inside joke there for some of my
students at a high level this is a
largely extemporaneous talk guided by a
handful of PowerPoint slides on a
lighter note hopefully it’s 12 to 15
minutes that addresses the really
important things you should be thinking
about for the next four to forty years
of your life so hopefully I haven’t set
the bar too high for myself so what I’d
really like to do is talk about a few
big educational ideas and do so through
the lens of some experimentation a
colleague of mine Scott strong and I
have been doing on some of the people in
the room students so some of the ideas
I’d like to address the idea of a growth
versus a fixed mindset so there actually
are quite a few really good TED talks
that have to do specifically with the
idea of a growth mindset this is the
idea that we can keep on learning we can
keep on improving or intelligence or
ability is not a fixed quantity but that
it can emerge and evolve and grow
throughout time the contrast of that
would be a fixed mindset the idea that
those are fixed characteristics I will
never be smarter tomorrow than I am
today and I will never have more
capabilities than I do today and those
are actually very restrictive ways to
think if one wants to be successful in
life there’s also the idea that as
engineering students as stem students
there really is room for some sort of
creative exploration although i would
say parenthetically it probably ought to
be guided otherwise chemistry labs will
be blowing up all over campuses and then
fundamentally what i really want to
focus my talk on is the power and the
importance of failure and this actually
ties in very tightly with the idea of a
when we look at a at least when Scott
and I were looking at our perceptions of
students our fear was that our students
may be tended to have a fixed mindset a
fear of failure and they were
risk-averse we couldn’t get creative
stuff out of them to the extent that we
wanted to and so we actually built a
slightly different paradigm that I’ll
get to in a few slides so the big
question i would start this off with is
from the students experiment experience
and i have to go back a while from to
draw in mind but my perception is these
ideas are formally discussed largely in
something like a freshman success
seminar that we have on campus here you
guys may or may not remember this but
you discuss these ideas and refreshment
success seminar that said it’s a one
half credit hour class that unless
you’re really not contributing to it
you’re going to get an A in so it
doesn’t have your undivided attention
your first term here next question how
do we reinforce these throughout the
curriculum I think we’re doing a better
job of this now than 25 years ago when I
was a student but my answer would be
this was not reinforced at all except
maybe accidentally by an exceptional
faculty member or two along the way this
talk hopefully we’ll explore well
definitely will explore some of my
thoughts and hopefully some of your
thoughts and I’m going to try to model
this and we know embody it and a few
quotes and silly gifts and this is a
thanks in no small part to my
collaborator Scott strong who I don’t
know has encouraged me to do the
following thing just to kind of mess
with students heads a little bit on
every assignment there is a quote that
quote may or may not have anything to do
whatsoever with the assignment these
quotes are drawn from great scientist
great mathematicians rappers books
literature movies you name it I think we
quoted the dude on an exam last semester
and then the silly gifts are well I had
to put the E in the tea into the TED
talk for those of you not aware this is
technology education not education
entertainment and design I’ll try not to
educate you silly gift first quote okay
what is experience experience is usually
what you get when you don’t get what you
wanted and it’s often the case that
experience is the most valuable thing
you have to offer so quote from randy
pausch his last lecture okay in addition
to watching TED Talks this is definitely
something worth watching on the internet
I would encourage you to do it why did I
choose this quote why did I choose this
gif if you focus on this image third guy
from the left pops right back up my
guess as somebody who’s fallen over on a
bike a handful of times is this is the
person that’s maybe experience this the
most and I suspect won the event okay so
how does this tie into my talk well
experience is what we want to give you
through the academic through the
intellectual growth process here and I’d
like to explore what kind of the
standard is that again at a high level
for learning objectives in STEM
education in the current age of course
there’s a certain knowledge base we
expect to expose all of our students to
we would like our students to be able to
extend and apply this knowledge in new
and innovative ways we’d like you all to
be able to communicate across
disciplines and across teams to solve
actual real-world meaningful problems
and we would like to instill in our
students a resilience and a curiosity
that leads towards lifelong learning and
an ability to persist through difficulty
because as it turns out stem is neither
static nor easy I think I think it’s
