Tips for neatening, formatting, and organizing self-study math homework?

December 6, 2016 9:39 AM

Please give me your tips on making handwritten math homework more attractive and useful, so I can enjoy reviewing my self-study math notebook.

I want to have nicer looking math notes. I'm reviewing high school math (algebra, geometry, trig) and studying college math I never had (calculus, linear algebra, whatever).

I have lots of great textbooks with problems and solutions.

When I'm working the practice problems, though, I just grab scratch paper and write things out haphazardly, often in as little space as I can (so I'll end up with three or four sloppy columns on the page).

I'd like to aim for something more attractive and legible, in the hope that I might enjoy looking back over them in the future.

So please give me all your best tips and ideas for creating my personal math notebook, writing out math homework attractively, and integrating it with notes (chapter summaries and so on). Links to examples would be great.

Please feel free to be very basic and explicit, like "write fractions so they take up two lines" or "circle the final answer" or "use lined paper" or "use graph paper" or whatever.

Suggestions on things to include besides worked problems (formats for chapter summaries, etc.) would also be great.

Thank you!

posted by kristi to Education (14 answers total)

Best answer: My HS math teacher had us do the following:

• fold lined notebook paper in half, lengthwise, so there was a vertical crease in the paper. This gives you two narrow columns to write problems in, since math problems rarely take up the entire width of a page.
• one line per operation when solving an equation
• at least one line between problems
• always circle the number of the problem you're working on, and draw a neat square around the solution.
• pencil only.

If I were doing this for myself, I would also use a different colored pen/pencil to write a short description of what I found difficult/tricky/insightful about the problem.

You may also like this article about keeping a "Commonplace Book" for tips on how to keep notes well-organized for your future self.
posted by homodachi at 9:47 AM on December 6, 2016 [2 favorites]

Best answer: Definitely use graph paper to line up your columns! For algebra and similar, write out the initial equation then put each step on its own line and mark what you're doing so when you review you can actually see the process (I'm adding dots because the spaces got stripped out when I previewed):

3x + 4 = 10
......-4... -4

3X = 6
÷3...÷3

X = 2
posted by Mrs. Pterodactyl at 9:56 AM on December 6, 2016

Best answer: I used to do something like homodachi suggests, except I would use the second column for all my "sidebar" calculations, e.g., factoring for some algebra thing or devising a scheme for integrating by parts or (pathetically) writing out some long division. It helped me to keep separate "thinking about applying a technique" and actually doing it. But having it all on the page let me remember where/how/why I had decided on that path.
posted by janell at 9:57 AM on December 6, 2016 [1 favorite]

Best answer: Give your equations an identifying number or letter so that you can refer back to them several lines later. Comment what you're doing as if someone else will have to understand it later.
posted by Obscure Reference at 10:08 AM on December 6, 2016

Best answer: Two general pieces of advice:

1. Make sure you give yourself enough room. You comment that you often write in as little space as you can. Don't do that. Give yourself all the space you need to be neat. I'm an intrinsically messy writer, but am able to have quite neat notebooks by giving myself lots of space.

2. Get a bound notebook to do your problems in. HOWEVER, do your "first draft" on scratch paper, NOT in your notebook. This accomplishes two things: 1) your writeup is much neater than it would be if you were just dumping your initial thoughts into the notebook and 2) re-writing it solidifies the ideas in your head and allows you to add commentary (e.g. "this was a tricky step, where I had to remember how to decompose vectors", etc.).

I personally like working on unlined, ungridded printer paper, but I understand that this is not generally regarded as The Thing To Do.
posted by Betelgeuse at 10:56 AM on December 6, 2016

Just an added point about my #2 above. I often make the analogy to my students of a paper in a literature class. You don't submit the rough draft; you submit a final paper that you've revised in order to most clearly make your points. In the same way, don't show me (or, in your case, yourself) every single little misstep along the way. Show me the work you did to get to the right answer, making sure to show me the steps you took. Just as any good paper should tell a story and/or lead its reader through a logical argument, so should the mathematical steps of a good problem writeup.
posted by Betelgeuse at 11:00 AM on December 6, 2016

Best answer: I minored in Math in college and did my best work (as did many others) on pads of paper like this engineering pad.

Basically, while the paper is on the pad, the grid shows through, but when you pull it off (to hand in to the instructor [or put in a binder in your situation]) the grid disappears and you have only your hand written lines unencumbered by lines.

Another thought, some of my friends who went deeper down the Math hole in university did much of their homework, labs, and research papers in LaTeX. I maxed out in the lower 300 level courses, so typed Math homework was never required.
posted by TomFoolery at 11:41 AM on December 6, 2016

Seconding Betelgeuse - in college math classes, I would recopy my homework from scratch paper to a fresh sheet, often with the problem statement either photocopied or manually written above the answer.

I was also a math grader for a number of years, and the students who did this generally had better results than the ones who tried to do the work in a small amount of space with a lot of erasures and overwriting.
posted by muddgirl at 12:06 PM on December 6, 2016

Nthing using plenty of space and commenting on your reasoning. Take your time writing so that your handwriting is legible. I would be sure to include attempts to solve problems that didn't work, with a sentence or two on why and how to avoid this in the future.

