  Based on the BESIII measurements on the reaction of $D_s^+\to
\pi^+\pi^0\pi^0$, we investigate this process by considering the $S$-wave
pseudoscalar-pseudoscalar interaction within the unitary chiral approach, and
the contributions from the intermediate resonances $f_0(1370)$ and $f_2(1270)$.
Our calculation could reasonably reproduce the experimental data, and our
results imply that the $f_0(980)$, dynamically generated from the $S$-wave
pseudoscalar-pseudoscalar interaction, plays an important role in this process,
and the contributions from the intermediate resonances $f_0(1370)$ and
$f_2(1270)$ are also necessary. The more precise measurements of this process
in future could shed light on the nature of the $f_0(1370)$ and $f_2(1270)$.