fair to say we’ve all experienced this
okay so those are the big high level
objectives next quote it’s a mistake to
think that you can solve any major
problem with just potatoes I found a
related gift somehow all right so our
problem is those objectives I just
listed those are highly aspirational and
non-trivial objectives how do we meet
those well what I’d like to do is kind
of start off by exploring the
traditional undergraduate experience in
stem what does this look like to you
guys it’s very very deep in disciplinary
content that’s delivered by experts with
an emphasis on procedural expertise in
John’s talk that big block in the middle
was all that these are all the facts you
have to know these are the formulas you
have to be able to apply and by God be
able to apply them well and here’s a
thousand problems to practice on there
are a lot of lectures their labs that
instill this this body have fixed this
fixed body of knowledge that is deeply
rooted in the past and necessarily so
right when Einstein are nine standing
when Newton said he was standing on the
shoulders of giants he was referring to
everybody that had laid the foundation
for him to develop the springboard into
physics and mathematics as we know it
now so we have to pay attention to the
past but our lectures and our activities
and classes tend to focus a lot more on
the past than in the future okay in
terms of how we judge and assess you
there’s a heavy emphasis on retention
and repetition of facts and on
competition on competency am i reading
the room okay is that a fair statement
okay I would say a DA from my
perspective this is a pretty low risk
thing for an instructor to do and for an
institution to do to deliver the
academic content in this manner however
I have to ask the question are we trying
to solve a major problem which is
potatoes
and I said and I’ve come to the
conclusion that yes we have alright
quote number three to hell with
circumstances I create opportunities
this should have special meaning to my
knowledge we’ve stopped calling the math
problems this semester we’re calling
them mathematical opportunities this is
also one of the best videos you’ll find
on the internet Bruce Lee is playing
ping-pong with his num drugs you should
all practice this at home okay so really
quickly just a short history of me as an
educator I am under a time limit so I
can’t brag about myself too much okay so
a couple things I started as an educator
at this institution as an instructional
faculty member when I was 24 I’m 47
today this is my 23rd year of this okay
I’ve been doing this a long time as a 24
year old I made a really key discovery
in the classroom you guys are smart and
if I expect a lot of you more often than
not I didn’t walk away disappointed John
might be cringing at the triple negative
i just used in that sentence so
philosophically I think students have a
tremendous amount of potential and I
think we often undervalue the existence
of that potential okay I will also say
that the traditional approach the
potatoes approach I excel at okay I
don’t mean that to be boastful it’s i
love the mathematics that I get to teach
students here I love that the students
are engaged in it that passion comes
across I can engage a room of 40 or 80
students in a lecture and I can do it
well and I can train them up on all the
little computational intricacies and I
can give them exams till they’re blue in
the face and they can do well on them
and as an educator for the
15 years I was doing this I got
increasingly good feedback for just that
approach in fact the last handful of
semesters that I really did everything
the traditional way I was often getting
perfect exact evaluations from my
students at the end of the semester
that’s 40 out of 40 students in a class
saying this was outstanding and I had to
ask myself is that good enough and this
is the answer I would like you to give
me if I’m giving you feedback like your
outstanding every week if I ask you is
that good enough probably not okay maybe
there’s some more potential there so
this led me to trying something
different and this gets me into really
the key components of this talk Scott
strong other colleagues and I would talk
all the time it just so happened that
Scott and I ended up landing a grant to
explore some of these conversations we
would sometimes have over coffee or beer
and we’d often discuss the fact that our
students are really good and they really
like what we’re doing when we do this
traditional approach to educating them
but we weren’t quite sure that we were
doing a total service to our students we
were maybe ignoring some of those things
that were the high level objectives for
how we educate engineering and stem
students and specifically we discuss a
lot the idea that you guys come in here
and your math is sound there are little
things that maybe are carryovers from
something goofy that happened in a high
school algebra class but you remediate
you figure it out you do really well
it’s almost impossible for us to break
freshmen and mathematics that’s my
perspective you guys might feel like we
try to break you quite often but I think
you’re good um what we don’t necessarily
do is help you become better learners
