Posted by: E (The Third Glance) | August 30, 2012

## Numbers

I’ve always been abnormally good with numbers. I remember them better than words or letters. I think in numbers quite often, though I couldn’t explain how that works. Patterns, numbers, factors, and math rule my brain. I’ve made my way through life counting, adding, multiplying, dividing, factoring, and more, taking in numbers and making them work with each other until a balance is met. When I was in kindergarten, I was the only student who knew how numbers worked. In 2nd grade, we had number-based logic puzzles that I finished every one of that the school had while my peers were still working on the first set. I figured out basic algebra in my head well before it ever had a name or reasons. I implicitly understood how different bases worked, and how to change numbers between them. I used to write out different number patterns in binary for fun. I was obsessed with Pascal’s triangle – the pyramid of numbers which has a 1 on each end of the rows, and then the rest of the numbers are defined by adding the two numbers above them, to make one. I would fill pads of graph paper with Pascal’s triangles, coloring in patterns, working in modular arithmetic, or different bases. Prime numbers were my favorites, and I spent hours trying to work out their mysteries. My favorite pastime was numbers. They were my friends, and I was theirs. We always played well together, and I loved them. I excelled at math in school and at home, and it brought me comfort.

But then one dark day, the Word Problems started. Suddenly my numbers were being marred with words. Nonsensical words. Who the heck cares if two trains are moving across the Siberian countryside? I certainly don’t! Or if Sally and Jim are walking together but Sally is taller than Jim and they have to take different numbers of steps. I don’t know Sally or Jim, and I don’t care. Word problems were my downfall from mathematical bliss. Those silly words and made up stories messed up my beautiful numbers and patterns. Don’t get me wrong, I had no trouble solving the equations these stupid “math” problems put forth. My issue wasn’t with the math. It was in the verbal translation of the story to the math problem that got me stuck. And don’t be fooled. When I say “stuck”, I mean, hours on end, in full meltdown-mode, unable to think or process ANY words, much less the frustrating words that were destroying my beautiful numbers and equations. I would try for HOURS, sobbing and beating myself up more and more as I failed to interpret the problems correctly, frustrating and confusing the people who tried to help me, because they didn’t understand the problem.

I almost failed math in 7th grade because of these stupid word problems. Not because I couldn’t do the math – I had no problem with that part, and that was the most puzzling thing for the educators. I was tested, and they found my mathematical abilities to be well above grade level. I could think and reason in numbers. I could perform advanced mathematical proofs of the type they teach in advanced university number theory. I obviously understood math. So why was I failing? No one knew, and I desperately did the best I knew how to do to prove them all wrong. I spent hours upon hours upon HOURS practicing the word problems. I spent my 30 minutes of “computer time” looking up word problems to practice with, and then the rest of my time doing them. I hated it, but I wanted to master this thing, that was getting in between me and my beloved numbers. I put myself through hell trying to make it right.

I never solved it. Sure, I got better at figuring out the word problems. Sure, the endless hours of sobbing over my math homework, listening to people tell me I’m incredibly stupid because I can’t figure out how high the man threw the football, or what time two cars would collide if they were traveling on the same road at two different speeds from two different distances. They shouldn’t be traveling in the same lane in the first place! I drew diagrams, counted squares, worked out insanely complex equations, far more complex than the problems called for, and did everything I could think of, to solve them. The instant I figured out what the equation was, I had the answer. That had always been the case. If someone would help me find the equation, I could solve that no problem. But I needed an equation, and translating from the confusing words to the equation was where I was stuck.

This issue continued to be a problem throughout the rest of my education. I thrived in math classes. I could solve even the most difficult equations. I taught myself Taylor Series (and the associated calculus) in 9th grade, because my history teacher introduced me to the “most beautiful mathematical equation of all time”: eiπ+1=0*, and I wanted to understand it, to prove it. So I did. But I always struggled with the last couple of homework questions, once all the equations were solved: the dreaded word problems.

