A couple of posts back I asked some of the tip-top students in my 280 class to write some hints on homework completion for their peers: what do they do that's made them successful so far this semester?
I've received a couple of responses so far, and I thought I'd share these two folks' suggestions in this post. I've left the suggestions as is, and I'll keep them anonymous.
Students (in any of my classes), please feel free to reply in the comments section.
1. A chronological checklist
A) I read the problems the day I get them or soon thereafter. I usually have to read them a lot of times before I even understand what is going on in them. But half the battle is knowing what's going on, so I try to get that done as soon as I can. I look for words I've heard before and think about whether I've seen anything similar. I usually write a "translation" to the side of the problem, something that helps me remember what the problem is asking when I go back to it later.
B) I scrawl. I write ideas down, even if they're stupid (and they probably are at first) or messy. They are usually very unorganized. I scrawl all over the homework paper and when I run out of room there, I scrawl all over notebook paper. This is just to get my ideas out, and if I don't have any ideas, I write out definitions that might be relevant, or really anything at all that might be relevant. For example, if the problem is to show two sets are equal, I write down what I know has to be shown for that to be true: containment in both directions. Just by writing that down and seeing it, I might think of the next step. For that matter, sometimes I just write down the entire problem in my own words.
C) I organize my scrawlings. Still on notebook paper, I write the problems out in order and compile all the ideas I had for each problem into one place. The answers might not be complete, but the ideas are at least organized.
D) I get frustrated and leave it alone for a while. Depending on how much time is left, I stop thinking about it for a few hours or a day so I don't burn out. These homeworks are really hard and if I think about it too much all at once I start getting mad and thinking "When am I ever gonna use this stuff???" Not productive. I take a break and do something completely different.
E) I come back fresh. I take my organized scrawlings to the math lab and crank it out. If no ideas ever came, I ask whoever is around if any ideas ever came to them, including Patrick, who lives right across the hall from the math lab, conveniently! I write out a dress rehearsal of my homework (the whole thing the way I want it to look Latexed, just on notebook paper).
F) I Latex it. I won't lie, this takes me forever. But I'm getting better at it and it comes much much easier than it did at first. I usually copy and paste an old homework into a new document and fill things in. That way, I don't have to start from scratch. Latexing it makes it SO much clearer and I can find mistakes more easily.
G) I revel in the beauty that Latex spits out. So lovely!
That's it mostly. It does take a lot of work but it feels so good to turn in a complete, correct, Latexed answer. That is, it's worth it.
2. Facebook is your friend
Timeline:
Upon receiving my homework sets, I usually read quickly through the problems. I do not really think about them critically or read very closely, but just to get an idea about what I am going to be asked to do in the upcoming week. I do pay special attention to the committee problems since they are due earlier.
When I find time over the weekend, I try to go ahead and get at least the committee problems completed. Usually these are due on Monday, and it’s not hard to get something down on paper that is constructive in two days, even if you work on weekends (I do!).
Next comes the bulk of the homework, which I try and get started on as quickly as possible. Usually I know that it will take about three or four hours to make my first run through the homework, not including waiting back on email responses from questions I have. I try and set out about that amount of time in split up in a couple of days. I don’t really think anyone could be sane if they tried to do all the homework at once. Four hours of induction is not really something my brain can take. However, I do try and work at least an hour or even two at a time. It keeps my mind from running off track and forgetting what I have already completed. Once I get that “draft” done, I will usually try and wait a little while, and then come back to it. By this time my mind has cleared and I am ready to get back to work. I read over each of my solutions to the problems, and then start doing corrections. I usually try and correct the simplest things first, because the more I have done on a homework set, the more anxious I am to get it finished. After I have got all of my changes done, I read over it again, and see if there is anything I can reword or make sound better, and of course make sure my proofs make sense. After that I am pretty much done! I do all of my work in LaTeX, so I usually don’t have more than the two “drafts,” the original and final, even though I may do numerous changes to the file.
