Modeling Instruction

In my reading of physics teacher blogs, one pedagogic buzzword comes up over and over “Modeling Instruction”. I got some pointers to papers in a comment by Jane Jackson, when I asked for references about peer instruction (a somewhat broader buzzword).

Unfortunately, I’ve found most of the papers on modeling instruction to be rather long, wordy, and not very useful for telling me what the technique was.  (They are heavy on measuring that the technique is useful, without actually saying what the technique is.)  I found Hake’s comments on the ap-physics mailing list and his web pages so aggressive and unhelpful that I could not bring myself to read more than one of his papers.  I got some useful information (about a page or two worth) out of the 32-page
Malcolm Wells, David Hestenes, and Gregg Swackhamer
A Modeling Method for high school physics instruction
Am. J. Phys. 63 (7), July 1995, 606-619.

The content can be pretty well summarized by their “box 2”:

BOX 2: MODELING METHOD Synopsis
The Modeling Method aims to correct many weaknesses of the traditional lecture-demonstration method, including the fragmentation of knowledge, student passivity, and the persistence of naive beliefs about the physical world.

Coherent instructional objectives

• To engage students in understanding the physical world by constructing and using scientific models to describe, to explain, to predict, to design and control physical phenomena.
• To provide students with basic conceptual tools for modeling physical objects and processes, especially mathematical, graphical and diagrammatic representations.
• To familiarize students with a small set of basic models as the content core of physics.
• To develop insight into the structure of scientific knowledge by examining how models fit into theories.
• To show how scientific knowledge is validated by engaging students in evaluating scientific models through comparison with empirical data.
• To develop skill in all aspects of modeling as the procedural core of scientific knowledge.

Student-centered instructional design

• Instruction is organized into modeling cycles which engage students in all phases of model development, evaluation and application in concrete situations—thus promoting an integrated understanding of modeling processes and acquisition of coordinated modeling skills.
• The teacher sets the stage for student activities, typically with a demonstration and class discussion to establish common understanding of a question to be asked of nature. Then, in small groups, students collaborate in planning and conducting experiments to answer or clarify the question.
• Students are required to present and justify their conclusions in oral and/or written form, including a formulation of models for the phenomena in question and evaluation of the models by comparison with data.
• Technical terms and representational tools are introduced by the teacher as they are needed to sharpen models, facilitate modeling activities and improve the quality of discourse.
• The teacher is prepared with a definite agenda for student progress and guides student inquiry and discussion in that direction with “Socratic” questioning and remarks.
• The teacher is equipped with a taxonomy of typical student misconceptions to be addressed as students are induced to articulate, analyze and justify their personal beliefs.

That was all very well, but still rather vague. There was an example running for several pages, but it didn’t help me much in seeing what characterized “modeling instruction”. Perhaps others would find it more informative.

I finally got a more satisfying answer from the ap-physics mailing list where I was directed to a series of blog posts: Salt The Oats: FIU Modeling Workshop.  These posts by Scott Thomas are reflections on a workshop that he took in June and July of 2011.  He offers the disclaimer

… if this interests you, please go to the workshop, don’t just rely on me.  Even after only one day I can tell that my recount will mean nothing for you without you attending.

Since I’m only planning on teaching physics once (and am almost halfway through), I’m unlikely to attend a two-week workshop, so reading Scott’s notes are about as close as I’m going to get.  His descriptions are fairly detailed, and I think I have a better idea of what modeling instruction involves from his description than from any of the more formal papers I’ve been pointed to.  (I’m not knocking the papers—they provide the evidence that the technique works—they just don’t provide enough information about the technique to come close to duplicating it.)

It is already too late for me to use some of the “modeling instruction” principles.  The students I have do read the book and understand the math, so much of the effort of getting the students to develop their own models would not be productive—they’d jump immediately to the “right” model and just verify that their data fits it well enough.

