Students in the Driver's Seat, Architects of Their Own Education
Relatively late in my career, about when we realized that Science One would be successful, several ideas about teaching and learning came together for my colleagues and me. None of them were particularly new to us, but together they were dynamite. Almost literally, they fueled an explosion of innovation in our institution as we designed other new programs and helped each other apply the ideas in our daily practice. I could go on about this for hours, but since my task here is to explore the idea of Students as Architects of their Own Education in narrative form, I will simply tell you some stories illustrating how the ideas can operate in the experience of individual students.
Mike Mayo was what I call a “mammal freak”. He loved all mammals the way many biologists love particular species like whales, wolves, or hummingbirds (or entities like mitochondria, chloroplasts or ecosystems), and tended to see the whole world in terms of their biology. Given this bias, it was no surprise that he asked a fascinating question about mammals in proposing a major research project in the Integrated Sciences course The Sizes of Things that I taught with Douw Steyn. In thinking about the challenge of reproduction, Mike argued that mammalian newborns should be related in size to the sizes of their mothers by the kind of relationship that we call a power law. His prediction was that the plot of these sizes, for all mammalian species, would be a straight line on log-log graph paper.
When we read his proposal, Douw and I grinned at each other, offered something like “Do you know where to find data to test your hypothesis?”, and sent him off to the literature with our encouragement. Sooner than I expected, Mike appeared at my office with a grin on his face and a piece of paper in his hand. For the several dozen mammal species he had plotted, the straight line of points indicated a perfect power law. Although I was as excited as Mike was about his discovery, it was too early in the term for him to finish his analysis and turn to writing. So as I congratulated him, I racked my brain for a way 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 they will all be easy to include.” We talked for a few minutes about what we expected to see in the analysis, and Mike went off to the library. When he returned a few days later, he was even more excited than he had been before. His first analysis had shown that for non-marsupial, eutherian mammals, the larger the mother the larger her newborns. Now he knew that, in contrast and to his surprise, all marsupials are born in the same small range of sizes, no matter how small the marsupial shrew or how large the kangaroo.
This presented a non-trivial problem for Mike to grapple with in writing. His proposal had developed an explanation for the power law he expected to find, but the non-relationship among marsupials was surprising from that perspective. He hadn’t thought about it yet and didn’t know how to explain it, at least at first. Mike eventually argued that whereas most mammals are born only once, marsupials are in effect born twice. The first time, they are the smallest mammals can be and still find their way from the birth canal to the pouch, some distance away, where they continue developing until their “second coming”. He wondered whether there should still be a weak power law relationship between the sizes of marsupial mothers and their newborns, because it should be farther from the birth canal to the teat on larger mothers. But he either couldn’t find enough data to detect the weak influence or for one reason or another concluded that it wasn’t there; I don’t remember.
In any case, Mike turned in his paper and we thought it was wonderful. It was fulfilling for Mike to have had such a rich experience of doing science as professional scientists do it, and wonderful that his discoveries were so exciting. And we didn’t have to teach him anything. Well, we taught him about power laws, and enough about data analysis to find them in a set of data. We didn’t teach him a thing about mammals, though, and didn’t help him in finding the data or analyzing them. He taught us.
Nancy Martin’s work in The Sizes of Things is another good example. Nancy was a long-distance runner, and just as Mike was biased by his love of mammals, Nancy saw the world through a runner’s eyes. In her proposal, she considered the simple fact that marathoners run more slowly than sprinters, and wondered what physiological processes determine the running speed for each distance.
Not surprisingly, given the major theme of the course, she argued that the slowing of running speed with distance should be described by a power law. She used the top three world record times for males and females at each distance from the shortest sprint to the longest ultramarathon to test this prediction, and, as Mike had, she expected a single straight line on log-log graph paper. However, she found not just one power law, as she had expected, but three of them, end to end (3 for males and 3 for females). Just as discovering fundamentally different “rules” of body size for marsupials than for other mammals created a significant creative problem of interpretation for Mike, Nancy’s surprise challenged her to explain it. Experientially, it plunged her from the relatively safe hypothetical world she had created in her proposal into the deep unknown, and any working scientist can tell you that this experience is both exhilarating and frightening.
An important key for Nancy was the striking fact that her three power laws corresponded with the three ranges of distance that runners and coaches call “sprints”, “middle distances”, and “long distances”. This reminded her that runners and even coaches usually specialize in one of the three ranges, that the tactics of training and competition are different in the three cases, and that different body types tend to excel at different distances. Considering these factors led her to propose, again after much reflection, many trips to many parts of the library, and consultation with several kinds of experts, a truly creative explanation.
In a nutshell, Nancy argued that sprints are fundamentally different than other races in that they are so short in duration. There is not enough time during a sprint to metabolize any kind of fuel to produce ATP, the metabolic “currency” of all cells. Instead, sprinters must rely on stored supplies of ATP, and the limiting factor is how fast they can mobilize it to generate motion. Middle distance races are long enough to completely expend stored supplies of ATP, so runners must regenerate it during the race. Nancy concluded that stored carbohydrates should be sufficient to fuel the longest middle distance race, and that the limiting factor is how fast runners can metabolize carbohydrate fuels to produce ATP. Long distance races are long enough to expend carbohydrate supplies, so runners must metabolize fats and oils to produce the ATP to finish the race. In each case, she argued, the critical rates should be linked to race duration by power law relationships.
