Exploring reflection in pre-service teacher education: a social perspective on the application, value and factors influencing reflection

This study explores the implementation of reflection from the perspective of teacher trainees in two ‘four-week’ teacher training courses in the southeast of the UK and provides a social perspective into reflection. The study reveals that participants conceptualise the different aspects of reflection, written, oral, and reflections made about others, differently in terms of their application and value, and shows a number of factors impacting the understanding and practice of such aspects. Accordingly, the application of written reflection is viewed as an idiosyncratic process and is understood as a systematic activity that is underexplored, while oral reflection is described as an interactional process, characterised by discussion and participation, and portrayed to be a practice of an important value. Participants’ views on the reflections made on others, both peers and experienced teachers, define such reflections in terms of a social process. Three factors impacting reflection are psychological involving trainees’ emotions, contextual, identifying aspects such as the context of reflection, trainees’ status as novice teachers, experience in reflection, and the guidance required, and social, revealing the impact of community dynamics on participants’ reflections. The study followed a qualitative approach and was framed within an ethnographic methodology with an autoethnographic aspect, recounting my insider experience during fieldwork. Data were collected in the two teacher training courses, using interviews, observations of the field, and an analysis of participants’ reflections, then analysed thematically. The findings of the study have methodological implications, focusing on the importance of insider experiences in research, pedagogical implications, suggesting a multi-dimensional framework for reflection, useful in teacher education contexts and beyond, and theoreticalimplications, proposing the integration of a social perspective to the study of reflection

A matrix-valued point interactions model

We study a matrix-valued Schr\"odinger operator with random point interactions. We prove the absence of absolutely continuous spectrum for this operator by proving that away from a discrete set its Lyapunov exponents do not vanish. For this we use a criterion by Gol'dsheid and Margulis and we prove the Zariski denseness, in the symplectic group, of the group generated by the transfer matrices. Then we prove estimates on the transfer matrices which lead to the H\"older continuity of the Lyapunov exponents. After proving the existence of the integrated density of states of the operator, we also prove its H\"older continuity by proving a Thouless formula which links the integrated density of states to the sum of the positive Lyapunov exponents

Effects of urban effluents on spatial structure, morphology and total phenols of Posidonia oceanica: Comparison with a reference site

In the Mediterranean, the discharge of urban effluents in coastal areas adversely affects Posidonia oceanica, since it induces nutrient enrichment and a decrease of water clarity, but data from the southern Mediterranean are very sparse. In this paper we examine the differences in P. oceanica parameters from a disturbed site (Bou Ismaïl) and a reference site (Kouali), at meadow level (shoot density, meadow cover), at individual level (leaf biometry, A coefficient, epiphytic index) and at biochemical level (total phenols). The differences were examined at the upper limit (− 5 m) and the lower limit (− 20 m), during an annual cycle. Results indicated a significantly lower mean meadow cover at the upper limits of the disturbed site compared to the reference site. The leaf length and leaf area were also lower at the disturbed site, and this difference was recorded all year round at the upper limit. The epiphytic index and the A coefficient of adult leaves were higher only in July and October at the upper limits of the disturbed site. In contrast, total phenol concentration of the leaves did not show any response to disturbances related to urban effluents. However, the biosynthesis of phenolic substances at the two sites was significantly higher in the intermediate leaves, in winter, when growth slows down. The unexpected higher value of total phenol concentration recorded in the intermediate leaves and sheaths in spring at the reference site is discussed

Localization for a matrix-valued Anderson model

We study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schr\"odinger operators, acting on L^2(\R)\otimes \C^N, for arbitrary $N\geq 1$. We prove that, under suitable assumptions on the F\"urstenberg group of these operators, valid on an interval $I\subset \R$, they exhibit localization properties on $I$, both in the spectral and dynamical sense. After looking at the regularity properties of the Lyapunov exponents and of the integrated density of states, we prove a Wegner estimate and apply a multiscale analysis scheme to prove localization for these operators. We also study an example in this class of operators, for which we can prove the required assumptions on the F\"urstenberg group. This group being the one generated by the transfer matrices, we can use, to prove these assumptions, an algebraic result on generating dense Lie subgroups in semisimple real connected Lie groups, due to Breuillard and Gelander. The algebraic methods used here allow us to handle with singular distributions of the random parameters

Positivity of Lyapunov exponents for a continuous matrix-valued Anderson model

We study a continuous matrix-valued Anderson-type model. Both leading Lyapunov exponents of this model are proved to be positive and distinct for all ernergies in $(2,+\infty)$ except those in a discrete set, which leads to absence of absolutely continuous spectrum in $(2,+\infty)$. This result is an improvement of a previous result with Stolz. The methods, based upon a result by Breuillard and Gelander on dense subgroups in semisimple Lie groups, and a criterion by Goldsheid and Margulis, allow for singular Bernoulli distributions

