Advances the idea that performance errors should contribute positively to the process of learning. Argues that errors do not occur randomly and that instructional theory should not condemn errors, but seek them. (PK)

Views on the need for a theory of mathematics education concern three interrelated components: meta-research and development of meta-knowledge on mathematics education as a discipline, development of a comprehensive view of mathematics education using a systems approach, and development of the dynamic regulating role of mathematics education. (MNS)

An overview to a session at the Fifth International Congress on Mathematical Education is given. Papers on research by Cooney, curriculum development by Goffree, reform in mathematics education by Stephens, and a summary by Nickson are included. (MNS)

The kaleidoscope is presented as a suitable topic for a preservice mathematics teacher's first contact with a nontrivial mathematical phenomenon. Included are historical notes on the kaleidoscope, explanation of the inner mechanisms of various kaleidoscope designs, and suggestions for further student investigations. (JJK)