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NSF Reports and Posters


  • 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


  • 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.


  • 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.


  • 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.


  • 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.


  • 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


  • 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.


  • 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).


  • Carraher, D., Schliemann, A.D., Brizuela, B., & Earnest, D. (2006).  Arithmetic and Algebra in early Mathematics EducationJournal 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.


  • 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.


  • 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 28th International Conference for the Psychology of Mathematics Education.




2000 and Earlier

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