I've come around to using bound notebooks so that everything is in chronological order, I find it's a pain to reorder looseleaf and move it to the right notebook. Leave a page or two blank at the beginning to create a table of contents and number the pages. Some lab notebooks come numbered and there's also a lot of information out there on structuring lab notebooks that you might find helpful. I like lined notebooks, but for working with matrices grids might be helpful. Whether you want to break the page into columns and if you need a commentary column may also vary with the subject. If I'm skipping between topics a fair amount, I reference the general topic in the margin (in my case, a 2-3 letter abbreviation for the project).
posted by momus_window at 12:16 PM on December 6, 2016

Best answer: Thoughts from someone who has taken a lot of notes, and trained students in how to take notes, particularly in math:

- use 1 cm dot matrix grid paper (I find that the dot matrix is less visually overwhelming than a regular grid, and if I need a true grid, I can connect the dots and draw the lines myself to create custom "containers" for my work)
- one digit per box on the grid paper
- use a colored pen or highlighter to box each problem and write the problem number (useful if you work out of order)
- plenty of space
- handwriting as neat as possible
- use a pen and cross things out with a single line if need be, instead of erasing pencil
- if you are a visual learner, use multiple colors
- create a key that identifies what you're doing with each color (draw and label a little box at the top of the page)
- give every page a clear topic/heading
- allow plenty of open space
- use as much paper as you need
- label what you're doing on a key problem (turn your problem into a diagram with arrows and headings)
- find a graphic organizer that you like and use it regularly (you can get a lot of mileage out of a t-chart, for example)
- google image search for phrases like "interactive (math) notebook examples," "how to take math notes," and "cornell notes math"
posted by the thought-fox at 1:20 PM on December 6, 2016

Best answer: I would like to argue against rewriting your work to show only the "clean" solution. Sometimes, knowledge of the back roads that you wandered on your way to a solution are as valuable as the solution itself.

If you end up way off base, writing the clean solution after the goose chase might be worthwhile.

I might use scratch paper for some of the basic arithmetic stuff that I can't do in my head, but I think that using the left side of the page for problem steps leaves plenty of scratch space on the right.

Pencil is fine for erasing minor flubs, but anything more than a few characters should be crossed out and written clean.

One thing that you might be missing out without a teacher in front of the blackboard is learning standard ways of formatting various problems when written out by hand.

For example, how many lines (and you need lines, if not grids or dots on your paper) does the quadratic equation take up when you write it? I won't say that you are "wrong" for using fewer than 2, but you set yourself up for failure when one of the parameters is a fraction.

What about summations? Where do you put the left side of the equation when the right takes two or more lines?

How is your Greek handwriting? Do your gammas look like y's? Is alpha distinct from a? Would a stranger recognize your deltas?
posted by sparklemotion at 4:25 PM on December 6, 2016 [1 favorite]

Best answer: Write bigger than you think. Like, think about the way double-spaced stuff looks. Writing big helps you think, I think -- it's part of the appeal of working on big chalkboards/whiteboards. It also forces you to write more clearly. I used to use big Crayola markers and an easel pad -- now I use a whiteboard, and just take pictures with my phone whenever I want to save something quickly. Maybe something like that would help with the "chicken scratch" stage.

(I say this as a small-writer -- I used to write two lines within a single college-ruled strip.)

Experiment with different formatting -- if you're writing stuff with a lot of subscripts, try making them REALLY BIG or really small or further down than you'd normally put them, and see if it looks clearer that way. For gross algebra problems involving lots of parentheses, make the big parentheses...big. Etc. A lot of this will depend on you -- give yourself room to experiment!

To figure out how worthwhile summarizing/rewriting your notes is, keep writing big and writing a lot and writing in chronological order, but make it easy for you to retrace your steps very quickly. Put big boxes around results, important formulas, etc., even if they're several pages apart. You don't have to write fresh reference pages from a blank slate; write over your previous notes (highlighting previous points as you come to understand their importance) and become familiar with them so that it's easier to "look up a formula" or a previous example or whatever. You'll need to do a lot of cross-referencing; pay attention to how long it takes to look things up, and see if you can reduce that time so that you don't have to interrupt your train of thought as long.

Then, if you decide that you really do need to condense, you'll know exactly what you need to write in your summaries, and where to look up more detailed info amidst your lengthier notes.

For some things (tables of basic derivatives, trig identities, various types of matrices, etc.) it might help to start compiling a single catch-all formula sheet, that you become intimately familiar with and that makes looking things up easy. The less latency there is between you and your notes, the more useful they'll be, and the more they'll help you!

For me personally, really "getting to know" my notes was the key. If you don't understand them, don't like looking at them, etc. -- how are you going to learn from them? They don't have to be perfectly written, because that (for me at least) just creates a lot of anxiety and is really missing the point. Write them for yourself. Draw little doodles or whatever. Go a little nuts with the boxing stuff and stylizing your Greek letters -- whatever will help personalize what you're learning, and make it your own.
posted by miniraptor at 7:16 PM on December 6, 2016

Best answer: Oh! And for big long strings of annoying algebra, I like to do something like this. (Say the question was "Show y(x) = 0.") Super easy to trace back through all the equals signs.
posted by miniraptor at 7:28 PM on December 6, 2016

Response by poster: Sorry to be so heavy on the best answer link, but these are all GREAT.

Thank you so much!
posted by kristi at 9:58 AM on December 9, 2016