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Agency as Inference: Toward a Critical Theory of Knowledge Objectification

  • Autores: José Francisco Gutiérrez
  • Localización: REDIMAT, ISSN-e 2014-3621, Vol. 2, Nº. 1, 2013, págs. 45-76
  • Idioma: inglés
  • Enlaces
  • Resumen
    • español

      Este artículo evalúa la verosimilitud de sintetizar la teoría del conocimiento objetivado (Radford, 2003) con investigación sobre equidad en didáctica de las matemáticas. Propongo el fenómeno cognitivo de inferencia matemática como un concepto prometedor para la investigación de los tipos de agencia de la equidad impulsadas por los estudiantes. Conceptualizo la apropiación de los estudiantes de los artefactos semióticos-culturales (p.e. símbolos y formas algebraicas) como medios para objetivar sus inferencias pre-simbólicas como condiciones de su agencia para construir cuidadosamente el significado de esos artefactos. A fin de basar empíricamente este enfoque emergente, este estudio se centra en la generalización algebraica (como un típo de inferencia matemática) y aplica el marco desarrollado por Radford a los datos de vídeo de dos iteraciones de una intervención educativa llevada a cabo en una escuela secundaria con jóvenes en riesgo. Se analizan y comparan las conversaciones de los estudiantes sobre la apropiación / obetivación, centradas en el patrón de enseñanza adoptado por cada una de las iteraciones ("instrucción directa" versus "basada en la investigación.") El análisis muestra que la ejecución que implica instrucción basada en la investigación permitió un acceso más equitativo a las oportunidades de inferencia agencia-como-matemática, mientras que la aplicación directa de la participación de la instrucción era aparentemente más productiva. Implicaciones para la investigación de acciones futuras que incluyan análisis de la cognición y la instrucción se discuten.

    • English

      This article evaluates the plausibility of synthesizing theory of knowledge objectification (Radford, 2003) with equity research on mathematics education.

      I suggest the cognitive phenomenon of mathematical inference as a promising locus for investigating the types of agency that equity-driven scholars often care for. In particular, I conceptualize students� appropriation of semioticcultural artifacts (e.g., algebraic symbols and forms) to objectify their presymbolic inferences as conditional on their agency to carefully and incrementally construct personal meaning for these artifacts. To empirically ground this emerging approach, this study focuses on algebraic generalization (as a type ofmathematical inference) and applies Radford�s framework to video data of two iterations of an instructional intervention conducted in a high school program for academically at-risk youth. I analyze and compare students� acts of appropriation/objectification during whole-class conversations centered on pattern-finding tasks, in relation to the instructional mode adopted for each of the iterations��direct instruction� vs. �inquiry-based.� The analysis shows that the implementation involving inquiry-based instruction enabled more equitable access to opportunities for agency-as-mathematical inference, whereas the implementation involving direct-instruction was ostensibly more productive. Implications for future equity research involving cognition-andinstruction analyses are discussed.

