Didactique des grandeurs en mesure et élèves en difficulté d'apprentissage du 2e cycle du primaire

Le programme -Une école adaptée à tous ses élèves-, qui s'inscrit dans la réforme actuelle de l'éducation au Québec, nous a amenée à nous intéresser aux représentations dans les grandeurs en mesure en mathématiques des élèves en difficulté d'apprentissage. Nous nous sommes proposés de reconduire plusieurs paramètres de la recherche de Brousseau (1987, 1992) auprès de cette clientèle. La théorie des champs conceptuels (TCC) de Vergnaud (1991), appliquée aux structures additives, a été particulièrement utile pour l'analyse et l'interprétation de leurs représentations. Comme méthode de recherche, nous avons utilisé la théorie des situations didactiques en mathématiques (TSDM), réseau de concepts et de méthode de recherche appuyé sur l'ingénierie didactique qui permet une meilleure compréhension de l'articulation des contenus à enseigner. Grâce à la TSDM, nous avons observé les approches didactiques des enseignants avec leurs élèves. Notre recherche est de type exploratoire et qualitatif et les données recueillies auprès de 26 élèves de deux classes spéciales du deuxième cycle du primaire ont été traitées selon une méthode d'analyse de contenu. Deux conduites ont été adoptées par les élèves. La première, de type procédural a été utilisée par presque tous les élèves. Elle consiste à utiliser des systèmes de comptage plus ou moins sophistiqués, de la planification aux suites d'actions. La deuxième consiste à récupérer directement en mémoire à long terme le résultat associé à un couple donné et au contrôle de son exécution. L'observation des conduites révèle que les erreurs sont dues à une rupture du sens. Ainsi, les difficultés d'ordre conceptuel et de symbolisation nous sont apparues plus importantes lorsque l'activité d'échange demandait la compétence "utilisation" et renvoyait à la compréhension de la tâche, soit les tâches dans lesquelles ils doivent eux-mêmes découvrir les rapports entre les variables à travailler et à simuler les actions décrites dans les énoncés. En conséquence, les problèmes d'échanges se sont révélés difficiles à modéliser en actes et significativement plus ardus que les autres. L'étude des interactions enseignants et élèves a démontré que la parole a été presque uniquement le fait des enseignants qui ont utilisé l'approche du contrôle des actes ou du sens ou les deux stratégies pour aider des élèves en difficulté. Selon le type de situation à résoudre dans ces activités de mesurage de longueur et de masse, des mobilisations plurielles ont été mises en oeuvre par les élèves, telles que la manipulation d'un ou des étalon(s) par superposition, par reports successifs, par pliage ou par coupure lorsque l'étalon dépassait; par retrait ou ajout d'un peu de sable afin de stabiliser les plateaux. Nous avons également observé que bien que certains élèves aient utilisé leurs doigts pour se donner une perception globale extériorisée des quantités, plusieurs ont employé des procédures très diverses au cours de ces mêmes séances. Les résultats présentés étayent l'hypothèse selon laquelle les concepts de grandeur et de mesure prennent du sens à travers des situations problèmes liées à des situations vécues par les élèves, comme les comparaisons directes. Eles renforcent et relient les grandeurs, leurs propriétés et les connaissances numériques.

Deficiência visual e educação científica: orientações didáticas com um aporte na neurociência cognitiva e teoria dos campos conceituais

The aim of this paper is to present an educational proposal with didactic and pedagogical orientations, to the Science Education for people with visual impairments. Then, we use as main reference, Gérard Vergnaud’s Theory of Conceptual Fields, joining with a translational focus, applying empirical results of Cognitive Neuroscience. Within this, we highlight the role of educational activities related with 'multisensory scientific literacy ', focusing on the linguistic triad: read, interpretation and textual representation. We hope this perspective, become in the future an important component on guidelines for composing a 'semiotic protocol' for Science Education. Realizing too, epistemological peculiarities, pedagogic and didactic specificities in this area, and, revealing such properties on the cognitive constructs, for science and technology education.

