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Bárbara M. Brizuela

Professor
Dean of Academic Affairs for Arts & Sciences

Publications:

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BOOKS:

2007:
Schliemann, A. D., Carraher, D., & Brizuela, B. M. (2007). Bringing Out the Algebraic Character of Arithmetic: From Children's Ideas to Classroom Practice. Mahwah, NJ: Lawrence Erlbaum and Associates.

Translated as: Schliemann, A. D., Carraher, D., & Brizuela, B. M. (2011). El carácter algebraico de la aritmética: de las ideas de los niños a las actividades en el aula. Buenos Aires: Editorial Paidós.

2004:
Brizuela, B. M. (2004). Mathematical Development in Young Children: Exploring Notations. NY: Teachers College Press.
Translated as: Brizuela, B. M. (2006). Desenvolvimento matematico na criança: Explorando notacões. Porto Alegre, Brazil: Artmed Editora.

Review: Warren, E. (2007). Children's Invented Notations as Insights Into Mathematical Thinking: A Review of Mathematical Development in Young Children: Exploring Notations. Journal for Research in Mathematics Education, 38(3), 322-326.

EDITED VOLUMES:

2016:
Brizuela, B. M., & Scheuer, N. (2016). (Eds.) Dynamic aspects of cognitive development and learning. Infancia y Aprendizaje/Journal for the Study of Education and Development, 39(4).

2013:

Brizuela, B. M., & Gravel, B. E. (2013). (Eds.) "Show me what you know" Exploring representations across STEM disciplines. New York: Teachers College Press.

Translated as: Brizuela, B. M., & Gravel, B. E. (forthcoming). Contract signed with Teachers College Press to be translated by Antonio Machado Libros, Madrid, Spain.

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

2000:
Brizuela, B. M, Stewart, J. P., Carrillo, R. G., & Berger, J. G. (Eds.). (2000). Acts of inquiry in qualitative research. Cambridge, MA: Harvard Educational Review.

ARTICLES IN REFEREED JOURNALS:

2017:
Blanton, M., Brizuela, B. M., Gardiner, A. M., Sawrey, K., & Newman-Owens, A. (2017). A Progression in First-Grade Children's Thinking About Variable and Variable Notation in Functional Relationships. Educational Studies in Mathematics, 95, 181–202.

2016:
Brizuela, B. M. (2016). Variables in Elementary Mathematics Education. Elementary School Journal, 117(1), 46-71.

Brizuela, B. M., & Scheuer, N. (2016). Investigating cognitive change as a dynamic process/Investigar el cambio cognitivo como proceso dinámico. Infancia y Aprendizaje/Journal for the Study of Education and Development, 39(4), 1-34.

Caddle, M., & Brizuela, B. M. (2016). Multiplication Principle Problems And Permutation Problems. The Mathematics Teacher, 109(6), 463-467.

Caddle, M., Bautista, A., Brizuela, B. M., & Sharpe, S. (2016). Evaluating mathematics teachers' professional development motivations and needs. Journal of Research in Mathematics Education/Revista de Investigación en Didáctica de las Matemáticas (REDIMAT), 5(2), 112-134. doi:10.4471/redimat.2016.2093

Cañadas, M. C., Brizuela, B. M., & Blanton, M. (2016). Second graders articulating ideas about co-variation with linear functions. Journal of Mathematical Behavior, 41, 87-103.

Cao, Y., & Brizuela, B. M. (2016). High school students' representations and understandings of the electric field in use of arrow diagrams. Physical Review Physics Education Research, 12(2), 020102.

Martí, E., Scheuer, N., Cavalcante, S., Trench, M., & Brizuela, B. M. (2016). Symbolic representation of the number three: a study with three-year-old children from contrasting socioeconomic environments. Journal of Cognitive Psychology, DOI: 10.1080/20445911.2016.1188821

Wilkerson-Jerde, M., Bautista, A., Tobin, R., Brizuela, B. M., & Cao, Y. (2016). More than Meets the Eye: Patterns and Shifts in Middle School Mathematics Teachers' Descriptions of Models. Journal of Mathematics Teacher Education, 19(2-3).

