This collection of papers was solicited from a variety of educators in an effort to provide direction to teachers, curriculum developers and textbook publishers on topics in mathematics education that are consistently mentioned in recent national reports and study groups. The consensus of reports sponsored by various professional associations suggests the topics addressed in this document. It contains papers on: (1) mathematics content; (2) geometry at the middle school level; (3) probability and statistics at the middle school level; (4) the inclusion of number theory in the mathematics curriculum; (5) estimation and mental computation; (6) problem solving; (7) mental images and visual thinking; (8) the role of technology in mathematics education; and (9) the development of teachers' conceptualization of mathematics. Because many of the professional groups addressing these topics have had difficulty in establishing definitions and directions for teachers, this document is an effort to address each topic as it would (should or could) appear in textbooks for students moving from arithmetic to algebra. (TW)