From conjecture generation by maintaining dragging to proof

In this paper we propose a hypothesis about how different uses of maintaining dragging, either as a physical tool in a dynamic geometry environment or as a psychological tool for generating conjectures can influence subsequent processes of proving. Through two examples we support the hypothesis that using maintaining dragging as a physical tool may foster cognitive rupture between the conjecturing phase and the proof, while using it as a psychological tool may foster cognitive unity between them.Comment: Research report at the 40th PME conference, Hungar

Maintaining dragging and the pivot invariant in processes of conjecture generation

In this paper, we analyze processes of conjecture generation in the context of open problems proposed in a dynamic geometry environment, when a particular dragging modality, maintaining dragging, is used. This involves dragging points while maintaining certain properties, controlling the movement of the figures. Our results suggest that the pragmatic need of physically controlling the simultaneous movements of the different parts of figures can foster the production of two chains of successive properties, hinged together by an invariant that we will call pivot invariant. Moreover, we show how the production of these chains is tied to the production of conjectures and to the processes of argumentation through which they are generated.Comment: Research report at the 40th PME Conference, Hungar

Reasoning By Contradiction in Dynamic Geometry

This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students’ work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we support the claim that a DGS can offer “guidance” in the solver’s development of an indirect argument thanks to the potential it offers of both constructing certain properties robustly, and of helping the solver perceive pseudo objects

Life of a Peruvian art collector: Guillermo Schmidt Pizarro and the fostering of public collections of pre-Hispanic art in the first half of the 20th century

Guillermo Schmidt Pizarro was a famous collector of Peruvian origins, active in Europe and the United States beginning in the early twentieth century. He traded numerous pre-Hispanic and colonial artifacts to the most important museums of the time. The focus of this preliminary work is to trace his biography and the sales he dealt with over thirty years of activity. Thanks to provenance information, the authors have been able to sometimes “virtually build up” fragments of textiles that he scattered among diverse public and private institutions. The importance of this research is consistent with the efforts of museums to trace the origin of every artifact in their collections. Guillermo Schmidt Pizarro fue un famoso coleccionista de origen peruano activo en Europa y en los Estados Unidos desde la primera mitad del siglo XX. Él estuvo en contacto con los museos más importantes de su época, ofreciéndoles numerosos artefactos prehispánicos y coloniales. El enfoque del presente trabajo preliminar es trazar su biografía y las ventas en las cuales estuvo involucrado durante más de treinta años de actividad. Gracias a los datos de provenance, las autoras en algunos casos han podido “reconstruir de forma virtual” los fragmentos de textiles que él ha disperso entre diversas instituciones públicas y particulares. La importancia de esta investigación queda en respaldar los esfuerzos de los museos para trazar el origen de cada artefacto en sus colecciones. Guillermo Schmidt Pizarro était un célèbre collectionneur originaire du Pérou qui opéra en Europe et aux États-Unis au début du XXe siècle. Il eut des rapports étroits avec les musées les plus importants de son époque auxquels il procura plusieurs artefacts préhispaniques et coloniaux. Le but de ce travail préliminaire est de tracer sa biographie et les ventes dont il s’occupa pendant plus de trente ans d’activité. Grâce aux informations de provenance, les auteures ont parfois pu « reconstruire virtuellement » les fragments de tissus dispersés parmi diverses institutions publiques et privées. L’importance de cette recherche constitue une contribution offerte aux musées pour retracer l’origine des artefacts de leurs collections

Temperature adaptation of glutathione S-transferase P1-1. A case for homotropic regulation of substrate binding.

Human glutathione S-transferase P1-1 (GST P1-1) is a homodimeric enzyme expressed in several organs as well as in the upper layers of epidermis, playing a role against carcinogenic and toxic compounds. A sophisticated mechanism of temperature adaptation has been developed by this enzyme. In fact, above 35 degrees C, glutathione (GSH) binding to GST P1-1 displays positive cooperativity, whereas negative cooperativity occurs below 25 degrees C. This binding mechanism minimizes changes of GSH affinity for GST P1-1 because of temperature fluctuation. This is a likely advantage for epithelial skin cells, which are naturally exposed to temperature variation and, incidentally, to carcinogenic compounds, always needing efficient detoxifying systems. As a whole, GST P1-1 represents the first enzyme which displays a temperature-dependent homotropic regulation of substrate (e.g. GSH) binding

Il trascinamento di mantenimento nella formulazione di congetture in ambienti di geometria dinamica

In ambienti di geometria dinamica, il trascinamento di mantenimento è una particolare modalità di trascinamento che consiste nel muovere un punto base di una figura in modo che la figura mantenga certe proprietà. L’uso del trascinamento di mantenimento è stato riscontrato nell’attività spontanea di studenti e, anni dopo, proposto esplicitamente ad alcuni allievi nel corso di un progetto di ricerca di cui questo articolo riporta alcuni dei risultati più significativi. In particolare, dopo l’analisi di un caso, sarà presentato un modello per l’analisi cognitiva dei processi di generazione di congetture con l’uso del trascinamento di mantenimento. Concluderemo con alcune riflessioni sulle implicazioni didattiche

Spatial and kinematic segregation in star-cluster merger remnants

Globular clusters that exhibit chemical and dynamical complexity have been suggested to be the stripped nuclei of dwarf galaxies(e.g. M54, ω Cen). We use N-body simulations of nuclear star clusters forming via the mergers of star clusters to explore the persistence of substructure in the phase space. We find that the observed level of differentiation is difficult to reconcile with the observed if nuclear clusters form wholly out of the mergers of star clusters. Only the star clusters that merged most recently retain sufficiently distinct density and kinematics to be distinguishable from the rest of the nuclear cluster. In situ star formation must therefore be included to explain the observed properties of nuclear star clusters, in good agreement with previous results