Outlines a model of mathematical understanding as a whole, dynamic, nonlinear, recursive growing process, entailing "folding back" for the reconstruction of inner level knowing. Presents examples from seventh graders' work. Discusses teacher awareness of student level of understanding, and implications for development of mathematics…

Issues concerning student intellectual development during college are considered in a symposium paper and in two reactions by faculty members. The symposium was sponsored by Bowling Green State University as part of the Academic Outcomes Project, which explores the effect of college on student growth and development. The reflective judgment model…