Physics was one of the hardest classes for me in high school (I took college level intro to calculus-based physics my last year of high school), and in college, because physics is just word-problem based math. They give you a scenario, and you have to use math to solve it. I used to work on physics problems for hours, trying to set up those damn equations. Once I had them, solving was the easy part. But translating from words to numbers was still no easy task. Yet I took advanced calculus, differential equations, and linear algebra, all the while struggling in physics**, because I loved the math, and it came easy. I’m one of those weird people who are great at math but sucks at physics. I haven’t met anyone (in MY experience) who shares this feeling. Most people I’ve talked to say they’re bad at math, and only understood it when they took physics. For me, math was always easy, but physics was difficult. Not because I don’t understand the math, but because I don’t understand the words motivating the math. This is a classic case of a brain wired differently. My autistic brain can deal with numbers, and it can sort of deal with words. But I’m missing the ability to translate between the two. Maybe I should’ve been a theoretical mathematician.

I share this story because I want it to serve as a reminder to educators. Sometimes those of us with different neurologies struggle for reasons very different from what you might assume. I had desperate trouble in math and physics, not because I didn’t understand the concepts, or because I couldn’t do the math. I could do both splendidly. I can expound on why things work the way they do. I could give beautifully sound mathematical proofs. I was quite comfortable in the land of multivariable calculus, and just as comfortable in the world of number theory. For me, the sticking point was, and remains, translating from the words that define the problem, to the math necessary to solve it. I don’t have a solution to this. If you give me the equation and say “use this equation”, I still can’t translate the words to it easily. I have to understand WHY, and what parts of the problem mean it calls for that particular equation. I have to figure out where the different words and bits of the problem fit. And if you give me the same sort of problem twice in a row, I can’t generalize it – the second will give me just as much trouble as the first. It’s still something I struggle with on a daily basis. Happily, though, I’m not a physicist. And even now, I play with numbers for the sheer joy of understanding their mysteries.

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* eiπ+1=0, a special case of Euler’s Formula, is beautiful for a number of reasons, including the fact that it contains the 5 most fundamental mathematical concept numbers: 1, 0, π, e, and i, all together in a very simple, beautiful equation.

** I use the word “struggling” here liberally. I got A’s in all my physics classes, I just had to work about 5 times more on physics than I did in anything else I ever did academically. I did it, because I wanted to. But it was never easy in the same way math and other subjects were. I would quite literally spend 40+ hours on the weekly physics problem sets, often forgetting to eat and losing sleep, because I couldn’t turn it in unfinished. Eventually I would stumble onto the right equation, and then solve it, but getting there was never easy. I would sob to my friend (online, through IM) who is a physics-minded person, as he very patiently walked me through the concepts (which I would easily respond to, with complete understanding, much to his frustration), until I figured out what the equations were and how to use them.

## Responses

1. A walk down memory lane : )

2. I dread word problems. I have mentioned this to you before. I love when you say, “They shouldn’t be traveling in the same lane in the first place!” That made me laugh out loud. The horrible part is, most IQ tests rely heavily on just these sorts of problems, which, it seems to me makes for a very inaccurate reading of actual intelligence.

3. I never struggled with Maths problems, but I failed miserably at an aspect of History GCSE. History GCSEs are split into three sections, the second of which is the “Document” section. You have to look at a document from the time, normally a political cartoon strip, then explain what it means. I got A*s on the first and last sections, but the document bit just continually eluded me. You were supposed to analyse the document like you would a poem in English Lit class. I got a book, I wrote down all of the different symbols, I regurgitated them in the exam and hoped for the best.

• Interesting. I never had to do stuff like that for history, but I was pretty epically terrible at it in English

4. I too loved Pascal’s triangles; but I became frustrated because someone told me the Fibbonacci sequence was nested inside of it, and I could never see how.

5. As for physics relying being based upon word problems, I’ve actually run into trouble at the higher levels of physics, because eventually you reach the point where its grounding in easily-explicable phenomena breaks down. If you were to take quantum mechanics, for example, you would probably find that it’s far easier to think of in terms of abstract multi-variable calculus. Of course, you would probably find the applications themselves kind of repetitive and boring, but nevertheless…

• Ahaha – I actually started to take lower-division quantum my freshman year (after making it through the rest of the calc-based physics series), but I was auditing it, didn’t need it, and it was in the middle of the day. If I took it, I had 2 x 1.5 hour stretches in lab. If I didn’t, I could spend an unbroken 5 hour stretch. I picked lab.

