Authorizes the Secretary of Education to award such grants if the applicant LEAs: (1) reduce class and school sizes for their public elementary and secondary schools to specified limits for various grade levels; (2) terminate the practice of social promotion in their public schools; (3) require that students be subject to State achievement standards in the core curriculum at key transition points, to be determined by the State, for all kindergarten through grade 12 students; (4) use tests and other indicators, such as grades and teacher evaluations, to assess student performance in meeting State achievement standards; (5) provide remedial education for students who fail to meet State achievement standards, including tutoring, mentoring, and summer and before- and after-school programs; and (6) provide equal matching funds from non-Federal sources.