Fig. 1.

Training protocol and sample tutoring materials. (a) Before training, children completed a WJ-III math fluency test, a strategy assessment, and received an introductory lesson for addition problem solving. Training sessions were spread across five days within a week and consisted of a variety of activities for solving 14 problems in the training set. The number of exposures to each problem in each activity is reported in parenthesis. Each problem was presented 14 times per day, and 70 times over the training period. At the end of training, children’s problem-solving strategies for trained and novel problems were reassessed. After training, children completed a fMRI task that involved solving trained and novel problems in the scanner. This was followed by a recognition memory task, outside of the scanner, in which children were asked to discriminate between problems they have practiced during tutoring and those they saw in the fMRI task. The type of problems presented at each stage are indicated below the training protocol. (b) Sample materials used in the tutoring. In flash cards, children verbally produced an answer to trained problems presented on a physical flash card. The tutor proceeded to the next problem once a correct answer was provided. Children completed untimed flash cards without a timer. In timed flash cards, the tutor marked the time children spent in each of three rounds (each round: full deck of trained problems) on a sailboat. Children were instructed to try to beat their previous time(s). In computerized flash cards, children typed in their answer to trained problems and received feedback on their response. In treasure hunt, children placed physical cards with trained problems on numbers corresponding to the answers in a ‘treasure map.’ Upon completion of all tutoring activities, children filled a treasure board and received a prize. (c) Sample lesson presented during tutoring. At pre-training and on training days 1–3, children reviewed a break-apart strategy with the problems in the training set and were encouraged to solve them using a method of their choice. On training days 4–5, children were asked to retrieve answers directly from memory whenever possible.