Where The Students Are

And the implications for the school closure decisions

I bemoaned in a previous article that at no point did the District Advisory Committee receive (or ask for) data about where students live. Fortunately, an SFUSD parent, Philippe Marchand, had already taken the initiative to file a public records act requesting the data behind all the criteria the district is using. He was kind enough to share the output with me. Included in the data was the number of students living in each zip code. I blended it with some general population data from the census bureau to create the following map.

The map is color-coded to show the number of SFUSD students who live in each zip code. If you mouseover a zip code, you can see the share of all students who live in that zip code and how that compares with that zip code’s share of the overall population. For example, zip code 94112 contains 9.1% of the total population of the city, 11.3% of the population under age 18, 16.0% of all SFUSD students, and 18.3% of all 9th grade students. At the other extreme, zip code 94123 (which includes the Marina) contains 3.0% of the total population, 2.4% of the children under 18, but only 0.4% of SFUSD students.

The four zip codes that cover the area from Ingleside to Hunter’s Point and from Visitacion Valley to the Mission (i.e. 94112, 94134, 94124, 94110) contain over 45% of all SFUSD students. The four zips that border the Pacific contain another 23%.

The next post will cover the implications of this for the school closure decisions. Today, the focus is going to be narrower: how it affects the School Access Criterion, which is the single most important of the ten criteria SFUSD has said it will use to inform its decision-making.

School Access Criterion

The School Access criterion was originally defined as the “average distance between the three closest schools with the same grade span”. The idea was that schools would be more likely to close if there were other similar schools nearby and less likely to close if similar schools were further away. Based on that definition, the district did a public survey to decide how to weight the criteria and School Access is now worth a massive 21% of the entire Composite Score¹.

Average Distance Between Schools

Here’s what the average distance to the three closest schools looks like. My numbers² may not match SFUSD’s because this sort of calculation requires a few assumptions and I may have made different assumptions than SFUSD. It’s unclear, for example, whether SFUSD’s definition of “same grade span” would group all elementary schools together or distinguish between TK-5, K-5, TK-8, and K-8 schools³.

Lafayette in the Richmond is the furthest from its neighbors (as shown by its deep blue color) because its proximity to the ocean means that it has no neighbors to its west or north. Similarly, there’s a ring of schools to the south and west in blue because you can’t have neighboring schools under the ocean or in another school district. Conversely, the schools with the closest neighbors are in the center of the city or near Chinatown. Cesar Chavez and Monroe have low scores in part because of their proximities to BVHM and SF Community, two K-8 schools. If the K-8 schools are excluded, then the four schools with the closest neighbors would all be in/near Downtown and Chinatown.

If SFUSD was still using the original definition of the criterion, the schools in red would have been more likely to close and the schools in blue would have been less likely to close.

Population Density Adjustment

The District Advisory Committee recommended adding student density as an additional criterion for school closures. They wanted to give a boost to schools in areas with lots of students. Here is the Superintendent’s response in full:

Do not add any additional criterion that the Community has not had an opportunity to weigh in on. In addition, there are two primary concerns with using population density as a criterion in the composite score. First, prior research has indicated that schooling options are causally related to residential sorting patterns (i.e., schooling options influence who is willing to live where). This means that population density is going to be responsive to the pattern of closures, mergers, and consolidations that will occur in the city. In other words, population density, as a criteria, is endogenous  to the process of reorganization, making it a suboptimal criteria. Second, it is inappropriate to think of a measure of population density as a criteria in the category of equity. In fact, population density around a school will likely operate, functionally, in the opposite direction as the other equity criteria, which, together and independently, attempt to compensate, in one way or the other, for historical and/or contemporary forms of inequity. The density of a neighborhood is not analogous or predictive of historical wrongs or disinvestments of a community. Therefore, we advise against using student density as a criteria  in the decision-making process for school closures and consolidation. Additionally, using this a density criteria could be misleading in the context of school closure or consolidation decisions. Research indicates that residential decisions are sensitive to local schooling options, and the closure of a school can significantly affect neighborhood desirability and subsequent population density. However, density will be added as a  metric for  the School Access criterion.

That’s a cogent, well-reasoned, argument right up until the last sentence. Having spent the whole paragraph pointing out the problems with using density as a criterion, it then casually announces that “density will be added as a  metric for  the School Access criterion”. More specifically, the definition of the School Access criterion was modified so that it now reads: “average distance between the three closest schools with the same grade span adjusted for population density of the zipcode of the school.”

Student Density

Now that we have the number of students in each zip code, it’s easy to calculate the density of students per zip code, as shown in the map below.

94102, which covers the Tenderloin, didn’t have a particularly high number of students but, because it covers a small area, its student density is the highest. 94124, which covers Bayview, has a density that’s a bit below average because so much of the zip code is used for industrial or commercial purposes. Other zips have lower densities than you might expect because of parks.