2015:
Bautista, A., Cañadas, M. C., Brizuela, B. M., & Schliemann, A. D. (2015). Examining How Teachers Use Graphs to Teach Mathematics in a Professional Development Program. Journal of Education and Training Studies, 3(2), 91-106

Blanton, M., Brizuela, B. M., Gardiner, A., Sawrey, K., & Newman-Owens, A. (2015). A Learning Trajectory in Six-Year-Olds' Thinking about Generalizing Functional Relationships. Journal for Research in Mathematics Education, 46(5), 511-558.

Brizuela, B. M., Blanton, M., Gardiner, A. M., Newman-Owens, A., & Sawrey, K., (2015). A first grade student's exploration of variable and variable notation / Una alumna de primer grado explora las variables y su notación. Estudios de Psicología: Studies in Psychology, 36(1), 138-165.

Brizuela, B. M., Blanton, M., Sawrey, K., Newman-Owens, A., & Gardiner, A. (2015). Children's Use Of Variables and Variable Notation To Represent Their Algebraic Ideas. Mathematical Thinking and Learning, 17, 1-30.

Cao, Y., & Brizuela, B. M. (2015). A Chinese Young Adult Non-Scientist's Epistemologies and Her Understandings of the Concept of Speed. International Journal of Mathematical Education in Science and Technology. DOI: 10.1080/0020739X.2015.1023857.

Sawrey, K., Brizuela, B. M., & Blanton, M. (2015). Student-Produced Representations as a Means for Interrupting the Flow of an Interview / Representaciones producidas por una alumna para interrumpir el flujo de una entrevista. Estudios de Psicología: Studies in Psychology, 36(1), 185-192.

2014:
Bautista, A., Brizuela, B. M., Glennie, C., & Caddle, M. (2014). Mathematics teachers attending and responding to students' thinking: Diverse paths across diverse assignments. International Journal for Mathematics Teaching and Learning. July Volume (28 pages). Retrieved from http://www.cimt.org.uk/journal/bautista.pdf

Bautista, A., Wilkerson-Jerde, M. H., Tobin, R. G., & Brizuela, B. M. (2014). Mathematics teachers' ideas about mathematical models: A diverse landscape. PNA, 9(1), 1-28.

Brizuela, B. M., & Blanton, M. (2014). El desarrollo del pensamiento algebraico en niños de escolaridad primaria. Revista de Psicología-Segunda Época (UNLP), 14, 37-57.

2013:
Brizuela, B. M., Martinez, M. V., & Cayton-Hodges, G. A.  (2013).  The Impact of Early Algebra: Results from a Longitudinal InterventionJournal of Research in Mathematics Education/Revista de Investigación en Didáctica de las Matemáticas, 2(2), 209-241.

Martinez, M. V., & Brizuela, B. M. (2013). Algebraic Modeling in a Proof Context. Journal of Mathematics Education. Education for All, 6(2), 70-81

2012:
Bautista, A., Pérez Echeverría, M. P., Pozo, J. I., & Brizuela, B. M. (2012). Piano students' conceptions of learning, teaching, assessment, and evaluation. Estudios de Psicología, 33(1), 79-104.

Schliemann, A.D., Carraher, D.W., & Brizuela, B. M. (2012). Algebra in Elementary School. In Coulange, L., Drouhard, J.-P., Dorier, J.-L., Robert, A. (Eds.) Recherches en Didactique des Mathématiques, Numéro spécial hors-série, Enseignement de l'algèbre élémentaire: bilan et perspectives (pp. 103-118). Grenoble: La Pensée Sauvage.

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.

Martinez, M. V., Brizuela, B. M., & Castro Superfine, A. (2011). Integrating Algebra and Proof in High School Mathematics: An Exploratory Study. Journal of Mathematical Behavior, 30, 30–47.

