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Next: The Method of Three Up: Physics 41, Homework 2008 Previous: List of Assignments for   Contents

How to Do Your Homework Effectively

By now in your academic career it should be very apparent just where homework exists in the grand scheme of (learning) things. Ideally, you attend a class where a warm and attentive professor clearly explains some abstruse concept and a whole raft of facts (too many, in fact, to fit in short term/working memory and with too little time to move most of them through into long term/working memory). You've forgotten many if not most of the facts, but if you were paying attention and really cared about learning the material you remember a handful of the most important ones, the ones that made your brief understanding of the material hang (for that moment) together.

Your professor gave you an assignment in support of the lecture. It is time to do it. How should you do it to both learn all that stuff you missed in lecture and to re-attain the moment of clarity that you then experienced, until eventually it becomes a permanent characteristic of your awareness and you know and fully understand it all on your own?

There are two general steps that need to be iterated to finish learning anything at all. They are a lot of work. In fact, they are far more work than attending lecture, and are more important than attending lecture. You can learn the material with these steps without ever attending lecture, as long as you have access to it in some media or human form. You in all probability will never learn it, lecture or not, without doing at least some of the work in these steps.

  1. Review the whole (typically textbooks and/or notes)
  2. Work on the parts (doing homework)
Let's examine these steps.

The first is pretty obvious. You didn't ``get it'' from one lecture. There was too much material if you were lucky and skillful and blessed with a good instructor you grasped it only for a moment but it is still flitting further and further away with every moment that passes. You need to review the entire topic, as a whole, as well as all its parts. A set of good summary notes might contain all the relative factoids, but there are relations between those factoids - a temporal sequencing, mathematical derviations connecting them to other things you know, a topical association with other things that you know. They tell a story, or part of a story, and you need to know that story in broad terms even if you can't remember every word.

Reviewing the material should be done in layers, skimming the textbook and your notes, creating a new set of notes out of the text in combination with your lecture notes, maybe reading in more detail to understand some particular point that puzzles you, reworking a few of the examples presented.

You do not have to work on memorizing the content. In fact, it is not desireable to try to memorize content at this point - you want the big picture first so that facts have a place to live in your brain.

Your brain is fabulously efficient at storing information in a compressed associative form. There are lots of experiments that demonstrate this - the simplest being trying to memorize a string of ten or so numbers at a glance (more than the 7 one can typically get into short term memory).

Try memorizing 1357902468 from just the one glance you got reading this sentence. No fair going back and repeating it to yourself, at least while looking at it! Now look at it and try to remember it. One strategy is to just repeat it to yourself until you get it right, but if you stare at it a while and think, you'll see that it has a very simple pattern embedded in it.

In fact, this number ``compresses'' to a single two-step rule - all the odd digits in ascending order followed by all the even digits ditto. You already know what a ``digit'' is, what odd and even numbers are, what ascending versus descending order is. You only need to remember "ascending" and "odd followed by even digits" - everything else is compressed.

This ability to compress goes far beyond what I can explain or you can easily imagine. When I play a game of chess, I've forgotten my first five moves by the time I've made my tenth move. By the time the game finishes, I have no idea how I got into the mess I'm probably in. A chess master, on the other hand, can finish the game and then can recontruct the entire game in order, and can criticize each move as they do so. In fact, they can probably remember the entire game they played yesterday, or the one they played last week. They've built a complex structure of associative memory so that they don't remember moves the same way your or I do.

On the other hand, I can often remember what mistakes a student of mine made a week after grading one of their papers. I many not remember the student's name (no good associative memory there) but I've got great structures for remembering how to solve or not solve physics problems.

This is the goal of your iterated review process. At first you are memorizing things the hard way, trying to connect what you learn to very simple hierarchical concepts such as this step comes before that step. As you do this over and over again, though, you find that new information takes you less and less time. Sometimes your right brain even figures something out and passes it off to your left brain, which ``discovers'' a missing part of the structure before you even read about it. By reviewing the whole, well-organized structure over and over again, you gradually build a greatly compressed representation of it in your brain and tremendously reduce the amount of work required to flesh out that structure with increasing levels of detail and remember them for a long, long time.

Now let's understand the second part of doing homework - working problems. As you can probably guess on your own at this point, there are good ways and bad ways to do homework problems. The worst way to do homework (aside from not doing it at all, which is far too common a practice as it is) is to do it all in one sitting, right before it is due, and to never again look at it.

It is left as a homework exercise for the student to work out why this is a bad idea from the discussion and facts given above. Let's see, it fails to repeat the material (essential for turning short term memory into long term in all cases). It exhausts the neurons, as one often ends up working on a problem far too long in one sitting just to get done. It fails to incrementally build up in your brain's long term memory the structures upon which the solution is based, so you have to constantly go back to the book to get them into short term memory long enough to get through a problem. Unfortunately, by not repeating they soon fade, often without a discernable trace in long term memory.

Just as was the case with memorizing the number above, the problems almost invariably are not going to be a matter of random noise. There is pattern and meaning there, but it takes time and repetition for the ``gestalt'' of it to spring into your awareness and burn itself into your conceptual memory is high order understanding. You have to give it time, and perform the repetitions.

You don't get strong by lifting light weights a single time. You get strong lifting heavy weights repeatedly. As with the body, so with the brain.

The following ``Method of Three Passes'' is a strategy for doing homework, especially problem oriented homework, that will pay off big in learning dividends should you adopt it.

next up previous contents
Next: The Method of Three Up: Physics 41, Homework 2008 Previous: List of Assignments for   Contents
Robert G. Brown 2008-11-05