Preliminaries 7
wandering attention) in lecture2
. Then watch as student performance and engagement
spirals into the stratosphere compared to what it was before…
Then pray. Some instructors have their egos tied up in things to the point where they cannot
learn, and then what can you do? If an instructor lets ego or politics obstruct their search for
functional methodology, you’re screwed anyway, and you might as well just tackle the material on
your own. Or heck, maybe their expertise and teaching experience vastly exceeds my own so that
their naked words are sufficiently golden that any student should be able to learn by just hearing
them and doing homework all alone in isolation from any peer-interaction process that might be of
use to help them make sense of it all – all data to the contrary.
My own words and lecture – in spite of my 31 years of experience in the classroom, in spite of the
fact that it has been well over twenty years since I actually used lecture notes to teach the course,
in spite of the fact I never, ever prepare for recitation because solving the homework problems with
the students “cold” as a peer member of their groups is useful where copying my privately worked
out solutions onto a blackboard for them to passively copy on their papers in turn is useless, in
spite of the fact that I wrote this book similarly without the use of any outside resource – my words
and lecture are not. On the other hand, students who work effectively in groups and learn to use
this book (and other resources) and do all of the homework “to perfection” might well learn physics
quite well without my involvement at all!
Let’s understand why working in groups has such a dramatic effect on learning. What happens
in a group? Well, a lot of discussion happens, because humans working on a common problem like
to talk. There is plenty of doing going on, presuming that the group has a common task list to work
through, like a small mountain of really difficult problems that nobody can possibly solve working on
their own and are barely within their abilities working as a group backed up by the course instructor!
Finally, in a group everybody has the opportunity to teach!
The importance of teaching – not only seeing the lecture presentation with your whole brain
actively engaged and participating in an ongoing discussion so that it makes sense at the time,
not only doing lots of homework problems and exercises that apply the material in some way, but
articulating what you have discovered in this process and answering questions that force you to
consider and reject alternative solutions or pathways (or not) cannot be overemphasized. Teaching
each other in a peer setting (ideally with mentorship and oversight to keep you from teaching each
other mistakes) is essential!
This problem you “get”, and teach others (and actually learn it better from teaching it than they
do from your presentation – never begrudge the effort required to teach your group peers even if
some of them are very slow to understand). The next problem you don’t get but some other group
member does – they get to teach you. In the end you all learn far more about every problem as
a consequence of the struggle, the exploration of false paths, the discovery and articulation of the
correct path, the process of discussion, resolution and agreement in teaching whereby everybody in
the group reaches full understanding.
I would assert that it is all but impossible for someone to become a (halfway decent) teacher
of anything without learning along the way that the absolute best way to learn any set of material
deeply is to teach it – it is the very foundation of Academe and has been for two or three thousand
2Perhaps by using Team Based Learning methods to structure and balance student groups and “flipping” classrooms
to foist the lecture off onto videos of somebody else lecturing to increase the time spent in the class working in groups,
but I’ve found that in mid-sized classes and smaller (less than around fifty students) one can get very good results
from traditional lecture without a specially designed classroom by the Chocolate Method – I lecture without notes and
offer a piece of chocolate or cheap toy or nifty pencil to any student who catches me making a mistake on the board
before I catch it myself, who asks a particularly good question, who looks like they are nodding off to sleep (seriously,
chocolate works wonders here, especially when ceremoniously offered). Anything that keeps students focussed during
lecture by making it into a game, by allowing/encouraging them to speak out without raising their hands, by praising
them and rewarding them for engagement makes a huge difference.
6 Preliminaries
tons of barley with a market value of ~v and a profit margin of q?
To learn this expression (for yes, this is a force law of nature and one that we very much must
learn this semester) we have to learn what the symbols stand for – q is the charge of a point-like
object in motion at velocity ~v in a magnetic field B~ , and F~ is the resulting force acting on the
particle. We have to learn that the × symbol is the cross product of evil (to most students at any
rate, at least at first). In order to get a gut feeling for what this equation represents, for the directions
associated with the cross product, for the trajectories it implies for charged particles moving in a
magnetic field in a variety of contexts one has to use this expression to solve problems, see this
expression in action in laboratory experiments that let you prove to yourself that it isn’t bullshit
and that the world really does have cross product force laws in it. You have to do your homework
that involves this law, and be fully engaged.
The learning process isn’t exactly linear, so if you participate fully in the discussion and the
doing while going to even the most traditional of lectures, you have an excellent chance of getting
to the point where you can score anywhere from a 75% to an 85% in the course. In most schools,
say a C+ to B+ performance. Not bad, but not really excellent. A few students will still get A’s –
they either work extra hard, or really like the subject, or they have some sort of secret, some way
of getting over that barrier at the 90’s that is only crossed by those that really do understand the
material quite well.
Here is the secret for getting yourself over that 90% hump, even in a physics class (arguably one
of the most difficult courses you can take in college), even if you’re not a super-genius (or have never
managed in the past to learn like one, a glance and you’re done): Work in groups!
