time, I only go back through those that seem incorrect or less elegant than I had assumed it would be.

From psychology I remember reading about instances (I can't remember the name for the concept) where one selectively dismisses the same errors, because their brain perceives the errors as being correct. If you leave the problem and come back to it, your brain has a better time noticing errors, because it isn't to fully immersed in the problem anymore.

I find this is definitely true for writing (which is why you write drafts and read through it at a later date) and I adapted this method to my maths.

Try developing a system similar to this and you will find fairly quickly, that you become very accustomed to going over problems multiple times, very efficiently and quickly.

However, I also do problems (what I would consider to be) very slowly, although I've never really compared my speed to anyone elses. Going through slowly and meticulously also seems to help reduce errors but I am also not in very high level maths or physics yet, so I am more able to go through my work more slowly.

Side Question:
Is speed really important or is the understanding and ability to work through problems effectively, a better method? I feel like I watch some kids practice pure speed and I feel like they fail to develop a deep understanding of the maths they are doing, or is this my perspective?

 

[Moonbear]

Side Question:
Is speed really important or is the understanding and ability to work through problems effectively, a better method? I feel like I watch some kids practice pure speed and I feel like they fail to develop a deep understanding of the maths they are doing, or is this my perspective?

It's a good question, and one I'm sure you'll get differences in opinions as people answer it. Here's my view on it:
In the working world, accuracy is more important than speed...mistakes cost time and money to fix. But, the catch is that if someone else can be just as accurate, but gets the job done faster, they will be the more valuable employee. So, you need to optimize both. One more catch is that unless you're doing a very mundane job where you're essentially doing the same thing over and over again many times a day, without developing an in-depth understanding, you will not be able to find solutions to novel problems. In the classroom, there's usually a right and wrong answer that you're trying to find. Beyond the classroom, the most valuable employees are the ones who understand what they are doing well enough to tackle the novel problems, and if you're talking about research rather than just the general world of business, the in-depth understanding is even more important. But, again, you need to understand it to the point where you can rapidly recall information of importance and apply it, or else you'll find yourself always a step behind everyone else.

 

[Trail_Builder]

relax, stress causes your brain to work incorrectly

well that's what i find

 

[verty]

I am speaking from a programming perspective, and there prevention seems to be vital. Going over a program later is something I pretty much can't afford. I suppose my lack of error-checking ability fits in with what I do then.

 

[moose]

I find that I am useless at looking for errors, perhaps it's a knack that some people have. For me, prevention is so much better.

Dont look for your mistake if it's an easy enough problem*, do it over again without making assumptions.


*With many problems, you don't have time to do this, unfortunately.

 

[dontdisturbmycircles]

Yea that is true moose. If it is a simple problem work it over again, I have one thing to add too. If you can, try to tackle it from a different angle, and if you come to the same answer through two different methods, you should start to have a warm fuzzy feeling inside.

 

[complexPHILOSOPHY]

I am speaking from a programming perspective, and there prevention seems to be vital. Going over a program later is something I pretty much can't afford. I suppose my lack of error-checking ability fits in with what I do then.

Oh, sorry! I don't have much experience with programming, just maths and physics.

 

[glueball8]

Wow, I'm the worest at theses... almost all the math marks I ever lose is because of this... 1+1=1 or 1*1=2 ... you name it...

 

[Howers]

I find the more advanced math I learn the worse I get in child's arithmetic =( Don't know if it has to do with age, I'm sitll in my 20s.

A few months ago it took me 10 seconds to confirm 7 + 4 = 11.

 

[sharkshockey]

I find the more advanced math I learn the worse I get in child's arithmetic =( Don't know if it has to do with age, I'm sitll in my 20s.

A few months ago it took me 10 seconds to confirm 7 + 4 = 11.

Same here... when math starts turning into the alphabet, I forget the basics. I lost 5 points on a math test for accidentally evaluating 2/3 + 2/3 as 4/9.

 

[leumas614]

The worst is the GRE which uses traps that are satistically most likely to fool you. Like which is bigger 0.82^6 or 0.82^5. And 4*2 is 6 while 4+2 is 8. The best approach is to come back to the problem afterwards and challenge even your basic assumptions because otherwise you may assume something to be true when it is really not. Unfortunately you can't do that on the GRE since it doesn't let you repeat questions.

