This resource book represents shared experiences of Project LINCS' (Lead teachers INvolved in making ConnectionS) teachers and staff in addressing the question, "Are we teaching mathematics so that all students will be empowered to use it flexibly, insightfully, and productively?" and other fundamental questions that are driving change in school mathematics. These questions affect: (1) the mathematics that middle school students learn; (2) the way the curriculum is organized; (3) the way students learn mathematics; (4) the roles of teachers; and (5) the climate and activities of our mathematics classrooms. The major portion of this resource book is devoted to sharing sample activities to assess, build on, and nurture student understanding and progress toward important mathematical goals. The teaching ideas are grouped under the major categories of algebra, alternative assessment, cooperative learning groups, geometry, number and computation sense, probability and statistics, problem solving, and writing to nurture and communicate understanding. Sample activities contain information to help teachers and students to focus, explore, disucss and reflect, and extend the activities. Each section contains references. (MKR)