This book is intended for everyone in California concerned about how well students are prepared for college. It describes the competencies in mathematics necessary for success in college and university work. This statement discusses the following: (1) an emphasis on encouraging students to experience the beauty and fascination of mathematics; (2) stress on building students' confidence in their reasoning power; (3) insistence on developing analytic reasoning ability; (4) advocacy of students' application of the concepts of algebra and geometry to the solution of unfamiliar problems; (5) recognition of the importance of students' developing complete understanding as a way of building their confidence in mathematics; (6) a call for students to have a history of successful experiences in finding solutions when encountering new mathematical situations; (7) stress on the need for students to discuss and write about mathematical ideas; and (8) an elaboration of appropriate uses of calculators. The book is divided into four parts: (1) "Expectations for Entering Freshman"; (2) "Prerequisites to Algebra 1"; (3) "Course Outlines for Algebra 1, Geometry, and Algebra 2"; and (4) "Outlines for Advanced Courses in Mathematics." The appendixes include: sample problems; competencies in speaking, listening, reasoning, and studying; the recommendation of the Board of Governors; and a discussion of the problems with calculus at the high school level. (KR)