An unpublished study* from the late 1990s showed that calculus students in classes of about 35 do no better than students in classes of 90 and larger. There was no statistical difference in the amount learned or in the drop-out rate. The large and small sections were taught by the same teachers. There were, however, significant differences among teachers.
This study suggests that at least under certain circumstances it may be more effective as well as less expensive to have the best teachers teach large lectures than to have many, less effective teachers teach smaller sections.
The paper actually discusses two studies at two different universities. The first compared small (30) to large (90), and neither large nor small classes had recitation sections. The second study compared small (20-35) to large (150-240) and both large and small had additional small recitation sections, so in one sense even the large sections had some small class time. In both cases teacher effect dwarfed all else, and the class size effect was not significant. Only at the second university did the study look at dropout rates.
David Bressoud, former president of the Mathematical Association of America, called section size
"a question I'm often asked and for which I know of no direct and meaningful evidence, at least with regard to undergraduate mathematics. ... Let me add that if a university chooses to go with small classes taught by graduate students and adjunct faculty, then coordinating and supervising the teaching of those classes is extremely important. I've seen disasters with small classes. Our study has also seen successes with large classes, but there are certain things that are critical to making them work: careful preparation and supervision of the recitation instructors, a highly supportive mathematics tutoring center with mechanisms for ensuring that students who need it use it, and the provision of feedback loops to the lecturers that foster active participation by the students in the class and give them a sense that the instructor is responsive to their questions and confusions. Clickers are one way of accomplishing this. One-minute quizzes, 'pair and share,' on-line feedback, or just long pauses built into the class to give students time to formulate questions are other techniques that can be employed successfully."
My own best personal experiences in teaching calculus have been with larger lectures: untypical special sections close to 100 at Williams, typical lectures of about 250 at MIT, and the very best a lecture of 100 at Rice. On the other hand, at least for more advanced courses, very small classes from about 10 to 20 seem much better. In general, the most popular courses at Williams are our signature Tutorials, in which students meet with faculty in groups of two once a week and present the material themselves.
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*"Class Size and Teacher Effects on Student Achievement and Dropout Rates in University-Level Calculus" by Tyler J. Jarvis of Brigham Young University.