Représentations dynamiques et tangibles dans l'enseignement mathématique

International audienceDynamic geometry environments offer a new kind of representation of mathematical objects that are variable and behave "mathematically" when one of the elements of the construction is dragged. The chapter addresses three dimensions about the transformations brought by this new kind of representation in mathematics and mathematics education: an epistemological dimension, a cognitive dimension and a didactic dimension. As so often stated since the time of ancient Greece, the nature of mathematical objects is by essence abstract. Mathematical objects are only indirectly accessible through representations (D'Amore 2003, pp. 39-43) and this contributes to the paradoxical character of mathematical knowledge: "The only way of gaining access to them is using signs, words or symbols, expressions or drawings. But at the same time, mathematical objects must not be confused with the used semiotic representations" (Duval 2000, p. 60). Other researchers have stressed the importance of these semiotic systems under various names. Duval calls them registers. Bosch and Chevallard (1999) introduce the distinction between ostensive and non ostensive objects and argue that mathematicians have always considered their work as dealing with non-ostensive objects and that the treatment of ostensive objects (expressions, diagrams, formulas, graphical representations) plays just an auxiliary role for them. Moreno Armella (1999) claims that every cognitive activity is an action mediated by material or symbolic tools. Through digital technologies, new representational systems were introduced with increased capabilities in manipulation and processing. The dragging facility in dynamic geometry environments (DGE) illustrates very well the transformation technology can bring in the kind of representations offered for mathematical activity and consequently for the meaning of mathematical objects. A diagram in a DGE is no longer a static diagram, representing an instance of a geometricalLes environnements de géométrie dynamique offrent un nouveau type d'objets mathématiques variables qui se modifient quand l'un des éléments de la construction est déplacé.Le chapitre aborde trois dimensions relatives aux transformations apportées par ce nouveau type de représentations en mathématiques et dans l'enseignement des mathématiques : une dimension épistémologique, une dimension cognitive et une dimension didactique

Reasons Seventh-day Adventist Parents Gave for Not Sending Their Children to Seventh-day Adventist Elementary and Secondary Schools

Problem. The Seventh-day Adventist elementary and secondary schools in the USA show a continuous enrollment decline. This study’s goal is to explore the reasons SDA parents give for why they do not send their children to SDA schools. Method. The participants were limited to the church members of the Lake Union Conference. Qualitative methodology was used in this study. Three groups of participants were selected using criterion sampling—non-home-schooling parents, home- schooling parents, and administrators. Data collection occurred through in-depth interviews, focus groups, and a one-question survey. The interviews were audiotaped. The tapes were transcribed verbatim, coded, and grouped into themes. Analysis and interpretation were verified by some participants, peer reviews, and triangulation. Results. Financial issues were the most cited reason for non-attendance. Home-schooling was the next great competitor. Home-schooling parents had noticed the lowering of school values and standards, and the strong influential power that some peers had on others. The students’ styles of dress, conversations, and demeanor no longer impressed them. Other non-home-schooling parents sent their children to public schools because these institutions have more resources, more qualified teachers, and better facilities. Public schools offered a wider range of subjects, competitive sports and scholarships, extracurricular activities, music, after-school programs, and other free services. Many SDA teachers work at public schools, and parents claimed that they took better care of their children. SDA academies were located too far away from home, and transportation caused parents to worry about their children’s safety. A few parents withdrew their children from SDA schools due to perceived unresolved conflicts. Changes in student population are affecting SDA schools, and some pastors were not supporting Christian education. Conclusion. Many SDA children are deprived of a Christian education due to lack of finance. Home-schooling parents are diligently controlling their children’s educational, spiritual, and moral training. Some non-home-schooling parents see public schools as better than SDA schools. Other non-home-schooling parents want schools to be located in close proximity to their homes. Parents, teachers, pastors, administrators, superintendents, and their staff must work together to educate all SDA children

²¹⁰Pb- ²²⁶Ra chronology reveals rapid growth rate of Madrepora oculata and Lophelia pertusa on world's largest cold-water coral reef

