<p>A layer of monodisperse circular steel disks in a nearly square horizontal cell forms, for small shear amplitudes, hexagonal close-packed regions that grow and merge until a single ordered domain fills the container. Increasing the shear amplitude leads to another reproducible regime in which a few large, locally ordered domains grow, shrink, and rotate with shear cycling, but do not evolve into a single ordered domain that fills the container. We use orientational order to describe the phenomena of order and disorder that we have observed. These results are robust within certain ranges of applied pressure and shear frequency. This work avoids two major limitations of sheared three-dimensional experiments: gravitational gradients and the difficulty of determining the interior three-dimensional structure.</p> Graphical Abstract <p></p>