In a food processor, combine one-third of the strawberries with 1/2 cup of the syrup and puree until smooth. Stir the strawberry puree into the syrup and freeze for 30 minutes. Using a fork, stir the ice crystals that form around the edges into the liquidy center and return to the freezer. Continue to stir and freeze until the mixture resembles soft snow, about 40 minutes. Stir in the remaining strawberries, freeze until just firm but not solid and serve.