  Motivated by suggestions of 'cosmic downsizing', in which the dominant
contribution to the cosmic star formation rate density (SFRD) proceeds from
higher to lower mass galaxies with increasing cosmic time, we describe the
design and implementation of the Redshift One LDSS3 Emission line Survey
(ROLES). ROLES is a K-selected (22.5 < K_AB < 24.0) survey for dwarf galaxies
[8.5<log(M*/Msun)< 9.5] at 0.89 < z < 1.15 drawn from two extremely deep fields
(GOODS-S and MS1054-FIRES). Using the [OII]3727 emission line, we obtain
redshifts and star-formation rates (SFRs) for star-forming galaxies down to a
limit of ~0.3 Msun/yr. We present the [OII] luminosity function measured in
ROLES and find a faint end slope of alpha_faint ~ -1.5, similar to that
measured at z~0.1 in the SDSS. By combining ROLES with higher mass surveys, we
measure the SFRD as a function of stellar mass using [OII] (with and without
various empirical corrections), and using SED-fitting to obtain the SFR from
the rest-frame UV luminosity for galaxies with spectroscopic redshifts. Our
best estimate of the corrected [OII]-SFRD and UV SFRD both independently show
that the SFRD evolves equally for galaxies of all masses between z~1 and z~0.1.
The exact evolution in normalisation depends on the indicator used, with the
[OII]-based estimate showing a change of a factor of ~2.6 and the UV-based a
factor of ~6. We discuss possible reasons for the discrepancy in normalisation
between the indicators, but note that the magnitude of this uncertainty is
comparable to the discrepancy between indicators seen in other z~1 works. Our
result that the shape of the SFRD as a function of stellar mass (and hence the
mass range of galaxies dominating the SFRD) does not evolve between z~1 and
z~0.1 is robust to the choice of indicator. [abridged]
