  We report on a new method for tracking the phases of the orbital modulations
in very short-period, near-contact, and contact binary systems systems in order
to follow starspots. We apply this technique to Kepler light curves for 414
binary systems that were identified as having anticorrelated O-C curves for the
midtimes of the primary and secondary eclipses, or in the case of non-eclipsing
systems, their light-curve minima. This phase tracking approach extracts more
information about starspot and binary system behavior than may be easily
obtained from the O-C curves. We confirm the hypothesis of Tran et al. (2013)
that we can successfully follow the rotational motions of spots on the surfaces
of the stars in these binaries. In ~34% of the systems, the spot rotation is
retrograde as viewed in the frame rotating with the orbital motion, while ~13%
show significant prograde spot rotation. The remaining systems show either
little spot rotation or erratic behavior, or sometimes include intervals of
both types of behavior. We discuss the possibility that the relative motions of
spots are related to differential rotation of the stars. It is clear from this
study that the motions of the starspots in at least 50% of these short-period
binaries are not exactly synchronized with the orbits.
