Hooks and Shifts: A Dialectical Study of Mediated Discovery
 Dor Abrahamson,
 Dragan Trninic,
 Jose F. Gutiérrez,
 Jacob Huth,
 Rosa G. Lee
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Abstract
Radical constructivists advocate discoverybased pedagogical regimes that enable students to incrementally and continuously adapt their cognitive structures to the instrumented cultural environment. Some sociocultural theorists, however, maintain that learning implies discontinuity in conceptual development, because novices must appropriate expert analyses that are schematically incommensurate with their naive views. Adopting a conciliatory, dialectical perspective, we concur that naive and analytic schemes are operationally distinct and that cultural–historical artifacts are instrumental in schematic reconfiguration yet argue that students can be steered to bootstrap this reconfiguration in situ; moreover, students can do so without any direct modeling from persons fluent in the situated use of the artifacts. To support the plausibility of this mediateddiscovery hypothesis, we present and analyze vignettes selected from empirical data gathered in a conjecturedriven designbased research study investigating the microgenesis of proportional reasoning through guided engagement in technologybased embodied interaction. 22 Grade 4–6 students participated in individual or paired semistructured tutorial clinical interviews, in which they were tasked to remotecontrol the location of virtual objects on a computer display monitor so as to elicit a target feedback of making the screen green. The screen would be green only when the objects were manipulated on the screen in accord with a “mystery” rule. Once the participants had developed and articulated a successful manipulation strategy, we interpolated various symbolic artifacts onto the problem space, such as a Cartesian grid. Participants appropriated the artifacts as strategic or discursive means of accomplishing their goals. Yet, so doing, they found themselves attending to and engaging certain other embedded affordances in these artifacts that they had not initially noticed yet were supporting performance subgoals. Consequently, their operation schemas were surreptitiously modulated or reconfigured—they saw the situation anew and, moreover, acknowledged their emergent strategies as enabling advantageous interaction. We propose to characterize this twostep guided reinvention process as: (a) hooking—engaging an artifact as an enabling, enactive, enhancing, evaluative, or explanatory means of effecting and elaborating a current strategy; and (b) shifting—tacitly reconfiguring current strategy in response to the hooked artifact’s emergent affordances that are disclosed only through actively engaging the artifact. Looking closely at two cases and surveying others, we delineate mediated interaction factors enabling or impeding hookandshift learning. The apparent cognitive–pedagogical utility of these behaviors suggests that this ontological innovation could inform the development of a heuristic design principle for deliberately fostering similar learning experiences.
Inside
Within this Article
 Introduction and Objectives
 Theoretical Background and Deliberations
 Data Source: A ConjectureDriven DesignBased Research Study of the Emergence of Proportional Reasoning from Guided EmbodiedInteraction ProblemSolving Activity
 Case Analyses: Progressive Mathematization Through Hooks and Shifts
 Conclusion: From Ontological Innovation to Design Heuristic
 References
 References
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 Title
 Hooks and Shifts: A Dialectical Study of Mediated Discovery
 Journal

Technology, Knowledge and Learning
Volume 16, Issue 1 , pp 5585
 Cover Date
 20110401
 DOI
 10.1007/s107580119177y
 Print ISSN
 22111662
 Online ISSN
 15731766
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Additive reasoning
 Cognition
 Conceptual change
 Designbased research
 Discovery
 Embodied interaction
 Functional extension
 Guided reinvention
 Mathematics education
 Proportion
 Proportional reasoning
 Remote control
 Sociocultural
 Symbolic artifact
 Virtual object
 Authors

 Dor Abrahamson ^{(1)}
 Dragan Trninic ^{(1)}
 Jose F. Gutiérrez ^{(1)}
 Jacob Huth ^{(1)}
 Rosa G. Lee ^{(1)}
 Author Affiliations

 1. Graduate School of Education, University of California, 4649 Tolman Hall, Berkeley, CA, 947201670, USA