Relatively late in my
career, about when we realized
Science One would be successful, several
ideas about teaching and learning came together
for my colleagues and me.  None of them were new,
but together they were dynamite.  Almost literally, they
fueled an explosion of innovation in our institution.
We designed other new programs and helped each
other apply the ideas in our daily practice.
The approach began to be applied
in other parts of UBC and
other parts of the
world.

One such innovation was
the Integrated Sciences Program, to
which students apply after  second year.
In their application, they design a two year
course of study integrating two different dis-
ciplines into a coherent vision of what
they want their lives to be like.  Some
of their plans were amazing.

In the first year, for
example, one applicant said she
wanted to become a science journalist.  She
showed that there was no way to do that at UBC or
anywhere else she’d looked.  She could prepare for
science or journalism, but there was no
way to meld those courses
of study into one. 

As a science student,
in fact, she wouldn’t even be able
to take most writing courses, which
were reserved for particular groups
of students. Not only that, but even
if other Faculties allowed it, her
own Faculty of Science
wouldn’t let her
take them.

Her plan was
to study one scientific discipline
in depth, pushing it to fourth year ocean-
ography courses without satisfying departmental
criteria for graduation, and take writing courses all
over  campus.   She needed  creative  writing  courses
in the Faculty of Arts, reporting courses in Journalism,
technical writing courses in Engineering, and so
on, and she was right that she couldn’t get into
them without our administrative and
bureaucratic help.

Sometimes, Deans’
Offices had to talk to Deans’ Offices
to make it happen, but really exciting proposals
were always accepted on their merits despite their
irregularity.  That student executed her plan
perfectly, graduated from ISP, not any
department, and became a
science journalist.

That early extreme
case was gratifying by supporting
an enormous assumption underlying
the program.  The basic idea, already manifest
in the application process, is that if you give students
power to own their own education and give them
the right tools, they will surprise you with
their accomplishments.

In addition to their
self-designed courses of study, ISP
students all took several ISP Courses that
bridged across disciplines in various ways.
In the first term of the first year of ISP there
was only one ISP Course, The Sizes of Things,
that I taught with atmospheric physicist
Douw Steyn for several years. 

The entire course
asked a single question: “What
difference does it make what size things
are?”  For our purposes, that question
was perfect in at least four ways.

“Things” could
be anything.  The sky was
the limit for what to consider, from the
edge of the universe down to subatomic particles,
from molecular biology to pure chemistry to global
warming.  The sizes of cultures, economies, and language
groups, class sizes in schools.  Engineering design,
airplane and boat design, and a range of issues
in medicine, business, and  the psychology
of learning in various sizes of groups.
It didn’t matter to us and
we didn’t care.

We already knew
from our own work that size
matters nearly everywhere we look.
We wanted  students to get that principle
in a way that could serve them the rest of their
lives.  Detecting these relationships in real data
requires sophisticated mathematical and statistical
tools.  We let them practice using them in team-
based exercises, then turned them loose to use
them in their own research as serious
scientists wanting answers.

We also knew
that to do this kind of research
well requires extensive knowledge of the
systems we study.  Even asking questions well
requires this, so we encouraged them to build
on their strengths by studying systems
they knew something about but
didn’t try to teach them
that content.

Students submitted
research proposals arguing that
some system should be expected to show
what we call a power Law relationship between
some aspect of size or scale and some aspect of how
the system worked.  They specified what data they
needed to test that hypothesis, how they would
analyze and interpret the results, and
how that might change anyone’s
view of the world.

They studied all kinds of
things, only a few of which Douw or
I knew much about.  We consulted with
students frequently, they shared progress
with each other regularly, and all of us learned
about many different systems. Here I’ll
tell you about three of those students
and their research projects.

Mike Mayo
Mike Mayo was what I call a
mammal freak. Mike loved mammals
with a passion, the way biologists love species
like whales, wolves, or hummingbirds, I confess,
or things like mitochondria, chloroplasts, ecosystems,
or artificial intelligence.  In some real sense we fall
in love with what we study and study what we
love, and Mike saw the world in terms
of mammalian biology. 

Given this bias,
it was no surprise that Mike
asked a fascinating question about
mammals in his proposal. Considering
the challenges of reproduction, he argued
that mammalian newborns must be large
enough to survive being born but small
enough to be born, which should
depend on the size of
the mother. 

For various
kinds of reasons, Mike expected
newborns’ sizes to be related to the sizes
of their mothers by a power law relationship,
and predicted that the plot of these sizes for all
mammal species would be a straight line on log-
log graph paper, expressing a particular power
law.  When we read Mike’s proposal we grinned
at each other, asked something like where Mike
would find data to test his hypothesis, and
sent him off to the literature with
our encouragement.

Sooner than
I expected, Mike showed
up at my office with a grin on his
face and graph paper in his hand.  For
the several dozen mammal species he had
plotted to date, the straight line of points
indicated a perfect power law and the
parameters of the law made sense
in terms of his hypothesis.

It amazed me
that I’d never read about that
relationship in the scientific literature before
and was as excited as Mike was about his discovery.
But it was still too early in the term for him to finish his
analysis and turn to writing.  As I congratulated him
on his result, I racked my brain for ways to keep
him going for a while.  “Did you include any
marsupials in your analysis, Mike?”,
I asked, grasping at a straw.

No, he replied,
I left out marsupials and a
few other groups but that’ll be easy.
I also need to get more  species from more
mammal groups and that’ll be even easier.
We talked for a minute about what we expected
to see in the marsupial analysis and he went back
to the library.  When he returned a few days
later he was even more excited than he
had been before and his new result
also excited me more than
it had before.

Before, he showed
that in non-marsupial, eutherian
mammals, the larger the mother the larger
her newborns by a power law specifying their sizes
more or less exactly.  To his surprise and in contrast
to his expectation, (that’s why it surprised him), it is not
that way at all for marsupials.  According to his analysis
of all the data he could find, all marsupials are born in
the same small range of sizes, no matter how small
the marsupial shrew or how large the kangaroo.
That was exciting science! It also created
a non-trivial problem for Mike to
grapple with in writing. 

In his proposal, he
developed a testable explanation
for a power law he predicted.  His first
analysis supported that idea strongly. But
only for eutherian mammals.  His analysis
of marsupials contradicted that same idea
and Mike had, somehow, to explain it.
Douw and I celebrated Mike’s
dilemma.

Mike eventually
argued that whereas most mammals
are born only once, marsupials are in effect born
twice, the first time the smallest mammals can be and
still find their way from the birth canal to the pouch,
some distance away through the fur.  Once they
get to the pouch, they lock onto a teat,
suck up food, and keep developing
til their second coming. 

Mike wondered about
a weak power law between the
sizes of marsupial mothers and their
newborns because it is farther from the
birth canal to the pouch on larger mothers.
But there weren’t enough data to detect a
weak influence, he tested but didn’t
find it, or he ran out of time.
I don’t remember.

His paper was
gripping scientific reading
about insightful, well-conducted, original
science.  It fulfilled him to actually “do” science
as professional scientists do it, which is rare for
undergraduates to experience.  His discoveries
were exciting and interesting in their own
right.  At least as importantly, his
study raised more questions
than it answered.

Even better for
all three of us, and for the rest
of the class, is that we didn’t teach him
anything about it.  We showed him some things
about power laws and how to find them in sets of
data.  We showed him how to ask questions that
point to their own answers, which is important.
But we didn’t teach him a thing about mammals,
help him find data or analyze them, or think
of the question in the first place.  Mike
taught us.  When it works, it
works better that way.

Nancy Martin
was a long-distance runner. Just
as Mike Mayo was biased by his love of
mammals, Nancy saw the world through a
runner’s eyes. She considered the simple fact
that marathoners run slower than sprinters,
and wondered what physiological
processes determine running
speed at each distance.

Not surprisingly,
given the theme of the course,
she argued that the slowing of running
speed with distance is described by a power
law, and used the top three world record times
for males and females at each distance, from the
shortest sprint to the longest ultramarathon, to test
that prediction statistically.  Like Mike, she expected
one straight line on log-log graph paper; either one
power law, or one each for males and females. Her
analysis revealed not just the one or two laws
she expected, but six.  Three power laws each
for males and females, end to end, over
three ranges of distance.

Just as discovering
different rules for birth weight in
marsupial and other mammals created
significant interpretive challenges for Mike,
Nancy’s surprise challenged her to explain it.
Experientially, that plunged her from the safe
hypothetical world of her proposal into the
deep unknown of the real world,
where running actually
occurs.

Any working scientist
can tell you that this experience is thrilling,
frightening, and close to the essence of our work.
It is a big part of what we live for professionally.
Hypothesis making. Hypothesis breaking.
What’s happening?  What’s going on?

