Ir al contenido

Documat


The Impact of Early Algebra: Results from a Longitudinal Intervention

  • Brizuela, Barbara M [1] ; Martinez, Mara V [2] ; Cayton-Hodges, Gabrielle A [3]
    1. [1] Tufts University

      Tufts University

      City of Medford, Estados Unidos

    2. [2] University of Illinois-Chicago
    3. [3] Educational Testing Service
  • Localización: REDIMAT, ISSN-e 2014-3621, Vol. 2, Nº. 2, 2013, págs. 209-241
  • Idioma: inglés
  • Enlaces
  • Resumen
    • In this paper, we provide evidence of the impact of early algebra (EA) over time.  We document this impact in the following ways: (a) by showing the performance over time of an experimental group of 15 children on an algebra assessment, from 3rd to 5th grade; and (b) by showing how the performance on an algebra assessment of children from an experimental group differs from the performance of a group of comparison students from their same elementary school who did not receive EA instruction from 3rd to 5th grade. We compared students’ scores through comparisons of means, correspondence factorial analyses, and hierarchical analyses.  Our results highlight the positive impact of an early access to algebra, indicating that this early access is associated, when we compare 3rd graders to 5th graders, with increased scores on items that involve inequalities and graphs.  When comparing experimental to comparison-group students we find increased scores on items that involve variables, functional relations, intra-mathematical contexts, tables, and algebraic expressions.  The study adds to a body of literature that has been arguing for EA as well as a need to thread algebra throughout the mathematics curriculum, starting in the earliest grades.

