This monograph represents an effort to build upon and extend beyond the literature on school mathematics as discussed in "Mathematics and Science: Critical Filters for the Future." Three significant changes in the political and educational landscape since 1985 are discussed. The first change is the introduction of mathematics standards to the education community. The role of standards in educational practice and policy making has gained traction, and today dominates discourse related to school mathematics and other subjects. A second change is a movement calling for educational leadership to more directly address issues of learning and teaching in schools. Significant changes are taking place in the ways the constructs of teaching and learning are now being defined by researchers, practitioners, and policymakers. Instructional leadership requires an in-depth understanding of research and development. Many state and federal policies now require school district instructional leadership to document the research base underlying local change strategies. This represents a new demand on those charged with district-wide and school-level improvements. A third and related change in the educational landscape is the No Child Left Behind Act of 2001 (NCLB), which calls for a new level of accountability by requiring each state to implement accountability systems covering all public schools and public school students. These systems must be based on rigorous state standards in mathematics, annual testing for all students in grades 3-8, and annual statewide progress objectives ensuring that all groups of students reach established levels of mathematical proficiency within 12 years. Setting rigorous state standards and related accountability models is placing significant pressure on school districts to rethink past practice and to look for effective and sound strategies to support the teaching and learning of mathematics. This monograph advocates that calls for rigorous standards require thoughtful action and planning, and that the building blocks for engineering mathematical progress in any school are time, quality, and design. If educators are eager to listen, open to a variety of educational solutions, never content with just trial and error methods, and pressed to know why a method works with students, they represent the type of teachers and instructional leaders who can engineer changes in mathematics education. Two appendices are included. (Contains 15 footnotes, 6 figures and 5 tables.) [For original monograph, see ED338758.]