A fascinating thing about Nancy’s project, which occurred in a surprising number of projects in that course, was that she was completely unable to find evidence that anyone before her had either asked or attempted to answer rigorously the question that informed her research. As far as she could tell from her review of the literature, she was exploring new territory. Because Nancy was a third-year student in The Sizes of Things, she decided to take an independent “directed studies” course the next year to do an exhaustive literature search, correspond with world experts about her work, and prepare a manuscript for publication. At the end of it, Nancy had failed to find any evidence of previous exploration and we concluded that she had done truly original research as an undergraduate.
Patrick came to Integrated Sciences from a technical background in atmospheric sciences, and he was biased to look to the air for his power laws. In an amazingly complex proposal, Patrick 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 that they produce. He tested his prediction using many years’ data from Vancouver International Airport, and his first discovery was that the data were so voluminous that no common statistical program could handle them. Patrick had to import and learn a specialized program that could handle the very large volume of data, and, after he did, he got another surprise. His plot of raindrop size against storm size showed two separate power laws for different size ranges of storms, presenting a challenge of interpretation.
Patrick guessed that the two ranges correspond to the two major mechanisms by which storms produce rain. In one, moving moisture-laden air is forced up by mountains or cold fronts in its path, cooling it enough to produce rain - - orographic precipitation. In the other, warm, moisture-laden air rises by convection , sometimes violently as in thunderstorms. Patrick predicted that the biggest raindrops come in thunder-type storms, but he couldn’t just sort the original data set by type of storm to test his new prediction because Vancouver’s nearby mountains and generally temperate marine climate bring it mainly orographic precipitation (and lots of it). From a long series of data from Gainesville, Florida, the thunderstorm capital of North America, he produced strong evidence that the two size ranges of raindrops are indeed generated by different types of rainstorms.
These three examples illustrate something important about teaching and learning, I think. Most importantly, they remind us that teaching can be more about guiding, supporting, and coaching students’ self-directed, curiosity-based work than about “teaching them” the so-called “content” of even difficult courses like ours. Of course, we did provide mathematical and statistical tools required for the research, and a series of small, structured, team-based opportunities to practice them prior to the major research project. Similarly, we did a great deal of coaching on other things like asking and answering powerful questions and expressing complex ideas simply in language, and introduced rigorous peer-editing procedures to ensure high-quality final products. But we didn’t think of ourselves as teachers of content, and neither did our students.
The content of that interdisciplinary course was unlimited, because it was about The Sizes of Things in general and in relationship rather than the size of any particular thing, and it varied from term to term depending on the interests of the students. The course was defined by an unlimited set of questions about the difference it might make what sizes things are and by a limited set of scientific tools for answering them. In four years of teaching it, we read fascinating projects on everything from the social psychology, economics, politics, and pedagogy of group size to the design of sailboats and human-powered airplanes, the dynamics of galaxy formation, and the partitioning of genetic information among chromosomes in cells. In very few cases did we know much if anything about the systems our students studied, and it didn’t matter a whit. In fact, we came to suspect that undergraduate courses taught by world experts in their content can easily suffer from the universal tendency of professors to profess what they know. Douw and I brought little more to our course than a few mathematical tools, a belief in their power to reveal much of interest about complex systems of all kinds, and a strong faith in the creative, self-actualizing power of our students.
An explicit objective of the program, which requires students to design their own two-year curriculum and use it to bridge across disciplines, is to “make them smarter” in the sense of “street smarts” rather than raw intelligence. To a truly fulfilling extent, we believe the program achieves this for both of our major constituencies. About half of Integrated Sciences students come to the program with strong backgrounds in a variety of scientific fields but seeking more freedom and broader education than they can find in most degree programs. The other half arrive with mediocre records and little sense of themselves as learners. Many have been rejected from elite programs with high entrance requirements and come seeking success . Once they get the hang of self-directed learning, though, both kinds of students tend to find what they came for in the learning environment Integrated Sciences provides, because working in it makes them smarter.
We have learned to expect stellar, sometimes publishable work from all of them, regardless of their backgrounds. Some of the personal transformations we witness in that environment are stunning, and many are sudden. For example, Mike Mayo discovered himself as a learner near the end of his last term as an undergraduate, and it literally changed his life.
It changes my life to witness such a thing.
For the historical, philosophical, and administrative background of this and two other interdisciplinary science programs at the University of British Columbia, see Benbasat, J. A. and C. L. Gass. 2002. Reflections on integration, interaction, and community: the Science One program and beyond. Conservation Ecology 5(2): 26. online
Mike Mayo’s reflections on his experience of the Integrated Sciences Program at UBC are posted on the ISP web site.
For insights into the biology and psychology of surprise, see Gass, C.L. 1985. Behavioural foundations of adaptation. In P.P.G. Bateson and P.H. Klopfer (eds.). Perspectives in ethology, Vol. 6, pp. 63-107. Plenum Press, New York.
After working in a government research laboratory, Mike Mayo is now employed as a scientist in a research laboratory at UBC. Nancy Martin had been a Science One student in first year before entering Integrated Sciences. She is now studying medicine at UBC. Patrick Little is now studying architecture at Dalhousie University.
Gass, C.L. 2002. An Exercise in Thinking, Writing, and Rewriting. Great Ideas in Teaching. Benjamin Cummings.