6. I just love these discussions of how our brains are all wired differently. I have a special love of those word problems because they always felt like ways to put order and organization to random situations. I used to love reading them and pulling the equation out. Like diagramming sentences in English class. The theoretical concepts of math were so over my head, I just could never quite wrap my brain around them without a more concrete real world point of reference. Thanks for sharing this.

7. I’m actually the opposite in a way. I always had trouble with math in general. Once I hit intermediate algebra, I was stuck. The math problems became a jumbled mess of symbols to me in my mind and I couldn’t remember how to do even the most basic of things like long division, once I had to learn synthetic (as an example). And I could never get it through to my brain how to do long division with a 2 digit number as a divisor. Word problems? Forget it. I skipped over them or guessed which answer “looked” the best. Because I would just have a meltdown over it if I even tried to answer it.

however, I loved basic algebra. I loved prime factorization. I loved simple equations like 12x + 5 = 10 (as a random example). I started to like factoring equations once I understood it. But it took me forever to understand it. Forever, and a few packs of markers for different colors. Lots of underlining, switching markers for each number, crossing things out. I had to see every little step of the way.

8. I am so glad you wrote this! I had the same issues with word problems and now my son is struggling with them. He just started second grade. I do home school (using virtual school) him so I am trying to work with him and see where I can help. He seems to get tripped up on the details. “Why did the balls bounce away? Why are the balls on the beach? Who is Jim and Jane and why are we talking about them? Why do we have to do math problems?”

If I only use the numbers he is a math whiz. I have started turning the math problems into stories before I read the word problem. After I tell him the made up story I read him the actual problem, then tell the story again asking for the solution. It is very time consuming, but seems to be helping him. I wish someone would have done that for me and cultivated my love of numbers. I love numbers and math, but I was labeled intermediate and felt like a failure so I gave up.

At least now I can spend all the time I want learning without anyone telling me that I am doing it the “wrong” way. I can also help my son keep his love of numbers and introduce him number theory and enjoy equations. They look like masterful art pieces to me . 🙂

• Yes, he sounds a lot like me… “why did the balls bounce away” is just one of those questions I’d ask, indignant… I’m glad you’ve found a way that seems to help. Like I said, I haven’t really found a way that helped me – I just spent hours and hours on it. Where I lack in smarts, I more than make up for in very VERY hard work… 🙂 Good luck!

9. Clearly, I am you. I didn’t have the same problems based on the words because I am also highly verbal, but it’s like “What do you mean “show your work?” I see the equation and I know the answer!” Mathmathmathmathmath. (Complex analysis was a little tougher because I couldn’t give it the time it needed, but even the time it would have needed wasn’t as much as my classmates were putting in.)

• 🙂 “show your work” was always a big difficulty for me. For one thing, my handwriting sucked. Showing my work meant writing down a bunch of stuff I thought so trivial that it shouldn’t count as a “step”, in my awful handwriting that took forever and looked horrible anyway. I used to get in trouble for “rushing”, when really, it had nothing to do with rushing and everything to do with the fact that showing my work was significantly harder and more useless.

• That is my son, exactly. And then he gets stuck on just what he needs or doesn’t need to show. He also is really discouraged (Algebra II, 10th grade), because he has to pay much more close attention and – dare I say – work to learn it, when math has always been a piece of cake for him before.

10. I love this: “Physics is just word-problem based math.” I hated physical science…

11. Once I got to high school math, I slowly hated word problems, too. That said, I ironically now am in a field where the licensing exam is word problems galore and the things I see are very applications based! Sure, it is based on the concepts I should know. But that licensing test can be very challenging if you are a slow reader and/or methodical test taker.

12. yes, yes, yes, thank you yet again, same here 🙂
“For me, math was always easy, but physics was difficult.”
always liked math, could sometimes get lost in it, but physics was a torture. Solving the equations was easy, but finding out how to set up an equation… a completely different story
still remember the meltdown I was having when trying to study physics at home for a test

btw, also loved fiction books as a child

it’s funny, I came across your blog while reading another one which listed a few blogs’ names and your immediately caught my attention – it was this “oh, I could have used a title patterned like this” sort of thing