2010:
Brizuela, B. M., & Alvarado, M. (2010). First graders' work on additive problems with the use of different notational tools. Revista IRICE Nueva Época, 21, 37-44.

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), 149-167.

2009:
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.

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

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

Translated as: 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.

Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2006). Arithmetic and Algebra in Early Mathematics Education. Journal for Research in Mathematics Education 37(2), 87-115.

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.W., Schliemann, A.D., & Brizuela, B.M. (2005). Treating the operations of arithmetic as functions. [Videopaper]. In D. Carraher & R. Nemirovsky (Eds.), Medium and meaning: Video papers in mathematics education research, Journal for Research in Mathematics Education Monograph, Vol. XIII. 2005. [On CD-ROM]. 11 min. video (204 MB), 34 pages text (170 KB), 32 images (974 KB).

2004:
Brizuela, B. M., & Schliemann, A. D. (2004). Ten-year-old students solving linear equations. For the Learning of Mathematics, 24(2), 33-40.

Translated as: 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.

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

1999:
Brizuela, B. M. (1999). Editor's Review. Harvard Educational Review, 69(4), 474-481.

Brizuela, B. M., & Sellers-García, M. J. (1999). School adaptation: A triangular process. American Educational Research Journal, 36(2), 345-370.

1998:
Soler-Gallart, M., & Brizuela, B. M. (1998). Cultural Action for Freedom: Editors' Introduction. Harvard Educational Review, 68(4), 471-475.

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

BOOK CHAPTERS:

Accepted:
Blanton, M., Ellis, A., Stephens, A., & Brizuela, B. M. (in preparation). Algebraic Reasoning in Grades K–8. Handbook of research on mathematics teaching and learning. Reston, VA: NCTM.

2016:
Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2016). Arithmetic and algebra in mathematics education. In E. Silver & P. Kenney (Eds.), More Lessons Learned from Research: Volume 2. Helping All Students Understand Important Mathematics (pp. 109-122). Reston, VA: NCTM.

2013:
Alvarado, M., & Brizuela, B. M. (2013). Herramientas notacionales en la solución de problemas aditivos con niños de primer año de primaria. In In C. Broitman (Ed.), Matemáticas en la escuela primaria [II]. Saberes y conocimientos de niños y docentes (pp. 99-119). Buenos Aires: Editorial Paidós.

Bautista, A., Brizuela, B. M., & Ko, Y.-Y. (2013). Middle school mathematics teachers' implicit conceptions about multiple representations for functions. In D. Halkias (Ed.), Psychology and the Search for Certainty in Everyday Life (pp. 31-48). Athens: ATINER.

Brizuela, B. M. (2013). La coherencia local y lógica en las producciones de notaciones numéricas en niños de 5 años de edad. In C. Broitman (Ed.), Matemáticas en la escuela primaria [I]. Números naturales y decimales con niños pequeños (pp. 129-146). Buenos Aires: Editorial Paidós.

Brizuela, B. M., & Cayton, G. (2013). Young Children's Self-Constructed Maps. In B. M. Brizuela & B. E. Gravel (Eds.), "Show me what you know" Exploring representations across STEM disciplines (pp. 22-42). NY: Teachers College Press.

Brizuela, B. M., & Gravel, B. E. (2013). Introduction. In B. M. Brizuela & B. E. Gravel (Eds.), "Show me what you know" Exploring representations across STEM disciplines (pp. 1-4). NY: Teachers College Press.

Gravel, B. E., Scheuer, N., & Brizuela, B. M. (2013). A case study of a student's efforts to make sense of air and the particle nature of gases through multiple representations. In B. M. Brizuela & B. E. Gravel (Eds.), "Show me what you know" Exploring representations across STEM disciplines (pp. 163-182). NY: Teachers College Press.

2012:
Brizuela, B. M., & Martinez, M. V. (2012). Aprendizaje de la comparación de funciones lineales. In M. Carretero, J. A. Castorina, & A. Barreiro (Eds.), Desarrollo Cognitivo y Educación: Procesos de Conocimiento y Contenidos Específicos (vol. 2, pp. 263-286). Buenos Aires: Editorial Paidós.

