Part of the Advances in Mathematics Education book series (AME)
Developing Algebraic Thinking in the Context of Arithmetic
Using classroom episodes from grades 2–6, this chapter highlights four mathematical activities that underlie arithmetic and algebra and, therefore, provide a bridge between them. These are:
Analysis of each episode provides insight into how teachers recognize the opportunities to pursue this content in the context of arithmetic and how such study both strengthens students’ understanding of arithmetic operations and enables them to develop ideas foundational to the study of algebra.
understanding the behavior of the operations,
generalizing and justifying,
extending the number system, and
using notation with meaning.
KeywordsNumber Line Number System Distributive Property Negative Number Mathematical Activity
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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- Behr, M. J., Erlwanger, S., & Nichols, E. (1980). How children view the equals sign. Mathematics Teaching, 92, 13–15. Google Scholar
- Blanton, M. (2008). Algebra and the Elementary Classroom. Portsmouth, NH: Heinemann. Google Scholar
- Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School. Portsmouth, NH: Heinemann. Google Scholar
- Harel, G., & Sowder, L. (1998). Students’ proof schemes. In E. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), Research on Collegiate Mathematics Education (Vol. III, pp. 234–283). Providence: AMS. Google Scholar
- Harel, G., & Sowder, L. (2007). Toward a comprehensive perspective on proof. In F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning. Reston, VA: National Council of Teachers of Mathematics. Google Scholar
- Kaput, J., & Sims-Knight, J. (1983). Errors in translations to algebraic equations: Roots and implications. Focus on Learning Problems in Mathematics, 5(3–4), 63–78. Google Scholar
- Kaput, J., Carraher, D., & Blanton, M. (Eds.) (2008). Algebra in the Early Grades. New York: Lawrence Erlbaum Associates. Google Scholar
- Kieran, E. J., Slaughter, Ml., Choppin, J., & Sutherland, J. (2002). Mapping the conceptual terrain of middle school students’ competencies in justifying and proving. In D. Mewborn, P. Sztajn, D. Y. White, H. G. Wiegel, R. L. Bryant, & K. Noney (Eds.), Proceedings of the 24 th Meeting for PME-NA, Athens, GA (Vol. 4, pp. 1693–1700). Google Scholar
- Russell, S. J., & Vaisenstein, A. (2008). Computational fluency: working with a struggling student. Connect, 22(1), 8–12. Google Scholar
- Russell, S. J., Economopoulos, K., Wittenberg, L., et al. (2008). Investigations in Number, Data, and Space (2nd ed.). Glenview, IL: Scott Foresman. Google Scholar
- Schifter, D. (2009). Representation-based proof in the elementary grades. In D. A. Stylianou, M. Blanton, & E. Kieran (Eds.), Teaching and Learning Proof Across the Grades: A K-16 Perspective. Oxford: Routledge—Taylor Francis and National Council of Teachers of Mathematics. Google Scholar
- Schifter, D., Bastable, V., & Russell, S. J. (1999). Developing Mathematical Ideas. Number and Operations, Part 1: Building a System of Tens Video. Parsippany, NJ: Dale Seymour Publications. Google Scholar
- Schifter, D. V., Bastable, V., & Russell, S. J. (2008a). Developing Mathematical Ideas. Number and Operations, Part 3: Reasoning Algebraically about Operations. Parsippany, NJ: Dale Seymour Publications. Google Scholar
- Schifter, D., Bastable, V., & Russell, S. J. (2008b). Developing Mathematical Ideas. Patterns, Functions, and Change. Parsippany, NJ: Dale Seymour Publications. Google Scholar
- Schifter, D., Monk, S., Russell, S. J., & Bastable, V. (2008c). Early algebra: What does understanding the laws of arithmetic mean in the elementary grades. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the Early Grades (pp. 413–447). New York: Lawrence Erlbaum Associates. Google Scholar
- Schifter, D., Russell, S. J., & Bastable, V. (2009). Early algebra to reach the range of learners. Teaching Children Mathematics, 16(4), 230–237. Google Scholar
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