1 year of geometry. Many districts and even some states have made it a goal that all students take algebra I by the 8th grade.

U.S. students are not yet, as a group, meeting the higher expectations of recent years. Trends in student achievement in mathematics, as measured by the National Assessment of Educational Progress (NAEP), have shown considerable improvement since 1990, but the 2009 results showed that just 39 percent of 4th graders and 34 percent of 8th graders are performing at or above the proficient level (National Center for Education Statistics, 2009). In the mathematics portion of the Third International Mathematics and Science Study (TIMSS), U.S. 4th and 8th graders scored above the median, but the nation was not among the top-performing nations (Gonzales et al., 2008). A 1998 comparison of the performance of older students showed that U.S. students were among the lowest performing group of the 21 nations in the study (National Center for Education Statistics, 1998).

At the same time, considerable evidence indicates that many teachers, especially in grades K-8, are not well prepared to teach challenging mathematics. The time allotted for mathematics content in the preparation of many elementary and middle school teachers is unlikely to be adequate, and many secondary school mathematics teachers (including those in the middle grades who are prepared as specialists) may also be receiving training that does not prepare them to teach advanced-level mathematics (e.g., algebra, geometry, and trigonometry). Mathematics teachers may also need specific preparation for the challenge of teaching mathematics in ways that engage all students and gives them a chance to succeed. Moreover, many of those who teach mathematics in U.S. secondary schools, especially in poor and underserved communities, lack appropriate certification and adequate content preparation. These concerns have been evident for a long time, and their persistence underscores the importance of assessing the status of the preparation of mathematics teachers.1

This chapter is organized as was the preceding one, beginning with a brief overview of the research base and then turning to our four key questions:

  1. What do successful students know about mathematics?

  2. What instructional opportunities are necessary to support successful students?

  3. What do successful teachers know about mathematics and how to teach it?


When possible, we have addressed the differing needs of K-8 teachers of mathematics and secondary mathematics teachers, but we note that much of the literature focuses on the teachers of younger students.

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