An important key
for Nancy was the striking fact
that her three sets of power laws corre-
sponded with sprints, middle distances, and
long distances.  That reminded her that runners
and coaches usually specialize in one range of
distance, that tactics of training and racing
differ in the three cases, and that differ-
ent body types excel at different
ranges of distance.

Considering
that pattern, she proposed,
again after much reflection, many
trips to many parts of the library and
much consulting with experts here
and abroad, a truly creative
explanation. In a nutshell,
Nancy argued that

Sprints
are fundamentally different
than other distances.   They are
so short that there’s no time during any
sprint to metabolize any kind of fuel to
produce ATP, the metabolic currency
of all cells, and sprinters’ muscles
use stored supplies of ATP.
The limiting factors are how
much ATP they store in
their muscles and
how fast they
metabolize it.

Middle distances
are long enough to exhaust
stored ATP and runners regenerate
it during races.  Nancy concluded that
stored cellular carbohydrates should be enough
to fuel the longest middle distance races and
that the limiting factors at those distances
are how much carbohydrate runners
store in their cells and how fast they
metabolize it to produce ATP.

Long distances
are long enough to exhaust
carbohydrate stores, and runners
must metabolize fats and oils, after depleting
stored ATP and carbohydrates, to produce enough
ATP to finish races.  Again, the limiting factors are how
much they store and how fast they metabolize it,
given all the other factors that determine
whether they can compete at the
world class level.

In each case, she argued,
the critical rates are linked to race duration
by power law relationships.

A fascinating thing
about Nancy’s study, in common
with a surprising number of other projects
in the course, was that she found no evidence
that anyone before her had ever either asked or
attempted to answer the question that informed
her research.  As far as she could tell from her
review of the literature and conversations
with experts in relevant fields, she was
exploring new scientific territory
even to ask the question,
let alone answer it.

Nancy was a
third year student in the course,
so she took an independent research course
the next year for an exhaustive literature search,
more correspondence with more world experts
about her results and her hypothesis. At the
end of it she still had no evidence of any
one before her. She did truly original
independent research as a student
in an undergraduate course.

Patrick Little
 came to ISP from a technical
background in atmospheric sciences and
was biased to look to the air for his power laws.
In an amazingly complex, highly mathematical
proposal, he argued that there should be a
power law relationship between the sizes
of rainstorms, measured by total
precipitation, and the sizes of
the individual raindrops
they produce.

********
Imagine Patrick
imagining that, as part of an
assignment in an undergraduate course
taught by people who have never
before thought about what he
imagined in such amazing
detail!
*******

Patrick tested
his prediction with many
years’ data from Vancouver International
Airport, and his first discovery came immediately.
The raindrop data were so unimaginably voluminous
that no common statistical program could handle them.
Patrick had to import and learn a specialized program
that could handle very large data sets.  When he could
analyze the data, he got another surprise: separate
power laws for different size ranges of storms,
which challenged Patrick to interpret and
explain the result.  He thought the two
ranges corresponded to the two
major ways  storms
make rain.

In orographic
precipitation, moving, moisture
laden air is forced up by mountains
or cold fronts in its path, cooling it to make
rain.  In convective precipitation, warm moist
air rises, cools, and makes rain, violently in thun-
derstorms or worse.  Big raindrops should come in
thunder-type storms and small ones from orograph-
ic.  Vancouver rain is mainly orographic, but from
a long series of data from Gainesville, Florida,
the thunderstorm capital of North America,
he produced convincing statistical evidence
that the two size ranges of raindrops
are indeed generated by different
types of rainstorms.

Reflections on the
Integrated Sciences Program
These three examples illustrate something
important about teaching and learning. Most of
all, they remind us that effective teaching may be more
about guiding, supporting, and coaching students’ self-
directed, curiosity-based work than teaching them
the so-called “content” of even technically
difficult courses like ours.

We provided ideas,
mathematical & statistical tools
and ways to use them, practice, and things
like asking and answering good questions and
insisting on high standards of communication in
describing complex relationships simply.  We used
rigorous peer-editing to help them learn to write
well, and gave them feedback any time they wanted
it, honestly and without holding back.  We didn’t
think of ourselves as teachers of content and
students didn’t either, but purveyors of
process and mindful, self directed,
curiosity-driven learning. 

The Sizes of Things
was about the sizes of things
in general, not any particular thing,
and its content varied from term to term
depending on the interests of our students.
The course was defined by unlimited numbers
of questions about differences it might make
what size things are, and by a limited
set of  tools for answering them.