Scattering theory of multilevel atoms interacting with arbitrary radiation fields

We present a generic transfer matrix approach for the description of the interaction of atoms possessing multiple ground state and excited state sublevels with light fields. This model allows us to treat multi-level atoms as classical scatterers in light fields modified by, in principle, arbitrarily complex optical components such as mirrors, resonators, dispersive or dichroic elements, or filters. We verify our formalism for two prototypical sub-Doppler cooling mechanisms and show that it agrees with the standard literature.

Non-Hermitian multichannel theory of ultracold collisions modified by intense light fields tuned to the red of the trapping transition

We develop a systematic scheme to treat binary collisions between ultracold atoms in the presence of a strong laser field, tuned to the red of the trapping transition. We assume that the Rabi frequency is much less than the spacing between adjacent bound-state resonances, In this approach we neglect fine and hyperfine structures, but consider fully the three-dimensional aspects of the scattering process, up to the partial d wave. We apply the scheme to calculate the S matrix elements up to the second order in the ratio between the Rabi frequency and the laser detuning, We also obtain, fur this simplified multichannel model, the asymmetric line shapes of photoassociation spectroscopy, and the modification of the scattering length due to the light field at low, but finite, entrance kinetic energy. We emphasize that the present calculations can be generalized to treat more realistic models, and suggest how to carry out a thorough numerical comparison to this semianalytic theory. [S1050-2947(98)04902-6].

Note on the nonuniqueness of the massive Fierz-Pauli theory and spectator fields

It is possible to show that there are three independent families of models describing a massive spin-2 particle via a rank-2 tensor. One of them contains the massive Fierz-Pauli model, the only case described by a symmetric tensor. The three families have different local symmetries in the massless limit and can not be interconnected by any local field redefinition. We show here, however, that they can be related with the help of a decoupled and nondynamic (spectator) field. The spectator field may be either an antisymmetric tensor B μν=-Bνμ, a vector Aμ or a scalar field φ, corresponding to each of the three families. The addition of the extra field allows us to formulate master actions which interpolate between the symmetric Fierz-Pauli theory and the other models. We argue that massive gravity models based on the Fierz-Pauli theory are not expected to be equivalent to possible local self-interacting theories built up on top of the two new families of massive spin-2 models. The approach used here may be useful to investigate dual (nonsymmetric) formulations of higher-spin particles. © 2013 American Physical Society.

The theory of electrostatic probes in strong magnetic fields : Thesis submitted to the Faculty of The Graduate School of the University of Colorado for the Degree Doctor of Philosophy Department of Aerospace Engineering Science

A theory is developed of an electrostatic probe in a fully-ionized plasma in the presence of a strong magnetic field. The ratio of electron Larmor radius to probe transverse dimension is assumed to be small. Poisson's equation, together with kinetic equations for ions and electrons are considered. An asymptotic perturbation method of multiple scales is used by considering the characteristic lengths appearing in the problem. The leading behavior of the solution is found. The results obtained appear to apply to weaker fields also, agreeing with the solutions known in the limit of no magnetic field. The range of potentials for wich results are presented is limited. The basic effects produced by the field are a depletion of the plasma near the probe and a non-monotonic potential surrounding the probe. The ion saturation current is not changed but changes appear in both the floating potential Vf and the slope of the current-voltage diagram at Vf. The transition region extends beyond the space potential Vs,at wich point the current is largely reduced. The diagram does not have an exponential form in this region as commonly assumed. There exists saturation in electron collection. The extent to which the plasma is disturbed is determined. A cylindrical probe has no solution because of a logarithmic singularity at infinity. Extensions of the theory are considered.

The measurement of perceived ontological deficiencies of conceptual modeling grammars

Over recent years, many scholars have studied the conceptual modeling of information systems based on a theory of ontological expressiveness. This theory offers four constructs that inform properties of modeling grammars in the form of ontological deficiencies, and their implications for development and use of conceptual modeling in IS practice. In this paper we report on the development of a valid and reliable instrument for measuring the perceptions that individuals have of the ontological deficiencies of conceptual modeling grammars. We describe a multi-stage approach for instrument development that incorporates feedback from expert and user panels. We also report on a field test of the instrument with 590 modeling practitioners. We further study how different levels of modeling experience influence user perceptions of ontological deficiencies of modeling grammars. We provide implications for practice and future research.

