At the beginning, of course, there was no work to show. Simple addition, subtraction, and the like. It had to be done in your head, because it was more or less a single operation, without intermediate results.

But that didn't last long. Multiplication, division, longer and longer problems. They all had multiple steps, multiple things to do.

I understood math well at the time. I was flying through problems, having little trouble. One of those people that understood the principles behind it, when other people in the class were still struggling to figure out what was going on.

It wasn't long before I ran into that command, that requirement that so many math teachers lay down. Show your work. Never mind the fact that I was the first one done on a test, and with one of the top scores. Never mind the fact that I really didn't have a way to cheat. I still had to show my work.

Anyone who is able to do longer problems in their head knows that you can go a lot quicker, and develop shortcuts that don't really translate into how you work it on paper. You have to actually slow down the rate in which you work.

Sadly, I also suspect that by being required to put it all down on paper, I needed less mental effort. I didn't have to remember as much, couldn't work as fast. I suspect that it in fact harmed me.

I know eventually I would have had to start showing my work regardless. There comes a point where there's just too much that needs to be done. Too bad I didn't get to wait until this point, but had to lose abilities I once had instead...

I wonder if it had anything to do with the slow decrease in interest and performance in my math classes...

Primarily the reason math teachers ask you to show your work in high school is to prepare you for advanced algebra and calculus. Perhaps it does slow you down, but at the same time, if you can't prove your work, it will be thrown out. For all anyone else knows, you got the answer by magic. This is a basic tenet of science and mathematics: reproducability. If someone else can't do the same thing you did and get the same result, then you (or anyone, in the case of new research) don't understand what you're talking about, or you can't pass on that understanding to the next person, thus making your work pointless.

Also, it's worth noting that it's much easier to understand where you went wrong if your entire process is written down. This means that not only can you go back and fix your mistakes, other people can too if they find them. Think of it as mathematical open source.

Wow. I just was going over old memories in my head and stumbled on some thoughts about math, and how I always suffered once I was forced to show my work. The thoughts that came to me on my own, before doing a basic google search for some terms that lead me here, are echoed fairly strongly in how the first post described the feelings. Yet I'd say that I was able to do it even better, and I was hurt even more when I was forced to slow down to show my work. When I write a journal, or any paper, I have the same trouble that my thoughts work way faster than my ability to write legibally. Sometimes before I even finish a thought I know how it ends, but I have to keep actually thinking it to pay attention to it and remember it for later. I'm sure part of this has to do with me being fairly ADD and never being "diagnosed", a fact that I am amazingly happy with since it is no problem if you learn how to manage your thoughts.

When I was forced to show all the steps of my work I would get the basic arithmetic wrong. It was the worst my senior year of HS when I took calculus. I earned a whopping F C F C in the four quarters, yet managed to get a perfect 5/5 on the AP exam for two years of college credit, and haven't taken math since. I do math with mental short-cuts. Way more than half the time I am not even aware of using them. Earlier today my friend wanted to know how much they just paid for their gym membership broken down by month since they paid it all up-front and wanted to see how much they really just saved. So they wanted to know 2 years at $410. So my head gets to a fairly close estimate extremely quickly with shortcuts, that took me a lot of thought later on to figure out what I really did.

I start out with 24 months * 2 would be 480, so if the dollar amount was $480 then it would be 20 a month. The difference between 240 and 480 is 120, which would be 360, and if $360 was the dollar amount then it would be $15 a month because thats the difference between $10 a month at 240 and $20 a month at $480. The difference between 360 and 480 is 60 (**EDIT** Hah! Perfect example! The difference between 360 and 480 is 120, not 60, but my answer is right. The 60 came from doing a smaller difference between the two to get the the $.5 answer below, but I wrote it out of turn even though I wasn't using it at that point. Showing work really does take a lot more effort for me, and results in dumb seeming simple arithmetic mistakes**EDIT**), which would be 420, so if the dollar amount was $420 then it would be $17.5 a month. $0.5 a month for 24 months would be $12 and $420-12 is $408. So it is somewhere between $17 and $17.5 a month, but a lot closer to $17 so around .1 or .2.

That answer is more than sufficient for an estimate of how much it costs them per month. That is a savings of around $13 a month. So if $17 a month is $410 then $13 should save them somewhere in the good $300's or so.

Do you know how much longer it took to type that, not to mention to figure out what the whole process was and write down each number at each point, all the while working backwards to figure out what I did to get the numbers I was using in the first place.

How long did the thought take to get that? Not all that many seconds.

Now imagine how much harder that would be for someone like me with calculus? Hah! All the steps and it just takes writing down one number wrong to get the answer off by some random little amount. Wish I would have been more like I am now back then, but you aren't really encouraged to speak your minds to your teachers. Easy enough to tell her to reserve her judgement, give me an F every time, and if by the end of the term I was still maintaining a near perfect score then to give me the benefit of the doubt that maybe my mind works a little different than the normal persons. Maybe its the ADD, maybe its what ADD is supposed to be when combined with intelligence. It is something though, and just because I can do something better than the teacher in a way that they can't quite grasp, and something that is just quick and easy common sense to my style of backwards thinking... I get to be penalized? I'm glad I didn't have to show my work in every other course and had a 4.6 GPA on a 4.0 scale so it didn't really matter what grade I got. Plus only 4 math classes counted towards your core GPA for outside the school, and calculus would technically be my 5th since I came from middle school with a +1 credit to skip a math so the grade really didn't count for anything. That teacher HATED me, lol, like most math teachers did. She was quite pissed when she saw my perfect score on the AP exam. Made my year. :)