I am trying (now) to get the two students to work together to set up and solve problems and to design labs (rather than my designing the labs)—we’ll see how that goes.  And I am trying to get them to use a more standardized layout for problem setup: drawing the free-body diagram, listing the initial and final state, writing out the appropriate fundamental equations.  I don’t know how much it is helping, as the students were already pretty high performing and good at setting up the right model without much fumbling around.  As we get to more complex problems, though, they may need a more disciplined approach, so I’ll try to provide the appropriate framework of generic questions and general-purpose tools (like free-body diagrams).

At least I was, from the beginning, using an approach that minimized memorization and re-derived things as much as possible from a few key formulas. I’ve always hated memorization (which is part of why I was a math major as an undergrad—almost no memory work). The textbook I’m using, Matter and Interactions, supports that approach pretty well—I believe that the authors were trying to get a bit of the modeling instruction flavor into their text (though the videos of Ruth Chabay’s lectures are very much a traditional lecture-demo style).

I am thinking about how much of the “modeling instruction” approach could be adapted for teaching introductory programming to biologists (my most challenging pedagogic task for next year). High-school and first-year college physics has only a few key concepts (the “models” of modeling instruction), and most of the effort in physics classes is in getting students to learn to do problem solving using that handful of models.  Are there equivalent key concepts in introductory programming?  Or are the problems beginning programmers have more like those of beginning biologists: too many unrelated factoids?  I think that programming is more like physics than like biology, with relatively few key concepts, applied to solve a wide range of problems, but that might be an unfamiliar way of thinking for the biology students who will be in the class.  So if I can find an approach that has the strengths of modeling instruction but applied to programming rather than physics, I’ll have a chance at getting most of the students to an acceptable level of programming skill.

Related articles

• NPR reports on peer instruction (gasstationwithoutpumps.wordpress.com)
• Preclass learning (gasstationwithoutpumps.wordpress.com)
• Numbers vs. symbols (gasstationwithoutpumps.wordpress.com)

Scientists don’t test hypotheses

On his Computing Education Blog, Mark Guzdial wrote about Nancy Nersessian’s work on how scientists really work: The Scientific Method is wrong: Scientists don’t test hypotheses, but build models.  He describes her idea as

Rather than test hypotheses, scientists do experiments to influence their models of how the world works.  The hypotheses they test come out of those models, …

That is hardly a new idea.  I’ve been trying to convince teachers for years that a hypothesis is not a guess, not even an educated guess, but the prediction of a model in a situation in which different models make different predictions. (See Science fair time again or Google science fair, for example).

I suppose that technically the term “hypothesis” should be used for the model, rather than for the prediction made from the model, because it comes from the Greek ὑπόθεσις (hypóthesis), meaning basis or supposition. But what gets stuck in the “hypothesis” box in science-fair forms is usually the prediction, not the model (if we should be so fortunate as to have a model rather than a wild-ass guess from the students).

Perhaps we should banish the term “hypothesis” from science fairs entirely, since it is used so badly. In its place we should ask students to provide the models that their experiment can distinguish among, and the predictions that would result from each model.  By making the models (always plural!) be the center of attention, rather than the prediction, I think we could correct a lot of the misunderstandings that abound about the scientific method.

Thoughts for revising a grad curriculum, part 3

Our department is thinking of doing a major overhaul of our graduate curriculum. This is the third in a series of posts on my thoughts about curricular design (earlier ones were Thoughts for revising a grad curriculum, part 1 and Thoughts for revising a grad curriculum, part 2).  The first post was applicable to almost any field, and the second post got more specific about some of the history, goals, and constraints of our department,but neither got down to the level of making specific proposals.

I’ll try to outline my ideas for a revised grad curriculum in this post, though I probably not get down to the level of detail needed for new catalog copy. I am still hoping to get pushback from colleagues around the world, former grad students, and even current grad students, so that our new curriculum design is the best we can manage.

