The Unabashed Academic

24 March 2011

Neuroscience, Education, and Reductionism

As an education researcher and a theoretical physicist, I’ve been very interested in the issue of how to think about education – how to develop a theoretical frame.*  So one thing I’ve been doing is studying a wide variety of topics about human thinking and learning – psychology, linguistics, and neuroscience.
I’ve been told by a number of my experimental neuroscientist friends that their science “has nothing for yet me” in my attempts to develop a phenomenology of learning, and to “come back in 50 years.”  They say, “a lot is really still up in the air.”
I think this attitude is based on a misunderstanding of the relation of reductionism to theory building in the natural sciences.  First, we theorists don’t “wait for experimentalists to get it right” before building theory.  The process of “getting it right” involves an intricate interplay of experiment and theory, a dance in which the leading partner can frequently switch roles.  Furthermore, the interplay need not be on the same level of reductionism – micro, meso, or macro.  Information flows across levels.  Work at a large scale can inform work on the small.
For example, in the 1860’s, James Clark Maxwell began the development of statistical physics that is the basis for what is perhaps the most powerful reductionism we know – the way to create an understanding of the macroscopic properties of matter as it emerges from the behavior of molecules 10 orders of magnitude smaller in linear dimension. 
But when Maxwell created his theoretical structure, very little was known about the properties of atoms and molecules.  Indeed, many leading physicists of the day were not even sure of their existence.  There was no convincing argument demonstrating molecular size (thought there were some hints), and chemical experiments suggested that their interaction properties were extremely complicated.
Maxwell succeeded in building a theory of gaseous matter using almost trivial assumptions about the nature of molecules.**  He treated them as if they were hard spheres – obviously a ridiculous and unsophisticated assumption given what we knew about chemistry at the time!  Even the simple fact that molecules form liquids and solids show clearly that there are attractive forces and that they are important.
Nonetheless, Maxwell was able to produce a beautiful and effective reductionism – and one that passed information back to the micro level.  His explanation of transport phenomenon (e.g., viscosity, which moves momentum across parallel layers of a flowing gas) showed that measurable macro properties depended on a small number of microscopic parameters in a straightforward way, allowing him to infer molecular properties (such as average speed and mean free path) from macroscopic experiments. Indeed, the confirmed predictions from his transport theory produced some of the most convincing arguments for the existence of molecules in the second half of the nineteenth century.  (Though that’s a topic for another post.)
Phenomena that are undetectable at the micro level can build up coherently when going to the macro level leading to clearer signals.  For example, the small deformations of an atom in response to an electric field – the electrons pushed one way, the nuclei pushed the other – cannot be measured at the atomic level.  But if every atom is pushed the same way, the resulting effect is observable at the macro level, thanks to the factor of 1023 in Avogadro’s number.  In this way quantum predictions of atomic polarizability can be confirmed via macro measurements.
Finally, there are complexities at the larger scales that are difficult, if not impossible, to deal with by reducing things to smaller levels.  We can’t really deal with the complexity of organic chemistry by reducing everything to the simple facts that there are atoms that interact and bind – and that there are only about 100 different kinds of atoms.  The fact that the thousands and thousands of chemicals that make up our every day experience are combinations of a small number of different kinds of atoms is a deep and powerful insight – but it doesn’t begin to let us understand the complexity of organic chemistry.  For that, we need organizing principles at a higher level.
So, for building a behavioral phenomenology of learning, my expectation is that some elements of neuroscience – even what we know today – are going to be important, even though the details might not be fully worked out.  But the interplay of knowledge between the macroscopic behavioral level to the microscopic is already important. [For example, see how neuroscientists use the implications of behavior associated with neural damage.***] Interactions between learning theory and neuroscience might wind up being of value both to the macro and micro researchers.

* A Theoretical Framework for Physics Education Research: Modeling student thinking, Edward F. Redish, in Proceedings of the International School of Physics, "Enrico Fermi" Course CLVI, E. F. Redish and M. Vicentini (eds.) (IOS Press, Amsterdam, 2004).
*** From Neuropsychology to Mental Structure, Tim Shallice (Cambridge U. Press, 1988).

