Computations underlying cognitive strategies in human motor learning are poorly understood. Here we investigate such strategies in a common sensorimotor transformation task. We show that strategies assume two forms, likely reflecting distinct working memory representations: discrete caching of stimulus-response contingencies, and time-consuming parametric computations. Reaction times and errors suggest that both strategies are employed during learning, and trade off based on task complexity. Experiments using pressured preparation time further support dissociable strategies: In response caching, time pressure elicits multi-modal distributions of movements; during parametric computations, time pressure elicits a shifting distribution of movements between visual targets and distal goals, consistent with analog re-computing of a movement plan. A generalization experiment reveals that discrete and parametric strategies produce, respectively, more localized or more global transfer effects. These results describe how qualitatively distinct cognitive representations are leveraged for motor learning and produce downstream consequences for behavioral flexibility.