Smaller Classes?

Table 17b in the 2016 Superintendent’s Annual Report (the latest available) includes data by division on the total numbers of “instructional positions” and students (“ADM”). 

The table contains data for principals and assistant principals, teachers (including technology instructors), teacher aides, guidance counselors, librarians, and district-wide instructors based on positions reported in school divisions’ Annual School Reports.  District-wide positions include Summer School, Adult Education, Pre-Kindergarten, and other non-regular day and non-LEA instructional positions.

The Average Daily Membership (ADM) shown in this table reflects all pupils (Pre-K through Post-graduate) served in the school division at the end of the year.

The (very nice) VDOE front end to the SOL database offers a plethora of data, including the division average SOL pass rates for 2016.

Combining those datasets for the reading tests gives the following:


The red diamonds are, from the left, the peer cities Newport News, Hampton, and Norfolk.  Richmond is the gold square.  The green diamond is Charles City; the blue diamond is Lynchburg.

The division average teacher/ADM ratio is 11.1%.  Richmond is 11.5%.  The average pass rate is 77.4%.

The fitted line suggests that the pass rate by division goes down as the Teacher/Pupil ratio increases, i.e., as the class size drops.  The R-squared, however, tells us that the two variables are only trivially correlated.

In short, by this measure smaller classes don’t perform any better.

The math data tell the same story.


The R-squared rises to 3.4%: Still not enough to bet on and, in any case, the correlation still goes in the wrong direction.

The average pass rate is 78.4%.

Finally, the average of the averages of the five subjects:


Unfortunately the available data do not give us the teacher numbers by grade, so we can’t refine the analysis down to the grade and school level.  Even so, these data suggest that the key to improved learning lies somewhere other than in class size.