Thoughts on Designing Interdisciplinary Courses I

Hi all,

Here are some thoughts on how to design a course that blends mathematics, biological science
and computation together.  It grew out an interest in following the recommendations of the Biology 2010 report
( CUBE. BIO 2010: Transforming Undergraduate Education for Future Research Biologists. Commit-
tee of Undergraduate Biology Education to Prepare Research Scientists for the 21st Century, National
Academies Press, 2003 ).  I began to do this in 2006 at the request of my Biological Sciences department
using textual materials, software and so forth of my own design.  By 2008, a first draft of the resulting
lecture notes was available as a Print on Demand Book from www.lulu.com which is an online publisher.
These notes are now in the Fourth Edition:
( Calculus For Biology: A Beginning – Getting Ready For Models
and Analyzing Models. Gneural Gnome Press: www.lulu.com/spotlight/GneuralGnome, 2012. )

I have taught about 100 students per academic year with this course which is a replacement for
Engineering Calculus Two.  The engineering calculus two was never a good fit for
the biologists and so my course trained biologists to be aware of both mathematical and computational
tools in the pursuit of biological insight.

However, the course was only taken by 100 students out of about 1500 majors.
The students who took the course were mostly required to do so by their curriculuum.
Approximately 75% of my students were PreMed also.  Hence, my enrollment was tightly
tied to the fact that most of the students who took the course were required to do to so.
Not all, of course, but most.


From this cadre of students, a small number ( 1 - 4) per semester would then take
further courses of this nature from me and some began to build biological models with me
during their sophomore through senior years.  But, the vast majority of both the biology majors
and the biology faculty do not like intellectual pursuits intertwined with mathematics and computational ideas
and so support within the biology department was limited.  Indeed, support within my own
mathematics department was limited as well.  I often felt like I was pretty much alone in these efforts.

My efforts appear to have been wasted as the biology department has just voted to

make any second calculus course optional for all their majors.  The only requirements are now

the first calculus course and a basic statistics course both of which can be satisfied by

a well prepared high school student with AP credit.  Hence, the vast majority of biology majors

will now go an entire four years of college without additional training in mathematics, statistics

and the use of computation.  This, of course, also impacts how they will learn physics, biochemistry

and so forth as more sophisticated treatment of the ideas in those disciplines will not be easy for them

to grasp do to inadequate background.

The enrollment is my Calculus for Biologist course will drop starting in Fall 2013 from 50 students

to probably 15 or so.  The enrollment in Spring 2014 will also drop from 50 to 15 so

I anticipate at most 30 students per year now rather than 100.  It could also be less too

and if the enrollment is too low the course won't be permitted to run.

It seems my grand experiment with the backing and approval of a small group of

biologists to try to implement some portion of the BIO 2010 recommendations has been

a complete and abject failure.

But I think the reasons for developing this course and the larger goals of the BIO 2010

report are worthy ones.  Over the last few years, I have written up some of my ideas

on how to design such a course and I thought I would share them on this blog.

The notes that follow were written in 2010 and I have changed them a bit for this blog.

Let me finish this introduction with a quote from an article in the Times Higher Education

from June 30, 2011:

``Competence in mathematics is desirable for everyone 

but vital for scientists, yet there is a widespread, 

deep-rooted fear of the subject. 

Stephen Curry insists that this can be overcome by 

making maths an 

integral part of science education''

That article is an interesting read.  I have been completely defeated by these deep seated fears

but perhaps other people at other institutions will find a way to do it better so that these

ideas can flourish.  

A White Paper on Interdisciplinary General Education:

Thoughts 2010 - 2013

James K. Peterson

Department of Biological Sciences

Department of Mathematical Sciences

1. Developing Literacy

When I was a younger man, I worked at Union Carbide as an operator

who helped run the equipment that made the plastic that is used in

baggies and the coating of telephone wires (among other things).

My responsibilities were split into an outside and an inside job.

Every other day, I would have the outside job which entailed me

walking around the plant looking for mechanical problems.

If I found some, I would shut equipment down and prepare it for

the maintenance staff by shutting valves and so forth.

