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Linear Algebra was easy, but I can't add 1+1 without using my fingers. WHAT.
March 10, 2012 12:12 AM   Subscribe

Basically, what it says. I've been brushing up on my math skills via Khan Academy, and I'm running into a problem I hit when I was in school. Basically, the math *concepts*, like Algebra, Trig, and the like? I'm able to get really easily. But, manipulating the numbers and doing the basic arithmetic? Hard. Sometimes even with a calculator, I'll miss carrying over a negative sign, and I'll get the problem wrong, despite knowing the concepts really, really well. What's going on here? Is my ADHD not under control? Are these symptoms of Dyscalculia? What? Ideas, hivemind!

Apologies for the length; I'll try to keep it short. I'm 42, in the software field, and really want to study higher math (Calculus and the like) to take some Computer Science classes. I'm brushing up using Khan Academy, and it's going great - except for messing up arithmetic.

All through school, math was always my worst subject, gradewise. Yet I'd do well on standardized tests. Yet, once I hit High School, I suddenly hit Geometry and Trigonometry - and finally math made sense. I liked these subjects, and they came to me easily. Same with some elements in Pre-Calculus, such as Matrices and Limits and graphing functions. Yet good grades would elude me, as I'd make arithmetic mistakes, and get marked way down. And with admonishments to 'pay more attention'.

College came along, I avoided math like the plague, got a Film degree, discovered I didn't want to work in film at all, and fell into software testing. And I'd like to take some Comp Sci classes to learn more. (And please don't start a debate on whether or not I need to even take this path to get ahead in my career, I want to do this.) Turns out that all this time I had problems in school? I had undiagnosed ADHD. Now my ADHD has been diagnosed and is being treated, but I don't think my dosage is high enough.

Fast forward 20 years later, and I'm revising math. And something different is happening - I'm finding it just fascinating. I understand Algebra for the first time ever, and I'm just loving learning new concepts and re-discovering old ones. I completed 262 out of 311 of the exercise modules, and I can't wait to finish the rest. And I am really looking forward to studying math in school, particularly Calculus and beyond. And the Linear Algebra modules in KA, even knowing that they were beginning level, I found easy. But I'm being plagued with the same difficulties doing basic arithmetic and manipulation, even with a calculator. I don't get it. This is pervasive, and really frustrating.

When I was a kid, I never got formally diagnosed with learning disabilities, even though a couple of teachers talked to me about possibly having Dyslexia. When I asked about this in college the first time around, they didn't find cause to test me, as they weren't obvious enough. I really don't want a second go at college to be tanked by the same thing, particularly since I'm really enjoying math for once in my life, and I want to continue, and go as far as I can with it. (And the world really needs more women who like math!)
posted by spinifex23 to Education (28 answers total) 21 users marked this as a favorite
 
As someone who teaches this stuff, I see your problem in my students, but as someone with ADHD, I don't share it. I had assumed that it could be overcome by a lot of practice, but I don't know for sure that this is true. Also that a deeper understanding would help (rather than an algorithmic approach to problem solving) but, again, I lack evidence to support this.

From my own experience with ADHD (and my observation of others with it) I have seen that the ability to concentrate varies with the object of concentration--that is, a strong interest/aptitude leads to hyperconcentration while boredom/tedium lead to its opposite. This is why I believe that a deeper understanding (along with an interest in the understanding) is the way to overcome this.
posted by Obscure Reference at 12:47 AM on March 10, 2012


OR,

That makes sense. I'm also thinking that maybe I shouldn't be trying to do this after a workday, when I'm tired. That could also be partially the cause of this all. And I forgot to add that in the post.
posted by spinifex23 at 12:56 AM on March 10, 2012


First, it's good to know you're getting a lot of enjoyment out of learning math. Math centers me.

Second, what you're describing sounds a lot like dyscalculia. If you were in high school in the 80s, it makes perfect sense that your (possible) learning disability went unobserved.

My wife has dyscalculia and has trouble retaining numbers in her head, even for a split second. If she's crunching algebra problems, she has to double/triple check what she's writing down. She is able to operate a cash register, but it takes a lot of effort to make sure she isn't reading dollar amounts in reverse. This is not to say she doesn't understand the concepts. She went as far as taking statistics (as was required for her major, social work) and she has a thorough understanding of the concepts. It just takes her longer to perform these tasks.

