The particular numbers on which I'm focused aren't cool ones like pi, although I suspect they're not entirely rational, either.
I teach at a public university in a state whose recent budget crises have been epic. That means that funding for sections of classes (and especially for the faculty who teach those sections of classes) has been tight.
My university is a teaching-focused university, which means that there has also been serious effort to ensure that the education students get at the university gives them a significant level of mastery over their major subject, helps them develop compentencies and qualities of mind and skills, and so forth. How precisely to ensure this is an interesting conversation, couched in language about learning objectives and assessments and competing models of learning. But for at least some of the things our students are supposed to learn, the official judgment has been that this will require students to write (and receive meaningful feedback on) a minimum number of words, and for them to do so in classes with a relatively small maximum number of students.
In a class where students are required to write, and receive feedback on, a total of at least 6000 words, it seems absolutely reasonable that you wouldn't want more than 25 students in the class. Do you want to grade and comment on more than 150,000 words per class section you are teaching? (At my university, it's usually three or four sections per semester.) That's a lot of feedback, and for it to be at all useful in assisting student learning, it's best of you don't go mad in the process of giving it.
There's a recognition, then, that on a practical level, for courses that help students learn by way of a lot of writing, smaller class sizes are good. From the student's point of view as well, there are arguably additional benefits to a smaller class size, whether being able to ask questions during lectures or class discussions, not feeling lost in the crowd, or what have you.
At least for a certain set of courses, the university recognizes that smaller classes are better and requires that the courses be no larger than 25.
But remember that tight funding? This means that the university has also put demands on departments, schools, and colleges within the university to maintain higher and higher student-faculty ratios.
If you make one set of courses small, to maintain the required student-faculty ratio, you must make other courses big -- sometimes very, very big.
But while we're balancing numbers and counting beans, we are still a teaching-focused university. That might mean that what supports effective teaching and learning should be a constraint on our solutions to the bean-counting problems.
We're taking as a constraint that composition, critical thinking, and chemistry lab (among others) are courses where keeping class sizes small makes for better teaching and learning.
Is there any reason (beyond budgetary expedience) to think that the courses that are made correspondingly large are also making for better teaching and learning? Is there any subject we teach to a section of 200 that we couldn't teach better to 30? (And here, some sound empirical research would be nice, not just anecdata.)
I can't help but wonder if there is some other way to count the beans that would better support our teaching-focused mission, and our students.