Interpreting the principal component analysis of multivariate density functions

Functional principal component analysis (FPCA) as a reduction data technique of a finite number T of functions can be used to identify the dominant modes of variation of numeric three-way data. We carry out the FPCA on multidimensional probability density functions, relate this method to other standard methods and define its centered or standardized versions. Grounded on the relationship between FPCA of densities, FPCA of their corresponding characteristic functions, PCA of the MacLaurin expansions of these characteristic functions and dual STATIS method applied to their variance matrices, we propose a method for interpreting the results of the FPCA of densities. This method is based on the investigations of the relationships between the scores of the FPCA and the moments associated to the densities. The method is illustrated using known Gaussian densities. In practice, FPCA of densities deals with observations of multidimensional variables on T occasions. These observations can be used to estimate the T associated densities (i) by estimating the parameters of these densities, assuming that they are Gaussian, or (ii) by using the Gaussian kernel method and choosing the matrix bandwidth by the normal reference rule. Thereafter, FPCA estimate is derived from these estimates and the interpretation method is carried out to explore the dominant modes of variation of the types of three-way data encountered in sensory analysis and archaeology

Localization Properties of the Chalker-Coddington Model

The Chalker Coddington quantum network percolation model is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We study the model restricted to a cylinder of perimeter 2M. We prove firstly that the Lyapunov exponents are simple and in particular that the localization length is finite; secondly that this implies spectral localization. Thirdly we prove a Thouless formula and compute the mean Lyapunov exponent which is independent of M.Comment: 29 pages, 1 figure. New section added in which simplicity of the Lyapunov spectrum and finiteness of the localization length are proven. To appear in Annales Henri Poincar

Optimal bandwidth matrices in functional principal component analysis of density functions

In order to explore and compare a finite number T of data sets by applying functional principal component analysis (FPCA) to the T associated probability density functions, we estimate these density functions by using the multivariate kernel method. The data set sizes being fixed, we study the behaviour of this FPCA under the assumption that all the bandwidth matrices used in the estimation of densities are proportional to a common parameter h and proportional to either the variance matrices or the identity matrix. In this context, we propose a selection criterion of the parameter h which depends only on the data and the FPCA method. Then, on simulated examples, we compare the quality of approximation of the FPCA when the bandwidth matrices are selected using either the previous criterion or two other classical bandwidth selection methods, that is, a plug-in or a cross-validation method

Nitrogen deficiency increases basal branching and modifies visual quality of the rose bushes

Rosebush architecture resulting from the spatial organisation of the plant axes induces plant shape and consequently within ornamental horticulture context, its visual quality and commercial value. This architecture can be modulated by environmental conditions, particularly in the horticulture context in which the possibilities to control growing conditions are numerous. The objectives of the study were to determine, in young rose bushes, (1) whether short periods of nitrogen deficiency affect branching and (2) whether this effect is sufficient to modify the visual quality of the plant in a sustainable manner. Between vegetative bud burst and the petal colour visible stage of the generated primary branch, young rooted cuttings of bush rose (cv Radrazz) were subjected to one of three nitrogen regimes: (1) no nitrogen deficiency, (2) continuous nitrogen deficiency, i.e. 35 days of N deficiency, and (3) nitrogen deficiency restricted to the flowering stages, i.e. 18 days of N deficiency. After the petal colour visible stage, all three groups of plants were supplied continuously with nitrogen. We observed the morphology of the axes and the kinetics of axillary bud burst. Twelve weeks after the petal colour visible stage, the visual quality of the rose bushes was evaluated by an expert jury. We found that nitrogen deficiencies (1) increased bud burst ratios in the medial and basal zones of the primary branch, (2) delayed the bud burst in the apical zone of the primary branch and (3) had long-term effects on plant visual quality. The continuous nitrogen deficiency regime produced flatter, more asymmetric and less vigorous rose bushes than the no nitrogen deficiency regime. By contrast, nitrogen deficiency during the flowering stages only resulted in more symmetric, taller and more vigorous rose bushes than the no nitrogen deficiency regime. Based on these results, the role of nitrogen on bud burst was discussed and candidate processes at the origin of the visual quality modification were suggested. This new approach combining ecophysiology and sensory assessment of ornamental plants enabled the identification of some early architecture components to be correlated with later visual quality characteristics and then to better target the physiological processes of interest

Assessment of the visual quality of ornamental plants: Comparison of three methodologies in the case of the rosebush

The quality of ornamental plants can be appraised with several types of criteria: tolerance to biotic and abiotic stresses, development potentialities and aesthetics. This last criterion, aesthetic quality, is specific to ornamental plants and objective measurements are required. Three methodologies for measuring aesthetic quality have been proposed. The first involves classical measurements of morphological features, such as flower number and diameter or leaf size. The second is based on sensory methods recently adapted to ornamental plants. The third, used by the International Union for the Protection of New Varieties of Plants (UPOV) for distinctness, uniformity and stability (DUS) tests, is based on morphological characteristics calibrated on specific reference varieties. The aim of this work was to compare these three methodologies for assessing some flowering and foliage characteristics of rosebushes. Six plants from 10 rose varieties identified by UPOV as reference varieties were cultivated for two years in a greenhouse and outdoors in Angers, France. They were measured and photographed weekly during flowering. Photographs of the plants in full bloom were submitted to a panel of judges for sensory assessment. The results of the three assessment methodologies were compared. Sensory and morphometric measurements were highly correlated and sensory measurements confirmed UPOV scales, whereas some morphometric measures diverged slightly from UPOV scales. We discuss the advantages, disadvantages and complementarity of these three methodologies