I grew up on military installations and attended some DoD schools. Some things unmentioned/underemphasized:

Families PCS (move) extremely often -- sometimes every school year, frequently every few years. Some places have DoD schools "on base", some do not, with students instead attend the local public schools. Some of those public schools are majority military kids, some are not.

DoD schools may have a consistent curriculum (not sure), but public schools across states/countries certainly do not. Constant moves mean students get a fractured, redundant curriculum. (Comically, I recall learning about the "Explorer" in History class no less than three times.)

Some bases are located in well-off areas with great public education, many others are not. Students might find themselves one year learning algebra, the next back to basic multiplication. Schools tend to be stubbornly inflexible and will not make accommodations on their own. Extremely attentive and pushy parents may get weak accommodations (e.g., letting students moving full grade levels up/down; something difficult to explain later), but it's rare.

Added to this is impact of constant social upheaval + stress of parents deployment, lack of lasting friendships, etc.

This is all to say -- you would not expect this population of kids to do well academically! The fact that they seem to (as measured in these tests at DoD schools) should be really surprising, and probably has little to do with the DoD schools themselves. They're after all only responsible for part (often a small part) of these kids' education.

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My main guesses at the real drivers here are:

1. (As mentioned in the article) It's a different world on base. Parents have a massive stake in their children's behavior -- and the students know this. No one wants their parent to get an earful from their CO, and it does happen. (This is most pronounced at DoD schools, but also extends off base.)

Drug and alcohol use is exceedingly rare, due to the above + how serious an offense it is on base.

It's true also that there's a modest baseline of economic + social support. Maybe not as much as the article suggests, but it's not nothing.

2. Simple reversion to the mean. The DoD schools are full of kids with a really diverse set of educational experience. Maybe some of the good experiences are even a bit "sticky" -- habits and skill learned transferring over to new environments, maybe even bad ones. Maybe it's not surprising that that population wins vs. the baseline (where kids only get a homogenous, mostly-good or mostly-bad experience). - If the good skills and habits are "contagious", maybe DoD schools even help spread them across this population.

3. The tests are mostly measuring the lower portion of the distribution. Well-off schools will have most students clipping the top end of the measurement. Many DoD students attend those schools! (At least for a time.)

This is going to seriously amplify (2), but also (1) and other things to the extent that they improve (or remove from the sample) the worst-off students.