  In this paper within the scope of FRW cosmology for k = 0, \pm1 we study the
dynamics of the universe for a cosmological model with a scalar field
nonminimally coupled to matter. By best- fitting the model parameters with the
observational data for the direct interaction between the dark sectors in the
model we obtain observational constraints on cosmological parameters. The
result shows that with the best fitted model parameters, only in flat universe,
the phantom crossing occurs twice in the past and once in the future, whereas
no crossing occurs for open and closed models of the universe.
