College Algebra

For a lot of reasons when I started college as a regular student, I had about 2 years of college but no math and almost none in high school other than 1 high school statistics class (another long story how that happened!). All I knew was that I had a B+ average on the all the general requirement classes, and that in MENSA, right after high school I tested and was 88% above the population, with a chance after college of being 90%, the bottom of the MENSA barrel of smarties.

So not a great background but I was fast on my feet and met most challenges reasonable well, so far in academics anyway. So I find that to take college algebra you need 2 years of high school math or 2 prerequisite algebra classes (the equivalent of high school).

Now this was for me a real show stopper. It meant I was going to have to spend 2 semesters, an additional year for to get at this level and then the real math classes I needed to take for physics would then begin. After another semester of calculus and trigonometry I would THEN be able to start my university level physics classes. This was not so clear ethier as they were saying I should take trigonometry after college algebra but before calculus, which would mean yet another semester. So almost a 2 year delay and I was already 5 years behind (Air Force and 1 year high school I dropped out no money and on my own, yes another story!!)

So, I decided I was just going to do this thing. I wasn't sure of all the details but I had had many challenges in my life and I wasn't going to let this one beat me. I talked to a number of people, with various opinions. I noted, that those with little or no math, had the most enthusiasm for the idea, whereas those who were in the know were more guarded and reserve.

All I knew to this point in my life was that I had overcome tremendous obstacles to this point, I wasn't vain, I was just confident in my ability to work hard and overcome. I knew I would dedicate myself and do anything it took to make it through but I had no idea the ordeal that was ahead of me.

I started classes. College Algebra, like many classes is an early morning class, 8 AM in fact. This was a painful time for me as I am so not a morning person, so as anxious as I was I usually came half dressed, late, and drossy, and yes slept through a few classes. It is also a daily class, Monday through Friday, five days a week.

Within that first week, you get to know the drill, she previews a little of what you will learn, then assigns what you will learn, the homework, and the next day, first thing, she asked how well you learned it and what problems you had. Within the first week, in this large class of 65 people, mostly business majors, by the way, I could feel the sinking feeling almost the first day, that I was in over my head and lost.

Within a month, I wasn't eating, I had lost weight like 20 lbs, dropped a class, and was coming to class with bloodshot eyes. To almost the exclusion of all else I studied college algebra. I got 1 then 2 paid tutors I studied with. I even went to a hypnotherapist! I studied at least 10 hours a day. If I was up I was studying algebra and I didn't understand it at all. I talked to my sister, Misty, she said she couldn't help me as she CLEP'ed out of College Algebra! Was this brutal or what? But although I had a small chuckle, it wasn't funny to me, I saw no future, because now not only didn't I think I could make it in this class, but I wouldn't get it even if I accepted all the extra time and started at the beginning.

By the way, my sister, Misty, pip that she was, also told me she took 18 hours per semester when she was in shool,

So mid-term comes, I get my test back, 12 out of a possible 200 points. I am devastated. My teacher, who never really talked to me personally, takes me after class, listen I know you are trying, I know you are smart, but its mid- term, and your grade is the lowest F, in fact you have the lowest grade for the entire class, no one else is even close to that low.

She let that sink in, seeing I was so despondent she puts her arm around me, which was quite a start for me. She was not a particularly warm woman, and I was not even a blimp on her radar. But she puts her arm around me and says, listen, I know you can do it, when you are ready but its crunch time, and tomorrow is the last day to drop without it affecting your grades. This is important because if your grades drop, you can lose your assistance, so not only this class, but all classes! Worse I was down from 5 classes to just 2, dropping this class would just give me 1 class, not even halftime time student and I would have to work at one of my other 3 jobs even harder. What a mess!

I went "home", the people who took me in to finish high school. Dad Ward, was in the kitchen, sitting there smoking a stogie and peeling an orange. I came in and sat down with a huge sigh. What's wrong, he asked. My life is over, I am a failure, I might as well kill myself, and few times in my life, I felt like it was true. It was over, I had no hope, I had run out of options, ideas, long ago, I was worn out and beaten. It was like a flood gate, I talked so fast, spilling out my tale of woe so fast, and though I didn't realize it I was crying by the time I was done, tears flowing.

