Children's Mathematical Representations - Bárbara M. Brizuela

My background is in psychology and education, and I am interested in general in cognitive development and educational processes. My research focuses on children's learning of written mathematical representations: written numbers, graphs, tables, algebraic notation, representations for space, data, and measurement, and idiosyncratic notations. My interests lie in understanding the interactions between children's written representations and their understanding of the conceptual aspects of mathematics. I am also interested in the role of notations within mathematics itself, both historically and in the development of children.

In this project, I investigate children's early learning of mathematical notations. I assume that conventional knowledge is built on prior understandings. From this assumption, it follows that children's ideas about mathematical notations could be constitutive of their later conventional understandings. One of the central tasks of the investigation is to document how children initially represent numerical and mathematical understandings and how they gradually assimilate conventional representations into their expressive repertoire.

Selected Publications:

Brizuela, B. M., & Cayton, G. A. (2010). Anotar números desde pre-escolar hasta segundo grado: el impacto del uso de dos sistemas de representación en la presentación. Cultura & Educación, 22(2).

Bautista, A., Pérez Echeverría, M. del P., Pozo, J. I., & Brizuela, B. M. (2009). Piano students' conceptions of musical scores as external representations: A cross-sectional study. Journal of Research in Music Education, 57(3), 181-202.

Brizuela, B. M. (2008). Notaciones empleadas por los niños para representar fracciones (Spanish translation of  "Young children's notations for fractions" published in 2006 in Educational Studies in Mathematics). 12(ntes) Enseñar Matemática. Nivel Inicial y Primaria, 3, 19-40.

Brizuela, B. M., & Schliemann, A. D. (2008). Alumnos de diez años de edad resolviendo ecuaciones lineales (Spanish translation of  "Fourth graders solving linear equations" published in 2004 in For the Learning of Mathematics). 12ntes. Enseñar Matemática Nivel Inicial y Primario, 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.

Brizuela, B. M., & Cayton, G. (2008). The roles of punctuation marks while learning about written numbers. Educational Studies in Mathematics, 68, 209-225.

Brizuela, B. M. (2006). Desenvolvimento matematico na criança: Explorando notacões. Porto Alegre, Brazil: Artmed Editora. (Portuguese translation of Mathematical Development in Young Children: Exploring Notations.)

Brizuela, B. M. (2006). Young children's notations for fractions. Educational Studies in Mathematics, 62(3), 281-305.

Alvarado, M., & Brizuela, B. M. (Eds.) (2005). Haciendo números. Las notaciones numéricas vistas desde la psicología, la didáctica y la historia. México: Editorial Paidós.

Alvarado, M., & Brizuela, B. M. (2005). Introducción. In M. Alvarado & B. M. Brizuela (Eds.) Haciendo números. Las notaciones numéricas vistas desde la psicología, la didáctica y la historia. (pp. 9-12). México: Editorial Paidós.

Brizuela, B. M. (2005). Relaciones entre representaciones: el caso de Jennifer, Nathan y Jeffrey. In M. Alvarado & B. M. Brizuela (Eds.) Haciendo números. Las notaciones numéricas vistas desde la psicología, la didáctica y la historia. (pp. 198-219). México: Editorial Paidós. (Spanish version of chapter in "Mathematical Development in Young Children: Exploring Notations".)

Brizuela, B. M. (2004). Mathematical Development in Young Children: Exploring Notations. NY: Teachers College Press.

Brizuela, B. M., & Schliemann, A. D. (2004). Fourth graders solving linear equations. For the Learning of Mathematics, 24(2), 33-40.

Brizuela, B. M. (2003). Números y letras: Primeras conexiones entre sistemas notacionales. In A. Teberosky & M. Soler-Gallart (Eds.), Contextos de alfabetización inicial (pp. 133-154). Barcelona: Editorial Horsori.

Brizuela, B. M., & Lara-Roth, S. (2002). Additive relations and function tables. Journal of Mathematical Behavior, 20(3), 309-319.

Brizuela, B. M. (2000). Algunas ideas sobre el sistema de numeración escrito en niños pequeños. In N. Elichiry (Ed.), Aprendizaje de niños y maestros. La construcción del sujeto educativo (pp. 15-27). Buenos Aires: Ediciones Manantial.

Brizuela, B. (1998). Invenções e convenções: Uma história sobre números maiúsculos. In A. Schliemann & D. Carraher (Orgs.), A compreensão de conceitos aritméticos. Ensino e pesquisa. São Paulo: Papirus Editora. (Portuguese version of "Inventions and conventions: A story about capital numbers".)

Brizuela, B. (1997). Inventions and conventions: A story about capital numbers. For the Learning of Mathematics, 17(1), 2-6.