Sarah Bolton, Associate Professor of Physics, Williams College
At Williams it was initially not clear how well tutorial education would work in the sciences. Some of the concerns about the success of science tutorials were very practical: how to accommodate large numbers of students? What to do about labs? Others had a more pedagogical bent: the perceived necessity for students to master broad a set of material, techniques too complex to learn without lectures, subjects that require mathematical (rather than prose) exposition, and inaccessibility of the primary literature to undergraduates. Over time, though, tutorials have become regular parts of the teaching in every department –some with significant adaptation from the traditional format, others hewing closely to that standard model. I’d like to give you a brief overview of the state of science tutorials at Williams, including a number of examples of courses taught by my colleagues, then talk a bit more specifically about tutorials in the Physics department, where I teach.
A few numbers: Williams has seven science departments: Astronomy, Biology, Chemistry, Computer Science, Geosciences, Math, and Physics. The number of science tutorials has been rising recently, and currently sits at about 15/year. These are distributed quite evenly among departments – most offer two tutorials each year. These tutorials have in common that students meet in pairs (or occasionally groups of three) each week with the faculty, but beyond that basic requirement the courses vary broadly, in terms of level (non-major, intermediate, and advanced courses) and format (traditional reading/writing papers, problem solving, programming, mixtures of all three).
Level: The majority of our tutorials are at the intermediate level- about 2/3 are 200 or 300 level courses, requiring several prerequisites in the major. Courses for the most advanced students make up most of the remaining 1/3, with one or two courses for non-majors added to the mix most years.
Role in major: No department requires that students take a tutorial in their major subject. In several departments (Physics, Computer Science, Geosciences) tutorials constitute 1/2 or more of the upper-level electives, thus ensuring that nearly all majors take one tutorial, and many take several. In Biology, Chemistry, and Math the tutorials are more sparse, so only a small fraction of the majors take a tutorial in their major subject. (Andrea will talk about some of the pedagogical reasons behind these differences.)
Format: Written work I: traditional approach: About 1/3 of science tutorials are taught in the traditional format used in the humanities and social sciences. (Students write a paper every other week, which is read aloud at the tutorial meeting, and critique the paper of a partner in alternate weeks.) In these courses students’ development as writers is emphasized in parallel with scientific argumentation, and most faculty provide detailed written comments on the papers each week. To give you a sense of the range of audiences that can be served well by this sort of tutorial, I offer a few examples from my colleagues.
Example 1: Non-majors’ courses: One of the most successful chemistry tutorials, “Applying the Scientific Method to Archaeology and Paleoanthropology”, is designed for students who are not majoring in chemistry, or even in science. The instructor says that this course lends itself particularly well to the tutorial method, as there is no one set of material that every student must master and students can choose those topics that interest them most. To get students started, the instructor creates folders with potential topics, each folder including primary literature articles, supplementary background reading (often from a text) and contextual archaeological material. Every student pair chooses a folder each week, and then does additional research before putting together a paper. The instructor reports that this is one of the most successful courses that she’s ever taught, in the sense that the students are extremely engaged with the material, and end up very invested in the course. The astronomy tutorial “Extraterrestrial life in the Galaxy: A sure thing, or a snowball’s chance?” has a similar spirit, and is geared for students not majoring in astronomy. The instructor in this course takes advantage of the very varied backgrounds of the students, intentionally setting up tutorial pairs so that the two students have contrasting expertise (a chemist with a geologist, for example).
Example 2: Intermediate and advanced courses: In the biology department, tutorials are most often sophomore electives. These students have already had at least three courses in Biology, including genetics, and are on the cusp of choosing a major. The department finds that tutorials “hit” these students at an ideal moment, when they have the tools to start reading the primary literature, and are ready to learn to analyze and critique it. Acquiring this skill as sophomores puts students in a strong position for upper level biology courses, which require reading (and digesting!) primary literature at a more rapid pace. For example, in the sophomore tutorial “Genomes, Transcriptomes, and Proteomes” the weekly reading typically consists of one major (40-50pp.) article reporting a new finding, such as the sequence of the human , mouse, or chimp genome. Students are a given a specific paper topic, which focuses on the meaning and value of the scientific information reported in the paper rather than on details of techniques. As example of a paper topic is as follows; “The paper by Smith et al compares gene expression in healthy versus cancerous tissue. The paper by Jones measures differences in gene expression between women who go on to relapse and those who remain healthy after treatment. Discuss the value of the information obtained in each of these studies, and compare their strengths and weaknesses.”
Written work II: mathematical and problem solving courses: About 2/3 of tutorials in the sciences have problem solving as a major focus, and thus require significant modifications from the standard tutorial arrangement. Most typically, intensive problem sets are assigned each week, and students alternate between presenting problems at the board and acting as a critic. Because these courses develop a hierarchical set of skills, they often require that both students do the problems each week. The alternation between presenter and critic may then take place several times over the tutorial hour, rather than in week –long segments. Many include a weekly meeting of the class as a whole in addition to tutorial meetings. This might be for a lecture/discussion to orient students to the upcoming material (as happens in some Physics and Mathematics courses), or be a lab (as in “Quantum Chemistry and Molecular Spectroscopy”.) I’ll tell you a bit about how these courses work in mathematics and Physics. Andrea will tell you more about the computer science model.
