Publications

NSF Reports and Posters

• NSF REESE #0633915 - "The Impact of Early Algebra on Later Algebra Learning"
  • Project Poster
  • Year 3 Activities Report - 2009
  • Year 3 Findings Report - 2009

Books

• Schliemann, A.D., Carraher, D.W., & Brizuela, B. (2011). El Carácter Algebraico de la Aritmética: De las ideas de los ninõs a las actividades en el aula. Buenos Aires: Paidøs.
• Kaput, J., Carraher, D. & Blanton, M.  (2008) (Eds.), Algebra in the Early Grades.  Mahwah, NJ, Erlbaum
• 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. [View abstract]

Articles and Book Chapters

2013

• Brizuela, B. M., Martinez, M. V., & Cayton-Hodges, G. A. (2013). The Impact of Early Algebra: Results from a Longitudinal Intervention. Journal of Research in Mathematics Education/Revista de Investigación en Didáctica de las Matemáticas, 2(2), 209-241.
• Carraher, D.W. & Schliemann, A.D. (in press). Early Algebra Teaching and Learning. In S. Lerman (Ed.). Encyclopedia of Mathematics Education. Springer.
• Schliemann, A.D., Carraher, D.W., Goodrow, A., Caddle, M., & Porter, M. (2013). Equations in elementary school. In A. M. Lindmeier & A. Heinze (Eds.). Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 161-168. Kiel, Germany: PME.
• Schliemann, A.D., Carraher, D.W., & Caddle, M. (2013). From Seeing Points to Seeing Intervals in Number Lines and Graphs. in B. Brizuela & B. Gravel (Eds.) Show me what you know: Exploring Representations across STEM disciplines. New York, NY. Teachers College Press.
• Carraher, D.W., Schliemann, A.D., & Schwartz, J. (2013). Algebra en la escuela primaria? In C. Broitman (ed.) Enseñanza y Aprendizage de Matematica. Buenos Aires, Argentina. Editorial Paidòs.

2012

• Brizuela, B. M., & Martinez, M. V. (2012). Aprendizaje de la comparación de funciones lineales. In J. A. Castorina, M. Carretero, & A. Barreiro (Eds.), Desarrollo Cognitivo y Educación (pp. 263-286). Buenos Aires: Editorial Paidós.
• Schliemann, A. D., Carraher, D. W., & Brizuela, B. M. (2012). Algebra in elementary school. In L. Coulange & J.-P. Drouhard (Eds.) Enseignement de l'algèbre élémentaire: Bilan et perspectives. Special Issue of Recherches en Didactique des Mathématiques, pp. 109-124.

2011

• Caddle, M., & Brizuela, B. M. (2011). Fifth Graders’ Additive And Multiplicative Reasoning: Establishing Connections Across Conceptual Fields Using A Graph. Journal of Mathematical Behavior, 30(3), 224-234.

2010

• Carraher, D.W. & Schliemann, A.D. (2010). Algebraic Reasoning in Elementary Classrooms. In D. Lambdin & F. Lester (Eds.) Teaching and Learning Mathematics: Translating Research to the Classroom. Reston, VA. NCTM.

2009

• Caddle, M.C. & Earnest, D. (2009). Slope as a procedure: The impact of axis scale. In Tzekaki, M., Kaldrimidou, M. & Sakonidis, H. (Eds.). Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 233-240. Thessaloniki, Greece: PME.
• Carraher D. W; Martinez, M. V & Schliemann, A. D. (2009). Introducción temprana al álgebra y a la generalización matemática. 12(ntes) Primer Ciclo, 4, pp. 7-42. Buenos Aires, Argentina.Editorial 12(ntes). ISBN 978-987-1540-07-5

2008

• Carraher, D.W., Martinez, M., & Schliemann, A.D. (2008).  Early algebra and mathematical generalization. ZDM – The International Journal on Mathematics Education (formerly Zentralblatt fur Didaktik der Mathematik), 40(1), 3-22.
• Brizuela, B.M. & Schliemann, A.S. (2008).  Alunos de diez años de edad resolvendo equaciones lineales.  Enseñar Matematica: Nivel Inicial y Primario, vol. 5, 7-24.
• Brizuela, B.M. & Earnest, D. (2008). 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 (pp. 273-301). Mahwah, NJ: Lawrence Erlbaum and Associates.
• Carraher, D.W., Schliemann, A.D. & Schwartz, J. (2008). 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.

