This document was initiated with the collection of 150 questions in telephone interviews of a national sampling of junior high school and high school teachers. A Mathematics Consultant Panel reviewed the questions, and selected topics were developed, for which there were research bases for answers. The material covers: (1) Effective Mathematics Teaching; (2) Individual Differences Among Mathematics Learners; (3) Communicating Mathematics; (4) Breaking Vicious Cycles: Remediation in Secondary School Mathematics; (5) Problem Solving: The Life Force of Mathematics Instruction; (6) Estimation: A Prerequisite for Success in Secondary School Mathematics; (7) The Calculator: An Essential Teaching Aid; (8) Understanding Fractions: A Prerequisite for Success in Secondary School Mathematics; (9) The Learning and Teaching of Algebra; (10) The Learning and Teaching of Geometry; and (11) The Path to Formal Proof. The document includes a 13-page bibliography. The document is set up so that each chapter may be read independently. Each begins with a question from a teacher, and the answer is constructed so that research information and classroom implications are clear. It is felt the material is of obvious use for individual study, and will prove useful for both pre- and in-service courses. It is hoped that teachers will take seriously the numerous invitations to replicate or validate the research cited. (MP)