Covariation between variables in a modelling process: The ACODESA (collaborative learning, scientific debate and self-reflection) method

Semiotic representations have been an important topic of study in mathematics education. Previous research implicitly placed more importance on the development of institutional representations of mathematical concepts in students rather than other types of representations. In the context of an extensive research project, in progress since 2005, related to modelling mathematical situations in Québec secondary schools (grades 8 and 9), we have addressed the problem of constructing a specific mathematical concept: covariation between variables as a prerequisite for the concept of function and its graphical representation. However, our research differs from previous studies as we attempt to take into consideration, in a cultural semiotic perspective, the spontaneous non-institutional representations that students produce when solving a problem situation in mathematics. We report our results with a group of students in grade 9, discussing the evolution of the representations the students produced to solve a problem situation, and the key role that the concept of covariation seems to play in helping students grasp the graphical representation of functions. We also discuss the different stages of the teaching method used, based upon collaborative learning, scientific debate and self-reflection (the ACODESA method of teaching) which aims to help the students acquire a cultural semiotic system.Conseil de Recherche en Sciences Humaines du Canada (No. 410-2008-1836, CID 130 252)

Sobre la comprensión en estudiantes de matemáticas del concepto de integral impropia : algunas dificultades, obstáculos y errores

En el presente trabajo mostramos algunas de las dificultades, obstáculos y errores que los alumnos universitarios encuentran al aprender los conceptos relativos a la integración impropia; algunos de ellos parecen inherentes al propio concepto de integral impropia y otros vienen relacionados con ausencia de significado o con otros conceptos del cálculo. Con el objetivo de analizar estas dificultades, obstáculos y errores construimos un marco teórico basado, principalmente, en la teoría de Duval sobre los registros semióticos de representación y construimos un modelo de competencia para evaluar la comprensión de nuestros alumnos.In this paper we present some difficulties, obstacles and errors university students face when learning the concepts relative to improper integration. Some of them seem to be inherent to the improper integral concept itself and some others are related to lack of meaning or to other concepts of calculus. With the aim of analysing these difficulties, obstacles and errors we built up a theoretical framework based, fundamentally, on Duval's theory of semiotic registers of representation and we designed a competence model to assess our students' comprehension

Deep inelastic scattering structure functions of holographic spin-1 hadrons with N f ≥ 1

Two-point current correlation functions of the large N limit of supersymmetric and non-supersymmetric Yang-Mills theories at strong coupling are investigated in terms of their string theory dual models with quenched flavors. We consider non-Abelian global symmetry currents, which allow one to investigate vector mesons with N f > 1. From the correlation functions we construct the deep inelastic scattering hadronic tensor of spin-one mesons, obtaining the corresponding eight structure functions for polarized vector mesons. We obtain several relations among the structure functions. Relations among some of theirmoments are also derived. Aspects of the sub-leading contributions in the 1/N and N f /N expansions are discussed. At leading order we find a universal behavior of the hadronic structure functions.Instituto de Física La Plat

The introduction of real numbers in secondary education. An institutional analysis of textbooks

In this paper we analyse the introduction of irrational and real numbers in secondary textbooks, and specifically the propositions on how these should be taught, in a sample of Brazilian textbooks used in state schools and approved by the Ministry of Education. The analyses discussed in this paper follow an institutional perspective (using Chevallard's Anthropological Theory of Didactics). Our results indicate that the notion of irrational number is generally introduced on the basis of the decimal representation of numbers, and that the mathematical need for the construction of the field of real numbers remains unclear in the textbooks. It seems that textbooks used in secondary teaching institutions develop mathematical organisations which focus on the practical block

Didactic Situations and Didactical Engineering in university mathematics: cases from the study of Calculus and proof

This paper discusses the use of the Theory of Didactic Situations (TDS) at university level, paying special attention to the constraints and specificities of its use at this level. We begin by presenting the origins and main tenets of this approach, and discuss how these tenets are used towards the design of Didactical Engineering (DE), particularly adapted at the tertiary level. We then illustrate the potency of the TDS-DE approach in three university level Research Cases, two related to Calculus, and one related to proof. These studies deploy constructs such as didactic contract, milieu, didactic variables, and epistemological analyses, among others, to design Situations at university level. We conclude with a few thoughts on how the TDS-DE approach relates to other approaches, most notably the Anthropological Theory of the Didactic