2007

• Carraher, D. W., & Schliemann, A. D.  (2007).  Early Algebra and Algebraic Reasoning.  In F. Lester (Ed.), Handbook of Research in Mathematics Education.  Greenwich, CT: Information Age Publishing, pp. 669-705.
• 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).

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(2), pp. 87-115.
• Martinez, M. V., & Brizuela, B. M. (2006). An unexpected way of thinking about linear function tables. In J. Novotná et al. (Eds.), Proceedings of the 30th Annual PME Meeting (vol. 4, pp. 153-160). Prague, Czech Republic: Charles University.
• Martinez, M. V., & Brizuela, B. M. (2006). A third grader's way of thinking about linear function tables. Journal of Mathematical Behavior, 25(4), 285-298.

2005

• 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.
• Earnest, D. & Schliemann, A.D. (2004). The dots problem: Third graders working with functions.  Proceedings of the 28^th International Conference for the Psychology of Mathematics Education.

2003

• Schliemann, A.D., et al. (2003). Algebra in Elementary School. Proceedings of the 27th International Conference for the Psychology of Mathematics Education. Honolulu, HI, July, 2003.
• Carraher, D., & Earnest, D. (2003). Guess My Rule Revisited. Proceedings of the 27th International Conference for the Psychology of Mathematics Education. Honolulu, HI, July, 2003. [View abstract]
• Brizuela, B.M. & Schliemann, A.D. (2003). Fourth graders solving equations. Proceedings of the 27th International Conference for the Psychology of Mathematics Education. Honolulu, HI, July, 2003. [View abstract]
• Goodrow, A., & Schliemann, A.D. (2003). Linear Function Graphs and Multiplicative Reasoning in Elementary School. Unpublished manuscript, Department of Education, Rhode Island College, January, 2003. [View abstract]

2002

• Brizuela, B. M. & Lara-Roth, S. (2002). Additive relations and function tables. Journal of Mathematical Behavior, 20 (3), 309-319. [View abstract]
• Carraher, D.W. & Schliemann, A.D. (2002). The transfer dilemma. Journal of the Learning Sciences, 11(1) 1-24.
• 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. [View abstract]
• Schliemann, A.D. & Carraher, D.W. (2002). The Evolution of Mathematical Understanding: Everyday Versus Idealized Reasoning. Developmental Review, 22(2), 242-266. [View abstract]
• 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.
• 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

2001

• Schliemann, A.D., Goodrow, A. & Lara-Roth, S. (2001). Functions and Graphs in Third Grade. Symposium Paper. NCTM 2001 Research Presession, Orlando, FL. [View abstract]
• 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. [View abstract]
• 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. [View abstract]
• 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. [View abstract]
• Carraher, D.W., Schliemann, A.D., & Brizuela, B.B. (2001). Algebra in the Early Grades. Hands On!, Spring 2001, Vol. 24, No. 1, 8-11.

2000 and Earlier

• Carraher, D., Schliemann, A.D., & Brizuela, B. (2000). Treating operations as functions. Plenary Presentation, XXII Annual Meeting for the Psychology of Mathematics Education, North American Chapter, Tucson, AZ, October 7-10.
• 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.). [View abstract]
• 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. [View abstract]
• 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.).
• 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. [View abstract]
• Carraher, D., Schliemann, A., & Brizuela, B. (1999). Bringing out the algebraic character of arithmetic. 1999 AERA Meeting (40 pp.). coming soon
• 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. [View abstract]