Perceiving and pursuing novelty : a grounded theory of adolescent creativity

Creativity plays an increasingly important role in our personal, social, educational, and community lives. For adolescents, creativity can enable self-expression, be a means of pushing boundaries, and assist learning, achievement, and completion of everyday tasks. Moreover, adolescents who demonstrate creativity can potentially enhance their capacity to face unknown future challenges, address mounting social and ecological issues in our global society, and improve their career opportunities and contribution to the economy. For these reasons, creativity is an essential capacity for young people in their present and future, and is highlighted as a priority in current educational policy nationally and internationally. Despite growing recognition of creativity’s importance and attention to creativity in research, the creative experience from the perspectives of the creators themselves and the creativity of adolescents are neglected fields of study. Hence, this research investigated adolescents’ self-reported experiences of creativity to improve understandings of their creative processes and manifestations, and how these can be supported or inhibited. Although some aspects of creativity have been extensively researched, there were no comprehensive, multidisciplinary theoretical frameworks of adolescent creativity to provide a foundation for this study. Therefore, a grounded theory methodology was adopted for the purpose of constructing a new theory to describe and explain adolescents’ creativity in a range of domains. The study’s constructivist-interpretivist perspective viewed the data and findings as interpretations of adolescents’ creative experiences, co-constructed by the participants and the researcher. The research was conducted in two academically selective high schools in Australia: one arts school, and one science, mathematics, and technology school. Twenty adolescent participants (10 from each school) were selected using theoretical sampling. Data were collected via focus groups, individual interviews, an online discussion forum, and email communications. Grounded theory methods informed a process of concurrent data collection and analysis; each iteration of analysis informed subsequent data collection. Findings portray creativity as it was perceived and experienced by participants, presented in a Grounded Theory of Adolescent Creativity. The Grounded Theory of Adolescent Creativity comprises a core category, Perceiving and Pursuing Novelty: Not the Norm, which linked all findings in the study. This core category explains how creativity involved adolescents perceiving stimuli and experiences differently, approaching tasks or life unconventionally, and pursuing novel ideas to create outcomes that are not the norm when compared with outcomes by peers. Elaboration of the core category is provided by the major categories of findings. That is, adolescent creativity entailed utilising a network of Sub-Processes of Creativity, using strategies for Managing Constraints and Challenges, and drawing on different Approaches to Creativity – adaptation, transfer, synthesis, and genesis – to apply the sub-processes and produce creative outcomes. Potentially, there were Effects of Creativity on Creators and Audiences, depending on the adolescent and the task. Three Types of Creativity were identified as the manifestations of the creative process: creative personal expression, creative boundary pushing, and creative task achievement. Interactions among adolescents’ dispositions and environments were influential in their creativity. Patterns and variations of these interactions revealed a framework of four Contexts for Creativity that offered different levels of support for creativity: high creative disposition–supportive environment; high creative disposition–inhibiting environment; low creative disposition–supportive environment; and low creative disposition–inhibiting environment. These contexts represent dimensional ranges of how dispositions and environments supported or inhibited creativity, and reveal that the optimal context for creativity differed depending on the adolescent, task, domain, and environment. This study makes four main contributions, which have methodological and theoretical implications for researchers, as well as practical implications for adolescents, parents, teachers, policy and curriculum developers, and other interested stakeholders who aim to foster the creativity of adolescents. First, this study contributes methodologically through its constructivist-interpretivist grounded theory methodology combining the grounded theory approaches of Corbin and Strauss (2008) and Charmaz (2006). Innovative data collection was also demonstrated through integration of data from online and face-to-face interactions with adolescents, within the grounded theory design. These methodological contributions have broad applicability to researchers examining complex constructs and processes, and with populations who integrate multimedia as a natural form of communication. Second, applicable to creativity in diverse domains, the Grounded Theory of Adolescent Creativity supports a hybrid view of creativity as both domain-general and domain-specific. A third major contribution was identification of a new form of creativity, educational creativity (ed-c), which categorises creativity for learning or achievement within the constraints of formal educational contexts. These theoretical contributions inform further research about creativity in different domains or multidisciplinary areas, and with populations engaged in formal education. However, the key contribution of this research is that it presents an original Theory and Model of Adolescent Creativity to explain the complex, multifaceted phenomenon of adolescents’ creative experiences.

