The papers contained in this document were originally presented at the May 1978 conference on Modeling Mathematical Cognitive Development sponsored by the Models of Learning Mathematics Working Group of the Georgia Center for the Study of Learning and Teaching Mathematics. Most have been revised to reflect comments and suggestions made at the meeting. The view of models presented includes the thinking of representatives of psychology, science, educational psychology, and philosophy, as well as mathematics educators. The efforts of those outside of mathematics education towards modeling as represented in this work are seen to be of great assistance in moving towards better models. Individual papers are titled: (1) What is a Model? Modeling and the Professions; (2) The Conception and Perception of Number; (3) Cognitive Microanalysis: An Approach to Analyzing Intuitive Mathematical Reasoning Processes; (4) An Information Processing Approach to Research on Mathematics Learning and Problem Solving; and (5) Reflections of Interdisciplinary Research Teams. Reactions to the first four titles are included. (MP)