I’ll organize this post as a series of questions, and try to provide my answers (which are not, of course the only possible answers).

How much research?

All PhD students have to do a thesis: an original piece of research.  MS students do not need to do original research, but do need to show high level of competence with the skills needed for  doing research.

Note the University of California grad requirements do not allow a “courses-only” masters program.  There must be some sort of capstone activity.  When we tried having this be a Master’s thesis, the projects grew to be too huge, and students were not completing the MS in several years, so we need to make sure that the capstone remains an appropriate size.  Our current requirement, that students do a one-quarter project with a written report and public oral presentation at the end, seems to be about the right size for the MS capstone.

I believe that PhD students need to develop skills in several areas and need to investigate several research questions before they start their theses.  The lab rotation system of biology programs, where students spend 3 quarters during their first year, each in a different lab,  is an excellent way to develop these skills, as well as providing a low-commitment way for faculty and students to explore the possibility of and adviser-advisee relationship.

Requirements:

• MS: 1 1-quarter research project (equivalent to a lab rotation) as a capstone.
• PhD: 3 1-quarter research projects (lab rotations) in the first year.

How many courses?

Before figuring what topics we need to cover and how to organize them into courses, we need to know how much room we have for making requirements.  This is constrained by how much student time we can dedicate to course work and by how much our faculty can teach.  Although the curricular redesign was prompted in large part by constraints on teaching time, I’m going to look at this problem primarily in terms of student time.

Based on my earlier discussion about the desire to have both MS and PhD programs, and to allow students to switch between them,I think that we want to have very similar course requirements for the MS and PhD programs. Ideally, a self-funded MS student doing courses full-time should be able to finish in a year, and a more typical MS student with teaching assistantships and a small research project should be able to finish in two.  We would also like most PhD students to choose an adviser at the end of their first year and declare candidacy by the end of their second year. These constraints puts an upper bound of 9 courses on the requirements for the MS,with the capstone project counting as one of the courses in the 9-course limit. The PhD students can be required do do a bit more, but not by much, or transition between the programs is too difficult.

Given that undergrad training in bioinformatics is still rare and our students come in with often quite lopsided training (heavy in only one of biology, computer science, and statistics), I don’t think that we can copy some PhD programs that have no required course work, only thesis research. Our filed changes very rapidly and our students are not likely to be prepared for the different fields and different problems they’ll be facing 5–10 years from now unless the required coursework forces them out of their comfort zone. Quite frankly, I don’t trust some of our faculty to advise students well on taking enough breadth—they  are so narrowly focused on students preparing for their current research projects that they will end up producing specialists who are only employable by their own research group.  There is certainly room for disagreement about the minimum number of courses to ensure this breadth, but I feel that the PhD students should be taking at least as many courses as the MS students.

There are a number of less-than-course-sized educational requirements I think are needed, like attending research seminars, getting lab safety training, and learning things like advanced library search techniques, voice projection, preparation of posters and slides, training to be a TA, … .  These are often packaged as 1-unit classes (much smaller than the usual 5-unit course here), so that we can keep track of the requirements with the usual student records.  It is much easier for staff to check a transcript than to have lots of extra requirements that need extra record keeping.

Proposed course numbers:

• MS:  8 “lecture” courses plus one project course. Also 3 quarters of attending research seminars and 1 how-to-be-a-grad-student mini-course covering a lot of the useful skills that are not tied to any specific subject matter.  Students with TAships would not be able to complete this program in a year, since a TAship is a half-time job and only allows time for 2 courses, not 3, in addition.
• PhD: 8–9 “lecture” courses, plus 3 project courses (lab rotations). Also 9 quarters of attending research seminars and 1 how-to-be-a-grad-student mini-course covering a lot of the useful skills that are not tied to any specific subject matter.  Students should take 5–6 lecture courses and 3 lab rotations their first year (which means at most one TAship in their first year), and 3–4 courses in their second year, with adviser-sponsored research filling up the rest of their schedule (except for one or two TAships).  I’m not sure whether the “lecture” course requirements should be 8 (to match the MS) or 9.