In four years
of teaching the course together,
we read fascinating studies of everything
from the social psychology, economics, politics,
and pedagogy of human group size in different
cultures to the design of sailboats, human powered
airplanes and other machines, the dynamics of galaxy
formation, and the partitioning of genetic information
among chromosomes in cells. We learned many things
we hadn’t known or thought about before about
everything including the sun, we had fun,
and we got paid for not teaching
them any content.

In very few cases
did we know much about what
our students studied and it didn’t matter.
In fact, we came to suspect that undergraduate
courses taught by world experts in the content can
easily suffer from the universal tendency of professors
to profess.  We brought little more to the course than
a few tools, belief in their power to reveal much
of interest in complex systems of all kinds,
and strong faith in the creative, self
actualizing power of students. We
did pull rabits out of our hats
on occasion, like with Mike
and his marsupials,
always intending
to bump learning
to deeper levels.

An explicit
objective of the ISP is to
‘make them smarter’.  Street smarts,
that is, not raw intelligence.  Students can’t
do anything about how intelligent they are.
But they can wise up, keep their wits
about them, and get smart,
day by day.

That’s what ISP is about.

To a truly
fulfilling extent, the program
achieves that objective for its two major
constituencies.  About half of the students, at
least in the beginning, came to the program with
strong backgrounds in a variety of scientific fields
but sought more freedom and a broader education
than they can find in most degree programs, and
the other half arrived with mediocre records
and little sense of themselves as learners.
Some had been rejected from elite
programs like pharmaceutical
sciences and sought
success.

Once they
get the hang of self directed
learning, both kinds of students find what
they come for in the ISP environment
because working in it makes
them smarter.

We  learned to
expect stellar, sometimes
publishable work from all students,
regardless of their backgrounds. Some personal
transformations we saw were stunning, and many
of them were sudden. When Mike Mayo discovered
himself as a learner, near the end of his final
term as an undergrad, it literally
changed his life.  It changes
my life to witness it.

There are
descriptions of the ISP and
other interdisciplinary science
programs in Integration, Interaction,
and Community and Reflections on Inte-
gration, Interaction, and Community, and the
rationale for that collection of publications is in
my introduction to the Special Feature of Ecology
and Society: Educating for Sustainability. I spoke
about them in Stories about Stories, Making
Magic Together, and A Decade of
Innovation in Science
Education.

For insights into
the biology and psychology of surprise,
see my book chapter Behavioural
foundations of adaptation.

I described the
peer editing approach we used in
An Exercise in Thinking, Writing,
and Rewriting.

In 2018, The Sizes of
Things was still being taught
in the ISP, 21 years after we started
it.  Here is its current official description.

Note on
Gainesville Florida
thunderstorms.  In Buzz Holling:
Heroes, Masters, and Wizards, I said Gainesville
is the thunderstorm capital of North America, and
mentioned a talk I gave there there about education.
I gave another talk on my hummingbird research
on the same visit, and right in the middle of it
the most violent thunderstorm I had
seen in my life started up. 

I could see the
lightning out the back window
of the room as I spoke, and that was more
interesting to me than my talk and concentrating
was difficult.  My host Peter Feinsinger stood up,
laughed, said it happens whenever visitors
start to speak, and suggested we all
take a break to enjoy the storm,
then return to the humming-
birds when I could
concentrate
again.

We
had enormous
thunderstorms at Grizzly
Lake too, and we lived right up
there in them.  But that Gainesville
storm impressed me greatly.  None
of that qualified me as an expert on
Patrick Little’s raindrop research,
but it made me more interested
in his question and results.

Near the beginning
of this story, I suggested that if
you give students power to own their own
education and give them the right tools, they will
surprise you with their accomplishments.  How I said
that was a nod to General George S. Patton, who
famously said “Don’t tell people how to do
things. Tell them what to do and let
them surprise you with
their results.”

Patton’s dictum
guided my whole teaching career,
but I see a contradiction in his words and
suggest a modification to resolve it. My reading
of the statement is that telling people how to do things
is telling them what to do.  But I don’t think that’s what
he meant.  In my version, he says “Don’t tell people how
to do things.  Tell them what they must accomplish
and they will surprise you with their results.”

Stories throughout
this site embody Patton’s dictum.
Frank Spear and the Pea Seeds, Teaching
for Creativity, and Five Questions to Change
Your Life give examples of this kind of learning.
Work on the Ugliest Part! addresses the issue in
Teaching & Learning, Sculpting & Art, and
Science & Nature.  So does What is
there about Risk?

Edited May 2022