L’incidence d’un dispositif de soutien en gestion de classe sur les pratiques disciplinaires et le sentiment d’efficacité d’enseignants débutants

Résumé Cette étude quasi expérimentale consistait à élaborer et à mettre à l’essai une mesure de soutien à l’intention d’enseignants débutants ainsi qu’à évaluer l’efficacité de celle-ci. L’une des particularités de cette mesure, appelée Dispositif de soutien en gestion de classe, était qu’elle était centrée essentiellement sur le développement de la compétence à gérer la classe. L’application du dispositif, échelonnée sur une année scolaire, portait sur une trentaine d’enseignants débutants œuvrant au primaire, en milieu défavorisé, à Montréal. Basé sur les trois phases du modèle théorique d’Archambault et Chouinard (2003), le dispositif se déclinait selon trois cycles de formation : l’établissement du fonctionnement de la classe, le maintien de celui-ci et le soutien à la motivation scolaire, ainsi que l’intervention pour résoudre des problèmes de comportement. Chaque cycle commençait par une journée de formation et d’appropriation (JFA) durant laquelle il y avait présentation d’un contenu théorique puis des ateliers d’appropriation. Par la suite, les enseignants effectuaient des mises en pratique dans leur classe. Pour terminer le cycle, un autre type de rencontre, la rencontre de suivi (RS), servait entre autres à objectiver la pratique. L’aspect original de cette mesure de soutien était que la première rencontre de formation était offerte une semaine avant la rentrée scolaire. Sur le thème « Commencer l’année du bon pied en gestion de classe », cette journée avait pour objectif de soutenir les enseignants débutants dans l’installation du fonctionnement de leur classe. L’efficacité du dispositif a été évaluée sur la base de trois dimensions : l’établissement et le maintien de l’ordre et de la discipline, le sentiment d’efficacité personnelle ainsi que la motivation professionnelle. Les perceptions du groupe d’enseignants débutants ayant pris part aux activités du dispositif (n = 27) ont été comparées à celles d’un groupe témoin (n = 44). Les participants avaient, en moyenne, 2,9 années d’expérience et leur âge variait de 23 à 56 ans. Les données ont été recueillies à l’aide d’un questionnaire auto rapporté rempli en deux temps, soit au deuxième et au huitième mois de l’année scolaire. Les scores des enseignants débutants du dispositif ont augmenté dans le temps pour l’ensemble des variables à l’étude. De plus, les analyses de variance à mesures répétées ont révélé que le dispositif a eu une triple incidence positive, attestée par des effets d’interaction. Les enseignants débutants engagés dans la démarche ont connu une augmentation de leur capacité à implanter les règles de classe, de leur sentiment d’efficacité personnelle à gérer les situations d’apprentissage et de leur motivation professionnelle. En effet, alors que, au début de l’étude, ils rapportaient des scores significativement inférieurs à ceux du groupe témoin, à la fin, les scores étaient équivalents. Les résultats ont aussi montré que les participants du groupe expérimental se distinguaient en affichant un meilleur sentiment d’efficacité à faire apprendre leurs élèves. L’étude nous apprend également que le sentiment d’efficacité personnelle à faire face aux problèmes de comportement et la capacité à gérer les comportements se sont renforcés de façon significative dans le temps chez l’ensemble des enseignants débutants. Finalement, aucun changement significatif n’a été détecté pour deux des huit variables à l’étude : le sentiment d’efficacité personnelle à avoir un effet sur le comportement des élèves et l’application des règles de classe. En définitive, ces résultats sont encourageants. Ils montrent l’enrichissement professionnel que les enseignants débutants peuvent retirer lorsqu’ils sont soutenus adéquatement. Nous croyons que la journée de formation portant sur l’installation du fonctionnement de la classe, avant la rentrée scolaire, a joué un rôle central dans les succès vécus par les enseignants débutants participants. C’est pourquoi nous recommandons ce type de formation assorti d’un suivi à long terme, où d’autres composantes entrent en jeu, afin de nourrir le sentiment d’efficacité personnelle et la motivation professionnelle des nouveaux enseignants.

Dunford-Pettis properties, Hilbert spaces and projective tensor products

We study complete continuity properties of operators onto ℓ2 and prove several results in the Dunford–Pettis theory of JB∗-triples and their projective tensor products, culminating in characterisations of the alternative Dunford–Pettis property for where E and F are JB∗-triples.

