Rank-size distribution of teaching excellence in the UIUC Physics department

Alfred Hubler, UIUC, Physics

The UIUC Physics Department publishes the names of teachers ranked as excellent by their students each semester. We do a longtudinal study of these data for the past 20 spring/fall semesters (fall 2000 - spring 2010). We count the number of occurences n, when a faculty member is listed for a course as an excellent or outstanding teacher. We do not consider sabbaticals, administrative leaves, arrival dates of new faculty and the departure dates of departing faculty. The size of the teaching faculty changes over the years somewhat. For this analysis we use the current faculty size. According to the UIUC Physics directory there a total of 58 teaching faculty members on December 1, 2010.

Figure 1 shows a rank-size distribution of the Physics teaching faculty. We find that an exponential distribution, n = N exp(-λ r) fits the experimental rank-size distribution well. A least squares fit provides the following fit parameters: N=20 and λ = 5 / faculty-size. Figure 1 contains a graph of the fitting function. In addition we find that 80% of the listings are received by 30% of the top ranked teachers, but the experimental distribution does not match Pareto's power law distribution for the 80-30 rule.


Figure 1. Rank-size distribution of number of times when a UIUC physics faculty member was ranked as an excellent teacher by the students. The continuous line is a fit with an exponential distribution. The fit values of the rate parameter is λ=5 / faculty-size. Therefore the median rank is rmedium = ln(2) / λ = 8.

Figure 2 is a semilog plot of the data shown in Fig.1. The data are consistent with a linear funtion. This suggests that the exponential distribution is a good fit.


Figure 2. Semilog plot of the rank-size distribution of number of times when a UIUC physics faculty member was ranked as an excellent teacher by the students. The continuous line is a fit with an exponential distribution.

Next we use the same data to evaluate course quality as a function of the course level. Figure 3 shows histogram of the number of courses ranked as excellent or outstanding versus the course level. Bin 100 contains the courses 100-199 and their lab sections, bin 200 contains the courses 200-299 and their lab ections and so on. Larger courses are co-taught by several faculty members.

Figure 3. Number of faculty members ranked as excellent teachers versus the course level during the past 10 years (20 fall and spring semsters). 100-level courses are large algebra-based general eductation Physics courses. 200-level courses are large calculus based Physics introductory courses for future scientists and engineers. 300-level and 400-level courses are designed for Physics majors and have a class size of 20-50 students. 500-level courses are courses designed for Physics gaduate students with class sizes btween 10 and 30 students.