This document contains final versions of papers that were conference contributions. This second conference, held in September 1978, was attended by 70 participants from 11 countries. Lectures were presented under the following five main sections: (1) Acquisition of Arithmetical Concepts; (2) The Learning of Generalization and Proof; (3) Interpersonal Aspects of Classroom Communication; (4) The Nature of Mathematical Thinking; and (5) Intuitive and Reflective Processes in Mathematics. The materials presented here are organized alphabetically. Whenever a particular contribution was presented under one of the five themes noted above, the number of this theme section is indicated in brackets in the contents list. The document opens with a brief discussion of the conference and provides some rationale and description of each of the five lecture categories. The bulk consists of individual papers. The material concludes with an alphabetized listing of conference participants. (MP)