For a work in progress, nice job! I really like his sense of touch and phrasing. For a second grader, he's above the curve there.
Couple things I would recommend working on:
-Really settle into the tempo. He has a tendency to rush into faster phrases, probably either because he is unsure of the notes or the speed at which he's playing. This is apparent at 0:06-0:09 especially (and, to some degree, every subsequent repeat of that phrase).
-Work on evenness. I know he's got small hands--what 2nd grader has large hands?--but the more even he can play the passages, the better. Look for tempo consistency, note duration, and volume. All three are critical, and if he learns it now, he won't have to relearn it later.
Can't wait to hear the final product.