Provided is an examination of the methodology used to study the problems of learning addition and subtraction skills used by developmental researchers. The report has sections on categories of theory and their methodologies, which review: (1) Behaviorist, Neo-Behaviorist and Piagetian Theories; (2) the Behaviorist and Piagetian Paradigms; (3) Soviet Studies, Constructivism, and Teaching Experiment; and (4) Artificial Intelligence, Information Processing, and Computer Simulation. A summary section draws together the discussions of the report by suggesting the need to make a global distinction between two categories of theory. A new model of intelligence is offered as an alternative to the psychometric group of models that dominate the field. The document concludes with some notes on the terminology used and references. (MP)