Ball, D.L, & Bass, H. (2003). Making mathematics reasonable in school. In J. Kilpatrick, W.G. Martin, & D. Schifter. A Research Companion to Principles and Standards for School Mathematics (pp. 27-44). Reston, VA: National Council of Teachers of Mathematics.
Blanton, M.L. & Kaput, J.J. (October 2003). Developing Elementary Teachers’ “Algebra Eyes and Ears”. Teaching Children Mathematics, (10)2, 70-77. (Available with NCTM membership.)
Blanton, M.L., Schifter, D., Inge, V., Lofgren, P., Willis, C., Davis, F. & Confrey, J. (2007). Early Algebra. In V.J. Katz (Ed.). Algebra: Gateway to a Technological Future (pp. 7-14). Washington, D.C.: The Mathematical Association of America.
Carpenter, T.P., Franke, M.L. & Levi, L. (2003). Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School. Portsmouth, NH: Heinemann.
Greenes, C.E. & Rubenstein, R. (Eds.). (2008). Algebra and Algebraic Thinking in School Mathematics: 70th Yearbook. Reston, VA: National Council of Teachers of Mathematics. This book includes the following chapter:
Schifter, D., Bastable, V., Russell, S.J., Seyferth, L. & Riddle, M. Algebra in the Grades K-5 Classroom: Learning Opportunities for Students and Teachers. Pages 263-277.
Kaput, J.J., Carraher, D.W. & Blanton. M.L. (Eds.) (2008). Algebra in the Early Grades. New York: Lawrence Erlbaum Associates. This book includes the following chapters:
Bastable, V. & Schifter, D. Classroom Stories: Examples of Elementary Students Engaged in Early Algebra. Pages 165-184.
Carraher, D.W., Schliemann, A.D. & Schwartz, J.L. Early Algebra Is Not the Same as Algebra Early. Pages 235-272.
Schifter, D., Monk, S., Russell, S.J., & Bastable, V. Early Algebra: What Does Understanding the Laws of Arithmetic Mean in the Elementary Grades? Pages 413-447.
Tierney, C. & Monk, S. Children's Reasoning about Change over Time. Pages 185-200.
Moses, R.P. & Cobb, C.E. (2002). Radical Equations: Civil Rights from Mississippi to the Algebra Project. Boston, MA: Beacon Press.
National Council of Teachers of Mathematics. (2000). The Algebra Strand, Pre-K-2 and 3-5. Principles and Standards in School Mathematics. Reston, VA: National Council of Teachers of Mathematics. Pages 37-40, 90-95, and 158-163.
Russell, S.J., Schifter, D. & Bastable, V. (January/February, 2006). Is It 2 More or Less? Algebra in the Elementary Classroom. Connect, Volume 19, Issue 3, 1-3.
Russell, S.J., & Vaisenstein,
A. (September/October 2008).
Computational fluency:
Working with a struggling
student. Connect,
Volume 22, Issue 1, 8-12.
Schifter, D. (1999). Reasoning
about Operations: Early
Algebraic Thinking, Grades
K through 6. In L. Stiff
and F. Curio (Eds.) Mathematical
Reasoning, K-12: 1999 NCTM
Yearbook. Reston,
VA: National Council of
Teachers of Mathematics.
Pages 62-81.
Schifter, D. (forthcoming). Representation-Based Proof in the Elementary Grades. In Stylianou, D.A., Blanton, M. & Knouth, E. (Eds.). Teaching and Learning Proof Across the Grades. Routledge – Taylor Francis and National Council of Teachers of Mathematics.
Schweitzer, K. (2006). Teacher as Researcher: Research as a Partnership. In S.Z. Smith & M.E. Smith (eds.) Teachers Engaged in Research: Inquiry into Mathematics Classrooms, Grades Pre-K-2 (pp. 69-94). Greenwich, CT: Information Age Publishing.
Algebra in the Elementary Grades: Other Resources
The Algebra Project -- Developed by mathematician and civil rights leader, Bob Moses, The Algebra Project is an interactive curriculum designed to provide "inner-city" and rural students with a better understanding of abstract mathematical concepts. It uses physical surroundings as tangible references for mathematical ideas.Two modules address algebra in the elementary classroom:
Schifter, D., Bastable, V. & Russell, S.J. (2008). Developing Mathematical Ideas. Patterns, Functions, and Change. Casebook, Facilitator's Guide, and DVD. Parsippany, NJ: Pearson Learning Group.
Schifter, D., Bastable, V. & Russell, S.J. (2008). Developing Mathematical Ideas. Reasoning Algebraically about Operations. Casebook, Facilitator's Guide, and DVD. Parsippany, NJ: Pearson Learning Group.