Note: this requirements are very similar to what we currently have—I think that the size of our current program is not far off from what is needed, and it is mainly the content and organization that needs changing.

How many different tracks?

Our department now covers several different fields, and we’ve already moved away from a one-size-fits-all curriculum. We can go in a couple of different directions: either very generic “number of courses” requirements with students crafting their own boutique programs to match what they need, or several specific “tracks” that point students to courses that are appropriate for different goals.

When I was a student, I liked being able to take whatever courses I wanted, and I used that freedom to take some challenging courses that I would not have been able to fit into a more structured program.  I also ducked some courses as an undergrad that I probably should have taken (like calculus-based physics), and I was never advised to take statistics, which I now see as an essential for many science disciplines (especially bioinformatics).  So while the flexibility was good for me in some ways, I did not get the intensive advising I should have gotten to optimize my education.

A really dedicated student who knows what they want to do and scours the course catalog for the entire university, looking for appropriate courses to patch weaknesses and build strengths, can put together a really great program if the constraints are as generic as possible.  A less dedicated student could use the same system to avoid challenging material, stay in their comfort zone, and get a truly inferior education.  Based on what I’ve seen of the past 25 years, we get students across the spectrum in dedication and ability to design their own curricula, from ones who could do as good a job at curricular design as any of the faculty to ones who have to be told every course to take, because they can’t figure out what they need to know or where to find it.  Typically (though not always), the PhD students have a better sense of what they need than the MS students, who need more specific direction.

This decision is, to a large extent, one of the cost and quality of advising. We could craft a custom program for each student, carefully matching their needs to the available courses.  This takes 2–4 hours of faculty time per student per year (in addition to any other advising), and adds a couple of hours to the staff record-keeping and graduation checking time.  With about 40 grad students in the program, half of whom need course advising, we’re talking about 80 hours of faculty time and 40 hours of staff time a year added for a “boutique”  degree program, contrasted to a checklist program.

Some of the faculty have not shown any interest in knowing about any courses other than their own, much less across the 7 or 8 departments that our students take classes from.  That means that custom programs would end up putting a heavy advising load on just two or three faculty, who would (in the way the university assigns “credit” for work) not being getting much, if any, reward for this advising time.

So I’d like to put together a system that allows the really dedicated students to challenge themselves without too many required courses filling up their time, but which forces students to move out of their comfort zones and get the breadth of education they should be getting.  I think that the MS programs should have very specific tracks, to reduce the faculty advising load and because the MS students generally need more specific advice.  The PhD program can be a bit more “boutique”, but students who don’t have the willingness or ability to design their own curricula should be able to use one of the MS tracks.

Suggested tracks:

• MS: emphasis on bioinformatics tool building:  Requires tool-using and tool-building courses in the department, Bayesian statistics and machine learning from outside the department.  This program may end up looking a lot like our current one, though we don’t currently have a tool-using grad-level course.
• MS: emphasis on computational biology: Requires tool-using and statistical inference, but only minimal programming.  Requires more biology than the tool-building track.  This track will require some new courses or refocusing of existing courses.
• MS: emphasis on biomolecular engineering: Requires minimal programming and tool-using, requires courses we may not currently have in molecular biology and bioengineering.  This track will require careful design, as I don’t believe we currently have a coherent program at the masters level in biomolecular engineering—we have an assortment of courses but the core that ties them together is not really working.  We may be doing ok for PhD students, though our offerings in biomolecular engineering are not as extensive or as polished as our bioinformatics, but the program is too scattered right now for a good MS degree.
• PhD: every student has to prepare a detailed curriculum, together with justification for each course and for the overall balance of courses, and provide a graduation checklist for the staff to use.  Any of the MS tracks can be used and will be provided in the required format to the students, so that those who do want to customize have detailed models to follow, and those who want to just do something standard don’t need to do anything.

