This document is the second of three related volumes. They present the rationale, background, and framework for a comprehensive monitoring system being developed for the National Science Foundation. The system is being designed to gather information about the effects of national, state, and local policy actions designed to change the teaching and learning of mathematics in the schools of America. The papers included were produced by project staff, commissioned, or reprinted from previous works. Expert reviews and critiques of sets of papers are included. In this volume the implications of psychology to the learning of mathematics is addressed, and the problems of assessing learning based on both the new mathematical fundamentals and knowledge of learning are examined. Part 1, related to implications from psychology, summarizes advances in cognitive psychology, research on intrinsic motivation, the role of intuition, as well as a synthesis of psychological research in relation to curriculum engineering. Part 2 begins to address the issue of determining a reasonable approach to assessing the outcomes of instruction in mathematics due to shifts in emphasis related to recent reforms. (PK)