“gives up” – they can simply “see” what the answer must be.
Where do these answers come from? The person has not “figured them out”, they have “recog-
nized” them. They come all at once, and they don’t come about as the result of a logical sequential
Often they come from the person’s right brain22. The left brain tries to use logic and simple
memory when it works on crosswork puzzles. This is usually good for some words, but for many of
the words there are many possible answers and without any insight one can’t even recall one of the
possibilities. The clues don’t suffice to connect you up to a word. Even as letters get filled in this
continues to be the case, not because you don’t know the word (although in really hard puzzles this
can sometimes be the case) but because you don’t know how to recognize the word “all at once”
from a cleverly nonlinear clue and a few letters in this context.
The right brain is (to some extent) responsible for insight and non-linear thinking. It sees patterns,
and wholes, not sequential relations between the parts. It isn’t intentional – we can’t “make” our
right brains figure something out, it is often the other way around! Working hard on a problem,
then “sleeping on it” (to get that all important hippocampal involvement going) is actually a great
way to develop “insight” that lets you solve it without really working terribly hard after a few tries.
It also utilizes more of your brain – left and right brain, sequential reasoning and insight, and if you
articulate it, or use it, or make something with your hands, then it exercieses these parts of your
brain as well, strengthening the memory and your understanding still more. The learning that is
associated with this process, and the problem solving power of the method, is much greater than
just working on a problem linearly the night before it is due until you hack your way through it
using information assembled a part at a time from the book.
The following “Method of Three Passes” is a specific strategy that implements many of the
tricks discussed above. It is known to be effective for learning by means of doing homework (or in
a generalized way, learning anything at all). It is ideal for “problem oriented homework”, and will
pay off big in learning dividends should you adopt it, especially when supported by a group oriented
recitation with strong tutorial support and many opportunities for peer discussion and teaching.
The Method of Three Passes
Pass 1 Three or more nights before recitation (or when the homework is due), make a fast pass
through all problems. Plan to spend 1-1.5 hours on this pass. With roughly 10-12 problems,
this gives you around 6-8 minutes per problem. Spend no more than this much time per
problem and if you can solve them in this much time fine, otherwise move on to the next. Try
to do this the last thing before bed at night (seriously) and then go to sleep.
Pass 2 After at least one night’s sleep, make a medium speed pass through all problems. Plan to
spend 1-1.5 hours on this pass as well. Some of the problems will already be solved from the
first pass or nearly so. Quickly review their solution and then move on to concentrate on the
still unsolved problems. If you solved 1/4 to 1/3 of the problems in the first pass, you should
be able to spend 10 minutes or so per problem in the second pass. Again, do this right before
bed if possible and then go immediately to sleep.
Pass 3 After at least one night’s sleep, make a final pass through all the problems. Begin as before
by quickly reviewing all the problems you solved in the previous two passes. Then spend fifteen
minutes or more (as needed) to solve the remaining unsolved problems. Leave any “impossible”
problems for recitation – there should be no more than three from any given assignment, as a
general rule. Go immediately to bed.
22Note that this description is at least partly metaphor, for while there is some hemispherical specialization of some
of these functions, it isn’t always sharp. I’m retaining them here (oh you brain specialists who might be reading this)
because they are a valuable metaphor.
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 (passively) 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 what you need to learn in some media or human form. You in
all probability will never learn it, lecture or not, without making a few passes through these steps.
a) Review the whole (typically textbooks and/or notes)
b) Work on the parts (do homework, use it for something)
(iterate until you thoroughly understand whatever it is you are trying to learn).
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 well prepared and blessed with a good instructor, perhaps you grasped some of
it for a moment (and if your instructor was poor or you were particularly poorly prepared you may
not have managed even that) but what you did momentarily understand is fading, 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 derivations 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, not try to memorize it
word for 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.
Lots of increasingly deep passes through it (starting with the merest skim-reading or reading a
summary of the whole thing) are much better than trying to work through the whole text one line
at a time and not moving on until you understand it. Many things you might want to understand
will only come clear from things you are exposed to later, as it is not the case that all knowledge is
ordinal, hierarchical, and derivatory.
You especially 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. If you build them a house, they’ll move right in without a fuss, where if you try
to grasp them one at a time with no place to put them, they’ll (metaphorically) slip away again as
fast as you try to take up the next one. Let’s understand this a bit.
As we’ve seen, your brain is fabulously efficient at storing information in a compressed associative
form. It also tends to remember things that are important – whatever that means – and forget things
that aren’t important to make room for more important stuff, as your brain structures work together
in understandable ways on the process. Building the cognitive map, the “house”, is what it’s all
about. But as it turns out, building this house takes time.
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 absorbing new information
takes you less and less time, and you remember it much more easily and for a longer time without
additional rehearsal. Sometimes your brain even outruns the learning process and “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 and be able to work with them for a long, long time. Him hum tum