On the other days, I would in inside the control room

operating the controllers which determined the kind of plastic

we were making on my shift.  I liked both jobs as they

were interesting and used different skill sets, but I particularly

liked the outside one as it let me rub elbows with some of the

master class maintenance people.  I remember in particular 

a pump repairman named Dave.  This was about 1973 and even then

an expert such as Dave was being ridiculed for his emphasis on

problem solving and correct technique. We used huge pumps

driven by as much as 5000 hp motors.  All of them had a typical

flange and seal design.  When the material they pumped began

leaking from the seal, the pump had to be shut down, the flange removed

from the head by unbolting it and a new seal put in.  This needed to be

done delicately and Dave used a dial indicator attached to the head

and the flange to make sure the heavy flange would be attached

absolutely level once the new seal was put in place.  Then, the flange

bolts would be tightened like we tighten the bolts on a tire

when we replace a flat: tighten bolts in pairs that are 180 degrees apart.

This ensured the flange seated properly against the seal.  Dave's

precise maintenance procedures led to rebuilt pumps lasting for many months

of continuous service.  The other guys in the pump repair crew

thought Dave was too fussy and didn't want to learn all these careful

and useful ideas.  They didn't value his skills and they didn't want

to learn his skill sets. 

They did not take as much care in their

maintenance procedures and the pumps they repaired

typically lasted only a month or so.   So, the general ability of the pump repair

crews at the Union Carbide plant I worked at went down each year.

Of course, it is also surprising that the engineering staff in charge of plant

operations accepted such lax behavior.  The message is clear.

If we want to encourage the development and retention of such mastery,

the work environment must encourage it.

Dave was a master craftsman whose way of looking at the world was

not valued by both his peers and by the plant managers; hence, it was not passed 

on to the next generation despite his many attempts to do so.  I used to listen

to him explain about pumps and all sorts of other things

in which he would try to make me see how to look into a machine

and feel its wrongness.  He was very good at taking a big problem

and breaking it down into smaller sub problems.  These smaller

sub problems were, of course, easier to solve.  He showed me

in a very real way how to make progress on a complicated thing, you

needed to subdivide the larger issues into pieces small enough

to work with.

I used to watch other craftsmen also at my plant.  Some worked

on metal lathes, some worked on assembly and disassembly of large

machinery and all of the good ones were masters of their

craft in the sense discussed above.

These early lessons for me occurred while I was

working full time and going to college part time

and so I was in the great position of being exposed

to both the abstraction I saw in college

and the pragmatism I saw in the trades.  In both

fields, the ability to move between theory and practice

is exemplified by the situational fluency of the expert craftsman, but I am afraid we

are moving away from it more and more.

The Nuts and Bolts Foundation is concerned that our young

people are losing this ability to connect practical

aspects of diagnosing problems and building solutions to

the theoretical knowledge they learn in high school and college.

They think (B. Bergeron. Mind/ Iron: Little hands build big dreams. Servo, 8(1):6–7, 2010)

``more has to be done in the American educational system.

For example, shop classes - once popular -

are now rare.  As a result, most students who

finish high school are functionally illiterate

when it comes to basic mechanical skills such as the

ability to read a ruler.  [Also, many employers

have a complaint about] new engineering graduates.

Apparently, they often can't build anything because

they don't know how things are made.  Theoretical

knowledge alone just doesn't cut it on the shop floor.''

They also believe 

``resources [must be] devoted to the pleasures

of 'tinkering' -- getting away from ... video games

and TV sets and into the backyard building things.

In that way, we will create the next generation of

artisans, inventors, engineers, repairman, and skilled

workers -- in short, a self-sufficient, self-sustaining

society.''

This idea of  tinkering and creative play

can also be applied to what 

(M. Resnick, J. Maloney, A. Monroy-Hernandez,

N. Rusk, E. Eastmond, K. Brennan, A. Millner,

E. Rosenbaum, J. silver, B. Silverman, and Y. Kafai.

Scratch Programming for All. Communications of the

ACM, 52(11):60–67, 2009.)

refers to as digital literacy.

