## 2016-02-22: A Very Simple Equation

There is a very simple equation that tells us a lot about the enrollment balancing issues in PPS:

• (total # of kids) / (total # of sections) = average kids-per-section

What does this mean? For a particular grade, say kindergarten, if we know the total number of kinders and the total number of kinder sections, then we can compute the average number of kinders per section.

If one is trying to balance enrollments in each section over all schools, then this "average kids per section" is what you get if you manage to perfectly balance enrollments. Balanced enrollments per section and per grade are how you build a foundation for equitable programming -- and it's the maximally-efficient way to make use of the limited capacity PPS currently has in its building stock.

Now for some actual numbers...

In 2014-15, there were 139.5 kindergarten sections and 2,878 kinder students on the east side, and 33.5 kindergarten sections and 803 kinder students on the west side, generating these average section sizes:

• East: 21 students per section (from actual section counts)
• West: 24 students per section (from actual section counts)

Looks great --- but there are two big problems hiding here: gross imbalances in section-sizes between schools and inflated section counts overall.

We know the "actual section counts" are unsustainably big, e.g. Chapman has extra sections squeezed into its basement. PPS published a "School Optimal Building Size Analysis" which is supposed to represent the actual capacity of PPS school buildings. Using those numbers, the "optimal section counts" for 2014-15 kindergarten add up to only 103 sections on the east side and 25 sections on the west side. The corresponding average section sizes are:

• East: 28 students per section (optimal section counts)
• West: 32 students per section (optimal section counts)

What does this tell us? Well, if we actually "right-sized" our schools with respect to building capacities, and even if we managed to optimally balance enrollment, then class sizes would have been too big even in 2014-15. To accommodate the present population and future growth, we will need more sections.

We can turn the equation around to figure out how many more sections we will need. Let's say we want an average of 25 students per section (though, if we are planning for growth, we should aim lower). If that's the target, it's easy to compute the number of sections needed:

• (total # of kids) / 25 = # of sections you need in district

Again using the 2014-15 kinder population, hitting the target requires around 115 sections on the east side and 32 on the west side. Compare this to the "optimal section counts", and that tells us we need another 12 sections on the east side and 7 sections on the west side. That tells you how many schools we're lacking, just to handle last year's kindergarten students --- e.g., we'd need to open 4 (three-strand) schools on the east and 2 (a three-strand and a four-strand) on the west.

Now, back to the other problem: gross enrollment imbalances between schools. These average section-sizes are only realizable by something like the Soft Neighborhood Model. The PPS Hard Boundary system comes nowhere close to filling sections evenly: over all neighborhood schools in 2014-15, actual kinder section-sizes ranged from 14 to 30 students per section. If the schools had been "right-sized" with the optimal section counts, the range is even wider, from 15 to 45 students per section! Hard Boundaries cannot fill sections evenly and predictably.