What topics do students need to learn?

Obviously, there are a lot of topics that could be taught and we can’t regard them all as essential.  What is essential for one student doing one research project may be just breadth for another, or may be totally irrelevant.  Also, the “essential” material will change over time, sometimes quite rapidly as the underlying technology that generates the data we use changes.

I’m not expert enough in biomolecular engineering to list core topics there, and I know too much bioinformatics to want to get down to the level of specific topics.  So for this post I’m going to try to group things into pretty broad categories, and give an idea of the overall balance I think the program should strive for.

• How to be a grad student: Students need to make a transition from education consumers to information generators. This is an on-going process that can take several years, but it is greatly facilitated by explicit teaching of presentation skills, library research skills, citation skills, co-authorship, research ethics, sharing of data, critical reading of papers, and so forth.  A mini-course (like the current BME 200) can start the process, but it needs to be supported by requirements for frequent (at least annual) oral and poster presentation and by lab-group journal clubs, required written documents (lab rotation reports, thesis proposal, and so forth), and research seminar attendance outside the lab group.
• Programming: all of our students will need to be able to do some programming.  The tool-builders will need to be expert programmers in two or three different languages, but even the tool users and biomolecular engineers will need to be able to write small programs in a scripting language (like Python) to be able to get tools to work together and to be able to do simple data analysis and presentation.  We should requires some training in programming (even if just a community college intro course) as a prerequisite for entering the program. Few of our students (even those with strong programming backgrounds) come in with much skill at Python programming, so one course with a strong emphasis on programming is useful, but it should not be the sole focus of any of our grad courses.
• Statistics: all of our students will need some statistics.  The tool-builders will need a strong background in Bayesian statistics, and everyone will need some classical statistical inference (so that they can understand an properly use notions like E-value).
• Biology: everyone will need some biology, probably to the level of an undergrad course in genetics and an undergrad course in cell biology.  The biomolecular engineers will need a lot more, both in terms of lab techniques and fundamental understanding of the field they are working in (which may be stem cells, viruses, protein nanopores, DNA replication, or any of a number of other things).  Again, we should require that our students come in with some training in biology, but some of the subjects we’ll expect students to know are not readily available at community colleges, so some students may have to make up missing course work after becoming grad students.
• Biochemistry: Because so much of our work is based on DNA and RNA sequence data and engineering of DNA and RNA molecules, students should have a thorough understanding of the biochemistry of the machinery for the fundamental dogma (transcription, RNA editing, reverse transcription, and translation).  Most of our students will not need enzyme mechanics and the biochemistry of metabolism or protein folding, but perhaps some will. There is some question about how much biochem should be prerequisite to entering the program and how much should be required after entering.  Given the fit between BIOC 100A and what our students need to know, we may want to require that course explicitly.
• Bioethics: Since its inception, our program has required that students take a full course in bioethics—not just the “be a good boy or girl” research ethics class that NSF and NIH expect, but a serious look at the potential consequences of new technologies and ways to reason about the ethical dilemmas they may pose, rather than having mainly emotional “new=good” or “new=bad” reactions.  I believe that we should continue such a requirement, though we may want to reconsider the various ways this can be met.
• Machine Learning: Many of our tools use classifiers and other tools from machine learning, and so tool-builders need to learn about various machine learning techniques—how they work, what their limitations are, and how to implement them.  Computational biology tool users need to know a little about the limitations of the tools, but do not need as detailed an understanding of how to build machine-learning tools.  It is not clear that biomolecular engineering students have any need for understanding machine learning.
• Bioinformatics tools: What tools and databases currently exist and how can we use them effectively to answer a variety of biological questions.  We have an intro course at the undergrad level for this, which may be able to share lectures with an intro grad course, but we probably also need some more advanced tool user courses, if we are to have a computational biology track for the M.S.
• Bioinformatics algorithms: We currently have a core course (BME 205) teaching models and algorithms, and several more advanced courses teaching a mixture of tool use and algorithms.  We may want to refactor these courses so that the tool use can be offered without the algorithms component to grad students from other departments, and perhaps even to computational-biology track MS students.  That will leave scattered bits of algorithm material that may need to be swept together into a more advanced algorithms course for tool builders.  The core course itself may need to be reorganized (with material from other courses) to be two course: one on the understanding of tools (with a lot of the background on stochastic modeling) and simpler Python scripting, and another on more advanced programming and more sophisticated algorithms (not just the dynamic programming of the current course, but some graph algorithms and some machine learning, perhaps).
• Biomolecular engineering: I’m not sure what topics we need to cover in our department to prepare students for research in the field.  There are all kinds of lab skills and engineering skills that may be needed, but I don’t know which ones are core and which ones are specific to one research lab.

