Resumen

Six widely used US Grade 1 curricula do not adequately address the following three developmental prerequisites identified by a proposed learning trajectory for the meaningful learning of the subtraction-as-addition strategy (e.g., for 13 – 8 think “what + 8 = 13?”): (a) reverse operations (adding 8 is undone by subtracting 8); (b) common part-whole relations (5 + 8 and 13 – 8 share the same whole 13 and parts 5 and 8); and (c) the complement principle in terms of part-whole relations (if parts 5 and 8 make the whole 13, then subtracting one part from the whole leaves the other part).