Definitely see about getting this assessed by a professional just so you can absolve some doubt as to what it is. If it is dyscalculia, I'm afraid the only way to overcome it is persistence, which, considering your apparent enthusiasm for math, shouldn't be a problem for you!
posted by triceryclops at 12:58 AM on March 10, 2012 [1 favorite]


When doing math problems write down everything! Write down each step, take no shortcuts. Do this every single time! Don't try to do steps in your head or anything like that, just write it all down. Write it out very neatly...generally from top to bottom.

In general I like to write down the givens or knowns, write the word problem into math terms and variables. Then write down the relevant or useful equations. Then work from what you know to what you want using the key equations.
posted by Mr. Papagiorgio at 1:00 AM on March 10, 2012 [5 favorites]


Sorry for thread sitting - really, I'm going to bed soon! But I did learn, the lard way, that I should write every step out. So, I do, down to even the addition and subtraction steps.

I did some reading, and apparently reading aloud the problems might help. Luckily, the roommate is at work tomorrow, so I'm going to also try that technique.
posted by spinifex23 at 1:03 AM on March 10, 2012


I think I have some symptoms of dyscalculia. I don't say I am dyscalculic because I just can't seem to line up ALL the symptoms (or an appropriate threshold of symptoms - I have good rhythm/spacial awareness etc.). But I did quite well at maths in high school but ALL my teachers said I had problems "making silly mistakes", so like you the concepts/difficult stuff was fine, but sometimes all the numbers would just get wonky. Working in retail in Australia was fine, the cents are to the nearest 5c coin "That'll be $5.25 please!" but when I moves to the UK "That come to £5.34, I mean £5.43!!"

For me the main difficulty is saying numers aloud, I'll have in my head the right number "66 Gosvernor Ave!" "You mean 69?" "Didn't O sy that?" and forget me reading information with dates pre the 20th.

However, I find the more I practice the better I am. I'm more than 10 years off high school so I notice my maths skills fade. When I worked I'm a bakery where the bread cost only certain price brackets my adding up of those numbers become quite good. Just when the bread prices changed... Ah! So you're studying maths! Awesome! Maybe we some regular arithmetic practice you can help your brain get more flexible?

FWIW my father is severely dyslexic, me, I'm fine with the letters, it's just those pesky letters.
posted by jujulalia at 1:23 AM on March 10, 2012 [1 favorite]


(My letters are better when I'm not typing on a smartphone... My letters are fine, it's just those pesky NUMBERS. But now I'm worrying about both!!)
posted by jujulalia at 1:27 AM on March 10, 2012 [2 favorites]


I see this a lot with my students... it's probably the most common problem, across the board. Things that help for people who don't have clinical-level problems: Practice, checking your work, and checking as you go by estimating what the answer will be before you start.

(By the way, the early programming parts of CS are all about precision. I'm not sure what a formal evaluation for dyscalculia and/or dyslexia would look like, but you might want to find out... If you have either one to a serious extent then CS will be very painful.)
posted by anaelith at 1:38 AM on March 10, 2012


I could have written a good portion of your description. I too found geometry and geometric calculus very intuitive but tended to flub the more elementary stuff for reasons I didn't understand.

I would be very hesitant to pathologize a tendency to drop your negative signs. This is more likely about not just learning the arithmetic manipulations, but internalizing the type of attention one has to pay to these processes.
posted by Emperor SnooKloze at 2:27 AM on March 10, 2012 [3 favorites]


When doing math problems write down everything! Write down each step, take no shortcuts. Do this every single time! Don't try to do steps in your head or anything like that, just write it all down. Write it out very neatly...generally from top to bottom.


In grad school I helped a friend raise her Finance (math and arithmetic heavy) exam score by a full grade (about 35% in marks) by simply teaching her how to identify the variables in the written word questions and put them down on the side of the sheet of paper (i.e. B = 34, Y=23 and Z = 89)

This then allowed her/us to use the formula sheets we were allowed to use for the exam to scan which formula used B, Y, Z and one more which was the variable to be solved for in the question very rapidly, thus allowing her to identify which to apply for the question accurately.

Then she revealed to me that she'd been brought up in the 'fuzzy math' era of American education (She would have been approx 27ish in year 2000) and had never been taught this pragmatic (rather engineering based approach) way of dealing with formulas, variables and basic arithmetic.

