Algebra in the Elementary Grades: A Bibliography

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.

Developing Mathematical Ideas (DMI) -- DMI is a professional development curriculum designed to help teachers think through the major ideas of K-7 mathematics and examine how children develop those ideas. At the heart of the materials are sets of classroom episodes (cases) illustrating student thinking as described by their teachers. In addition to case discussions, the curriculum offers teachers opportunities: to explore mathematics in lessons led by facilitators; to share and discuss the work of their own students; to view and discuss videotapes of mathematics classrooms; to write their own classroom cases; to analyze lessons taken from innovative elementary mathematics curricula; and to read overviews of related research.

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.