  We perform a "fossil record" analysis for ~800 low-redshift spiral galaxies,
using STARLIGHT applied to integral field spectroscopic observations from the
SDSS-IV MaNGA survey to obtain fully spatially-resolved high-resolution star
formation histories (SFHs). From the SFHs, we are able to build maps indicating
the present-day distribution of stellar populations of different ages in each
galaxy. We find small negative mean age gradients in most spiral galaxies,
especially at high stellar mass, which reflects the formation times of stellar
populations at different galactocentric radii. We show that the youngest
(<10^{8.5} years) populations exhibit significantly more extended distributions
than the oldest (>10^{9.5} years), again with a strong dependence on stellar
mass. By interpreting the radial profiles of "time slices" as indicative of the
size of the galaxy at the time those populations had formed, we are able to
trace the simultaneous growth in mass and size of the spiral galaxies over the
last 10 Gyr. Despite finding that the evolution of the measured light-weighted
radius is consistent with inside-out growth in the majority of spiral galaxies,
the evolution of an equivalent mass-weighted radius has changed little over the
same time period. Since radial migration effects are likely to be small, we
conclude that the growth of disks in spiral galaxies has occurred predominantly
through an inside-out mode (with the effect greatest in high-mass galaxies),
but this has not had anywhere near as much impact on the distribution of mass
within spiral galaxies.
