The invention relates to compositions and methods for modifying cementitious materials such as by reducing setting time. Polymer compositions of the invention are derived by polyetherifying mono-glycerols, optionally with alkylene glycols, to obtain polyglycerol homopolymers or copolymers, and then carboxylating the obtained polyglycerol homopolymers and/or copolymers with an organic acid having at least two carboxylic functionalities. The set retardation effect of the carboxylated-carboxylic polyglycerol polymer compositions in cementitious materials is reduced is compared to polyglycerol polymer not having the carboxylated-carboxylic groups, while its water reducing ability is maintained without loss of early compressive strength. Cementitious compositions and methods involving the carboxylated-carboxylic polyglycerol are also covered by the invention.