Translated as: Brizuela, B. M., & Martinez, M. V. (2014). Aprendendo a comparação de funções lineares. In M. Carretero, J. A. Castorina, & A. Barreiro (Eds.), Desenvolvimento Cognitivo e Educação: Processos do Conhecimento e Conteúdos Específicos (vol. 2, pp. 246-267). São Paulo, Brazil: Penso Editora.

2008:
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.

2005:
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".)

2003:
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.

2000:
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.

Soler-Gallart, M., & Brizuela, B. M. (2000). Editors' introduction. In P. Freire, Cultural action for freedom (pp. 1-5). Cambridge, MA: Harvard Educational Review.

1998:
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".)

PAPERS IN REFEREED CONFERENCE PROCEEDINGS:

2016:
Morales, R., Cañadas, M. C., Brizuela, B. M., & Gómez, P. (2016). Relaciones funcionales identificadas por estudiantes de primero de educación primaria y estrategias de resolución de problemas que involucran funciones lineales. In J. A. Macías, A. Jiménez, J. L. González, M. T. Sánchez, P. Hernández, C. Fernández, F. J. Ruiz, T. Fernández, & A. Berciano (Eds.), Investigación en Educación Matemática XX (pp. 365-375). Málaga, Spain: Sociedad Española de Investigación en Educación Matemática (SEIEM).

2014:
Caddle, M., & Brizuela, B. M. (2014). Using Interviews To Explore Teacher Knowledge Profiles In The Area Of Permutations. Proceedings of the Joint 38th Annual Meeting of the International Group for the Psychology of Mathematics Education [PME] and the 36th Annual Meeting of the North American Chapter for the Psychology of Mathematics Education [PME-NA]. Vancouver, Canada: PME/PME-NA.

2013:
Bautista, A., Wilkerson-Jerde, M. H., Tobin, R., & Brizuela, B. M. (2013). Diversity In Middle School Mathematics Teachers' Ideas About Mathematical Models: The Role Of Educational Background. In B. Ubuz, Ç. Haser, & M. A. Mariotti (Eds.), Proceedings of the 8th Congress of the European Society for Research in Mathematics Education [CERME] (pp. 960-969). Ankara, Turkey: Middle East Technical University.

2011:
Portsmore, M., & Brizuela, B. (2011). First Grade Students' Planning and Artifact Construction While Working On An Engineering Design Problem. Proceedings of the Annual Conference of the American Society of Engineering Education. Vancouver, BC. 2011 Honorable Mention for Best Paper in ASEE K-12 Division.

2009:
Martinez, M., & Brizuela, B. M. (2009). Modeling and proof in high school. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd Annual Meeting of the International Group for the Psychology of Mathematics Education (vol 4, pp. 113-120). Thessaloniki, Greece: PME.

2008:
Brizuela, B. M., & Cayton, G. A. (2008). First and second graders' spontaneous use of punctuation marks within written numerals. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepúlveda (Eds.), Proceedings of the 32nd Annual Meeting of the International Group for the Psychology of Mathematics Education (vol. 1, p. 241 México: Cinvestav-UMSNH.

Cayton, G. A., & Brizuela, B. M. (2008). Relationships between children's external representations of number. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepúlveda (Eds.), Proceedings of the 32nd Annual Meeting of the International Group for the Psychology of Mathematics Education (vol. 2, pp. 265-272). México: Cinvestav-UMSNH.

Huang, W., Brizuela, B. M., & Wong, P. (2008). Integrating Algebra and Engineering in the Middle School Classroom. Proceedings of the American Society for Engineering Education.  Pittsburgh, PA.

2007:
Cayton, G. A., & Brizuela, B. M. (2007). First graders' strategies for numerical notation, number reading and the number concept. In J.-H. Woo, H.-C. Lew, K.-S. Park, & D.-Y. Seo (Eds.), Proceedings of the 31st Annual Meeting of the International Group for the Psychology of Mathematics Education (vol.2, pp. 81-88). Seoul, Korea: Seoul National University.

