Agency as Inference : Toward a Critical Theory of Knowledge Objectification
Gutiérrez, José Francisco (University of California at Berkeley)

Data:	2013
Resum:	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 cultural artifacts (e. g. , algebraic symbols and forms) as semiotic means of objectifying their pre-symbolic 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 of mathematical 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 iterationsâ€""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-and-instruction analyses are discussed.
Drets:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Algebraic reasoning ; Agency ; Equity ; Generalization ; Inference
Publicat a:	REDIMAT : Revista de Investigación en Educación Matemática, Vol. 2 Núm. 1 (Febrero 2013) , p. 45-76, ISSN 2014-3621

Adreça alternativa: https://hipatiapress.com/hpjournals/index.php/redimat/article/view/525

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