  • Referencias bibliográficas
    • Bednarz, N., Kieran, C., & Lee, L. (1 996). Approaches to algebra: Perspectives for research and teaching. Dordrecht,...
    • Bednarz, N., & Janvier, B. (1 996). Emergence and development of algebra as a problem-solving tool: continuities and discontinuities with...
    • Bednarz, N. (2001 ). A problem-solving approach to algebra: accounting for the reasonings and notations developed by students. In H. Chick,...
    • Bodanskii, F. (1 991 ). The formation ofan algebraic method ofproblem solving in primary school children. In Davydov, V. (Ed.), Survey of...
    • Booth, L. R. (1 984). Algebra: Children's strategies and errors. Windsor, UK.: NFER-Nelson.
    • Brenner, M. E. & Moschkovich, J. N. (Eds.). (2002). Everyday and Academic Mathematics in the Classroom. Monographs of the Journal for...
    • Brizuela, B. M., & Earnest, D. (2008). Multiple notational systems and algebraic understandings: The case of the "best deal" problem....
    • Bruer, J. T. (1 993). Schools for thought: A science of learning in the classroom. Cambridge, MA: MIT Press.
    • Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary...
    • Carraher, D. W., & Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In F. K. Lester (Ed.), Second Handbook of Research...
    • Carraher, D. W., Schliemann, A. D. & Schwartz, J. (2008). Early algebra is not the same as algebra early. In J. Kaput. D. Carraher, &...
    • Carraher, T.N., Carraher, D.W. & Schliemann, A.D. (1 985). Mathematics in the streets and in schools. British Journal of Developmental...
    • Chazan, D., & Yerushalmy, M. (2003). On appreciating the cognitive complexity of school algebra: Research on algebra learning and directions...
    • Chevallard, Y. (1 989). Le passage de l’arithm´etique a l’algébrique dans l’enseignement des mathématiques au collège [The passage from the...
    • Davis, R. (1 967). Exploration in Mathematics: A Text for Teachers. Palo Alto, Reading, MA, London, Don Mills, Ontario: Addison-...
    • Davis, R. (1 971 -72). Observing children's mathematical behavior as a foundation for curriculum planning. The Journal of Children's...
    • Davis, R. (1 985). ICME-5 Report: Algebraic thinking in the early grades. Journal ofMathematical Behavior, 4(2), 195-208.
    • Davis, R. (1 989). Theoretical considerations: Research studies in how humans think about algebra. In S. Wagner & C. Kieran (Eds.), Research...
    • Davydov, V. (Ed.) (1 991 ). Survey ofapplied Soviet research in school mathematics education, The University of Chicago,...
    • Demana, F., & Leitzel, J. (1 988). Establishing fundamental concepts through numerical problem solving. In A. F. Coxford & A. P. Shulte...
    • diSessa, A., Hammer, D., Sherin, B., & Kolpakowski, T. (1 991 ). Inventing graphing: Meta-representational expertise in children. Journal...
    • Dubinsky, E., & Harel, G. (1 992). The concept of function: Aspects of epistemology and pedagogy. Washington, DC: Mathematical...
    • Fujii, T., & Stephens, M. (2001 ). Fostering an understanding of algebraic generalization through numerical expressions: the role of quasi-variable....
    • Goldin, G. (1 998). Representational systems, learning, and problem solving in mathematics. Journal of Mathematical Behavior, 17(2),...
    • Goldenberg, E. P., & Shteingold, N. (2008). Early algebra: The math workshop perspective. In J. Kaput. D. W. Carraher, & M. Blanton...
    • Hall, R. (1 990). Making mathematics on paper: Constructing representations of stories about related linear functions (Technical...
    • Hall, R., Kibler, D., Wenger, E., & Truxaw, C. (1 989). Exploring the episodic structure of algebra story problem solving. Cognition and...
    • Izsák, A. (2004). Students' coordination ofknowledge when learning to model physical situations. Cognition and Instruction, 22(1 ),...
    • Kaput, J. (1 991 ). Notations and representations as mediators of constructive processes. In E. von Glasersfeld (Ed.), Radical constructivism...
    • Kieran, C. (1 981 ). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317-326.
    • Kieran, C. (1 989). The early learning of algebra: A structural perspective. In S. Wagner & C. Kieran (Eds.), Research Issues in the Learning...
    • Kobayashi, M. (1 988). New ideas of teaching mathematics in Japan. Tokyo: Chuo University Press.
    • Lebart, L., Morineau, A., & Piron, M. (1 995). Statistique multidimensionnelle [Multidimensional statistics]. Paris: Dunod.
    • MacGregor, M. (1 996). Curricular aspects of arithmetic and alegbra. In J. Gimenez, R. Lins & B. Gomez (Eds.), Arithmetic and Algebra...
    • Martinez, M. V., & Brizuela, B. M. (2006). A third grader’s way of thinking about linear function tables. Journal of Mathematical Behavior,...
    • Meira, L. (1 995). The microevolution of mathematical representations in children’s activities. Cognition and Instruction, 13(2),...
    • Moss, J., Beatty, R., McNab, S. L., & Eisenband, J. (2006). The potential ofgeometric sequences to foster young students’ ability...
    • Nunes, T., Schliemann, A.D., & Carraher, D.W. (1 993). Mathematics in the Streets and in Schools. Cambridge, U.K: Cambridge...
    • Pearson Scott Foresman. (1 998). Investigations in Number, Data, and Space. Glenview, Ill., Author.
    • Radford, L., Bardini, C., & Sabena, C. (2007). Perceiving the general: the multisemiotic dimension of students' algebraic activity....
    • Sadovsky, P. (2005). Enseñar matemática hoy: Miradas, sentidos y desafíos [Teaching mathematics today: Perspectives, meanings, and...
    • Saporta, G. (1 990). Analyse des donnees et statistiques. Editions Technip.
    • Scheuer, N., de la Cruz, M., Pozo, J. I., Huarte, M. F., & Sola, G. (2006). The mind is not a black box: Children's ideas about the...
    • Schliemann, A. D., Carraher, D., & Brizuela, B. M. (2007). Bringing Out the Algebraic Character of Arithmetic: From Children’s Ideas...
    • Schliemann, A. D., Carraher, D. W., & Brizuela, B. M. (2012). Algebra in Elementary School. In Coulange, L., Drouhard, J.-P., Dorier, J.-L.,...
    • Schwartz, J. (1 996). Can technology help us make the mathematics curriculum intellectually stimulating and socially responsible? Paper...
    • Smith, J. & Thompson, P. (2008). Quantitative Reasoning and the Development of Algebraic Reasoning. In J. Kaput. D. Carraher, & M....
    • Usiskin, Z. (1 988). Conceptions of school algebra and uses of variables. In A. F. Coxford & A. P. Shulte (Eds.), The ideas of algebra:...
    • Vergnaud, G. (1 982). A classification of cognitive tasks and operations of thought involved in addition and subtraction problems. In T....
    • Vergnaud, G. (1 985). L'enfant, la mathématique et la réalité : problèmes de l'enseignement des mathématiques áa l'école...
    • Vergnaud, G. (1 988). Multiplicative structures. In J. Hiebert &M. Behr (Eds.), Number concepts and operations in the middle grades...
    • Vergnaud, G. (1 994). Multiplicative conceptual field: What and why? In G. Harel & J. Confrey (Eds.), The development of multiplicative...
    • Verschaf el, L., Greer, B., & De Corte, E. (2002). Everyday knowledge and mathematical modeling of school word problems. In K. Gravemeijer,...
    • Wagner, S. (1 981 ). Conservation of equation and function under transformations of variable. Journal for Research in Mathematics Education,...
    • Zhang, J. (1 997). The nature of external representations in problem solving. Cognitive science, 21 (2), 179-217.
    • Zhang, J., & Norman, D. A. (1 994). Representations in distributed cognitive tasks. Cognitive Science, 18, 87-122.
    • Zhang, J., & Norman, D. A. (1 995). A representational analysis of numeration systems. Cognition, 57, 271 -295.

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno