National Council of Teachers of Mathematics. (2000). *Principals and standards for school mathematics*. Reston, VA: Author. Available at http://www.nctm.org/standards/content.aspx?id=16909

This document from the National Council of Teachers of Mathematics lists a) the principles that should guide decisions made by teachers and school administrators related to mathematics curriculum, and b) the algebra standards across grade spans, K-12.

California Department of Education. (1999). *Mathematics content standards for California public schools: Kindergarten through grade twelve*. Sacramento, CA: Author. Available at http://www.cde.ca.gov/be/st/ss/documents/mathstandards.pdf

This document provides the academic content standards in mathematics for California PubliSchools, K-12, adopted by the California State Board of Education in December 1997.

Reys, B.J., Dingman, S., Olson, T.A., Sutter, A., Teuscher, D., Chval, K., Lappan, G., Larnell, G.V., Newton, J., Ok-Kyeong, K., & Kasmer, L. (2006). *The intended mathematics curriculum as represented in state-level curriculum standards: Consensus or confusion?* Greenwich, CT: Information Age Publishing, Inc. Available at http://www.mathcurriculumcenter.org/st_std_exec_sum.pdf

This report by the Center for the Study of Mathematics Curriculum examines in detail the mathematics learning goals specified for each grade level, K-8, across all states in the U.S. Researchers examined the extent to which there is consistency across state documents on when students should master particular skills. For algebra instruction, they found substantial variation across states in the grade levels at which K-8 students focus on particular topics. The report offers a series of recommendations for those engaging in the development of grade-level specifications, including limiting learning goals at each grade level to deepen learning and collaborating across states to build consensus on mathematics standards for each grade level.

** Schifter, D., Bastable, V., Russell, S.J., Seyferth, L., & Riddle, M. (2008). Algebra in the grades K-5 classroom: Learning opportunities for students and teachers. In Greens, C.E., & Rubenstein, R. (Eds.), Algebra and algebraic thinking in school mathematics (pp. 263-277). Reston, VA: The National Council of Teachers of Mathematics, Inc. Available for purchase at http://www.nctm.org/store/Products/70th-Yearbook--Algebra-and-Algebraic-Thinking-in-School-Mathematics-Chapter-19-(PDF-Downloads)/

In this chapter, the authors explore how early algebraic thinking can be introduced into grade K-5 classrooms. Using data from two classroom case studies, the authors argue that as children learn about basic operations (understanding the operation of models, sorting out the different representations, and figuring out how to compute), they “observe and comment on regularities in the number system.” The recognition of these patterns becomes the foundation for “formulating, testing, and proving generalizations”- the practices that define early algebra. Finally, the authors present evidence from a professional development seminar to illustrate how teachers can develop the knowledge and skills needed to support early algebraic reasoning.

Paek, P. L. (2008, January). Intensive mathematics program: Grant High School. Case study from *Practices worthy of attention: Local innovations in strengthening secondary mathematics*. Austin, TX: Charles A. Dana Center at the University of Texas at Austin. Available at http://www.utdanacenter.org/pwoa/downloads/grant.pdf

This profile highlights an intensive mathematics program that involves giving students double periods of mathematics for two years. In the two years of study, students complete three years’ worth of mathematics—Pre-Algebra, Algebra I, and Geometry. (This description is part of a compilation of “*Practices Worthy of Attention*,” a joint initiative of Achieve, Inc. and the Charles A. Dana Center.)

**This document is considered a priority reading.