Could there be, even in principle, a lean math department? What would it be?
Which is a great question, to which I started a rambling response; I figure I might as well turn it into a rambling blog post instead.
Where do I even start thinking about that? What does a math department do? Produce theorems, teach students, I guess. Two pretty different goals; can we find waste in either of them?
What sort of waste do we look for? Situations where we aren’t processing but could be? Hard to say – in both of those scenarios, there’s a fair amount of down time, when students are doing something other than overtly learning math, when researchers are doing something over than overtly producing theorems. But you can’t always tell when learning and thinking are happening; I’m not sure if that will lead us anywhere useful. Though there are situations where you would be able to discover more results more quickly if you could talk to the right person at the right time; maybe we could analyze why that doesn’t happen and come up with something.
On the teaching side, can we see push systems that we can consider turning into pull systems? I bet there’s something to that, if we dig enough. Math departments generate courses, syllabuses, degree requirements the way they see fit, and then force students to take them (or not, as the case may be); I don’t see that as really being driven by the students’ desires for results, in general. (Other than in the most banal way, as in a pre-med wanting the result of admission to med school, which can be helped by having passed a course for which a calculus course is a formal requirement.) Admittedly, it’s not like Toyota will make whatever car I can imagine, but I still think there’s something to the idea that we need more pull in education.
So I guess I’d start with that: what are the outcomes that students want? Are we meeting them? If not, do a five whys analysis to try to uncover root causes, and see where that leads us. One basic thing to ask about: if a student is taking a course, and doesn’t get a good grade in the course, what’s going on there? Does the student have goals that aren’t a good fit for the course? (If so, why is the student in the course, and what can we learn from that?) Or are the student’s goals a good fit for the course, but the student didn’t meet those goals? (If so, how can we, especially the professor but also the student, improve the situation to increase the chance of meeting the goals?) Or were the student’s goals met, but the professor gave the student a bad grade anyways? (Just what is the purpose that the grade is serving? What need of students are we trying to meet by giving them grades? Are we sure that grades are the best way to do that?)
Also, I’m fairly sure that schools do a good deal more batching than is necessary. Maybe work on single-student flow: break down the groupings of courses, semesters, … Or is a semester the takt time? Seems kind of long for that, though.
I guess the upshot of this rambling response is: yes, there could in principle be a lean math department. The basic shift, I think, would involve in starting from the point of view of the students’ desired outcomes (if we want to make teaching leaner) and from the point of view of theorems (if we want to make research leaner). (A theorem is a funny sort of customer; I suspect that there’s something I’m missing there, but I can’t quite figure out a better customer to take the place of a theorem.) Are the students acquiring knowledge/skills/whatever as quickly and thoroughly as possible? If not, ask five whys each time we can identify a place where we aren’t. Are we producing theorems as quickly and profoundly as possible? If not, ask five whys.
Also, I’m fairly sure that schools could use a healthy dose of “respect for the individual”. In particular, I find them schockingly disrespectful of students, and adjunct faculty also have a lot to complain about.
Anybody else have any suggestions? I think there must be some people who have used lean ideas in education; I’ll see if I can dig up anything. For research, I guess lean product development would be the obvious parallel; I wonder if some of the ideas there (e.g. set-based design) would help research proceed more smoothly?
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