That’s it. Nothing really complex or horrible, just get together with your friends who are also
taking the course and do your homework together. In a well designed physics course (and many
courses in mathematics, economics, and other subjects these days) you’ll have some aspects of the
class, such as a recitation or lab, where you are required to work in groups, and the groups and group
activities may be highly structured or freeform. “Studio” or “Team Based Learning” methods for
teaching physics have even wrapped the lecture itself into a group-structured setting, so everything
is done in groups/teams, and (probably by making it nearly impossible to be disengaged and sit
passively in class waiting for learning to “happen”) this approach yields measureable improvements
(all things being equal) on at least some objective instruments for measurement of learning.
If you take charge of your own learning, though, you will quickly see that in any course, however
taught, you can study in a group! This is true even in a course where “the homework” is to be
done alone by fiat of the (unfortunately ignorant and misguided) instructor. Just study “around”
the actual assignment – assign yourselves problems “like” the actual assignment – most textbooks
have plenty of extra problems and then there is the Internet and other textbooks – and do them in
a group, then (afterwards!) break up and do your actual assignment alone. Note that if you use a
completely different textbook to pick your group problems from and do them together before looking
at your assignment in your textbook, you can’t even be blamed if some of the ones you pick turn
out to be ones your instructor happened to assign.
Oh, and not-so-subtly – give the instructor a PDF copy of this book (it’s free for instructors,
after all, and a click away on the Internet) and point to this page and paragraph containing the
following little message from me to them:
Yo! Teacher! Let’s wake up and smell the coffee! Don’t prevent your students from doing
homework in groups – require it! Make the homework correspondingly more difficult!
Give them quite a lot of course credit for doing it well! Construct a recitation or review
session where students – in groups – who still cannot get the most difficult problems
can get socratic tutorial help after working hard on the problems on their own! Inte-
grate discussion and deliberately teach to increase active engagement (instead of passive
Preliminaries 5
is basically sedentary – you’re still just sitting there while somebody or something else makes it all
happen in your brain while you aren’t doing much of anything. At best it grabs your attention a bit
better (on average) than lecture, but you are mentally passive.
In all of these forms of learning, the single active thing you are likely to be doing is taking notes
or moving an eye muscle from time to time. For better or worse, the human brain isn’t designed
to learn well in passive mode. Parts of your brain are likely to take charge and pull your eyes
irresistably to the window to look outside where active things are going on, things that might not
be so damn boring!
With your active engagement, with your taking charge of and participating in the learning
process, things change dramatically. Instead of passively listening in lecture, you can at least try to
ask questions and initiate discussions whenever an idea is presented that makes no intial sense to you.
Discussion is an active process even if you aren’t the one talking at the time. You participate! Even
a tiny bit of participation in a classroom setting where students are constantly asking questions,
where the instructor is constantly answering them and asking the students questions in turn makes
a huge difference. Humans being social creatures, it also makes the class a lot more fun!
In summary, sitting on your ass1 and writing meaningless (to you, so far) things down as some-
body says them in the hopes of being able to “study” them and discover their meaning on your own
later is boring and for most students, later never comes because you are busy with many classes,
because you haven’t discovered anything beautiful or exciting (which is the reward for figuring it
all out – if you ever get there) and then there is partying and hanging out with friends and having
fun. Even if you do find the time and really want to succeed, in a complicated subject like physics
you are less likely to be able to discover the meaning on your own (unless you are so bright that
learning methodology is irrelevant and you learn in a single pass no matter what). Most introduc-
tory students are swamped by the details, and have small chance of discovering the patterns within
those details that constitute “making sense” and make the detailed information much, much easier
to learn by enabling a compression of the detail into a much smaller set of connected ideas.
Articulation of ideas, whether it is to yourself or to others in a discussion setting, requires you
to create tentative patterns that might describe and organize all the details you are being presented
with. Using those patterns and applying them to the details as they are presented, you naturally
encounter places where your tentative patterns are wrong, or don’t quite work, where something
“doesn’t make sense”. In an “active” lecture students participate in the process, and can ask
questions and kick ideas around until they do make sense. Participation is also fun and helps you
pay far more attention to what’s going on than when you are in passive mode. It may be that
this increased attention, this consideration of many alternatives and rejecting some while retaining
others with social reinforcement, is what makes all the difference. To learn optimally, even “seeing”
must be an active process, one where you are not a vessel waiting to be filled through your eyes
but rather part of a team studying a puzzle and looking for the patterns together that will help you
eventually solve it.
Learning is increased still further by doing, the very essence of activity and engagement. “Doing”
varies from course to course, depending on just what there is for you to do, but it always is the
application of what you are learning to some sort of activity, exercise, problem. It is not just a
recapitulation of symbols: “looking over your notes” or “(re)reading the text”. The symbols for any
given course of study (in a physics class, they very likely will be algebraic symbols for real although
I’m speaking more generally here) do not, initially, mean a lot to you. If I write F~ = q(~v × B~ ) on
the board, it means a great deal to me, but if you are taking this course for the first time it probably
means zilch to you, and yet I pop it up there, draw some pictures, make some noises that hopefully
make sense to you at the time, and blow on by. Later you read it in your notes to try to recreate
that sense, but you’ve forgotten most of it. Am I describing the income I expect to make selling B~
1
I mean, of course, your donkey. What did you think I meant?