| Full-Time Faculty
 Bárbara M. Brizuela
Associate Professor
Department Chair
Director, Mathematics, Science, Technology, and Engineering Education Program
- Ed.D., Harvard University
- M.A., Tufts University
- Licenciada en Ciencias Pedagógicas, Universidad de
Belgrano, Argentina
- Licenciada en Psicopedagogía, Universidad de Belgrano, Argentina
Bárbara studied in Argentina and the U.S., where she moved in
1995. She has been a kindergarten and seventh grade teacher in
Argentina as well as a Spencer Foundation research training
grantee. In 2008-2009 Bárbara was a Spencer Fellow, a Fulbright
Senior Scholar, and a Schuster Family Faculty Fellow in Arts &
Sciences (Tufts University). Her current research focuses on
children's learning of the notational number system, notational
aspects of mathematics,
children's learning of elementary mathematics, including
early algebra, and mathematics teachers' learning and professional development.
Since 1998, she has also been involved in a research project on
children's early algebraic reasoning and teaching elementary
school children, exploring the intertwined nature of arithmetic
and algebra (see
www.earlyalgebra.org). In the past, she has also
investigated the connections between engineering and algebra
through a project funded by the General Electric Foundation. Her
main areas of interest are early childhood education, cognitive
development, and mathematics education. Her research is grounded
on the fundamental belief that our primary goal as educators is to understand
and highlight children's thinking and reasoning in productive ways.
Click here to view Bárbara's
CV.
Click
here to access Bárbara's wiki
(secured access only; for MSTE Education
Faculty Committee and Search Committees)
Current projects:
In the News:
2010:
Interview by Magazine Desde La Patagonia, published by Centro Regional
Universitario Bariloche, Universidad Nacional del Comahue, reporting on
my Fulbright Fellowship at their institution.
2009:
Let x=x. Tufts Journal, April 2009. Article by Marjorie
Howard on the Early Algebra project and our summer camp.
Interview on the television program 12(ntes) [Teachers], which appears weekly on public television in Argentina. Volume 4, 2009.
Aprender Matemática Puede Ser Divertido. Acción, 4(28), 8-9. 2009 Article in the
outreach magazine of the Ministry of Science and Technology, Province of Córdoba,
Argentina, reporting on a two-day workshop held for in-service teachers in May 2009.
Reflexões no papel. Álgebra desde cedo. Revista Nova Escola on line, edição 227 – Noviember
2009, by Beatriz Santomauro.
Report on an invited presentation given in October 2009
as part of "Education Week" organized by the Victor Civita Foundation with the
purpose of celebrating teachers' day in Brazil. São Paulo, Brazil.
2003:
The wedding of two programs will help kids learn
mathematics. Tufts Journal, March 2003. Article by Marjorie
Howard on the Building Math project.
2001:
Algebra in elementary school? No sweat.
Tufts Journal, November 2001. Article by Marjorie
Howard on the Early Algebra Project.
Publications:
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holder.
BOOKS:
2011:
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 (Spanish translation of Bringing Out the Algebraic Character
of Arithmetic: From Children's Ideas to Classroom Practice ).
Buenos Aires: Editorial Paidós.
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.
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.)
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: Amazon Mission.
Portland, ME: Walch Publishing. (Winner of "Distinguished Achievement Award"
from the Association of Educational Publishers, 2008.)
2006:
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.)
2004:
Brizuela, B. M. (2004).
Mathematical Development in Young Children:
Exploring Notations.
NY: Teachers College Press.
EDITED VOLUMES:
Brizuela, B. M., & Gravel, B. E. (forthcoming). (Eds.)
"Show me what
you know" Exploring representations across STEM disciplines. Book contract
signed with Teachers College Press.
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:
2012:
Bautista, A., Pérez Echeverría, M. P., Pozo, J. I., &
Brizuela, B. M. (in press, 2012). Piano students'
conceptions of learning, teaching, assessment, and
evaluation. Estudios de Psicología, 33(1).
Schliemann, A. D., Carraher, D. W., & Brizuela, B. M.
(2012, in press). Algebra in elementary school and its impact
on middle school learning. Recherches en Didactique des
Mathématiques, Paris, France.
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.
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).
Fourth graders solving
linear equations.
For the Learning of Mathematics, 24(2), 33-40.
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.
ARTICLES IN NON-REFEREED JOURNALS:
2008:
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.
2001:
Carraher, D., Schliemann, A. D., & Brizuela, B. M. (2001).
Algebra in
the Early Grades.
Hands On!, 24(1), 1-6.
BOOK CHAPTERS:
Forthcoming
Brizuela, B. M., & Martinez, M. V. (forthcoming).
Aprendiendo acerca de la comparación de funciones lineales.
In J. A. Castorina, M. Carretero, & A. Barreiro (Eds.),
Desarrollo Cognitivo y Educación. Buenos Aires: Editorial Paidós.
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:
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.
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 31rst 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.
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.
REVIEWS OF MY PUBLISHED WORK:
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.
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