Learning Sciences

Radical constructivists advocate discovery-based 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 mediated-discovery hypothesis, we present and analyze vignettes selected from empirical data gathered in a conjecture-driven design-based research study investigating the microgenesis of proportional reasoning through guided engagement in technology-based embodied interaction. 22 Grade 4–6 students participated in individual or paired semi-structured tutorial clinical interviews, in which they were tasked to remote-control 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 two-step guided re-invention 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 hook-and-shift 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.

Abstract: Learning scientists are only beginning to appreciate the potential of synergy between two concurrent developments—theory of embodied cognition and technology of embodied interaction. We characterize and evaluate this prospective synergy from a sociocultural perspective. First we analyze learning in explicitly embodied cultural practices (eg, surfing), then analogize to the implicitly embodied practice of mathematics.

Recent theories of cognition model human reasoning as tacit simulated action. Implications for the philosophy, design, and practice of mathematics instruction may be momentous. We report on findings from a pioneering design-based research study into the embodied roots of proportional reasoning that also explored the pedagogical potential of embodied-interaction (EI), a form of technology-enabled immersive activity.

We chart a historical analysis of a collaborative design-based research project investigating the emergence of mathematical meaning from embodied interaction with a technological trackingsystem supporting the learning of proportionality. Recounting iterative cycles of a conceptually critical perceptual feedback element, we articulate three interconnected images of researchbased designers: (a) Janus the two-headed keeper of passageways who sees artifacts alternately as a student would or as an expert would; (b) an investigator searching to explicate design decisions coherently in light of learning-sciences theory; and (c) a reflective practitioner who embraces tradeoffs and is open to constructive criticism and to implementing radical changes to design and theory. Ultimately, we posit, we as researchers are continuously developing professional vision for our own design even as the design changes.

This on-going design-based research study focuses on Grade 4-6 students' guided task-based interaction with a novel computer-based hand-tracking system built to suggest the limitations of naïve additive schemes and create opportunities to develop core notions of proportionality as elaborations on these schemes, even before engaging numerical semiotic forms. Study participants struggled with canonical issues inherent to rational numbers. They formulated a string of insights leading up to a new type of equivalence class. Reported as a case study of Itamar, a 5 th -grade middle-achieving student, our analyses reveal emergence of conceptually critical mathematical meanings in an activity that initially bears little mathematical significance.

" Community " has become a commonplace term in the learning sciences. Alongside this popularization comes the view that communities are, in general, something to strive towards. We draw on contemporary trends to problematize this assumption and motivate a discussion for the productivity of dissent.

Familiarity with the construction, test, and refinement of computational algorithms is of critical importance to many disciplines in the 21st century. We introduce a novel learning environment that lowers the threshold to participation in algorithmic practices including using functions to transform input, using conditionals to selectively transform or manipulate input, creating simple and complex algorithms, and testing and debugging algorithms to iteratively improve them. Our learning environment leverages VR technology and principles of embodied cognition that prioritize "hands in" learning. Instead of creating algorithms through traditional computational programming (which often renders the structure and components of an algorithm opaque), students using our technology build "concrete algorithms" in the form of a virtual Rube Goldberg-type machine that makes the algorithm's structure, components, and functioning visible.