The reality is that the poorer school districts have fewer resources, so they have larger class sizes and very often that happens in predominantly African American neighborhoods.
I'm sure you know that; I'm just letting you know that I know it too. One of the tragic things about it is that I think most of these kids have a lot of potential that will not be realized.
I disagree with your assertion that putting them in areas with dividers would be bad for them. First of all I'm not suggesting that all kids should be in computer labs with dividers all day, and I'm not suggesting that all kids be put in areas with dividers at all. I'm merely suggesting that for certain subjects and certain students that demonstrate an ability to work self-paced; we put them in an environment like that for some class periods. I'm not advocating for having all students in an environment like that all day. They'd all end up with no social skills (like engineers 
).
I appreciate your engineering analogy, but one of the things about engineering is the review process. You don't build a structure without a review by an engineer from the government. The materials have to be approved by an engineer. A lot of engineering is about studying failure. There are engineering properties for every kind of material and those properties are used in the calculations that are submitted for approval to the city. We know the limit of these materials because experiments are performed in labs until the material fails. Steels have a 'modulus of elasticity' based on those failure tests and forces and moments are determined based on load. Then a factor of safety is applied. I'm not a structural engineer, but it seems like a factor of 3 to 4 is standard. In other words; you determine the maximum load and then multiply that times 3 or 4 to size your materials.
I only tell you this because that's what I'm talking about with students. Obviously you can't develop a 'formula' for how many kids can be confined to a cubicle for a self-paced segment of the day that is applicable across all neighborhoods, but evaluation criteria can be developed to optimize such factors as 'cubicle size', 'distance between adult monitors', 'check in frequency/student' etc.
If the problem is that we need to reduce class size; that's how I would approach the problem: Have larger class sizes for students who need less individual attention, so that more educators can be dedicated to the students that need more individual attention. I don't believe there is a 'style they learn best' that fits all children. The style you describe did not work for my kids; they performed best when allowed to work at their own pace.
Determining optimum size would be an iterative process. As i said, I would start with 200. Maximum acceptable may turn out to be only 30, in which case the entire study would have turned out to be a failure, but studying failure is a big part of engineering.
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