Example: Mathematics courses. In the department of Mathematics and Statistics most tutorials require only two or three math courses as prerequisites, and may be taken by sophomores, juniors, and seniors. These courses are explicitly designed to foster skills in mathematical argumentation, built around particular applications that differ between the courses. In “Biological Modeling with Differential Equations” students choose topics that interest them – from epidemiology to population dynamics of endangered species-and present them at tutorial meetings. The tutorial hour consists of three student presentations, with questions/critique on each presentation from the two listening students. In “Numerical Problem Solving”, which draws students from Math, Physics, and Computer Science, students spend about half the tutorial session presenting problems on the board, and half demonstrating programs they have written (using a projection setup). The math department has also set up special tutorial-based sections of some of its large 200-level courses that are required for the major. In contrast to their non-tutorial versions, which emphasize particular content, the tutorial sections emphasize developing and critically analyzing mathematical argumentation (as applied to the particular content of the course).
Physics tutorials:
In the physics department we teach all of our or “second courses” in a subject as tutorials – these are “Applications of Quantum Mechanics”, “Electromagnetic Theory”, and “Advanced Classical Mechanics”. These courses all emphasize advanced mathematical problem solving, and seek to hone students’ ability to present physical arguments both orally and in writing. A secondary goal is for students to learn to “teach themselves” new material from a text or research paper. Each course is based out of a particularly readable text-book (and these are hard to find in physics!), from which students are assigned the major weekly readings.
Because we push students somewhat beyond the material in texts, and because we often assign quite open-ended problems, we have found that starting each week with a group meeting on Friday is very helpful. At this meeting we motivate the upcoming reading, try to clarify a tricky spot or two, and introduce some of the more opaque problems in the assignment. The reading and problem set assigned on Friday typically take students 15-20 hours to complete.
Tutorial meetings then consist of a discussion of the problems of the week. Students take turns presenting their solutions at the board, while the instructor and tutorial partner ask questions. Sometimes students are stuck and we spend time talking about approaches they could take to finish the problem. Often we also discuss extensions to the problem and implications the results. For students, this portion of the tutorial is a combination of presenting work that’s fully prepared in advance, and thinking on their feet about extensions and challenges to their solutions.
Tutorial partners often work together in their preparations, and thus come to tutorial with similar solutions and questions. While we support student collaboration on the problems (indeed, many of them are designed to be too hard to do alone), we find that students tend to use short-hand in presenting a solution to a partner who knows their thinking well. Similarly, student critics tend not to demand careful explanations of solutions they’ve helped devise. As a result, we’ve added a weekly “presentation problem” to each assignment. This problem is assigned to a single student, and must be completely finished in advance (with help from me, if necessary). Unlike the rest of the problem set, the “presentation problem” demands a polished ten- minute presentation, which students will have practiced at the board before tutorial. We ask that students consider pacing, optimal board layout, careful justification of arguments, etc. We’ve found that the addition of this problem gives students much more practice in thinking about the nuances of clear oral presentation of mathematical arguments.
Students have 24 hours to complete the write-up of their problem sets after tutorial. This gives them a chance to incorporate the tutorial discussion into their thinking and complete any problems on which they were stuck. Students end up writing something like 20 pages of problem solutions each week. To encourage students to develop their skills as clear writers of mathematics, some problems are assigned to be written up in “text book” form – that is, with significant prose commentary such as one finds in a fully developed text book example.
Practical issues/Enrollments Our tutorials enroll between10-30 students each term. We have chosen to keep these courses as tutorials despite the significant enrollment pressures, in large part due to student commentary about their value. (Andrea will talk more about student response). 2/3 of physics majors take more than one physics tutorial – 1/3 of our majors take all three.
Outcomes. The development of students’ skills across tutorials is striking. In their first tutorials, even the very best students tend to stop once they get a solution. They are hesitant to interpret their results, or go beyond them, and they are quite scared to stand up and speak at the board. By the end of that first term, and especially in a second tutorial, they are wholly different people at the board. Solving the problems is just the start of their preparation. They’ll follow that up by considering their solution in various limits and connecting it to previous ideas. They’ll often choose to write a numerical simulation to demonstrate the behavior of the solution in cases where analytic plots are difficult, or instead put together an approximation scheme that shows how the solution behaves away from the simple limits. They regularly come in with results I haven’t thought of, and questions I can’t answer. Some students really respond to the idea of learning to present well –taking very seriously commentary about effective lines of presentation, board work, etc., and asking for additional commentary from myself and their partner. These students are sometimes not the strongest mathematically, but end the semester making presentations that are remarkably strong – both scientifically and pedagogically. Perhaps the biggest change we see during a tutorial semester is in confidence. By the end of the term even our shy students are visibly anxious to get their hands on the chalk and get up to the board. They develop a sense of mastery - of both the content and the presentation – which is unmatched in our other courses. When students come back to visit from graduate school they often say “Well, I’d taken fewer physics courses than my peers from larger undergrad programs. But because of those tutorials, I really know what I know, and I know how to argue at the board. That’s put me in a good place.”