She had been taught to "hold on to it in your head" and of course its much harder to do that than to write it out clearly in a way that allows you to assess which pattern of variables shows up in which formula or equation and recognize it quickly.

Would this shift to fuzzy math in middle school also have happened for you perhaps given that you are close to the same age group?
posted by infini at 2:53 AM on March 10, 2012


The thing that helped me immensely with arithmetic errors was discovering Maple while at university. I'm “good at maths”, but can't add for shit. I still had to know exactly what I was doing, but Maple (or frankly any other CAS) kept track of all the terms.

(and as for handing in my assignments typeset in TeX rather than my usual scrawl ...)
posted by scruss at 4:46 AM on March 10, 2012


I have young students and often when there are problems with negative signs or basic calculations it is sometimes due to a) not writing out all steps or b) writing with handwriting so bad that they confuse their own 3 for a 5 or negative sign for part of an equals sign etc. Just an idea.
posted by bquarters at 5:07 AM on March 10, 2012 [4 favorites]


Now that I'm awake, other things have occurred to me. One is handwriting. You need to write things in a legible and mathematically correct way. That is make your minus signs obvious. Don't under or over extend lines for fractions or radicals. use equal signs to mean things are equal, not to mean you've performed the next step.

Give names to your repeated mistakes. For example, a common error of my students is to take a fraction like (14x+3)/(7x+3) and cancel the 7 into the 14. I call that "term cancelling."

Khan academy has a recipe approach to problem solving which often hides why things work behind rules. I'm always thinking, whenever I'm doing something, "what allows me to do this?" So, for example, if I have X^2 = Y^2, can I take square roots of both sides and have X=Y ? Why would that be valid? (It isn't necessarily.)

Do problems in several different ways and see if they come out the same. Make up new ways.
Our text says that the way to solve sqrt(x-2) -2 = -x is to bring the 2 to the right hand side and square both sides, but what if, after bringing over the 2, instead of squaring, you divide both sides by sqrt(x-2)? Or what if you substitute Y^2 for (x-2)? (and would that be allowed?)

And as someone said above, estimate what the answer should look like (or even what intermediate results should look like.) One problem in our text had a bicycle covering a distance in 15 minutes and asked for the average speed of the cyclist in miles per hour. Students who just plugged numbers into a formula neglected to convert from minutes to hours and had a bike capable of going 200 miles per hour. It never occurred to many of them that this is unlikely in the real world.
posted by Obscure Reference at 6:02 AM on March 10, 2012 [2 favorites]


I have dyscalculia to such a degree that I struggle read analogue clocks and to dial, let alone retain, telephone numbers. My story regarding math is virtually identical to yours. I struggled severely until geometry, at which I excelled. If there is any possibility that this could be you, I would strongly suggest you be assessed by a learning specialist.

If you do have dyscalculia you will be vastly more successful in your maths endeavours with specialist tutoring and sheer, tedious rote memorisation of the different steps required for different calculations. (I would, at this point have to re-learn these even for the most rudimentary long division.) There are now also well rated books for dyslexic and dyscalculic learners that may suffice if your disability is mild.
posted by DarlingBri at 6:21 AM on March 10, 2012 [2 favorites]


Yet, once I hit High School, I suddenly hit Geometry and Trigonometry - and finally math made sense. I liked these subjects, and they came to me easily. Same with some elements in Pre-Calculus, such as Matrices and Limits and graphing functions.

This is because the "big ideas" in mathematics are usually quite easy to grasp. Many of the things are very natural. Students often wonder why a proof of something like the intermediate value theorem is even needed, and they ask me "isn't that just obviously true?" Limits are almost unbearably easy to understand when you're looking at graphs of functions which are piecewise continuous.

I see that Obscure Reference tells you to be sure that you're using mathematical notation correctly. The symbol "=" does not mean "and now I've done this". Just a few days ago, I had two different students on two different occasions say "and then" when they wanted me to write "+"! I couldn't believe it.

I cannot stress the importance of correct use of mathematical notation. Being good at this takes time, and lots of it. This is what I imagine is happening with you, and unless you scan some problems you've worked that have the kinds of errors you're talking about and mefimail them to me, I can't be sure why you keep dropping negative signs and so forth.