Approach:
When I first start doing my homework; I pick out the problem I think will be easiest to prove. As I said before, the more I have done, the better off I am. I do everything in LaTeX, just because for me, I don’t have to worry about my chicken scratch handwriting, and the entire proof starts out organized, which helps me. Many times, I will have two different ways I think the problem may work out. Therefore just start typing the ideas for one, and if I get stuck start typing the other ideas. Eventually things will start to work out, or one idea will play off the other, or the ideas may end up combining. Who cares if I spend an extra ten minutes writing down an entire problem and getting the wrong answer, if it helps me understand what is going on, isn’t that what counts?
Committees work beautifully in one of two ways. In the first case, suppose I have absolutely no idea what is going on, or am just not really sure how to go about setting up the problem. I usually go as far as possible, even if it’s only two lines of LaTeX, and then I write comments asking how it should be set up, or how to get moving again on the problem. In the second case, suppose I nail it and know I have it right, or at least I am pretty sure I have it right. What is more encouraging that turning in the paper, and two days later seeing comments on your paper from friends saying “Awesome Job!”?
What happens when I really get stuck? Well may I first say that in every homework set, about two of the problems I end up getting stuck. My first method of attack on this is to take a break. Go grab something to eat. Let your mind wonder to the GPA killer, Facebook, for a little while. If you smoke go get a cig and make your way to the closest designated smoking area. Even play a round of Gears of War 2. Whatever you consider as something to just chill you out, do it. But while taking a break, I always try and keep in mind what I am stuck on. How on earth can this possibly work? Usually with this I can get at least one problem figured out. Taking a break is good too, because as stated before, trying to do all of this at once is insanity. If I can’t tackle all of my problems this way, I next EMAIL Patrick. I do stress email, because in fact going and talking face to face I have found doesn’t work for me. The reason is, I get back and start doing my homework, and I will forget exactly what was said. But if I send an email, I have it in writing right in front of me to stare at until it’s no longer needed. Usually after receiving my response (Which kudos to Patrick for the average 15 second wait time it takes to receive a response) I read the email a few times. Sometimes I may look at an email literally 20 to 30 times, constantly switching between my TeXmaker and my email windows. It’s what works for me. The emails are always helpful, usually contain examples, and are usually encouraging. I am pretty sure I have never got an email describing my idiocy, though I don’t know how Patrick resists. This is just what I do. The math lab really doesn’t work for me, but if it works for other people then that’s awesome! Use that! Find whatever works, Find someone that you can understand and get constructive comments out of. I assure you though, at the least shooting an email to Patrick won’t hurt, and usually gets you a fast response that you can then study.
A couple of things I always keep in mind while I am doing the homework:
- The problem will always work out. No matter what. There is a solution. If the problem asks you to prove a theorem, you know that the theorem will hold. It’s just a matter of getting to that solution. You got this! Just work it out!
- It all comes back to, and sometimes I start my proofs by actually listing these: What you know, and what you want. The theorem is obviously what you want, and the definitions of the parts of that theorem you can usually count on being what you know.
- I always go back to the definition if I start going in some horrid direction to nowhere. Usually between the notes from class and what is given in the question, you have exactly what you need. Since we are trying to prove something in general, it almost always goes back to the definition.
LaTeX really seems to help me get my homework done neatly and correctly. The PDF is REALLY easy to look over and it’s REALLY easy to see if you have made any mistakes. Also, after you do it enough, it is not hard at all and is faster than writing it down in most cases. The code is extremely easy to figure out, because it’s all logical tags. If you have to take CSCI 201, you have to learn java, and that’s much harder because not all the code makes sense. But in LaTeX, if you want a fraction, its \frac{}{} or a union sign its \cup, which the union sign looks like a cup. LaTeX is very logical and only takes a very small amount of practice to learn and get good at. Also, if you use TeXmaker, it will actually predict the code for you, and it’s also got buttons on the side that will insert the code right into the document! It’s so EASY! Once you do learn it, it makes the homework so much easier to work on, and then you don’t have to worry about keeping up with three or four drafts that is barely readable. You just have one file that you can edit anytime you want with ease.
The homework just takes a little bit of time and thought. It really is a very do-able piece of work. All that needs to be done is to find a system that works, stick to it, and ride that through the rest of the semester.
That's for starters. My thanks to the thorough job these two folks have done! (I promise, I've not paid them for their remarks. It's all pro bono.) I've got three or more people on the hook, and I hope they'll chime in with their own advice soon, too.
Anyone else?
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