General theory of stigmergy : modelling stigma semantics

Stigmergy is a biological term used when discussing a sub-set of insect swarm-behaviour describing the apparent organisation seen during their activities. Stigmergy describes a communication mechanism based on environment-mediated signals which trigger responses among the insects. This phenomenon is demonstrated in the behavior of ants and their food gathering process when following pheromone trails, where the pheromones are a form of environment-mediated communication. What is interesting with this phenomenon is that highly organized societies are achieved without an apparent management structure. Stigmergy is also observed in human environments, both natural and engineered. It is implicit in the Web where sites provide a virtual environment supporting coordinative contributions. Researchers in varying disciplines appreciate the power of this phenomenon and have studied how to exploit it. As stigmergy becomes more widely researched we see its definition mutate as papers citing original work become referenced themselves. Each paper interprets these works in ways very specific to the research being conducted. Our own research aims to better understand what improves the collaborative function of a Web site when exploiting the phenomenon. However when researching stigmergy to develop our understanding we discover a lack of a standardized and abstract model for the phenomenon. Papers frequently cited the same generic descriptions before becoming intimately focused on formal specifications of an algorithm, or esoteric discussions regarding sub-facets of the topic. None provide a holistic and macro-level view to model and standardize the nomenclature. This paper provides a content analysis of influential literature documenting the numerous theoretical and experimental papers that have focused on stigmergy. We establish that stigmergy is a phenomenon that transcends the insect world and is more than just a metaphor when applied to the human world. We present from our own research our general theory and abstract model of semantics of stigma in stigmergy. We hope our model will clarify the nuances of the phenomenon into a useful road-map, and standardise vocabulary that we witness becoming confused and divergent. Furthermore, this paper documents the analysis on which we base our next paper: Special Theory of Stigmergy: A Design Pattern for Web 2.0 Collaboration.

Experimental verification of the modified spring-mass theory of fiber Bragg grating accelerometers using transverse forces

A fiber Bragg grating (FBG) accelerometer using transverse forces is more sensitive than one using axial forces with the same mass of the inertial object, because a barely stretched FBG fixed at its two ends is much more sensitive to transverse forces than axial ones. The spring-mass theory, with the assumption that the axial force changes little during the vibration, cannot accurately predict its sensitivity and resonant frequency in the gravitational direction because the assumption does not hold due to the fact that the FBG is barely prestretched. It was modified but still required experimental verification due to the limitations in the original experiments, such as the (1) friction between the inertial object and shell; (2) errors involved in estimating the time-domain records; (3) limited data; and (4) large interval ∼5 Hz between the tested frequencies in the frequency-response experiments. The experiments presented here have verified the modified theory by overcoming those limitations. On the frequency responses, it is observed that the optimal condition for simultaneously achieving high sensitivity and resonant frequency is at the infinitesimal prestretch. On the sensitivity at the same frequency, the experimental sensitivities of the FBG accelerometer with a 5.71 gram inertial object at 6 Hz (1.29, 1.19, 0.88, 0.64, and 0.31 nm/g at the 0.03, 0.69, 1.41, 1.93, and 3.16 nm prestretches, respectively) agree with the static sensitivities predicted (1.25, 1.14, 0.83, 0.61, and 0.29 nm/g, correspondingly). On the resonant frequency, (1) its assumption that the resonant frequencies in the forced and free vibrations are similar is experimentally verified; (2) its dependence on the distance between the FBG’s fixed ends is examined, showing it to be independent; (3) the predictions of the spring-mass theory and modified theory are compared with the experimental results, showing that the modified theory predicts more accurately. The modified theory can be used more confidently in guiding its design by predicting its static sensitivity and resonant frequency, and may have applications in other fields for the scenario where the spring-mass theory fails.