beyond just our class and so what Scott
and I decided to do and it was supported
in large part by
successfully writing a grant and getting
support and really leverage to convince
our department head that it’s okay for
us to do something crazy was to rather
than focus entirely on mathematics in
our freshman honors calculus 3 class
this is a class for students that come
in they’re placed out of two semesters
of calculus already in order to get
there they have either taken calculus in
concurrent enrollment in another
university or cooked to your school or
they got the highest possible score on
the hardest possible AP math exam we
can’t break those mathematically so this
is from our perspective a low risk pool
of students to experiment on so here’s
the big idea let’s try something very
different and the different thing we
decided to try was okay these students
have done very well in every math test
they’ve ever taken some of you are in
the room right now you’ve done very well
in every math test you’ve ever taken
ninety-five percent is a disappointment
we come in day one and we said we don’t
care we’re not going to judge you that
much on how well you do your mathematics
in this class instead we’re going to
judge you on how well you think about
your mathematics and communicate that to
us a little bit of a paradigm change
okay so we created a studio environment
that focused on often problem sets that
weren’t even possible and we turn
students loose in groups and we saw what
they would do with it and we told our
TAS judge them harshly if they don’t
organize their thoughts well or
demonstrate reflective practice okay so
what could go wrong with it with an
approach like this well there was some
student pushback particularly in year
one I think it was better this year so
we’ve been doing this for a couple of
years there were disastrous assignments
Joshua in the front row was nodding his
head as i was talking about impossible
problems sometimes we just throw an idea
on the page and see what students do
with it this is not something you
typically do with freshmen you do it
with grad students but we thought why
not try I would also say I had a handful
of colleagues that told me I was just
flat crazy i buy extra contact time with
students
my evaluations are going to go to an
there’s just there’s no good that can
come of this the flip side of that is
what could possibly go right so the
students that engaged in this we asked
them to keep journals we asked them to
write reflectively we asked them to do
even when we give them practice problems
do those reflectively let’s just look at
some things that happened here so they
adopted a reflective set of practices so
I’m just going to put up a few exemplary
this is a math assignment it’s a toupee
page handwritten essay on growth mindset
that’s kind of cool this is a set of
math practice problems in fact this is a
set of math practice problems that were
done wrong and then revisited in the
journal with corrections in different
colors and notes about what I what
misconception did I demonstrate in this
that’s reflective practice here’s
another one a student in it doesn’t
quite pop on the screen but you’ve got
the work and then in dark red a dialogue
about how I think about this type of
problem what else could go right well
students explore concepts and tools
represented to them and went way beyond
anything we asked in assignments so one
of our early assignments was actually a
junior or senior level partial
differential equations problem where we
asked students to play around with
Mathematica and explore the behavior of
a particular two dimensional wave
equation okay they were given the tools
to play with this they were asked to
animate a simple case I had one student
come to me and say look what I did is
that kind of cool and she actually
figured out how to mouse over and click
and get this to actually add note modes
what else happened students succeeded on
assignments that were well above the
level of the course so this is a midterm
project I want to get to the last bit of
it this is just a handful of a 22-page
right up in latex and the graph you have
embedded there it demonstrates quadratic
approximations through the second-order
Taylor approximate
asian to an egg great-looking function
to characterize critical point behavior
using linear algebra seventeen-year-old
in a freshman class so those are the
kinds of things that can happen when we
take the wheels off we’ve also been able
to engage TAS in multiple years and we
have students developing content so I’m
just going to give you a couple of
really quick thoughts some constraints
on the model their resource constraints
there was a penalty for evaluation when
we made it way too hard the first
semester students were not kind to us I
would say there’s no silver bullet this
is I think working for me I don’t think
it’s the answer for everybody and I want
to leave you with an audience assignment
as students as educators we should
always be thinking about what can we do
to make our experience better how can we
recognize how we learn and how can we do
things better how can we push ourselves
further and on that I’ll leave you with
a comic strip thank you very much [Applause]