Remember this, though. Unless this happens on every single problem you work, it may not really be a sign of anything. I have been studying mathematics for years and years, and I still do exactly the same things you describe (only occasionally, not every time). I'll lose a negative sign. 3+2 = 6, 5/2 = 5.5, whatever. Weird errors crop up like this with everyone, even (or possibly especially) with the most lucid mathematicians among us. In fact, when I post all the solutions to all the quizzes and tests online for my students, I tell them they can earn 5 points for every error they find. Boy howdy, do they find errors (most are typographical, but still). You can never completely eliminate errors.

And the world really needs more women who like math!

This is absolutely true. I hope you are successful!
posted by King Bee at 6:26 AM on March 10, 2012 [2 favorites]


I don't have a lot to add here, but I'll say this by way adding some perspective...

Even those of us that aced math are prone to misplacing our minus signs, making arithmetic mistakes and the like. While I did that too, I would mostly catch my mistakes because of things like:

- Doing a rough estimate to see if my answer was in the right ball park
- Put some numbers into equations and see if what comes out makes sense
- Check the boundary conditions... Does this make sense if x is 0? Very large? etc
- Working things out two different ways and comparing the results
- Carefully reviewing all the steps

i.e. It's as much about catching and correcting mistakes as not making them

Also it's true about most things that a belief like "I'm no good at X" tends to become self-fulfilling. Even if there's some underlying reason there, the self-talk and self-doubt you burden yourself with and the emotions that come up because of that amplifies it all many times over.

Lastly, congratulations on the progress you're making. It sounds pretty awesome.
posted by philipy at 6:40 AM on March 10, 2012 [2 favorites]


So much good advice in this thread.

To this I'll add that showing work, to me, means organizing your information in a way that will make it easy to check.

Another thing I always try to do is to find a different way to solve the problem, and to do it that way, too. You can use the two answers to check each other, and finding different approaches builds your insight/intuition.

Also, a big part of showing your work isn't just about handwriting, but about leaving yourself enough room. Don't be afraid to use an entire sheet of paper for a single problem if you need to.

Also, if you're checking your answers in the back of a book, check after each problem rather than checking all answers in a problem set after you're done, in case you've picked up a bad habit and are repeating it.

If you find you've made a mistake, go back and do the problem from start to finish again, maybe even again after that, so a correct, coherent version of the problem sticks in your head instead of an incorrect train of thought with a list of errata.

You may also want to try rubber duck debugging, as described in this thread. I've busted this out with my students, and a lot of them really like explaining their work out loud to these things, and find it helps clarify their thinking as they go along.

Data points: I teach remedial math to 4-8th graders, and I hated math when I was in grade school due to many of the same difficulties you're describing.
posted by alphanerd at 9:54 AM on March 10, 2012 [2 favorites]


Lots of good stuff so far, just chiming in with a few random thoughts:

Don't under or over extend lines for fractions or radicals.

I recommend putting a down-tick on the end of your roots. It really helps, especially if you have the square root of three, times x, next to the square root of (three times x).

If you don't want to use reams of paper, get a page-sized white board and use that. Or, yes, type your math (it's fantastic and easier than you think).
posted by anaelith at 11:36 AM on March 10, 2012 [1 favorite]


I was a kid with ADD in the 80s, and I had and have all the same problems - struggling mightily with computation of every type, inability to hold a number in my mind while doing the next step, inability to carry without writing it down. My standardized tests always came back with verbal scores in the 99th percentile and math in the 60s. I nearly failed Algebra I, sailed through geometry, then nearly failed Algebra II. Back in elementary school, my first grade teacher wrote on my report card, "Jocelyn needs to learn to stop counting on her fingers." Thirty years later, I'm still trying to accomplish that. And my math-avoiding tactic was to study theatre!

As long as I can use a calculator, I'm pretty much okay. I succeeded at statistics, finance, and accounting through studying way more than other people, and ended up doing work where I used Excel all the time. It turns out I had a gift for data analysis - as long as I had a spreadsheet I could set up to do the calculations.

When you embark on college again, take advantage of the resources for this before you need them - disability services may test you, or you can be tested and get accommodations. And there'll be options for tutoring. It sounds like you have a good attitude about this and are not carrying around a lot of shame about it - that augurs well for you advocating for yourself to get the help you may need.
posted by jocelmeow at 12:18 PM on March 10, 2012 [1 favorite]


Now that I'm awake and have had my coffee...