Degenerate detectors are unable to harvest spacelike entanglement

We show, under a very general set of assumptions, that pairs of identical particle detectors in spacelike separation, such as atomic probes, can only harvest entanglement from the vacuum state of a quantum field when they have a nonzero energy gap. Furthermore, we show that degenerate probes are strongly challenged to become entangled through their interaction through scalar and electromagnetic fields even in full light contact. We relate these results to previous literature on remote entanglement generation and entanglement harvesting, giving insight into the energy gap’s protective role against local noise, which prevents the detectors from getting entangled through the interaction with the field

Accidental catheter removal in critically ill patients: a prospective and observational study

INTRODUCTION: The importance of accidental catheter removal (ACR) lies in the complications caused by the removal itself and by catheter reinsertion. To the best of our knowledge, no studies have analyzed accidental removal of various types of catheters in the intensive care unit (ICU). The objective of the present study was to analyze the incidence of ACR for all types of catheters in the ICU. METHODS: This was a prospective and observational study, conducted in a 24-bed medical/surgical ICU in a university hospital. We included all consecutive patients admitted to the ICU over 18 months (1 May 2000 to 31 October 2001). The incidences of ACR for all types of catheters (both per 100 catheters and per 100 catheter-days) were determined. RESULTS: A total of 988 patients were included. There were no significant differences in ACR incidence between the four central venous access sites (peripheral, jugular, subclavian and femoral) or between the four arterial access sites (radial, femoral, pedal and humeral). However, the incidence of ACR was higher for arterial than for central venous catheters (1.12/100 catheter-days versus 2.02/100 catheter-days; P < 0.001). The incidences of ACR/100 nonvascular catheter-days were as follows: endotracheal tube 0.79; nasogastric tube 4.48; urinary catheter 0.32; thoracic drain 0.56; abdominal drain 0.67; and intraventricular brain drain 0.66. CONCLUSION: We found ACR incidences for central venous catheter, arterial catheter, endotracheal tube, nasogastric tube and urinary catheter that are similar to those reported in previous studies. We could not find studies that analyzed the ACR for thoracic, abdominal, intraventricular brain and cardiac surgical drains, but we believe that our rates are acceptable. To minimize ACR, it is necessary to monitor its incidence carefully and to implement preventive measures. In our view, according to establish quality standards, findings should be reported as ACR incidence per 100 catheters and per 100 catheter-days, for all types of catheters

Growth mode transition involving a potential-dependent isotropic to anisotropic surface atom diffusion change. Gold electrodeposition on HOPG followed by STM

The electrodeposition of gold on highly oriented pyrolytic graphite (HOPG) from acid aqueous solutions was studied by using electrochemical techniques complemented with ex-situ scanning tunneling microscopy (STM). The kinetics of gold electrodeposition is consistent with a nucleation and three-dimensional growth process under diffusion control from the solution side. As the applied potential moves in the negative direction, the gold crystal density increases, and the crystal shape changes from a Euclidean to a dendritic fractal morphology. This transition can be assigned to the anisotropic surface diffusion of gold adatoms induced by the applied electric potential. A model including a potential-dependent energy barrier at step edges accounts for the morphology transition for gold electrodeposition on HOPG.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA)Facultad de Ciencias Exacta

Introduction to the papers of TWG14: University mathematics education

Research on university level mathematics education is a fast developing field as evident in the growth of the CERME University Mathematics Education (hereafter UME) Thematic Working Group. TWG14 was launched in CERME7 (Nardi, González-Martín, Gueudet, Iannone & Winsløw, 2011). After CERME8 (Nardi, Biza, González-Martín, Gueudet, & Winsløw, 2013), its leader team – in collaboration with TWG14 participants and others – worked towards a Research in Mathematics Education Special Issue on Institutional, sociocultural and discursive approaches to research in university mathematics education (Nardi, Biza, González-Martín, Gueudet & Winsløw, 2014) which focused on research that is conducted in the spirit of the following theoretical frameworks: Anthropological Theory of the Didactic, Theory of Didactic Situations, Instrumental and Documentational Approaches, Communities of Practice and Inquiry and Theory of Commognition

Deep inelastic scattering structure functions of holographic spin-1 hadrons with N f ≥ 1

Two-point current correlation functions of the large N limit of supersymmetric and non-supersymmetric Yang-Mills theories at strong coupling are investigated in terms of their string theory dual models with quenched flavors. We consider non-Abelian global symmetry currents, which allow one to investigate vector mesons with N f > 1. From the correlation functions we construct the deep inelastic scattering hadronic tensor of spin-one mesons, obtaining the corresponding eight structure functions for polarized vector mesons. We obtain several relations among the structure functions. Relations among some of theirmoments are also derived. Aspects of the sub-leading contributions in the 1/N and N f /N expansions are discussed. At leading order we find a universal behavior of the hadronic structure functions.Instituto de Física La Plat