We present an analysis of the data produced by the MaNGA prototype run (P-MaNGA), aiming to test how the radial gradients in recent star formation histories, as indicated by the 4000AA-break (D4000), Hdelta absorption (EW(Hd_A)) and Halpha emission (EW(Ha)) indices, can be useful for understanding disk growth and star formation cessation in local galaxies. We classify 12 galaxies observed on two P-MaNGA plates as either centrally quiescent (CQ) or centrally star-forming (CSF), according to whether D4000 measured in the central spaxel of each datacube exceeds 1.6. For each galaxy we generate both 2D maps and radial profiles of D4000, EW(Hd_A) and EW(Ha). We find that CSF galaxies generally show very weak or no radial variation in these diagnostics. In contrast, CQ galaxies present significant radial gradients, in the sense that D4000 decreases, while both EW(Hd_A) and EW(Ha) increase from the galactic center outward. The outer regions of the galaxies show greater scatter on diagrams relating the three parameters than their central parts. In particular, the clear separation between centrally-measured quiescent and star-forming galaxies in these diagnostic planes is largely filled in by the outer parts of galaxies whose global colors place them in the green valley, supporting the idea that the green valley represents a transition between blue-cloud and red-sequence phases, at least in our small sample. These results are consistent with a picture in which the cessation of star formation propagates from the center of a galaxy outwards as it moves to the red sequence.