Thank you all for the excellent advice. I think what's happening to me is a few different things:

1. My handwriting is horrid, and I often can't read it afterwards. Always has been, always will be. I also have Spastic Paraparesis, which often makes it difficult as well.

2. I fully admit, I do tend to rush through things. And when frustrated, I don't take breaks nearly as often as I should. I do also take a medication that makes me sleepy (Baclofen), and that certainly doesn't help. But that's why there's caffeine!!!

3. It doesn't happen with every problem. And I can usually do math in my head OK, such as calculating tips and the like. I still may have a touch of Dyslexia and/or Dyscalculia; I mix up directions all the time, as well as transposing letters and numbers when writing. But it may come out more when frustrated or distracted or fatigued. Or when also watching reruns of Glee.

4. Luckily, I literally have reams of paper to go through, as every night I collect the paper in my office's recycle bins to use as scratch paper. I do try to be methodical about writing out every single step. Sometimes it feels like I'm slogging through mud doing so, but I tend to get better results.

5. I also tend to do better when the numbers are written larger, and with more white space. I need to start doing that more. I don't have to worry about wasting paper that was going to be recycled anyways.

6. And with word problems, I try to be conscious of what the answer could actually be in the real world - but sometimes I forget, and I've calculated Alvaro's age to be -8473723.4. And then I'll put it in, and blink when I get it wrong, because I've gotten so lost in the abstractness of the problem that I forget its real-world applications.

7. Luckily, having years of real world software QA and testing experience have drilled the 'paying attention to the details' into my head, so I think I'm OK on that one.

And 8. When I go back to school, I do have to talk to the Disabilities Office about accommodations for my ADHD and Spastic Paraparesis; the latter makes it hard for me to write for any length of time. So, I'm going to ask for a Notetaker. I may bounce the Dyscalculia/Dyslexia issue off of them, if my changes to my work habits don't improve the situation.


At least I'm tackling the issue now, and not waiting until I hit school in the Fall or Winter. Thanks!
posted by spinifex23 at 12:48 PM on March 10, 2012


And 9. Use a calculator for every single simple calculation, no matter how small it is. Because, no matter how rested I am, I cannot trust myself to be able to multiply 3 x 3 correctly. And ask for this also as an accommodation.
posted by spinifex23 at 1:28 PM on March 10, 2012


And take my ADHD meds every single day I attempt to do math. Just took my Ritalin. Let's hope it kicks in soon.


Yes, I'm still really frustrated, and having a bad time of it. I really don't want to face that I can't do this.
posted by spinifex23 at 1:30 PM on March 10, 2012


Use a calculator for every single simple calculation, no matter how small it is.

Maybe try and wean yourself off of this, though. No doubt, if you're taking a university-level calculus course, ask for this as an accommodation during a test or whatever. When you're doing exercises at home, do them first without a calculator, then with. See if the answer comes out differently. Sometimes the calculator is wrong too (although this is usually due to pilot error).

Also, if you have a "fancy" calculator, the kind that can do everything except experience the complex emotion of love, for the love of Jeff please learn how to use it. I see a lot of my students with these things who don't know that the calculator can compute limits, derivatives, even symbolic integrals, etc.
posted by King Bee at 1:35 PM on March 10, 2012


A common joke is that a lot of math students can't do arithmetic. This is exaggerated, but there's some truth in it: Being good at math and being good at arithmetic aren't the same skill, and you can be good at one without being good at the other.

Admonishments to "pay more attention" are annoying, but that's what helped me. I'm still not great at arithmetic, but I made a significant improvement just by being more systematic about how I approached problems. The problem was that the arithmetic parts seemed like they should be so easy that I just sped through them, not really thinking about what I was doing.

You aren't very specific about your problems. What happens when you try to do long division, for example? Do you not understand the algorithm? Do you have trouble recalling what "5+2" is? Or do you know what "5+2" is, but for some reason you write down "8" instead of "7"?

If it's the last:

Slow down.

Write out each step, systematically, even if you don't think you need to. Do it in an organized fashion even if your handwriting is terrible. (That is, don't use any available blank space. Go by line. Waste paper.)

Mentally check each step.

Avoid using a calculator when you're practicing. Check your work with one, but do the problems by hand first. If you're having trouble writing and need to use the calculator, don't just punch in the numbers, but narrate what you're doing.