Sufficiency of Favard's condition for a class of band-dominated operators on the axis

The purpose of this paper is to show that, for a large class of band-dominated operators on $\ell^\infty(Z,U)$, with $U$ being a complex Banach space, the injectivity of all limit operators of $A$ already implies their invertibility and the uniform boundedness of their inverses. The latter property is known to be equivalent to the invertibility at infinity of $A$, which, on the other hand, is often equivalent to the Fredholmness of $A$. As a consequence, for operators $A$ in the Wiener algebra, we can characterize the essential spectrum of $A$ on $\ell^p(Z,U)$, regardless of $p\in[1,\infty]$, as the union of point spectra of its limit operators considered as acting on $\ell^p(Z,U)$.

Fourier transform, null variety, and Laplacian's eigenvalues

We consider a quantity κ(Ω)—the distance to the origin from the null variety of the Fourier transform of the characteristic function of Ω. We conjecture, firstly, that κ(Ω) is maximised, among all convex balanced domains of a fixed volume, by a ball, and also that κ(Ω) is bounded above by the square root of the second Dirichlet eigenvalue of Ω. We prove some weaker versions of these conjectures in dimension two, as well as their validity for domains asymptotically close to a disk, and also discuss further links between κ(Ω) and the eigenvalues of the Laplacians.

Spectral analysis of diffusions with jump boundary

In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case of a large drift and prove that there is a threshold drift above which the bottom of the spectrum no longer depends on the drift. As a corollary to our result we are able to answer two questions concerning elliptic eigenvalue problems with non-local boundary conditions formulated previously by Iddo Ben-Ari and Ross Pinsky.

The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.

Uniqueness of signature for simple curves

We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p-variation, 1≤p<2, are in fact moments of its winding number. This relation allows us to prove that the signature series of a class of simple non-smooth curves uniquely determine the curves. This implies that outside a Chordal SLEκ null set, where 0<κ≤4, the signature series of curves uniquely determine the curves. Our calculations also enable us to express the Fourier transform of the n-point functions of SLE curves in terms of the expected signature of SLE curves. Although the techniques used in this article are deterministic, the results provide a platform for studying SLE curves through the signatures of their sample paths.

On the Fucik spectrum of the Laplacian on a torus

We study the Fucik spectrum of the Laplacian on a two-dimensional torus T(2). Exploiting the invariance properties of the domain T(2) with respect to translations we obtain a good description of large parts of the spectrum. In particular, for each eigenvalue of the Laplacian we will find an explicit global curve in the Fucik spectrum which passes through this eigenvalue; these curves are ordered, and we will show that their asymptotic limits are positive. On the other hand, using a topological index based on the mentioned group invariance, we will obtain a variational characterization of global curves in the Fucik spectrum; also these curves emanate from the eigenvalues of the Laplacian, and we will show that they tend asymptotically to zero. Thus, we infer that the variational and the explicit curves cannot coincide globally, and that in fact many curve crossings must occur. We will give a bifurcation result which partially explains these phenomena. (C) 2008 Elsevier Inc. All rights reserved.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

Local solvability for a class of evolution equations

Motivated by the celebrated example of Y. Kannai of a linear partial differential operator which is hypoelliptic but not locally solvable, we consider it class of evolution operators with real-analytic coefficients and study their local solvability both in L(2) and in the weak sense. In order to do so we are led to propose a generalization of the Nirenberg-Treves condition (psi) which is suitable to our study. (C) 2009 Published by Elsevier Inc.

Banach spaces without minimal subspaces

We prove three new dichotomies for Banach spaces a la W.T. Gowers` dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers` program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size K I into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability. (c) 2009 Elsevier Inc. All fights reserved.

Spectral bounds and basis results for non-self-adjoint pencils, with an application to Hagen-Poiseuille flow

We obtain eigenvalue enclosures and basisness results for eigen- and associated functions of a non-self-adjoint unbounded linear operator pencil A−λBA−λB in which BB is uniformly positive and the essential spectrum of the pencil is empty. Both Riesz basisness and Bari basisness results are obtained. The results are applied to a system of singular differential equations arising in the study of Hagen–Poiseuille flow with non-axisymmetric disturbances.

Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

Characterizations of logarithmic Besov spaces in terms of differences, Fourier-analytical decompositions, wavelets and semi-groups.

We work with Besov spaces Bp,q0,b defined by means of differences, with zero classical smoothness and logarithmic smoothness with exponent b. We characterize Bp,q0,b by means of Fourier-analytical decompositions, wavelets and semi-groups. We also compare those results with the well-known characterizations for classical Besov spaces Bp,qs.