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Welcome
About Early Algebra
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Publications
NSF Reports and Posters
- NSF REESE #0633915 - "The Impact of Early
Algebra on Later Algebra Learning"
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 28th
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]
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