[BaO]

Consider the equilibrium shown. An additional piece of solid CaCO3 is added to the equilibrium above. The rate of dissolving and rate of crystallization have 
            CaCO3 (s) <-> Ca⁺² (aq) + CO₃^-2 (aq)
   
answer : dissolving increased ; crystallization increased

please check my explanation : the rate of dissolving has increased because the surface of CaCO3 has increased
                                          ---------------crystalization---------------------------  there are more solid present

[BaO]

but anyway, do you think that is the correct answer?
 i dont think both dissolving and crystalliztion rates increase at the ssame time.

[Yggdrasil]

The answer makes sense to me.  Adding solid leaves the system in equilibrium (i.e. K_sp = [Ca²⁺]*[CO₃^2-] says the same after the addition of solid), so by the definition of equilibrium:

rate of dissolution = rate of crystalization

Therefore, adding more solid increases both the rates of crystalization and dissolution because of the increased surface area of solid.  This makes sense because both rates must increase by the same amout for the system to remain in equilibrium.