  • Referencias bibliográficas
    • Abrahamson, D. (2009). Orchestrating semiotic leaps from tacit to cultural quantitative reasoning—the case of anticipating experimental...
    • Arcavi, A. (1 994). Symbol sense: informal sense-making in formal mathematics. For the Learning ofMathematics, 14(3 ), 24-35.
    • Ball, D. L., Battista, M. T., Harel, G., Thompson, P. W., & Confrey, J. E. (201 0). Keeping the mathematics in mathematics education...
    • Boaler, J. (2008). Promoting 'relational equity' and high mathematics achievement through an innovative mixed-ability approach....
    • Boaler, J., & Greeno, J. G. (2000). Identity, agency, and knowing in mathematics worlds. In J. Boaler (Ed.), Multiple perspectives on...
    • Cobb, P., & Hodge, L. L. (2002). A relational perspective on issues of cultural diversity and equity as they play out in the mathematics...
    • Confrey, J. E. (201 0). “Both And”—equity and mathematics: a response to Martin, Gholson, and Leonard. Journal of Urban Mathematics Education,...
    • Diversity in Mathematics Education (DiME). (2007). Culture, race, power, and mathematics education. In F. K. Lester (Ed.), Second handbook...
    • Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics,...
    • Esmonde, I. (2009). Ideas and identities: Supporting equity in cooperative mathematics learning. Review of Educational Research,...
    • Filloy, E., & Rojano, T. (1 989). Solving equations: the transition from arithmetic to algebra. For the Learning of Mathematics, 9(2),...
    • Gresalfi, M., Martin, T., Hand, V., & Greeno, J. G. (2009). Constructing competence: an analysis of student participation in the activity...
    • Gutiérrez, J. (201 0). "I don't know--I'm just genius!": distinguishing between the process and the product of student...
    • Gutiérrez, R. (2002). Enabling the practice of mathematics teachers in context: toward a new equity research agenda. Mathematical Thinking and Learning,...
    • Heid, K. (201 0). Where’s the math (in mathematics education research)? Journal for Research in Mathematics Education, 41 (2), 1 02-1 03 .
    • Herscovics, N., & Linchevski, L. (1 994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27,...
    • Kaput, J. J. (2007). What is algebra? What is algebraic reasoning? In J. J. Kaput, D. W. Carraher & M. Blanton (Eds.), Algebra in the...
    • Ladson-Billings, G. (1 998). It doesn't add up: African American students' mathematics achievement. In C. Malloy & L. ...
    • Lee, C. D. (2006). The teaching and learning of intellective competence. In E. W. Gordon & B. L. Bridglall (Eds.), Afirmative development:...
    • Martin, D. B., Gholson, M. L., & Leonard, J. (201 0). Mathematics as gatekeeper: power and privilege in the production of knowledge. Journal...
    • Moses, R., & Cobb, C. (2001 ). Radical equations: math literacy and civil rights. Boston: Beacon Press.
    • National Science Board (NSB). (2008). Science and engineering indicators 2008. Arlington, VA: National Science Foundation.
    • Oakes, J., Joseph, R., & Muir, K. (2004). Access and achievement in mathematics and science: inequalities that endure and change. In J....
    • Pickering, A. (1 995). The mangle ofpractice: time, agency, and science. Chicago: University of Chicago Press.
    • Radford, L. (2003 ). Gestures, speech, and the sprouting of signs: a semiotic–cultural approach to students' types of generalization....
    • Radford, L. (2006). Elements of a cultural theory of objectification. Revista Latinoamerecana de investigacion en Matematica Eduactiva,...
    • Radford, L. (2008). Iconicity and contraction: a semiotic investigation of forms of algebraic generalizations of patterns in dif...
    • Radford, L. (201 0). Algebraic thinking from a cultural semiotic perspective. Research in Mathematics Education, 12(1 ), 1 -1 9....
    • RAND Mathematics Study Panel. (2003 ). Mathematical proficiency for all students: toward a strategic research and development program...
    • Rivera, F. D. (2008). On the pitfalls of abduction: Complicities and complexities in patterning activity. For the Learning of Mathematics,...
    • Sánchez-Jankowski, M. (2008). Cracks in the pavement: social change and resilience in poor neighborhoods. Berkeley, CA: University...
    • Schoenfeld, A. H. (2007). Early algebra as sense-making. In J. J. Kaput, D. W. Carraher & M. Blanton (Eds.), Algebra in the early grades...
    • Schoenfeld, A. H., Smith, J. P., & Arcavi, A. (1 993 ). Learning: the microgenetic analysis of one student’s evolving understanding of...
    • Sfard, A. (2007). When the rules of discourse change, but nobody tells you: making sense of mathematics learning from a commognitive standpoint....
    • Willis, P. (1 977). Learning to labor: how working class kids get working class jobs. New York, NY: Columbia University Press.
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