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ERIK DEMAINE: Yeah, so
one of the exciting parts

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of this class is that we ran
an optional session where

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whoever is interested
in doing the research

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side of the material could
solve open problems together.

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So we call this a
problem-solving session.

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But it's-- all the problems
are unsolved in the field.

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And so it's not a required
part of the class,

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because it's OK to just
learn the material.

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But if you really want to engage
with what we're learning about,

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then you should try
to advance the field

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and solve new problems beyond
what we know how to solve.

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And so every week I have
this session for two hours.

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That seems to be
about the sweet spot.

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And I would come with a couple
of new open problems inspired

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by the material that
we've just covered

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in the last week of lectures.

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So this is, I find, a
really powerful combination

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in teaching, where you've
just covered in one week

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the latest that everyone knows.

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Everyone's at the
state of the art.

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They've just learned what the
best results are in the field.

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And so it's natural to
ask, well, what's next?

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What would be the next step?

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How can we improve
these results?

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What would be the
next thing to analyze?

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And so the open
problem session nicely

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dovetails with the
lectures, where

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it's just been a
couple of lectures,

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so it's still fresh in the mind.

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And now we know all
these techniques,

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can we conquer this new problem?

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So the hardest part, of course,
as a teacher is picking out

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what is the right
unsolved problem

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to work on, because they have
to be easy enough that you have

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the hope of solving them in
two hours, though, some of them

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we continue through
multiple weeks.

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But at least you want to make
some progress in two hours.

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Otherwise, you feel like
you're wasting time,

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and it's kind of discouraging.

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But you also don't
want the problem

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to be so easy that it's not
worth writing a paper about.

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So the challenge is
to find this balance,

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and also hoping
that the problem is

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within the scope of the material
that you've just taught,

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because it's unsolved.

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No one knows whether these
techniques will apply.

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But by bringing a few
problems to the table,

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and also by the
end, students were

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bringing in their own suggested
problems, you can get lucky.

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And so in the
session, there were

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about a dozen people typically
who'd show up each week.

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It would shift a little bit
who has the time, because it

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is kind of extracurricular.

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But we would get together, I
would describe the problems

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usually within
just a few minutes

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and remind people of the
past problems from past weeks

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and update.

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If people had any progress
since the last week,

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then they would present
what their ideas were

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or what their things were.

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But then most of the time
is spent brainstorming.

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So often-- we were
in a room that

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had lots of little
kind of corners, each

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with white boards.

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And so often, different
people would say, oh,

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you want to work
on this problem?

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And if so, come to
this little corner.

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And then they would work in
that corner on their problem.

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And so there would be
a few different groups,

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each of like three or
four people brainstorming

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about some problem,
maybe we could

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do this, what if we applied
this technique that we just

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learned from class,
and this sort of thing.

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And then I would jump around
from corner to corner and try

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to give my advice like,
oh, have you tried this?

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Oh, this paper seems relevant,
maybe you should read this one.

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And then in the span
of those two hours,

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often, we would solve the
problems we would look at.

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Certainly, not all of them.

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But I would say maybe
half of the problems

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that we set out to solve,
we actually did by the end.

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Many of those turned
into the final projects

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for students in the class,
so that was another motivator

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for people to come.

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And many of them have
been published since,

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so they are now papers
in the literature.

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And it's been a
nice way to progress

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the field of hardness proofs.

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And I think I think
this approach is really

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powerful in general
for-- probably

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for more advanced classes,
like advanced undergraduate

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and graduate classes.

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Anywhere people are comfortable
going that extra step

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and trying out
research, I think,

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this is a really
powerful technique

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of combining teaching the
latest material in an area

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and then trying to
push those frontiers

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and solve new problems.

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It takes extra effort, but
most professors are also

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researchers in
addition to teachers,

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so they should all try it.

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And I'd be happy to give
them advice for how to do it.

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I've been doing it
for several years

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in all of my advanced classes.

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And in the beginning
it was a little--

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there are lots of kinks to
work out of figuring out what's

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the right level of
problem, but now

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it works pretty well
and pretty consistently.

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I think one key to making
these problem sessions

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work is you can't be
the only driving force.

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You need to orchestrate
the students

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to be willing to speak up.

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I mean, it's always a
challenge in lectures to get

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students to ask questions.

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But this is like way
beyond asking questions,

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now they have to like suggest
answers and suggest ideas.

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And they have to be
in an environment

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where they're comfortable
voicing their ideas

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and not being too
self-critical, because when

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you're solving problems,
it's really-- usually--

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most ideas don't work.

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That's life.

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But silence is like the worst
thing for solving problems.

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So even if you have like a kind
of lame idea, like you know

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it doesn't work, it's
still worth saying it

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because it might inspire
someone else to have

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a second idea and a third idea.

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And just keeping
the conversation

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going is really critical.

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So I think whatever
you can do to encourage

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that kind of like--
including yourself, asking

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silly questions that may not--
the answer doesn't really

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tell you-- well,
what's the right way--

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being comfortable not
knowing the answers

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and asking initially stupid
questions that might lead

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into interesting
directions, I think,

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will encourage students
to do the same.

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And it doesn't
work for everyone.

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Some students remain quiet
throughout the whole semester.

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But hopefully, they at least
got to see this picture

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of how research happens.

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That's sort of the goal.

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The problem sessions
are definitely

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much more personal
interaction with me,

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and so they feel a lot
more comfortable around me

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as the professor.

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And so, yeah, they're definitely
more comfortable asking

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questions in lecture.

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It just generally leads to
a nice kind of-- I mean,

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it's really a bonding
experience, I would say.

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So I see it especially
within the group

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that they're super comfortable
working with each other

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because they've solved so
many problems together.

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There's this camaraderie
of we can tackle anything.

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And so this problem
session is continued way

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past the end of semester.

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It's been going for
another year since.

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Hopefully, it will
continue going.

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Of course, some students
will graduate and leave.

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But it's actually been
great for my research.

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If I have a new
hardness problem,

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I can bring it to
the problem session,

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and like wolves
they'll attack it.

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And usually we'll get a
solution within a few weeks.

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So it's really-- and a
big part of that, I think,

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is because they've
shared this experience,

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and they've solved so
many things together

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that it really-- they have a lot
of confidence in this context.