Putting the “right” number of students into a building does not guarantee the “right” number of students goes into each room. In fact, in most high schools, it’s not possible under the Carranza Hybrid plan.

Why not?

First period, my school, juniors and seniors.  Normally we’d have about 200 upperclassmen divide into 7 classes, anywhere from 20 to 34 in a class. Mostly upper 20s. I’ve got last fall’s program in front of me: AP English Literature and Composition, Vectors and Matrices, Calculus AB, Vertebrate Physiology, AP English Language and Composition, Spanish Level III, AP US History

But today, socially distanced and hybridized, only 50 upperclassmen are in, divided into 7 classes, carefully selected so that there are 5 to 9 in a class. Mostly 7 or 8.

Those are good numbers. Our classrooms are small, and most have capacity between 7 and 11, including teacher.

The bell rings, second period. 7 classes again. AP English Literature and Composition. AP Spanish, Vectors and Matrices, AP Biology, AP English Language and Composition, Spanish Level IV, AP US History. Good, right?

Wrong. There are way too many kids in Spanish Level IV and AP Bio (15 each) and the rest of the classes are low. Can we fix it?  We might send a few kids home, and replace them with others, so that first AND second periods now fit, socially distanced in each period. That would take some serious work, carefully considering each student’s schedule.

But then third period, and now we have more classes over socially distanced capacity. And this time we can’t fix it without messing up first or second.

But wait, we’ve barely started. Because when we chose 50 upperclassmen whose classes worked for 1st and 2nd period, we were leaving 150 home. Next we would have needed to find another 50 whose numbers worked for 1st, 2nd, 3rd…  It wasn’t going to happen. Even if someone cleverly got further along in the process than I can, by the time they hit the 3rd cohort, the entire effort would collapse.

## Why does this happen?

Individual schedules

High school students follow individual schedules. They move during the day, and have some classes with some other students, other classes with different groups of students. This is not elementary school were class 405 stays with class 405 the entire day.

High school students have different levels of mathematics, and of foreign language, depending on how advanced they are. They might even study different languages. There is not a rule of thumb that students who study Vectors also take Mandarin while students who study Calculus take beginning German while students who study Algebra II study advanced German. It is mix and match.

High school students in most schools have some choice of Advanced Placement courses. High school students may have specialized CTE electives. High school students have other electives. And some high school students repeat courses.

Variation

The more options, the more variation. In general, younger students’ schedules have less variation. In my school, freshman schedules vary only in math, foreign language, and a choice of skills courses (which we choose, then reverse, and which does not add any complexity to the schedule). That creates six course variations – and in most years we see all six. But by the time students become seniors, the number of options that are really the students’ options have grown – in theory there are about 240 course variations – but we are likely to see requests for maybe 40 – 50 of them. (this excludes make-up classes, we always have a few, and college classes – which is a different, longer discussion).

The specific courses, and the kind of courses, that may vary school to school. But in the vast majority of high schools in NYC (and I would say across the US) schedule variation increases as kids move towards senior year.

Uneven Numbers

The numbers requesting each course in high school are not equal. For freshmen maybe that’s not true. Maybe there are the same number of sections of English 9 as there are of Global History 1. That’s how it is in my school. But by senior year – oy! We can have 48 kids for AP Biology and 32 kids for Public Policy, 70 for AP Calculus and 90 for AP English Literature and Composition. Not only are the numbers of sections different depending on the course, but the average size of the sections is different. And, even without hybrid, balancing junior and senior classes has been a very imperfect art.

When we move from classes of 32, 30, 28, 28, 28, 26 and 20 to classes of 32, 32, 32, 30, 28, 26, and 20, the flows (arrows pointing from one class to another) will be uneven, in a complicated way.

Correlation

If our courses were tightly correlated it would make the scheduling more predictable, more regular. If there was zero correlation, that would loosen things up, and make scheduling and balancing easier. But neither is the case. What do I mean?

If every kid who took AP Calculus also took AP Bio, I could link the two courses in the schedule, reducing the complexity. Even if every kid who took Bio also took Calc, that would help. But neither one of those is true.

On the other hand, if there was no relation between AP Calc and AP Bio, if the requests were random, then I could keep the flows (arrows pointing from one class to another) pretty even.

Unfortunately, neither is the case. Kids who take Calc are more likely to take AP Bio than kids who don’t, but it’s roughly 50% of the kids who take Calc, and 25% of those who do not. So there’s correlation, but no guarantees. And the exceptions are too common to just be considered exceptions. This is true for most pairs of our APs and electives – lots of weak correlation, very little strong correlation.

Is this the same in every high school?

The names of the courses are different. And the sticking points (Advanced Placement vs Special Arts courses vs CTE courses vs Elective vs Make Up courses) are different. And the numbers are different – though there are many more small high schools (300 – 600) in NYC than there are large high schools, but the range is tremendous. But yes, most high schools will run into the same constraints, for the same reasons.

Is there anything that can be done to make a cohort model work in a high school?

To get past this difficulty, yes. Run about twice as many cohorts as the DoE says you need. They are planning for you to fill every room every period. But the student flows mean you will end up violating capacity pretty much all the time, in a minority of rooms. Instead, plan for rooms to be filled at 50% of socially distanced capacity (the limit is 10 – plan for 6), and then the “bulges” won’t go over 10. Since most high schools seem to “need” 3 or 4 cohorts – planning for 6 or 7 or 8 cohorts might make the numbers work. But, and I am choosing the word carefully, this is ridiculous.

Are there other reasons a cohort model won’t work in a high school?

Well, yes, lots. But this one is huge, and is worth talking about separately.

Does this problem affect middle schools, too?

Many of them, yes. Those that do not keep their students together in the same group all day.

Does that mean that Elementary Schools and Middle Schools that don’t use individual programs are going to be fine with the hybrid cohorts models?

No. There are many more problems than the one I describe above. This is one problem that elementary schools won’t have. (Just as parent pick up and drop off, a big issue in elementary, will not be an issue in most high schools).

So what should we do?

Mulgrew already knows this. I assume Carranza knows this. And yet, we still have been handed unworkable choices. The right answer?

“We cannot choose. There is not a model that works for high school.”