Ok here is the crucial part of the paper:

It's a difference in differences design, using individual-level test scores and de-seasonalized data (p. 13). Their wording is:

> Y_igst is the outcome of interest for student i in grade g in school s in time period t, HighAct_s is an indicator for high pre-ban smartphone activity schools, D_t is a series of time period dummies (t = 0 indicates the first period after the ban took effect), δ_s is school fixed effects, and θ_g is grade fixed effects. In this setting, β_t are the parameters of interest, reflecting the difference in the outcome of interest between treatment and comparison schools for each period, with the period before the ban serving as the omitted category, holding grade level constant.

To me some modeling choices seem a bit heavy-handed, but I'm not an economist and could not do better.