On Intergenerational Inertia

Instruction seems to have an immense intergenerational inertia.  Why else, in an age of ubiquitous calculators, do we insist on subjecting 5th graders to the torture of trying to learn to add multiple columns of numbers with perfect reliability or learn the mechanics of long division?

I conjecture that this is because our instruction goes back to a curriculum developed in 1900 when three-quarters of Americans worked on farms.  (Elementary school education didn’t become compulsory throughout the US until 1918.)  An appropriate job for a grade-school educated person was an account keeper or salesperson in a shop – where all calculations had to be carried out by hand.

As that motivation decays over decades, instead of changing our educational practice, we seem to continually re-invent ex-post-facto justifications for continuing to do what we know how to do.  Today, we might justify it on the basis of “helping students to develop a number sense.”  But there are much better ways to do this. [My favorite involved a program Judah Schwartz created called “What do you do with a broken calculator?”  In this, students had to figure out how to carry out calculations when one of the keys on their computer-screen calculator failed to work.] 

This inertia may be in part responsible for our tendency to create overly broad introductory physics courses.  As teachers, we know all the things we learned a generation ago.  They must be important, since we learned them and we did OK – and anyway they seem much easier to us after years of practice.*  We also know that modern instruction requires us to update our teaching by including new topics.  So we try to squeeze them in without removing the old.  Of course the result is an increasingly superficial treatment – a course a mile wide and an inch deep.

When I first taught physics I was assigned to teach E&M to a class of physics majors.  They had serious trouble learning the basic concepts of electricity and magnetism in a 15-week semester devoted entirely to the subject.  Why should I imagine 40 years later that biology majors – students less well motivated and prepared in physics and math than self-selected physics majors, and with other equally difficult courses competing for their study time – should be able to master these ideas in 6 weeks?

Figuring out what students need to learn now – and what they need to do to learn it – is a much harder task than we typically assume, especially at the university level where teaching is a second tier activity that you are supposed to be able to do in your spare time when you’re not working on your research.  This approach guarantees that we won’t have the time to be as thoughtful as the task needs, that we will have to fall back on what we learned when we were young a generation ago.  This ill serves our students who will still be working a generation from now.

*Reverse Engineering the Solution of a "Simple" Physics Problem: Why learning physics is harder than it looks, E. F. Redish, R. E. Scherr, and J. Tuminaro,  The Physics Teacher44, 293-300 (May, 2006).

20 March 2011

On service courses

In physics departments, a lot of the students we teach are not going to be physics majors.  They are going to be engineers, chemists, computer scientists, biologists, and doctors.  Everybody (that is, all physicists) agrees that physics is good for all future scientists since physics is the basis of all other sciences – at least that’s the way it seems to physicists. We tend to be reductionists.  That is, we build everything up from fundamental low-level principles.  Thus, in principle, quantum mechanics is a consequence of quantum field theory, chemistry is a consequence of quantum mechanics, biology is a consequence of chemistry, and medicine and social science are a consequence of biology.  Therefore, every science is based on physics.  Of course none of those connections (even the first) are filled in yet – or are likely to be filled in for many years, if ever.  But that’s a topic for another essay.  If those “in principle” reductionist connections are not why we teach physics to other scientists, what is?

I think that there are still lots of good reasons for other scientists to take physics.  The first and most obvious is that physics actually plays a role in the actual practice of all those sciences.  Chemists need to understand electricity and quantum physics, biologists need to understand fluid flow and energy, and doctors need to understand forces and torques as parts of their knowledge collection.  But more important than the specific bits of physics is the “physics way of thinking”.

The core of the approach that physics takes to science is that of finding and reasoning from a small core of fundamental principles.  And the deeper and more advanced we go in physics, the fewer and more powerful the principles become.  At the macroscopic level, we learn conservation of energy and momentum and they are fundamental principles that allow us to think about and solve many complex situations.  At a more advanced level, the fundamental principles become that our laws of physics should not depend on where we are or when we apply them.  This invariance with respect to space and time turns out to imply energy and momentum conservation.

One result of this “push for principle” in physics is that we tend to simplify.  Einstein said, “Physics should be as simple as possible, but not simpler.”  We seek the simplest possible problem that illustrates the application of the principle we are trying to teach.  I call these touchstone or toehold problems.  Once we understand these simple examples thoroughly, then more complex situations can be built around them.  The toehold examples provide starting points, ways of going forward or of organizing what we know in order to make sense of the complexity. 