I continued looking at me, with his orange. Then he thought and chewed on his cigar as was his habit when he was thoughtful. He said, so you want some help? Yes, I said resoundingly. And you would listen to my advise? Anything, anything I said exasperatedly. He didn't say anything for a moment, and the pause, while seconds seemed like an eternity, I said I would piss on a spark plug if it would help. I volunteered all the exotic things I had tried, was trying, I was ashamed but I told him everything.

He said, do you have your book with you, I said out in the car, he motion to go get it. He said, do you have some homework, I said of course! Okay well do some, I said here? He said yes. I got my fancy paper, ti-25 calculator, .5mm pencil, and opened my book, and started working on the first problem. After a few minutes, he said okay that's enough, close your book.

I said, what?! He said I know your problem. At this point, you have to understand, as well intentioned as he was, and he was a very smart man, this guy had a 6th grade education. In my mind, I was spinning a million miles an hour, going no way, does he have anything, especially after a few minutes of observation.

He said, yes, you are too smart. Well that was it, that was IT. Come on Dad, I said, come on, I am flunking out of college, worst in my class, and you are sitting there saying that. He looked at me nonplused, and said, are you done? I nodded, he said ready to listen? Yes. He said grab the egg timer. He said about how long should it take to complete a problem? I droned on about each was different level of complexity, how it was hard to gauge, how I had to...he waved me to stop and said, okay we will give it 5 minutes. 5 minutes I said, come on, I can't even get the problem down. He looked at me again, I nodded okay, okay...and? He said every day you get homework? I said yes. He said okay here is what you are going to do.

Put the timer on, do each problem until 5 minutes, when it is done, reset the timer and go to the next. When you are done with the set, close the book, and go out and swim, or study something else, but do not go back to the book. At this point, I couldn't even get my mind around this idea, so I just nodded dumbly, but so not in agreement in my mind. Then at class does the teacher ask if there are any questions, I said first thing she does do, is ask that. He said do you ask questions?

No I replied and started explaining why, how far behind I was that my questions were so stupid and out of place, and the answers were even more confounding, and...he waved me to stop. Okay so go to the first Problem and ask her to help, show her what you did, how far you got, and let her help you work through it Do this until you get to the end. When its done, when she ask if there are more question go to your next problem. I cant do that! Come on, he said why? I said I will eat all the classes time, they will riot on me. And I will take all class for just a few problems, cause I am soooo far behind. He said, you said you would do anything, right? Yes I said.

You paid for the classes like everyone else, you have a right to her time like everyone else, have you ever taken up her time with questions? And before I could answer, he said I know you havent' Now, you have to be greedy for you, you have to put yourself first, you have to be fearless. Is anyone else failing like you? No, I am at the very bottom. He said so its fair to say, no one needs help more than you? Yes I said. Good, so that is what the classes are for, ask until the class is over. Do you have time after, I said yes 2 hours before my next class, so if she has time, and is willing continue as long as she will tolerate you.

Has she ever told you to stop, no I said. So do this. Then do this the next day and continue. I shook my head, this was so not going to work. But he made me feel not bad for taking the time for questions, yes they wouldn't race ahead and yes I would pull them back, but he was right I had just as much right as anyone else, and I did promise to take his advise and I always try to keep my promises. This was a whooper.

So I started, I applied the formula, sometime I varied the time for a problem I couldn't abide by that, it was an indulgence, and made me feel like I was cheating a little, but never more than a half hour for one, but I once the timer went off, I did move on and I followed his simple plan .

At first it was so grueling and the students were not buying it. I got so many people shaking their heads at me, some even left, and quit coming to class. Some said come one, this is nuts, move on, MOVE on, I wouldn't be swayed. They were all passing, all but me and this was my only chance.

I got my next test back, and ready for this, it was an A, just a few minor mistakes! I teared up. And I got faster, I caught up, but I used almost all the time still, as I was working every problem that I had until I was clear. Now I got to the point I wasn't behind, I was even with them, I wasn't an idiot, I was informed, in the know, and had well formed questions and even some insights.

I tried very hard, not to think about the success I was experiencing, I really thought she made a mistake on the test, and came to her, and went over each question to look for the mistakes she must have missed. The math was right, it took an hour to convince me but I couldn't argue, I understood the problem, the solution, and unbelievably, amazingly the math was right, and here was the most amazing part, I KNEW it was right!

