Three addresses by internationally renowned mathematics researchers and a fourth paper on the role of research are presented. Each of the addresses focuses on the learning process, but from different points of view. Heinrich Bauersfeld provides an analysis of the miscommunication inherent in many teacher-student interactions. Four deficient areas of research are discussed. Efraim Fischbein directs attention to the role of intuition in learning. Hans Freudenthal traces the growth of number and geometry ideas in one child. The fourth paper, by Richard Lesh, identifies four problem areas needing research. (Author/MK)