The Components of Number Sense

Ball D. L. (1990). Elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education, 21(2), 132–144.

Ball D. L. (1992, Summer). Magical hopes: Manipulatives and the reform of math education. American Educator, 16, 14–18, 46–47.

Ball D. L. (2008). Implications for special education on teaching math. Retrieved February 24, 2009, from The Council for Exceptional Children Web site: CEC.sped.org.

Ball D. L. Cohen D. (1996). Reform by the book: What is—or might be—the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), 6–8, 14.

Baxter J. A. Woodward J. Olson D. (2001). Effects of reform-based mathematics instruction on low achievers in five third-grade classrooms. Elementary School Journal, 101(5), 529–548.

Cain C. Doggett M. Faulkner V. Hale C. (2007). The Components of Number Sense. Raleigh, NC: NC Math Foundations Training, Exceptional Children's Division of the North Carolina Department of Public Instruction (NCDPI).

Carpenter T. P. Franke M. L. Levi L. (2003). Thinking mathematically: Integrating arithmetic & Algebra in elementary school. Portsmouth, NH: Heinemann.

Dehaene S. (1997). The number sense: How the mind creates mathematics. New York: Oxford University Press.

Deizmann C. M. English L. D. (2001). Promoting the use of dioramas as tools for thinking. In Cuoco A. A. (Ed.), The roles of representation in school mathematics (pp. 77–89). Reston, VA: National Council of Teachers of Mathematics.

Garet M. S. Porter A. C. Desimone L. Birman B. F. Yoon Suk K. (2001). What makes professional development effective: Results from a national sample of teachers. American Educational Research Journal, 38(4), 915–945.

Gersten R. Clarke B. S. Jordan N. C. (2007). Screening for mathematics difficulties in K-3 students. Portsmouth, NH: Center on Instruction. Available from www.centeroninstruction.org/index.cfm.

Gersten R. Ferrini-Mundy J. Benbow C. Clements D. H. Loveless T. Williams V. (2008). Report of the Task Group on Instructional Practices. In U.S. Department of Education (ED), National Mathematics Advisory Panel: Report of the task groups and subcommittees (section 6; pp. 1–201). Washington, DC: Education Publications Center.

Gersten R. Jordan N. C. Flojo J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38(4), 293–304.

Gonzalez P. Guzman J. C. Partelow L. Pahlke E. Jocelyn L. Kastberg D. (2004). Highlights from the Trends in International Mathematics and Science Study (TIMSS) 2003 (NCES Report No. 2005–005). Washington, DC: U.S. Government Printing Office.

Griffin S. (2003). The development of math competence in the preschool and early school years: Cognitive foundations and instructional strategies. In Royer J. M. (Ed.), Mathematical cognition (pp. 1–32). Amherst, MA: Information Age.

Griffin S. (2004). Teaching number sense. Educational Leadership, 61(5), 39.

Hiebert J. Stigler J. W. (2000). A proposal for improving classroom teaching: Lessons from the TIMSS video study. Elementary School Journal, 101(1), 3–20.

Hill H. C. Rowan B. Ball D. L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.

Kalchman M. Moss J. Case R. (2001). Psychological models for the development of mathematical understanding: Rational numbers and functions. In Carver S. M. Klahr D. (Eds.), Cognition and instruction. Mahwah, NJ: Lawrence Erlbaum.

Knuth E. (2002). Teachers' conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teacher Education, 5(1), 61–88.

Lemke M. Sen A. Pahlke E. Partelow L. Miller D. Williams T. (2004). International outcomes of learning in mathematics literacy and problem solving: PISA 2003 results from the U.S. perspective (NCES Report No. 2005–005). Washington, DC: U.S. Government Printing Office.

Lesh R. Post T. R. Behr M. (1988). Proportional reasoning. In Hiebert J. Behr M. (Eds.), Number concepts and operations in the middle grades (pp. 93–118). Reston, VA: National Council of Teachers of Mathematics.

Ma L. (1999). Knowing and teaching elementary mathematics: Teachers understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum.

National Center for Education Statistics. (1999). Highlights from TIMSS: Overview and key findings (NCES Report No. 1998–081). Washington, DC: Author.

National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press.

Post T. R. (1991). Intermediate teachers' knowledge of rational number concepts. In Fennema E. Carpenter T. P. Lamon S. (Eds.), Integrating research on teaching and learning mathematics (pp. 177–198). Albany, NY: SUNY Press.

Stigler J. W. Hiebert J. (2004, February). Improving mathematics teaching. Educational Leadership, 61(5), 12–17.