What topics do we need to teach?

This question is a bit different from the previous one, as we hope that courses offered by other departments can serve a number of our students’ needs.  Because we have a tiny department and we can’t dedicate all of our teaching resources to the grad program (we have bioinformatics and bioengineering undergrad courses to teach also!), we have to have out students taking some of their grad education from other departments. Many of the topics in the previous section are best handled by other departments (statistics by AMS, machine learning by computer science, biology by MCD bio, biochem by chemistry, …).

We will probably also have to rely heavily on other departments (like electrical engineering, computer engineering, microbiology, and chemistry) for some of the more technical training the biomolecular engineers will need.

We will have to teach bioethics, bioinformatics tool usage, and bioinformatics algorithms. We’ll probably have to teach some of the more specific biomolecular engineering techniques (whatever those turn out to be).  We may even have to teach a little programming, or at least provide occasions in classes where students are forced to practice their programming.

Questions for the part 2 post that I still haven’t addressed:

• How do we integrate the biomolecular engineering students grad students fully into the department?  It would be a real shame to have them disappear into faculty advisers’ labs for 4 years, and not interact with the other grad students. (This is already a serious problem with our 10 faculty currently spread over 4 buildings, and soon to be spread over 5 buildings.)
• Are there any core subjects that all our students should take, regardless of their eventual research? Having a common core helps develop camaraderie between the grad students and leads to fruitful collaborations between labs (grad students are often the vectors for the infection of collaboration).
• Are there further subjects that are core to different tracks?
• What do we do about subjects that we see as essential, but that do not fit the campus’s one-size-fits-all grad-course size (35 lecture hours, with about 100 hours outside class)?  Should we create mini-courses?  Portmanteau classes that have multiple, nearly independent topics?
• How will the revised graduate curriculum support the (fairly small) number of bioinformatics undergrads, who currently are expected to take 2 or 3 of the first-year grad courses?
• Is there a way to get any synergy between the graduate biomolecular engineering courses and the (fairly large) number of bioengineering undergrads?

I’ve also not yet addressed the question of how the things we need to teach are broken up into courses and how we write the requirements so that they don’t need to be rewritten every couple of years as other departments tweak their curricula.

Marmoset song

I rarely embed videos in my blog, but the pun in this one was too good to pass up:

USA causes of death

A few weeks ago I came across an interesting statistics site, which shows causes of death in the USA as maps.  It is really astonishing how the life expectancy changes geographically, and how many different causes of death show the same geographic distribution.

You can get maps of individual states (down to the county level).  The county I live in is doing pretty well on most health measures (8th longest male life expectancy in California, at 78.1 years—compared to 77.79 statewide and 75.93 nationally, and 9th longest female life expectancy at 82.6 years—compared to 82.76 statewide and 81.07 nationally).  A big part of the difference is probably from more exercise and less smoking here than elsewhere, but there are probably other factors (since death rate due to accidents is also low).

Although the black-background web pages are a bit annoying to read, the data and the maps are cool.