I want to point out a number of serious, practical problems with using these zip-code based densities as an adjustment.

• If the density were calculated as, say, the number of students living within a one-mile radius of the school, it would not be subject to the discontinuities that are present when it is calculated per zip code. Consider José Ortega and Sheridan. They are 0.4 miles apart in Ingleside and each is the other’s closest neighbor. By my calculations, the average distance to the three closest schools was 0.78 miles for Sheridan and 0.87 miles for Ortega. Those are both a bit above average, meaning that the schools would be less likely to close based on this criterion. If you drew a circle of radius one mile around each school, there would be large overlap between the two circles, implying that the number of students living within a one-mile radius of each school is probably pretty similar. But because the boundary between zip codes 94132 and 94122 is an entirely arbitrary vertical line that happens to run between them, the density adjustment for Ortega is 572 students / sq mile and for Sheridan is 2,371 students / sq mile. Unless the adjustment is carefully defined, the School Access criterion will end up being more about the population densities than the distance to the nearest schools.

• There are plenty of these discontinuities. If Dolores Huerta elementary were on the east side of San Jose Avenue instead of the west side, its population density adjustment would be based on 1,827 students per square mile instead of 621. If Sunnyside were one block to the north, it would be in 94127 (density: 588 per square mile) instead of 94112 (density: 2,371 per square mile). If Sherman elementary were two blocks east, it would be in 94109 (density: 1,347 per square mile) instead of 94123 (density: 206 per square mile)

• The adjustment is based on the zip code of the school, not the zip codes of where the students are from. Everett and Lick middle schools are both in zip code 94114 (523 students per square mile) but both draw a plurality of their students the Mission which is in zip code 94110 (1,827 students per square mile).

• Normally, when you adjust a variable by some other variable there is a relationship between them. If you’re trying to calculate if someone is overweight, you might adjust their observed weight for their height and sex. This makes sense because, on average, taller people weigh more than shorter people and men weigh more than women. If a person’s weight is far above that predicted by their height and sex, we might conclude that they’re overweight or obese. In contrast, the relationship between student density and distance to neighboring schools is weak.

  

• Besides, the goal is not to control for student density. We’re not trying to identify schools whose distance to neighboring schools is above or below that which would be predicted by the student density of their zip code. Instead, as the DAC members who requested this change made clear, the motivation was to give a boost to all schools in high density areas. To make schools in high density areas less likely to close, the adjustment has to increase distances in high density areas by more than it increases distances in low density areas.

• The district hasn’t specified how they’re going to do this so we’re on our own. My first idea was just to multiply the two numbers (i.e. distance * density). One person I asked suggested multiplying the density by the square of the distance. The units for the resulting number would at least then be people instead of people per mile. In the end, I decided to follow the logic of my complaints about the adjustment and treat student density as a completely separate metric from distance. I calculated a mean and standard deviation for the student densities of each school and used those to calculate a student density z-score for each school. I then just added this to the distance z-score shown above to calculate a combined score⁴. For example, Sheridan’s distance z-score was 0.86 and its density z-score was 1.83, giving a total of 2.69. Meanwhile, Ortega, which was on the wrong side of the zip code line, had a distance z-score of 1.40 and a density z-score of -1.08, for a total of 0.32.

It’s not worth delving into the precise numbers because the method I used won’t match SFUSD’s method. But if we look at how the colors changed between the unadjusted and adjusted maps, we can get a sense of how the adjustment will affect the results. It’s almost certainly true that the density adjustment will make it much more likely that schools in the center of the city will close and make it much less likely that schools on the southern edge of the city will close. Schools that were previously vulnerable because they were so close to their neighbors are now much less vulnerable because they’re in high density zip codes.

1. It gets 5.0/12 of the Equity score, which is in turn 50% of the Composite Score. 5/12 * 0.5 = 21%.

2. I’m showing the values as z-scores because that’s what SFUSD will use to calculate the composite score for each school. See this presentation for an explanation. The map would look identical if I showed the actual distances instead. Z-scores become useful when blending numbers that represent completely different concepts (like distances and culture/climate survey results).

3. It seems obvious to me that there should be one elementary school group rather than two (elementary and K-8) or four (K-5, TK-5, K-8, TK-8). The people who apply to Key, Sunset, and Stevenson are likely to also apply to Lawton (a nearby K-8 school) and vice versa. The people who apply to Chavez, Moscone, and Flynn are likely to also consider Buena Vista Horace Mann and vice versa. Rooftop should be compared to Clarendon and Alvarado, not Alice Fong Yu and Buena Vista Horace Mann. Few parents limit their choices to K-8 schools.

4. Effectively, I have made student density a new criterion and given it the same weight as the average school distance. A nice feature of this approach is that if I didn’t like the output, I could easily give the student density a higher or lower weight in order to get closer to my desired output. There’s no right or wrong weight.