1. There are three Critical Foundations of Algebra: conceptual understanding, computational fluency, and problem-solving skills.
2. State curriculum standards, textbooks, and end-of-course assessments should focus on specific, identified Major Topics of School Algebra (see report for specifics).
3. By the end of Grade 7, students should master 11 benchmarks associated with three distinct clusters of concepts and skills: fluency with whole numbers, fluency with fractions, and particular aspects of geometry and measurement.
4. When introductory algebra teachers were surveyed about students’ mathematics preparation, the teachers reported students’ backgrounds as weak, especially in (1) rational numbers and operations involving fractions and decimals and (2) solving word problems.
5. Internationally, high achievement is associated with teaching for proficiency in a few topics; U.S. math instruction should follow a coherent progression and avoid revisiting topics year after year.
6. All school districts should ensure that students are prepared for and have access to an authentic (i.e., aligned with the Major Topics mentioned above) algebra course by Grade 8.
7. Many textbooks and curriculum materials are not mathematically accurate; publishers need to ensure accuracy.
8. Teacher education programs and licensure tests need to incorporate the Critical Foundations and Major Topics mentioned above.
9. Many teachers, especially in rural areas, have limited options for improving their practice. Developing teacher leaders can be a powerful strategy for improving mathematics teaching and learning, especially in resource-poor school districts.
10. Improving math achievement for students—even in high-poverty schools—can be accomplished through active district-school partnerships that focus on using data and building teachers’ knowledge and skills. These partnerships can include local or regional colleges and universities.
*Items 1 to 8 are from Chapter 3: Report of the Task Group on Conceptual Knowledge and Skills in Foundations for Success from The Final Report of the National Mathematics Advisory Panel (2008, U.S. Department of Education), available online at
www.ed.gov/about/bdscomm/list/mathpanel/report/conceptual-knowledge.pdf.
Items 9 and 10 are from A Legacy of Leadership and Lessons Learned: Results From the Rural Systemic Initiatives for Improving Mathematics and Science Education (2007, Edvantia), available online at www.edvantia.org/products/pdf/rsi_report_0706.pdf.
