Another problem that is becoming more of an issue recently is that the "energy efficient sealing" of rooms is causing carbon dioxide to rise higher than expected. Installing air filters may be a proxy for mixing carbon dioxide better with outside air. <shrug>

In short, this study has no real controls, a lot of problems, and not a lot of evidence.

As a side note, it is not like the kids live in the classroom, they are exposed nonetheless - when outside the classroom - to "normal" air, let's say that in a week they are 30 hours or less in class and the remaining 138 hours they are not.

So these magical filtering allows for intellectual improvements when impacting roughly 30/168=17.8% less than 20% of inhaled air?

That's the whole point of the article. The author proposes a new title, "New study finds no evidence of educational benefits from installing air filters in classrooms."