Recent research on solving addition and subtraction word problems has resulted in the construction of theoretical models of children's problem-solving processes. Some of these models have been translated into computer programs. Characteristics and predictions of the theoretical analysis developed by Riley, Greeno, and Heller (1983) are discussed in this paper, and tested in a study with 30 first graders. They were administered a series of Piagetian, memory, and counting tasks, plus eight addition and subtraction word problems, in interviews conducted with individuals three times during the 1981-82 school year. Six student protocols are included to illustrate the findings. A number of results confirm several predictions and implications of the computer mode. However, some important findings are not in agreement with these models. These specific findings, concerning answer patterns, appropriate problem representations, correct solution strategies, and the nature of errors, are discussed. (MNS)