It got stranger from here. I have to stop the story and give you a brief aside. There are 3 levels of physics. 1 is a survey level, that basically exposes a student to some concepts, there is almost no math except a few simple formulas. The second is college level and uses college algebra. There are simple formulas like kinetic energy, acceleration etc. and to solve problems you have to use simple, rules, but for at least the first course, rudimentary algebra. With these tools you can solve simple problems, typically like you would find on a SAT test. The 3rd series is University level physics. This is the same type of problems but much more difficult and based on Calculus. The reason you need calcus is because not only are these more real time problems and closer to reality but they deal with aspects of change.

For instance, in College series level (CSL), you would work on a car traveling at constant speed over a fixed distance, in one of its forms, v=dt, in University series level (USL) you would deal with a car speeding up and slowing down at irregular intervals, v, becomes the limit 0-v over intervals(variable acceleration). Its not so important if you don't understand, but what is important is that the closer to real life a problem is, the more complex the mathematics become.

So the only other class I ended up with was college physics, not for a requirement but to prepare for University level. I was learning the algebra I need as almost as fast as I need to use it. During this class, dealing with matrices, we were also dealing with them in college algebra, but during my physics class, I saw a pattern and first I just could show it but not explain it. As I worked more with it, and later, with help, seeing how to prove it, I was able to develop even more "patterns" .

I took it to my algebra teacher, and said, here is an idea that I got from you and see it applied here but I don't know how to prove what cases it will or wont work for except by brute force of trying all cases, which is impossible! She became intrigued, and helped me formulate a mathematical construct, known as a proof. When we were done, she asked if I minded if she published it for me, I said not at all and a few months later, she brought me a opened pamphlet, with my idea, rob's rule, and our proof for it. I was truly humbled and in awe. Could life be any better?

But I said, I have a new problem, she said which is? I said well since that time I have formulated a set of rules, dealing with matrixes as well as some other things and the proofs are a bit beyond me, I showed her what I had and she helped me through the difficult math which only mathmatains truly understand. After a few of these, I knew I would probably never be good at proofs and would always need assistance but that the idea was the main thing for me and I could sort of stumble around in the world of proof enough to basically explain the basic concept.

Okay, well back to the story. At the close of the semester, she called me after class, she said well you have now made a big problem for me. Up to mid-term you had an F average, the lowest F, from that point on you have almost an A average. So together, they average to a C. But this isn't really representative of your body of work. I was high, "body of work", wow, I repeated it over and over. She said, I tell you what I will do, You had the lowest F, if you make the highest A on the final, I will give you an A for the course.

I tell you what, I couldn't really wrap my mind around the conversation. It was a surreal moment, from where I had come, we are negotiating, the idea of an "A". I just was speechless. I let her steer the boat, cause I was flabercasted. Yes I had worked hard, but I had worked hard, even harder before, now I was doing less and getting more, something must be wrong but again, I reminded myself that I would not cast dispersions on my luck.

The final came, she circled my A with 198 out of 200 points, and pointed to it and shook her head yes and I knew. Later in her office, she wouldn't say but this girl, who was always the top preferformer had I think tied or a few points above me and I think she waived it anyway, but I will never know as she maintained I have to say one more thing, every time I got my paper back without red ink, I would flip through the test, over and over, looking and looking for the marks that used to be so thick I could barely make out my work. I swear it was like it wasn't even my own work, I had to stare at it, I knew it was my hand, I knew those were my answers, but I just couldn't connect to it. Believe it or not, I would shrug my shoulders and unbelieving, just say oh well, and just move forward. Because to me it was all to incredible to believe.

So that's more or less my math story. It was a grueling, humbling experience. Imagine, just apply such a simple stradgey, and that is all it takes. They thing he noticed, if you hadn't discerned it yet, when he said I was too smart, what he observed was that I immersed myself and focused on that one problem, to the exclusion of all else. The next day, drained, frustrated, I had a small part of one problem solved. The trick was to do as much as you can of EACH problem, learning some of what the lesson is about. Otherwise all you know is that one problem, this way you have learned more, more rules, more tools, even if unsuccessful, you have some idea and each day, you build on those ideas. You get a tool bag instead of one bent, chewed up mangled, worn out screwdriver.

From there I took over 30 hours of advanced mathematics, Calculus 3, differential equations, discrete mathematics, and on and though I had some tough times, my next challenges were not in mathematics any longer and never again. I hope this helps you or someone with their math woes. 33108_340.jpg As Einstein is often quoted as saying: "Do not worry about your difficulties in Mathematics. I can assure you mine are still greater."