 

[snkk197]

I find the more advanced math I learn the worse I get in child's arithmetic =( Don't know if it has to do with age, I'm sitll in my 20s.

A few months ago it took me 10 seconds to confirm 7 + 4 = 11.

It's a bit of a relief to read this forum. Doing mundane jobs outside of uni, I am convinced are making me more stupid. I can practically feel the IQ points dropping out of me head. I was fantastic at mental arithmetic when I was at school, the fastest in my class. Now, even though I love math and am about to embark on a degree in physics, when I sell chocolate bars and ice-cream, or check my supermarket receipt, I struggle to add a string of numbers accurately.

I wonder if it's worth practicing mental arithmetic - multiplication tables, fast methods of multiplying large numbers, fun things you learn at school and then forget when you get on to the more advanced stuff. I don't mean spend hours drilling, but a few mins a day, while brushing your teeth, on the bus or whatever. Would that, (along with lots of sleep, good diet, plenty of exercise) help improve accuracy?

NB: I used to think sudoku might sharpen my brain, but for me personally it's a massive and fruitless waste of time!

 

[glueball8]

I think we should stop using calculators...

 

[MathematicalPhysicist]

for the title question, my answer is stop living.

cause life is about making those mistakes, and the more you interact the more you will make mistakes.

 

[guguma]

It is much better to make a simple mistake and look back to it for a good laugh, than to insist on the truth about a horrible wrongdoing.

If you want to accomplish great things, small mistakes are nothing (I hate time limited tests or competitions just because of this reason). But if you are writing a thesis with an intention to prove that stars are actually tied to a celestial dome with gigantic steel strings and making no small mistakes then you just judge yourself.

In a quantum mechanics test I got a horrible mark from a question just because I miscalculated a stupid integral due to constants (horrible handwriting I guess). I discussed the answer of the particular question with a friend after the test, he said to me "dude, I memorized the solution of that problem from the solutions manual, I did not work it out" in my amazement. Guess what he got full marks...

MORAL:

I can work that question out whenever I need, and many similar ones, if I make a mistake it will come out sooner or later and I will correct it, the other guy can't.

Damn, I hate the education system, just throw us some money and food and let us think and study in peace without rushing anything will you!

 

[glueball8]

Damn, I hate the education system, just throw us some money and food and let us think and study in peace without rushing anything will you!

I guess you can quit school like Einstein...

 

[guguma]

I guess you can quit school like Einstein...

The essence of the problem abides in your suggestion. Why should Einstein quit school to be Einstein?

And no I would not quit school, if you are serious in your suggestion.

 

[cristo]

I think we should stop using calculators...

I don't like this suggestion. Maybe in school children should be encouraged to use calculators as little as possible, but I don't see the point in memorizing multiplication tables etc once you're through high school.

 

[Sheneron]

I think prevention of mistakes is better strategy then searching for mistakes you could have possibly made. What I do is to take time and answer each question carefully and fully. I answer a question and check my work with each step in order to prevent mistakes. Whenever I finish I never go back and check my work because I take my time and have no need to check over work that was already checked. I find its more beneficial to spend time answering a question completely and correctly versus doing the test fast in order to save time checking you work at the end.

There is no need to check for mistakes when you know you have answered the question correctly.

 

[glueball8]

I don't like this suggestion. Maybe in school children should be encouraged to use calculators as little as possible, but I don't see the point in memorizing multiplication tables etc once you're through high school.

Well I'm in high school. Hmm this year they changed the AMC 12 to no cal. and that killed me... (I knew the day on the contest). I don't mean for everything, like trying to divide 1236543241234/23452 you have to use the cal but for simple stuff we should try not to...

Ps. lol what my mom says...

 

[xfoo]

I think we should stop using calculators...

I agree with this when the student is still learning the math (beyond this, use whatever you need to be efficient). I guess I am a fan of learning 'by hand' before using the tools that make it easier, instead of just jumping straight to the tools. I see people use calculators all the time and don't even recognize when they have punched in something wrong because they have no intuitive feel for numbers.