A key goal in cognitive training research is understanding whether cognitive training enhances general cognitive capacity or provides only task-specific improvements. Here, we developed a quantitative model for describing the temporal dynamics of these two processes. We analyzed data from 1300 children enrolled in an 8 week working memory training program that included 5 transfer test sessions. Factor analyses suggested two separate processes: an early task-specific improvement, accounting for 44% of the total increase, and a slower capacity improvement. A hidden Markov model was then applied to individual training data, revealing that the task-specific improvement plateaued on the third day of training on average. Thus, training is not only task specific or transferable but a combination of the two. The models provide methods for quantifying and separating these processes, which is crucial for studying the effects of cognitive training and relating these effects to neural correlates.