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The Early Algebra project writes for researchers, educators, and policy-makers. Generally, we include specific examples from classroom episodes and students' work.
Click on the size of the respective abstract, e.g., [1k], to view a short description of a publication.
Click on the size of the full file, e.g., [263 k], to download a full version of the paper in PDF (portable document format) file onto your computer. You need Acrobat Reader (it's free) to read the article in this format.
2008
Martinez, M., Carraher, D.W. & Schliemann, A.D. (forthcoming). Early Algebra and mathematical generalization. Zentralblatt fur Didaktik der Mathematik.
2007
Brizuela, B.M. & Earnest, D. (2007). Multiple notational systems and algebraic understandings: The case of the "best deal" problem. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the Early Grades. Mahwah, NJ: Lawrence Erlbaum and Associates (now Taylor & Francis).
Carraher, D.W. & Schliemann, A. D. (2007). Early Algebra and Algebraic Reasoning. In F. Lester (ed.) Second Handbook of Research on Mathematics Teaching and Learning: A project of the National Council of Teachers of Mathematics. Vol II. Charlotte, NC: Information Age Publishing, pp. 669-705.
Carraher, D.W., Schliemann, A.D. & Schwartz, J. (2007). Early algebra is not the same as algebra early. In J. Kaput. D. Carraher, & M. Blanton (Eds.), Algebra in the Early Grades. Mahwah, NJ, Erlbaum, pp. 235-272 (now Taylor & Francis).
Peled, I. & Carraher, D.W. (2007). Signed numbers and algebraic thinking. In J. Kaput. D. Carraher, & M. Blanton (Eds.), Algebra in the Early Grades. Mahwah, NJ, Erlbaum, pp. 303-327 (now Taylor & Francis). [608 k]
Schliemann, A.D., Carraher, D.W., & Brizuela, B. (2007). Bringing Out the Algebraic Character of Arithmetic: From Children's Ideas to Classroom Practice. Lawrence Erlbaum Associates (now Taylor & Francis).
2006
Carraher, D., Schliemann, A.D., Brizuela, B., & Earnest, D. (2006). Arithmetic and Algebra in early Mathematics Education. Journal for Research in Mathematics Education, Vol 37. [3 mb]
Martinez, M. V., & Brizuela, B. M. (2006). An unexpected way of thinking about linear function tables. In J. Novotn‡ et al. (Eds.), Proceedings of the 30th Annual PME Meeting (vol. 4, pp. 153-160). Prague, Czech Republic: Charles University. [4.5 mb ]
Martinez, M. V., & Brizuela, B. M. (2006). A third graderŐs way of thinking about linear function tables. Journal of Mathematical Behavior, 25(4), 285-298.
2005
2005-1 Carraher, D., Schliemann, A.D., & Brizuela, B. (2005). Treating operations as functions. In D. W. Carraher, & R. Nemirovsky (Eds.) Media and Meaning. CD-ROM issue of Monographs of the Journal for Research in Mathematics Education.
2004
Brizuela, B.M., & Schliemann, A.D. (2004). Ten-year-old students solving linear equations. For the Learning of Mathematics, 24(2), 33-40. [432 k]
2003
Schliemann, A.D., et al. (2003, in press). Algebra in Elementary School. Proceedings of the 27th International Conference for the Psychology of Mathematics Education. Honolulu, HI, July, 2003. [128 k]
Carraher, D., & Earnest, D. (2003, in press). Guess My Rule Revisited. Proceedings of the 27th International Conference for the Psychology of Mathematics Education. Honolulu, HI, July, 2003. [1k] [112 k]
Brizuela, B.M. & Schliemann, A.D. (2003, in press). Fourth graders solving equations. Proceedings of the 27th International Conference for the Psychology of Mathematics Education. Honolulu, HI, July, 2003. [1k] [448 k]
Goodrow, A., & Schliemann, A.D. (2003). Linear Function Graphs and Mulitplicative Reasoning in Elementary School. Unpublished manuscript, Department of Education, Rhode Island College, January, 2003. [1k] [2.1 M]
Schliemann, A.D., Carraher, D.W., & Brizuela, B. (in press). Bringing Out the Algebraic Character of Arithmetic: From Children’s Ideas to Classroom Practice. Studies in Mathematical Thinking and Learning Series. Mahwah, NJ: Lawrence Erlbaum Associates. [1k] [1.4 M]
