Developing algebraic reasoning in the elementary school

Understanding Mathematics and Science Matters

Volumn , Issue , 2005, Pages 81-98

  Carpenter, Thomas P ^a   Levi, Linda ^a   Berman, Patricia Williams ^a   Pligge, Margaret ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54049148484     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.4324/9781410612618     Document Type: Chapter

References (25)

1. Bastable, V, & Schifter, D. (1998). Classroom stories: Examples of elementary students engaged in early algebra. In J. Kaput (Ed.), Employing children's natural powers to build algebraic reasoning in the content of elementary mathematics. Unpublished manuscript, National Center for Research in Mathematical Sciences Education, Madison, WI.
2. Behr, M., Erlwanger, S., & Nichols, E. (1980). How children view the equal sign. Mathematics Teaching, 92, 13-15.
3. Carpenter, T. P. & Lehrer, R. (1999). Teaching and learning mathematics with understanding. In E. Fennema & T. A. Romberg (Eds.), Mathematics classrooms that promote understanding. (pp. 19-32). Mahwah, NJ: Lawrence Erlbaum Associates.
4. Carpenter, T. P., & Levi, L. (2000). Developing conceptions of algebraic reasoning in the primary grades (Research Report No. 00-2). Madison, WI: National Center for Improving Student Learning and Achievement in Mathematics and Science, Wisconsin Center for Education Research.
5. Chailkin, S., & Lesgold, S. (1984, April). Pre-algebra students'knowledge of algebra tasks with arithmetic expressions. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.
6. Clement, J. (1982). Algebra word problem solutions: Thought processes underlying a common misconception. Journal for Research in Mathematics Education, 13, 16-30.
7. Collis, K. E (1975). The development of formal reasoning. Newcastle, Australia: University of Newcastle.
8. Davis, R. B. (1964). Discovery in mathematics: A text for teachers. Reading, MA: Addison-Wesley.
9. Erlwanger, S., & Berlanger, M. (1983). Interpretations of the equal sign among elementary school children Proceedings of the North American Chapter of the International Group for the Psychology of Mathematics Education.
10. Falkner, K. P. Levi, L. & Carpenter, T. P (1999). Children's understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6, 231-236.
11. Kaput, J. (1998). Transforming algebra from an engine of inequity to an engine of mathematical power by "algebrafying" the K-12 curriculum. In National Council of Teachers of Mathematics (Ed.), The nature and role of algebra in the K-14 curriculum. (pp. 25-26). Washington, DC: National Academy Press.
12. Kaput, J. & Clement, J. (1979). Letter to the editor. Journal of Mathematical Behavior, 2, 208.
13. Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317-326).
14. Kieran, C. (1989). The early learning of algebra: A structural perspective. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teaching of algebra. (pp. 35-56). Reston, VA: National Council of Teachers of Mathematics.
15. Kieran, C. (1992). TThe learning and teaching of school algebra. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning. (pp. 390-419). New York: Macmillan.
16. Koehler, J. (2002). Algebraic reasoning in the elementary grades: Developing an understanding of the equal sign as a relational symbol. Unpublished master's thesis: University of Wisconsin-Madison.
17. Matz, M. (1982). Towards a process model for school algebra errors. In D. Sleeman & J. S. Brown (Eds.), Intelligent tutoring systems (. (pp. 25-50). New York: Academic Press.
18. National Council of Teachers of Mathematics (1997). Algebraic thinking [Special issue]. Teaching Children Mathematics, 3, (6).
19. National Council of Teachers of Mathematics (1998). The nature and role of algebra in the K-14 curriculum. Washington, DC: National Academy Press.
20. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.
21. Rosnick, P. & Clement, J. (1980). Learning without understanding: The effect of tutoring strategies on algebra misconceptions. Journal of Mathematical Behavior, 63, 3-27.
22. Saenz-Ludlow, A. & Walgamuth, C. (1998). Third graders' interpretations of equality and the equal symbol. Educational Studies in Mathematics, 35, 153-187.
23. Schifter, D. (1999). Reasoning about algebra: Early algebraic thinking in Grades K-6. In L. V. Stiff & F. R. Curcio (Eds.), Developing mathematical reasoning in Grades K-12. (pp. 62-81). Reston, VA: National Council of Teachers of Mathematics.
24. Tierney, C. & Monk, S. (1998). Children reasoning about change over time. In J. Kaput (Ed.), Employing children's natural powers to build algebraic reasoning in the content of elementary mathematic. (pp. 62-81). Unpublished manuscript: National Center for Research in Mathematical Sciences Education, Madison, WI..
25. Valentine, C. Carpenter, T P. & Pligge, M. (in press). press). Developing concepts ofjustification and proof in a sixth-grade classroom. In R. Nemirovsky & A. Rosebery B. Warren, & J. Solomon (Eds.), The encounter of everyday and disciplinary experiences. Mahwah, NJ: Lawrence Erlbaum Associates.