Research on mathematics instruction is reviewed in order to respond to two questions: (1) Has the influx of talented people who have entered the mathematics instruction field over the last three decades changed anything? and (2) Will any of the work being done actually improve mathematics instruction? The different ways in which parents, students, teachers, non-teaching professionals, and other groups perceive and use mathematics is discussed to illustrate the sometimes conflicting views of mathematics and how these views affect instruction. Ten statements, based on analysis of research on diagnosis and evaluation in mathematics, are discussed: (1) Schools mostly teach rote aspects of mathematics and neglect strategy, analysis, heuristics, decision making, intuition, flexibility, and creativity; (2) Typical students are creative and can be resourceful in mathematics if appropriately taught; (3) Most instructional programs do not recognize students' creativity; (4) Students are confused about mathematics; (5) Complex mathematical ideas can be taught through building upon previous learning; (6) Consistent errors signal misunderstanding; (7) Representations determine problem-solving ability; (8) Students solve problems through stimulus-response; (9) Mental tasks in mathematics are diverse; and (10) Many students can learn substantially more mathematics than they presently do. (CJ)