Here we show the use of the 210Pb- 226Ra excess method to determine the growth rate of two corals from the world's largest known cold-water coral reef, Røst Reef, north of the Arctic circle off Norway. Colonies of each of the two species that build the reef, Lophelia pertusa and Madrepora oculata, were collected alive at 350 m depth using a submersible. Pb and Ra isotopes were measured along the major growth axis of both specimens using low level alpha and gamma spectrometry and trace element compositions were studied. 210Pb and 226Ra differ in the way they are incorporated into coral skeletons. Hence, to assess growth rates, we considered the exponential decrease of initially incorporated 210Pb, as well as the increase in 210Pb from the decay of 226Ra and contamination with 210Pb associated with Mn-Fe coatings that we were unable to remove completely from the oldest parts of the skeletons. 226Ra activity was similar in both coral species, so, assuming constant uptake of 210Pb through time, we used the 210Pb- 226Ra chronology to calculate growth rates. The 45.5 cm long branch of M. oculata was 31 yr with an average linear growth rate of 14.4 ± 1.1 mm yr -1 (2.6 polyps per year). Despite cleaning, a correction for Mn-Fe oxide contamination was required for the oldest part of the colony; this correction corroborated our radiocarbon date of 40 yr and a mean growth rate of 2 polyps yr -1. This rate is similar to the one obtained in aquarium experiments under optimal growth conditions. For the 80 cm-long L. pertusa colony, metal-oxide contamination remained in both the middle and basal part of the coral skeleton despite cleaning, inhibiting similar age and growth rate estimates. The youngest part of the colony was free of metal oxides and this 15 cm section had an estimated a growth rate of 8 mm yr -1, with high uncertainty (∼1 polyp every two to three years). We are less certain of this 210Pb growth rate estimate which is within the lowermost ranges of previous growth rate estimates. We show that 210Pb- 226Ra dating can be successfully applied to determine the age and growth rate of framework-forming cold-water corals if Mn-Fe oxide deposits can be removed. Where metal oxides can be removed, large M. oculata and L. pertusa skeletons provide archives for studies of intermediate water masses with an up to annual time resolution and spanning over many decades. © 2012 Author(s)

La muerte y la doncella : diseños para xilografía

El proyecto de esta obra gráfica tiene un origen en el conocimiento y la valoración de la música de Franz Schubert, en especial del cuarteto en re menor «La muerte y la doncella»

Protein-membrane interaction and fatty acid transfer from intestinal fatty acid-binding protein to membranes: Support for a multistep process

Fatty acid transfer from intestinal fatty acid-binding protein (IFABP) to phospholipid membranes occurs during protein-membrane collisions. Electrostatic interactions involving the α-helical "portal" region of the protein have been shown to be of great importance. In the present study, the role of specific lysine residues in the α-helical region of IFABP was directly examined. A series of point mutants in rat IFABP was engineered in which the lysine positive charges in this domain were eliminated or reversed. Using a fluorescence resonance energy transfer assay, we analyzed the rates and mechanism of fatty acid transfer from wild type and mutant proteins to acceptor membranes. Most of the α-helical domain mutants showed slower absolute fatty acid transfer rates to zwitterionic membranes, with substitution of one of the lysines of the α2 helix, Lys27, resulting in a particularly dramatic decrease in the fatty acid transfer rate. Sensitivity to negatively charged phospholipid membranes was also reduced, with charge reversal mutants in the α2 helix the most affected. The results support the hypothesis that the portal region undergoes a conformational change during protein-membrane interaction, which leads to release of the bound fatty acid to the membrane and that the α2 segment is of particular importance in the establishment of charge-charge interactions between IFABP and membranes. Cross-linking experiments with a phospholipid-photoactivable reagent underscored the importance of charge-charge interactions, showing that the physical interaction between wild-type intestinal fatty acid-binding protein and phospholipid membranes is enhanced by electrostatic interactions. Protein-membrane interactions were also found to be enhanced by the presence of ligand, suggesting different collisional complex structures for holo- and apo-IFABP.Instituto de Investigaciones Bioquímicas de La Plat

A predictive inline model for nonlinear stimulated Raman scattering in a hohlraum plasma

In this Letter, we introduce a new inline model for stimulated Raman scattering (SRS), which runs on our radiation hydrodynamics code TROLL. The modeling follows from a simplified version of a rigorous theory for SRS, which we describe, and accounts for nonlinear kinetic effects. It also accounts for the SRS feedback on the plasma hydrodynamics. We dubbed it PIEM because it is a fully PredIctivE Model, no free parameter is to be adjusted \textit{a posteriori}~in order to match experimental results. PIEM predictions are compared against experimental measurements performed at the Ligne d'Int\'egration Laser. From these comparisons, we discuss PIEM ability to correctly catch the impact of nonlinear kinetic effects on SRS

Vital Humanities. Their educational Potential

In Classical Greece, conversation was considered the supreme form of human expression, in that it was the most human way that a person uses his/her body. Learning to speak properly—as H.I. Marrou asserts— meant thinking and living properly. Eloquence was what differentiated civilized human beings from barbarians.1 It is from these beginnings that the importance and meaning of the Humanities were understood in the most generic sense of the word. The aim of this paper is to reexamine the Humanities insofar as they have a genuine educational dimension. The first part contemplates the Humanities from a classical perspective and its situation in present day knowledge-based society. The second part examines what happened to the Humanities in the nineteenth-century Western world, and compares that to what happened later. In the third part, some lines of argument are presented, which show how vital the Humanities are to education. This paper concludes that the Humanities are necessary to modern-day goals, both in the educational and social contexts