We spend a lot of time working on the simple case of a mass attached to a spring since this provides us with a way of thinking about any oscillating system.  The core ideas behind oscillation are restoring force and inertia.  The is some stable equilibrium of the system such that when the system is deformed away from it, there is a force that attempts to pull it back to the equilibrium point.  Typically, that force gets stronger the farther you get from equilibrium and vanishes at equilibrium.  As that system is pulled back towards equilibrium, it starts going faster.  When it reaches equilibrium, the restoring force vanishes.  But at that point it is moving and has inertia.  Since there is no more force to stop it, it keeps going, goes past its equilibrium and we start all over.  This pattern can be working out in detail for the mass on a spring and provides the basis for describing damped oscillations, driven oscillations, coupled oscillations and resonance, as well as (perhaps surprisingly) a basis for the theory of motion of protons and neutrons in a nucleus or the theory of light in quantum field theory.

Besides this “drive for the simple”, physics thinking has a number of other characteristics such as looking for coherence, thinking about physical mechanism, taking multiple ways of looking at things, and making the connection to everyday experience.  (This last sometimes needs some refinement of our everyday experience to reconcile it with the science we have developed.)  There are valuable tools that we commonly use to achieve these ends such as doing dimensional analysis or considering limiting cases.

In an attempt to make physical thinking more explicit in our traditional service courses, my colleagues and I at the University of Maryland have spent the past decade learning about our biology clients in our algebra-based service course and refining the course to help them learn to strengthen their scientific reasoning skills.  [The method and results are laid out in our paper, Reinventing College Physics for Biologists: Explicating an Epistemological Curriculum , E. F. Redish and D. Hammer, Am. J. Phys., 77, 629-642 (2009).]  We had good success with this class.  On standardized mechanics conceptual tests (FMCE) we get much better pre-post fraction of the possible gain ( ~ 0.45-0.50) than in traditional classes ( ~ 0.15-0.30), and we get strong gains on our Maryland Physics Expectations (MPEX) survey, something not seen in most traditional classes.  

Anecdotal comments from students are also often positive and supportive (though they sometimes complain that there is too much hard work for a 100 level class).  Many students have said that the course changed the way they think about science for the better. (Some anecdotes are reported in the above-cited paper.)  But a recent comment from a student brought me up short. 

The week before the beginning of the second term, a student who had been in my first semester class came by to tell me I would be seeing him and his two friends from the class again.  He said they had enjoyed the class very much, worked together on the homework (as I had encouraged them to do), and felt they learned a lot.  As a result, they signed up for the second semester right away, choosing my course over some competing courses in their major.  He added that they wanted to take my course, despite the fact that they were biology majors and therefore it wasn’t of much relevance for them.

Well!  Despite the fact that I had thought carefully about what might be useful for biologists in their future careers, and focused on developing deep scientific thinking skills, it suddenly became clear that I had failed in an important part of my goal.  I had managed to teach some good knowledge and good thinking skills, but I had not made the connection for my students to the role of that knowledge or those skills in their future careers as biologists or medical professionals.  The occasional problem I had included with a biological or medical context did not suffice.

I now see that often I taught my principles and simple examples without making a real connection to show how those principles imbed in complex situations.  This can make my basic principles and the problems I give seem more like puzzles and games than ways of parsing a more complicated problem. 

I therefore propose we who are delivering service courses for other scientists – and I mean mathematicians, chemists, and computer scientists as well as physicists – ought to measure our success not just by the scientific knowledge and skills that our students demonstrate, but by their perception of their value to themselves as future professionals.  We can tell ourselves, “Well, they’ll see later how useful all this is,” and they might, but that is really wishful thinking on our part.  If our students see that what we provide is valuable now, they will maintain and build on what they have learned in our classes.  Otherwise, it is likely that what we have taught will fade and our efforts will have been largely in vain.

 For years I have been asking my students an extra credit question on my final exams, “Have you learned anything in this class that you think will be of any use to you in five years?  If so, what?  If not, why not?” (5 points for any thoughtful answer)  Up to now I have been looking at the results with interest and amusement.  I now intend to take those answers much more seriously and will use them as a significant measure of what I see as overall success in my service courses.