This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the Institute for Mathematical Studies in the Social Sciences and delivered to students in schools in a computer-assisted-instruction mode. Probabilistic automata were defined and tested for basic addition, subtraction, and multiplication exercises. Results of detailed application of the register machine models are unpublished and will appear subsequent to the date of this final report. The results of analyses indicate that the kinds of models developed can be applied to learning and performance in elementary mathematics, and have implications for detailed pedagogical procedures of instruction in these basic skills. (Author/DT)