A question of agency : applying Sen’s theory of human capability to the concept of secondary school student career ‘choice’

In this paper, we seek to operationalize Amartya Sen's concept of human capability to guide a scholarly investigation of student career choice capability. We begin by outlining factors affecting youth labour markets in Australia; a prosperous country that is affected by a ‘two-speed’ national economy. We then examine recent government initiatives that have been designed to combat youth unemployment and cyclical disadvantage by enhancing the aspirations and career knowledge of secondary school students. We argue that these policy measures are based on four assumptions: first, that career choice capability is a problem of individual agency; second, that the dissemination of career information can empower students to act as ‘consumers’ in an unequal job market; third, that agency is simply a question of will; and finally, that school education and career advice – as a means to freedom in the space of career development – is of equal quality, distribution and value to an increasingly diverse range of upper secondary school students. The paper concludes by outlining a conceptual framework capable of informing an empirical research project that aims to test these assumptions by measuring and comparing differences between groups in the range of freedom to achieve and, therefore, to choose.

A theory of process modeling impact

Process modeling – the design and use of graphical documentations of an organization’s business processes – is a key method to document and use information about the operations of businesses. Still, despite current interest in process modeling, this research area faces essential challenges. Key unanswered questions concern the impact of process modeling in organizational practice, and the mechanisms through which impacts are developed. To answer these questions and to provide a better understanding of process modeling impact, I turn to the concept of affordances. Affordances describe the possibilities for goal-oriented action that a technical object offers to a user. This notion has received growing attention from IS researchers. The purpose of my research is to further develop the IS discipline’s understanding of affordances and impacts from information objects, such as process models used by analysts for information systems analysis and design. Specifically, I seek to extend existing theory on the emergence, perception and actualization of affordances. I develop a research model that describes the process by which affordances emerge between an individual and an object, how affordances are perceived, and how they are actualized by the individual. The proposed model also explains the role of available information for the individual, and the influence of perceived actualization effort. I operationalize and test this research model empirically, using a full-cycle, mixed methods study consisting of case study and experiment.

Gauge theory of a group of diffeomorphisms. II. The conformal and de Sitter groups

The extension of Hehl's Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.

Space in Musical Semiosis : An Abductive Theory of the Musical Composition Process

Space in musical semiosis is a study of musical meaning, spatiality and composition. Earlier studies on musical composition have not adequately treated the problems of musical signification. Here, composition is considered an epitomic process of musical signification. Hence the core problems of composition theory are core problems of musical semiotics. The study employs a framework of naturalist pragmatism, based on C. S. Peirce’s philosophy. It operates on concepts such as subject, experience, mind and inquiry, and incorporates relevant ideas of Aristotle, Peirce and John Dewey into a synthetic view of esthetic, practic, and semiotic for the benefit of grasping musical signification process as a case of semiosis in general. Based on expert accounts, music is depicted as real, communicative, representational, useful, embodied and non-arbitrary. These describe how music and the musical composition process are mental processes. Peirce’s theories are combined with current morphological theories of cognition into a view of mind, in which space is central. This requires an analysis of space, and the acceptance of a relativist understanding of spatiality. This approach to signification suggests that mental processes are spatially embodied, by virtue of hard facts of the world, literal representations of objects, as well as primary and complex metaphors each sharing identities of spatial structures. Consequently, music and the musical composition process are spatially embodied. Composing music appears as a process of constructing metaphors—as a praxis of shaping and reshaping features of sound, representable from simple quality dimensions to complex domains. In principle, any conceptual space, metaphorical or literal, may set off and steer elaboration, depending on the practical bearings on the habits of feeling, thinking and action, induced in musical communication. In this sense, it is evident that music helps us to reorganize our habits of feeling, thinking, and action. These habits, in turn, constitute our existence. The combination of Peirce and morphological approaches to cognition serves well for understanding musical and general signification. It appears both possible and worthwhile to address a variety of issues central to musicological inquiry in the framework of naturalist pragmatism. The study may also contribute to the development of Peircean semiotics.

Gauge theory of a group of diffeomorphisms. I. General principles

Any (N+M)-parameter Lie group G with an N-parameter subgroup H can be realized as a global group of diffeomorphisms on an M-dimensional base space B, with representations in terms of transformation laws of fields on B belonging to linear representations of H. The gauged generalization of the global diffeomorphisms consists of general diffeomorphisms (or coordinate transformations) on a base space together with a local action of H on the fields. The particular applications of the scheme to space-time symmetries is discussed in terms of Lagrangians, field equations, currents, and source identities. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.