``It has become commonplace to refer to young people as ``digital natives''

due to their apparent fluency with digital technologies.  Indeed, many

young people are very comfortable sending text messages, playing online games,

and browsing the web.  But does that really make them fluent with new

technologies?  Though they interact with digital media all the time, few are able

to create their own games, animations, or simulations.  It's as if they can ``read''

but not ``write''.

As we see it, digital fluency requires not just the ability to chat, browse, and interact

but also the ability to design, create, and invent with new media.  To do [this],

you need to learn some type of programming.  The ability to program provides important

benefits.  For example, it greatly expands the range of what you

can create (and how you can express yourself) with the computer.  It also

expands the range of what you can learn. In particular, programming supports

``computational thinking,'' helping you learn important problem-solving and

design strategies (such as modularization and iterative design) that carry

over to non programming domains.  And since programming involves the creation

of external representations of your problem-solving processes, programming

provides you with opportunities to reflect on your own thinking, even to think

about thinking itself.'' ''

So it would be nice to return to undergraduate courses designed to 

develop a sense of general literacy in the students.  This would

include the ability to use computation and simulation to develop insight,

to build appropriate blends of mathematically enabled science for the purpose of

exploration and utilize creative play in generalized learning.

These attitudes would, of course, 

enhance the student's ability to problem solve and integrate theoretical and practical knowledge.

A general philosophy might be one I often use in my own classes.  We should be

developing tool builders rather than tool users.  No matter how careful the training,

all classwork is eventually obsolete in the light of rapidly advancing technology and science.

Hence, what is of paramount importance, is to teach students how to think for themselves;

to learn how to rapidly scan lots of information in books and manuals to gather the gist

and to know when to assemble a new tool from scratch to efficiently solve their current problem.

In many of my engineering jobs, I was routinely simply handed a mountain of information in the form

of poorly written manuals and hand written documentation and told to make something happen

in a few days.  Well, you just can't read all of the stuff in a few days, so you have

to be good at sifting through the pile for the useful nugget.  This also means

you have to be good at taking the task you are given and breaking it down into smaller

problems more amenable to attack and then use tools to develop more insight.

This definitely involves what Resnick said above. You have to create new representations

of the process you are using to solve the problems given to you and reflect on how you

are thinking about your tasks.  

So how to we inculcate this kind of attitude in a class?

I myself always try to get the students engaged intellectually

by asking questions verbally, by applying the things we discuss

to real problems and reiterating that it is important to carry a lot

of material locally in your head.  ``Look'', I'll say, 

``if you are working for a company and are at the water cooler or lunch

when you get into conversations with your boss, the boss will appreciate

your ability to think on your feet.  If you always say you have to go

look it up, your boss will slowly but surely learn to rely on others

who can have an informed opinion using their skills on the fly.''

So the bottom line is that a student does need to master their

coursework in such a way that they can draw on it in real life

situations without access to a book or notes.  They become leaders then

and that is what we need.  

We also need students to be able

to pull out of complicated situations and data, the bones of the underlying

ideas buried inside the mess.  My own training has been very much in the

physical sciences, but I'll mention a few examples to show how I was

trained to abstract out of messiness underlying principles.

A. When I was in grade school in the sixties, we had to outline

every chapter we read in our textbooks as our first assignment.

We were being taught how to quickly find the main points of our reading.

Oh, we complained, but since we all had to do it, it soon became second nature.

B. In grade school, we also had to write all of our homework in ink

and we were not allowed to erase anything.  So, if we made a mistake, we

had to rewrite the whole page!  This sounds horrible today, but it had

a huge benefit for us.  We very quickly learned to write well in our

minds prior to committing to paper.  It made a lot less work for us

to organize first and write second.  Also, not being allowed erasures

made us learn real fast how to do it right the first time.

I am sure these simple demands helped shape my ability to

pick out main ideas, shape my arguments efficiently and so on.

And it was just what is now considered an onerous exercise.

