With the goal of understanding and improving the performance of Air Entraining Agents (AEA), we are studying the nucleation and growth of ice in cement paste. We begin by re-examining an elegant experiment by Helmuth (1962), who inserted thermocouples into blocks of cement paste that were undercooled, then frozen; the rate of ice growth was indicated by the time at which the thermocouples responded to the heat of fusion as the ice passed by. He found a growth rate comparable to the interface-controlled rate measured in thin capillaries. However, the internal temperature of the concrete rose to a value independent of the external temperature, indicating that growth was heat-flow controlled. These seemingly contradictory observations were confirmed in our experiments. The explanation, revealed by our numerical simulations (using a level set method), is that the ice forms dendrites whose shape allows rapid growth. Using a phase field model at the pore scale, we examined the dependence of crystal morphology on water volume fraction and pore size distribution. The simulations indicate that the dendrites may exist on a scale much larger than the pore size, if the volume fraction of ice is high. Preliminary experiments indicate that propagation of a dendrite through the body triggers growth of ice in the air voids, so the quality of frost protection will depend on the interaction of dendrites and voids.