Teachers. Students learn best from teachers with strong content knowledge and pedagogical skills. Lack of access to high-quality teachers may preclude some students, especially minorities and those living in poverty, from pursuing advanced study. All 50 states require licensing of public school teachers; none requires special certification for those providing advanced study. High school teachers see themselves as subject area specialists. They teach up to 175 students per day, and have little opportunity to work with colleagues to improve curriculum or instruction. They frequently cite inadequate support, lack of student motivation, and student discipline problems as reasons for leaving teaching.

Coordination. Academic preparation for advanced study begins in middle school. Mathematics and science courses in these grades often lack focus, cover too many topics, repeat material, and are implemented inconsistently. In mathematics, states are moving toward offering algebra in eighth grade. Increasing numbers of middle schools are instituting integrated science curricula that de-emphasize disciplines. Middle and high school teachers rarely have opportunities to coordinate curricula or instruction for grades 7–12.

Curricular Differentiation. More than 80 percent of middle schools and many high schools direct or allow students to choose their classes in mathematics, science, and other subjects. Other schools offer core curricula that are narrowly focused on academic subjects and allow students few choices. Early differential placement steers some students away from rigorous academic programs. Research indicates that constrained curricula are more effective and equitable in helping students pursue advanced study.

Sequencing. The typical progression of courses in high school mathematics leading to calculus is Algebra I, geometry, Algebra II, trigonometry, and precalculus. Most state high school graduation requirements also include 2 years of science, although college-bound students traditionally take more, usually biology, chemistry, and then physics.

Standards. In science, standards developed by the American Association for the Advancement of Science and the National Research Council call for increased emphasis on inquiry and in-depth study of fewer topics. In mathematics, the standards from the National Council of Teachers of Mathematics emphasize learning of concepts and helping students understand mathematics more deeply. Forty-nine states have developed standards and

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