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ERIC Number: EJ1112193
Record Type: Journal
Publication Date: 2013-Feb
Pages: 33
Abstractor: As Provided
ISBN: N/A
ISSN: EISSN-2014-3621
EISSN: N/A
Agency as Inference: Toward a Critical Theory of Knowledge Objectification
Gutiérrez, José Francisco
REDIMAT - Journal of Research in Mathematics Education, v2 n1 p45-76 Feb 2013
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 semiotic-cultural artifacts (e.g., algebraic symbols and forms) to objectify 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 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-and-instruction analyses are discussed.
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Publication Type: Journal Articles; Reports - Research
Education Level: Secondary Education; High Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: California
Grant or Contract Numbers: N/A