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

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

Kinetic effects in stimulated Brillouin scattering

The role of ion and electron kinetic effects in the nonlinear evolution of stimulated Brillouin scattering (SBS) is investigated by means of particle-in-cell numerical simulations. The simulations were carried out in one and two spatial dimensions (1D and 2D), with a full PIC code, in which both ions and electrons are kinetic. The full PIC simulations are compared with those obtained from a hybrid PIC code (kinetic ions and Boltzmann electrons), making it possible to determine in which limit the electron kinetic effects are important. The simulation geometry corresponds to a coherent laser beam interacting with an expanding plasma slab. In the 1D simulations, the interaction becomes incoherent, as time goes on, in a domain that spatially begins in the plasma region close to the laser light entrance, and that ends within the plasma at a frontier which moves faster than the ion acoustic wave (IAW) velocity. The higher the laser intensity, the faster moves the frontier of this spatial domain. The SBS reflectivity drops at the very moment when this domain fills entirely the plasma. Two regimes have to be distinguished. In the regimes of low laser intensity, strong sub-harmonic generation of the excited IAW is observed to take place in this moving spatial domain, so that the SBS reflectivity drop is interpreted as being due to sub-harmonic generation. In the opposite regime of high laser intensity, there is no evidence of strong sub-harmonic generation, whereas a strong ion heating is observed, so that the reflectivity drop is interpreted as being due to enhanced ion damping. In the 1D simulations the electron kinetic effects are found to be able to smooth temporally the SBS reflectivity, although the overall picture remains the same when the electrons are taken as a Boltzmann fluid. In the 2D simulations, the SBS reflectivity is observed to drop rapidly in time because of the efficient nonlinear Landau damping on the ions, as previously reported by Cohen et al. [1]. In these 2D simulations, the electron kinetic effects are found to play a negligible role as compared with the ion kinetic effects

The carbon concentrating mechanism in Chlamydomonas reinhardtii: Finding the missing pieces

The photosynthetic, unicellular green alga, Chlamydomonas reinhardtii, lives in environments that often contain low concentrations of CO2 and HCO3-, the utilizable forms of inorganic carbon (Ci). C. reinhardtii possesses a carbon concentrating mechanism (CCM) which can provide suitable amounts of Ci for growth and development. This CCM is induced when the CO2 concentration is at air levels or lower and is comprised of a set of proteins that allow the efficient uptake of Ci into the cell as well as its directed transport to the site where Rubisco fixes CO2 into biomolecules. While several components of the CCM have been identified in recent years, the picture is still far from complete. To further improve our knowledge of the CCM, we undertook a mutagenesis project where an antibiotic resistance cassette was randomly inserted into the C. reinhardtii genome resulting in the generation of 22,000 mutants. The mutant collection was screened using both a published PCR-based approach (Gonzalez-Ballester et al. 2011) and a phenotypic growth screen. The PCR-based screen did not rely on a colony having an altered growth phenotype and was used to identify colonies with disruptions in genes previously identified as being associated with the CCM-related gene. Eleven independent insertional mutations were identified in eight different genes showing the usefulness of this approach in generating mutations in CCM-related genes of interest as well as identifying new CCM components. Further improvements of this method are also discussed. © 2014 Springer Science+Business Media Dordrecht

Integrating DGSs and GATPs in an Adaptative and Collaborative Blended-Learning Web-Environment

The area of geometry with its very strong and appealing visual contents and its also strong and appealing connection between the visual content and its formal specification, is an area where computational tools can enhance, in a significant way, the learning environments. The dynamic geometry software systems (DGSs) can be used to explore the visual contents of geometry. This already mature tools allows an easy construction of geometric figures build from free objects and elementary constructions. The geometric automated theorem provers (GATPs) allows formal deductive reasoning about geometric constructions, extending the reasoning via concrete instances in a given model to formal deductive reasoning in a geometric theory. An adaptative and collaborative blended-learning environment where the DGS and GATP features could be fully explored would be, in our opinion a very rich and challenging learning environment for teachers and students. In this text we will describe the Web Geometry Laboratory a Web environment incorporating a DGS and a repository of geometric problems, that can be used in a synchronous and asynchronous fashion and with some adaptative and collaborative features. As future work we want to enhance the adaptative and collaborative aspects of the environment and also to incorporate a GATP, constructing a dynamic and individualised learning environment for geometry.Comment: In Proceedings THedu'11, arXiv:1202.453

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

Immunohistochemical subtypes predict the clinical outcome in high-risk node-negative breast cancer patients treated with adjuvant FEC regimen: results of a single-center retrospective study

Prognostic factors for disease-free survival in patients treated before 2005 September: multivariate analysis. (DOCX 15 kb