Provided are methods for producing carbonate-containing compositions comprising silicon-based material (e.g., pozzolanic material) from a source of carbon dioxide, a divalent cation-containing solution, and a source of proton-removing agents. In such methods, divalent cations of the divalent cation-containing solution are provided by digestion of material comprising metal silicates. Also provided are methods for producing carbonate-containing compositions comprising little or no silicon-based material. In such methods, silicon-based material (e.g., silica, unreacted or undigested silicates, aluminosilicates, etc.) may be separated and processed separately from carbonate-containing compositions. Silicon-based material and carbonate-containing material may be blended at a later stage to produce a pozzolanic material, which may be further processed and blended with, for example, Portland cement.