C.  In calculus, we learn to integrate functions which are very simple at first.

Then, we learn to use a technique called substitution which allows

us to see how buried in a very complicated integral is a much simpler

pattern we can find by using the substitution idea.  The details of the

mathematics are irrelevant.  The point is by doing many of these sorts of

problems, I was training myself to recognized underlying patterns buried

in ostensibly complicated expressions.  After awhile, any of us being

taught this way, had a light bulb go on in our head. Forever after,

we would always see the simpler pattern buried in the complicated one.

We could then take this new found skill and use it when we looked at

interactions of people, insects, gases etc. and start to see

laws that governed interaction.  Hence, a simple rote

training exercise using a mathematical tool was actually a much

bigger exercise in helping us to see how abstraction

-- the process of pulling patterns out of complexity --

was useful.  

As a final comment on how we are trained, consider that I learned to write

themes on paper by hand in ink.  I was not constrained to use short and simple

sentences and constructions; the pristine white of the page was my playground.

We have now transitioned to doing most of our creative writing on laptop screens.

The geometry of the page we write on is very different now.  It is easy to

start thinking in terms of 24 line, 80 column text as it fits nicely on our

display.  But make no mistake, this limits us.  We are now moving towards

new writing and reading display which are even smaller -- Ipod screens and the like.

This is having a profound effect on how we both create and process written information

which we are seeing in our students.  Also, note the rapid move to

e-reader technology where the normal book size has been reformatted to

5 by 7 or smaller.  This will inevitably push printed content

delivery towards shorted sentences, simpler paragraphs and so forth.

Also, note large complicated diagrams such as are common in technical text

and mathematical equations are harder to deliver on the e-reader platform.

This will also create a strong move towards the removal of such technical content.

Now, of course, interdisciplinary work does require such technical material:

messy and very dense blocks of information for the students to absorb.

Our technologies are moving us away from this.

There are similar things that crop up when you

look at how a person learns to program. I learned to program in the

late sixties and seventies before there were terminals, text editors and the like.

I had to type my programs onto cards and any mistake meant I had to type the

whole card again.  Needless to say, my early grade school training was helpful.

Yes, it was annoying and I was happy to move on to better tools for writing

my programs but I suspect my early training actually helped a lot.

Of course, all of this stuff is lost now and I think that has a lot to do

with why programming and other abstract endeavors are so hard for our students now.

With that said, new techniques to help students with implementing

problem solving strategies in programming are available.  For example,

there is  a really good programming environment called Scratch

(Lifelong Kindergarten Research Group. Scratch. MIT

Media Lab, 2010.)

which enables young people pre college and even pre high school

to learn how to assemble building blocks of code to solve problems.

Image how such kids trained in this fashion in their early years will develop!

I believe we need to rethink our approaches to the freshman and sophomore

courses at the university to stress the ideas mentioned above:

learn literacy in problem solving, tool building not just tool using and

the ability to skim lots of information quickly to get the basics assimilated.

The problem with all of this, is that the teacher's role is huge!

All students are essentially unique and helping a student with

their journey towards becoming their best requires a lot of effort

tailored for each student.  In 

(D. Hecht. Land of Echoes. Bloomsbury Publishing, 2004.)

a comment is made about how a particularly ineffective psychologist

looks at their patient load:

``He was ... one of that breed of psychologists

who looked for a tidy, encompassing theory that

wrapped the human psyche into a neat diagnostic bundle.

The trailing ends, the parts that didn't fit, were to be

ignored or cut to size.  It was the outlook of a man

accustomed to dealing with human problems in quantity:

to treating an unending flow of short-term patients,

managing their acute stages and referring them on, but never

having to dig in for the long haul and the messy, irregular, 

and highly individual process of healing.''

Of course, if you simply replace psychologist by

teacher, it is clear this comment is equally relevant

to my teaching and research profession.

Many teachers want to automate their assignments with

standardized testing, large class sizes so economies

of scale can be brought to bear on resource allocation issues

and evaluation procedures that minimize subjectivity.

The problem is that in all of my years in teaching,

there are always students who don't fit into any grading

scheme I devise.  My life is easier if they do, but 

it seems like my job is to help them find their path

to greatness, if possible.  The students have many problems

of their own to work out and that will always be so; however,

in the classes we teach we need to offer them tools to

help with that process rather than hinder it.