Carraher, D., Schliemann, A.D., & Brizuela, B. (accepted for publication). Treating operations as functions. In D. W. Carraher, R. Nemirovsky, & C. DiMattia, C. (Eds.) Media and Meaning. CD-ROM issue of Monographs for the Journal of Research in Mathematics Education. [1.9 M]
2002
Brizuela, B. M. & Lara-Roth, S. (2002). Additive relations and function tables. Journal of Mathematical Behavior, 20 (3), 309-319.  [1k]
Carraher, D.W. & Schliemann, A.D. (2002). The transfer dilemma. Journal of the Learning Sciences, 11(1) 1-24. [352 k]
Carraher, D. & Schliemann, A.D. (2002). Empirical and Logical truth in Early Algebra activities: From guessing amounts to representing variables. Symposium paper NCTM 2002 Research Presession. Las Vegas, Nevada, April 19-21. [1k] [1.4 M]
Schliemann, A.D. & Carraher, D.W. (2002). The Evolution of Mathematical Understanding: Everyday Versus Idealized Reasoning. Developmental Review, 22(2), 242-266. [1k] [352 k]
Carraher, D.W. & Schliemann, A.D. (2002). Is everyday mathematics truly relevant to mathematics education? In J. Moshkovich & M. Brenner (Eds.) Everyday Mathematics. Monographs of the Journal for Research in Mathematics Education, 11, 131-153. [256 k]
Carraher, D.W. & Schliemann, A.D. (2002). Modeling reasoning. In K. Gravemeijer, R., Lehrer, B., Oers, and L. Verschaffel (Eds.). Symbolizing, Modeling and Tool Use in Mathematics Education. The Netherlands: Kluwer Academic Publishers, pp. 295-304. coming soon [160 k]
2001
Schliemann, A.D., Goodrow, A. & Lara-Roth, S. (2001). Functions and Graphs in Third Grade. Symposium Paper. NCTM 2001 Research Presession, Orlando, FL. [1k] [288 k]
Carraher, D., Brizuela, B. M., & Earnest, D. (2001). The reification of additive differences in early algebra. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra: Proceedings of the 12th ICMI Study Conference (vol. 1). The University of Melbourne, Australia. [1k] [400 k]
Schliemann, A.D., Carraher, D.W. & Brizuela, B.M. (2001). When tables become function tables. Proceedings of the XXV Conference of the International Group for the Psychology of Mathematics Education, Utrecht, The Netherlands, Vol. 4, 145-152.  [1k] [80 k]
Carraher, D., Schliemann, A., & Brizuela, B. (2001). Can Young Students Operate on Unknowns? Proceedings of the XXV Conference of the International Group for the Psychology of Mathematics Education, Utrecht, The Netherlands (invited research forum paper), Vol. 1, 130-140.  [1k] [112 k]
2000 and Earlier
Brizuela, B., Carraher, D., & Schliemann, A. (2000). Mathematical notation to support and further reasoning ("to help me think of something"). Symposium paper, 2000 NCTM Research Pre-session Meeting (18 pp.). [1k] [96 k]
Carraher, D., Brizuela, B. & Schliemann, A., (2000). Bringing out the algebraic character of arithmetic. Instantiating variables in addition and subtraction. In T. Nakahara & M. Koyama (Eds.) Proceedings of the XXIV Conference of the International group for the Psychology of Mathematics Education. Hiroshima, Japan, Vol. 2, 145-152. [1k] [128 k]
Schliemann, A., Carraher, D., & Brizuela, B. (2000). From Quantities to Ratio, Functions, and Algebraic Relations. Symposium paper. 2000 AERA Meeting. New Orleans, April (31 pp.). [112 k]
Carraher, D., Schliemann, A.D., & Brizuela, B. (2000). Children's Early Algebraic Concepts. Plenary address. XXII Meeting of the Psychology of Mathematics Education, North American Chapter, Tucson, AZ, October, 2000.  [1k]
Carraher, D., Schliemann, A., & Brizuela, B. (1999). Bringing out the algebraic character of arithmetic. 1999 AERA Meeting (40 pp.). coming soon [560 k]
Schliemann, A.D., Carraher, D.W., Brizuela, B., & Pendexter, W. (1998). Solving algebra problems before algebra instruction. Second Early Algebra Meeting. University of Massachusetts at Dartmouth/Tufts University. [1k] [160 k]