Memorize your times tables if you haven't already.

Arithmetic is tedious, and boring, and frustrating, and any number of other negative descriptors, but it is also a skill, one that many people can't do well automatically without a lot of practicing.

Now, I'm sure you're at the point where you want to smack anyone who says that you should just pay more attention. I was there too. I majored in math, and constantly made simple errors in my assignments and exams that cost me miscellaneous points here and there. I reached a ceiling - I could never get an A on an exam where arithmetic was graded, even if I knew how to do all of the problems. I felt like there must be something going on, but the truth was that I was just going too fast.

To be honest, the fact that these problems are sporadic - that is, you can do these problems but are just often making errors - makes me suspect that something like dyscalculia isn't the answer. It may be, in which case ignore me and pay attention to actual experts. If not, it may be that you're just not that good at arithmetic and need to compensate for it by being meticulous.
posted by Kutsuwamushi at 2:27 PM on March 10, 2012


If you are going to use a calculator, get one with a 2-line or multi-line display, like this, not like this. I often see students making errors when they input calculations into the calculator. With a 2-line or multi-line display, you'll be able to review what you entered. If you think you've entered "2 * 3" and you got "5", look at the display. You mistakenly entered "2 + 3" instead. I see this problem all the time. A 2-line display makes this problem easier to check and eliminate.

When you get an answer plug your answer into your original problem and see if it results in a true statement. For example, after you solve "16x + 4 = 0", if you get a correct answer of "-1/4", plug it back in to the original problem, like "16(-1/4) + 4 = 0". Do the calculations and make sure it comes out true. If you make a mistake when solving the original equation and get an incorrect answer like positive "4", when you plug this result back into your original equation, "16(4) + 4 = 0", you should be able to see that this answer doesn't work, and it will alert you that you need to review your work to locate the error and retry.

Do this kind of checking in all your work, and it will become second nature. When studying with online tools or doing textbook homework, students often rely on the online tool or the back of the textbook to tell them if they have the right answer, so they don't develop the practice of checking their work. Then, when they go to take a test, since they aren't in the habit, they see this step as work that they aren't comfortable doing and the will take too much time, and so they skip this essential step, and get wrong answers. When taking a test, the students with the best grades are the last ones to turn in the test. They are using every available minute to review their work, testing their answers and looking for any possible errors. When doing your homework either from a book or online, it's fine to check the back of the book or the online tool to tell you if you've got the right answer, but ONLY after you have done the work yourself to verify your answer.
posted by marsha56 at 3:04 PM on March 10, 2012 [1 favorite]


I have to thank you all for your help again.

Reading the answers has been helpful, and now that I have a clear mind and sufficient caffeine, I think I found one of my main issues: I rush through the problems, and I don't double check. So, going back to the math I was having problems with last week, I completed all of the problem set and got them all right by doing these things:

1. Giving myself l o t s of space to write things out.
2. writing out *every single step*, no matter how small.
3. Double checking *every single step*, no matter how small.
4. Using the calculator to double check calculations, but also going with what I know, and trusting that.
5. Walking away from it when I feel the frustration starting to rise up, instead of trying to push through it. This is key, and I really need to remember this. Even if it's only for 5 minutes or so.

And I did it! I may tap you for help later on, but I think I have it now. And criticism is OK, I'm just glad that this seems to be an issue of sloppy habits that can be corrected. So I'd rather correct them now than when I hit class.
posted by spinifex23 at 12:31 PM on March 12, 2012 [2 favorites]


I feel the same way. I love conceptual math (calculus and up), and can do the stuff on paper with a calculator (if I am familiar with the calculator), but when it comes to doing simple math problems in my head, including simple subtraction, I was horrible at it.

I got a lot better reading a book about doing mental math. You can find it here: Secrets of Mental Math

I know the title sounds cheesy, but it really is an awesome book and arms you with techniques to never feel inept at elementary school math again!
posted by Peregrin5 at 4:31 PM on March 15, 2012 [1 favorite]


So, I marked this with a 'Resolved' tag, as the advice here has been seriously helpful. Taking breaks, using all the paper I need, writing out every step, and most importantly, having confidence in my abilities have all helped a lot. Thank you again.
posted by spinifex23 at 12:42 PM on April 9, 2012 [1 favorite]


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