kind of silly/simple question with probably a simple answer.

Jan 2016
61
7
United States
Hey, I have a reoccurring problem in math, and it's that I make a lot of really simple mistakes, and I don't really mean mistakes related to understanding the concepts or the math. I don't even mean computational mistakes when doing mental math. The kind of mistakes where I might have some function say (1 + x)^3. Then in the next step I'll rewrite it as (1 + x) without the exponent. Or I'll add 16 + 8 or something simple in my head and get the correct answer of 24, but instead of writing 24 down on the paper I'll sometimes put something completely different. like I may write 3 instead.. Or I'll randomly forget to apply chain rule. Admittedly this just sounds like I'm distracted, and that may be the case but I feel like this happens way too often. I feel silly asking this because these kinds of questions tend to have obvious answers like slow down, double check your work, make sure you get enough sleep, etc. But since this forum has a lot of people that may have been doing math way longer than I have I thought some of you might have some tips or insight I might not have realized.

Any advice is welcome :spin:
 

romsek

Math Team
Sep 2015
2,690
1,489
USA
doing your match in columns one statement at a time might help
mistakes will stand out much more readily than if you have several statements per line.

I like to do math on blank white paper. I hate doing math on lined paper.

get in the habit of quickly checking the current line against the previous line at the point you are going to start the next line. It's your last chance to catch errors before they propagate.

Get proficient with the available software tools. You might not be able to use them for your homework/tests at present but you eventually will be able to. They are invaluable.
 
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Jan 2016
61
7
United States
I really like the idea of using plain white paper, and while I normally try for my work to be neat as possible it's not to extent of of line per step I'll give that a try!

And good point with reading the previous line. Of course I do it every now and then but more than likely not as often as I should.. Now that I think about it, that's probably one of those things that should be ingrained into muscle memory like looking both ways before crossing the street or checking your rear view mirrors periodically while driving.
 
Jan 2016
61
7
United States
Also I'd like to add this question in:

What do you guys find generally works best for you as review material? Do you periodically go back and do a few problems, do you reread the proofs, or do you have a collection of particularly good problems you've previously solved which offer nice insight into some topic, or maybe something completely different?
 

romsek

Math Team
Sep 2015
2,690
1,489
USA
problems

they may lead you to re-read some stuff but I find just trying to read math without actually pushing a pencil is useless.

depending on what math you are studying problems are very likely proofs.
 
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