The plot thickens: The aesthetic dimensions of a captivating mathematics lesson

We present an analysis of a sixth-grade mathematics lesson in which an aesthetically-rich moment of mathematical surprise, inspired by a decontextualized integer addition problem, spurred students to ask mathematical questions and actively sustain inquiry into the lesson’s central ideas. In order to understand how the unfolding mathematical content enabled this moment, we interpret the lesson as a mathematical story. Using this narrative framework, we describe the aesthetic dimensions of the story including its plot, density, coherence, and rhythm, and connect them to the unfolding mathematical content. This analysis demonstrates how these aesthetic elements of a lesson can be recognized and how they help explain the students’ productive engagement. This framework offers a potential tool for researchers and practitioners who seek to understand, design, and enact captivating mathematical experiences.Accepted manuscrip

Adult participation in children’s word searches: on the use of prompting, hinting, and supplying a model

Although word searching in children is very common, very little is known about how adults support children in the turns following the child’s search behaviours, an important topic because of the social, educational and clinical implications. This study characterises, in detail, teachers’ use of prompting, hinting and supplying a model. From a classroom dataset of 53 instances, several distinctive patterns emerged. A prompted completion sequence is initiated by a ‘word retrieval elicitor’ (‘fishing’) and is interpreted as a request to complete the phrase. Non-verbal prompting is accomplished through a combination of gaze and gesture and, also, as a series of prompts. Hinting supplies a verbal clue, typically via a wh-question, or by specifying the nature of the repairable. In contrast, the strategies that supply a linguistic model include both embedded and exposed corrections and offers of candidates. A sequential relationship was found between prompting, hinting and supplying a model which has implications for how clinicians and teachers can foster self-repair

Atlas.txt : Exploring Lingusitic Grounding Techniques for Communicating Spatial Information to Blind Users

Peer reviewedPostprin

Experimental String Field Theory

We develop efficient algorithms for level-truncation computations in open bosonic string field theory. We determine the classical action in the universal subspace to level (18,54) and apply this knowledge to numerical evaluations of the tachyon condensate string field. We obtain two main sets of results. First, we directly compute the solutions up to level L=18 by extremizing the level-truncated action. Second, we obtain predictions for the solutions for L > 18 from an extrapolation to higher levels of the functional form of the tachyon effective action. We find that the energy of the stable vacuum overshoots -1 (in units of the brane tension) at L=14, reaches a minimum E_min = -1.00063 at L ~ 28 and approaches with spectacular accuracy the predicted answer of -1 as L -> infinity. Our data are entirely consistent with the recent perturbative analysis of Taylor and strongly support the idea that level-truncation is a convergent approximation scheme. We also check systematically that our numerical solution, which obeys the Siegel gauge condition, actually satisfies the full gauge-invariant equations of motion. Finally we investigate the presence of analytic patterns in the coefficients of the tachyon string field, which we are able to reliably estimate in the L -> infinity limit.Comment: 37 pages, 6 figure