2006:
Martinez, M. V., & Brizuela, B. M. (2006). An unexpected way of thinking about linear function tables. In J. Novotná, H. Moraová, M. Krátka, & N. Stehlíková (Eds.), Proceedings of the 30th Annual Meeting of the International Group for the Psychology of Mathematics Education (vol. 4, pp. 153-160). Prague, Czech Republic: Charles University.

2003:
Brizuela, B. M., & Schliemann, A. (2003). Fourth graders solving equations. In N. A. Pateman, B. J. Dougherty, & J. Zilliox (Eds.), Proceedings of the 2003 joint meeting of PME and PMENA (vol. 2, pp. 137-144). Honolulu: University of Hawai'i.

Schliemann, A. D., Carraher, D., Brizuela, B. M., Earnest, D., Goodrow, A., Lara-Roth, S., & Peled, I. (2003). Algebra in elementary school. In N. A. Pateman, B. J. Dougherty, & J. Zilliox (Eds.), Proceedings of the 2003 joint meeting of PME and PMENA (vol. 4, pp. 127-134). Honolulu: University of Hawai'i.

2002:
Schliemann, A. D., Carraher, D. W., & Brizuela, B. M. (2002). From unknown amounts to representing variables. In Proceedings of the XIV Annual Meeting Psychology of Mathematics Education, North American Chapter (pp. 127-129). Athens, GA: ERIC Clearinghouse.

2001:
Brizuela, B. M., & Lara-Roth, S. (2001). Additive relations and function tables. 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, pp. 110-119). The University of Melbourne, Australia.

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.

Carraher, D., Schliemann, A. D., & Brizuela, B. M. (2001). Can young students operate on unknowns? In M. van der H.-P. (Ed.), Proceedings of the 25th conference of the International Group for the PME (vol. 1, pp. 130-140). Utrecht, The Netherlands: Freudenthal Institute.

Schliemann, A. D., Carraher, D., & Brizuela, B. M. (2001). When tables become function tables. In M. van der H.-P. (Ed.), Proceedings of the 25th conference of the International Group for the PME (vol. 4, pp. 145-152). Utrecht, The Netherlands: Freudenthal Institute.

2000:
Carraher, D., Brizuela, B. M., & Schliemann, A. D. (2000). Bringing out the algebraic character of arithmetic: Instantiating variables in addition and subtraction. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th conference of the International Group for the PME (vol. 2, pp. 145-152). Hiroshima, Japan: Hiroshima University.

TEACHING MATERIALS:

2006:
Wong, P. Y., & Brizuela, B. M. (2006). Building Math: Amazon Mission. Portland, ME: Walch Publishing. (Winner of "Distinguished Achievement Award" from the Association of Educational Publishers, 2008.)

Wong, P. Y., & Brizuela, B. M. (2006). Building Math: Everest Trek. Portland, ME: Walch Publishing. (Winner of "Distinguished Achievement Award" from the Association of Educational Publishers, 2008.)

Wong, P. Y., & Brizuela, B. M. (2006). Building Math: Stranded. Portland, ME: Walch Publishing. (Winner of "Distinguished Achievement Award" from the Association of Educational Publishers, 2008.)

ARTICLES IN NON-REFEREED JOURNALS:

2001:
Carraher, D., Schliemann, A. D., & Brizuela, B. M. (2001). Algebra in the Early Grades. Hands On!, 24(1), 1-6.

BOOKNOTES:

Brizuela, B. M. (1999). The kindness of children. Harvard Educational Review, 69(2), 212-214.

Brizuela, B. M. (1998). Revolutionary multiculturalism: Pedagogies of dissent for the new millennium. Harvard Educational Review, 68(2), 259-261.

Brizuela, B. M. (1997). The essential Piaget: An interpretive reference and guide. Harvard Educational Review, 67(4), 835-836.