Pre-Service Teachers’ Knowledge of Relational Structure of Physics Concepts : Finding Key Concepts of Electricity and Magnetism

Peer reviewe

Concept networks of students’ knowledge of relationships between physics concepts : finding key concepts and their epistemic support

Abstract Concept maps, which are network-like visualisations of the inter-linkages between concepts, are used in teaching and learning as representations of students’ understanding of conceptual knowledge and its relational structure. In science education, research on the uses of concept maps has focused much attention on finding methods to identify key concepts that are of the most importance either in supporting or being supported by other concepts in the network. Here we propose a method based on network analysis to examine students’ representations of the relational structure of physics concepts in the form of concept maps. We suggest how the key concepts and their epistemic support can be identified through focusing on the pathways along which the information is passed from one node to another. Towards this end, concept maps are analysed as directed and weighted networks, where nodes are concepts and links represent different types of connections between concepts, and where each link is assumed to provide epistemic support to the node it is connected to. The notion of key concept can then be operationalised through the directed flow of information from one node to another in terms of communicability between the nodes, separately for out-going and in-coming weighted links. Here we analyse a collated concept network based on a sample of 12 original concept maps constructed by university students. We show that communicability is a simple and reliable way to identify the key concepts and examine their epistemic justification within the collated network. The communicabilities of the key nodes in the collated network are compared with communicabilities averaged over the set of 12 individual concept maps. The comparison shows the collated network contains an extensive set of key concepts with good epistemic support. Every individual networks contain a sub-set of these key concepts but with a limited overlap of the sub-sets with other individual networks. The epistemically well substantiated knowledge is thus sparsely distributed over the 12 individual networks

Concept Networks in Learning and the Epistemic Support of their Key Concepts

Peer reviewe

Modelling students' knowledge organisation : Genealogical conceptual networks

Learning scientific knowledge is largely based on understanding what are its key concepts and how they are related. The relational structure of concepts also affects how concepts are introduced in teaching scientific knowledge. We model here how students organise their knowledge when they represent their understanding of how physics concepts are related. The model is based on assumptions that students use simple basic linking-motifs in introducing new concepts and mostly relate them to concepts that were introduced a few steps earlier, i.e. following a genealogical ordering. The resulting genealogical networks have relatively high local clustering coefficients of nodes but otherwise resemble networks obtained with an identical degree distribution of nodes but with random linking between them (i.e. the configuration-model). However, a few key nodes having a special structural role emerge and these nodes have a higher than average communicability betweenness centralities. These features agree with the empirically found properties of students' concept networks. (C) 2017 Elsevier B.V. All rights reserved.Peer reviewe

Pre-Service Teachers’ Declarative Knowledge of Wave-Particle Dualism of Electrons and Photons: Finding Lexicons by Using Network Analysis

Learning the wave-particle dualism of electrons and photons plays a central role in understanding quantum physics. Teaching it requires that the teacher is fluent in using abstract and uncommon terms. We inspect the lexical structures of pre-service teachers’ declarative knowledge about the wave-particle dualism of electrons and photons in the context of double-slit interference. The declarative knowledge is analyzed in the form of a lexical network of terms. We focus on lexical structures because, in teaching and learning, knowledge is communicated mostly through lexical structures, i.e., by speaking and writing. Using the lexical networks, we construct the lexicons used by pre-service teachers to express their knowledge of electrons and photons in the context of double-slit interference. The lexicons consist of eight different key terms, each representing a set of closely-related or synonymous terms. The lexicons by 14 pre-service teachers reveal remarkable variation and differences, and are strongly context-dependent. We also analyzed lexicons corresponding to two didactically-oriented research articles on the same topic and found that they also differ. Lexicons paralleling both texts are found among the pre-service teachers’ lexicons. However, only some of the pre-service teachers use such rich vocabulary as would indicate multi-faceted understanding of quantum entities

Pre-Service Teachers’ Declarative Knowledge of Wave-Particle Dualism of Electrons and Photons: Finding Lexicons by Using Network Analysis

Learning the wave-particle dualism of electrons and photons plays a central role in understanding quantum physics. Teaching it requires that the teacher is fluent in using abstract and uncommon terms. We inspect the lexical structures of pre-service teachers’ declarative knowledge about the wave-particle dualism of electrons and photons in the context of double-slit interference. The declarative knowledge is analyzed in the form of a lexical network of terms. We focus on lexical structures because, in teaching and learning, knowledge is communicated mostly through lexical structures, i.e., by speaking and writing. Using the lexical networks, we construct the lexicons used by pre-service teachers to express their knowledge of electrons and photons in the context of double-slit interference. The lexicons consist of eight different key terms, each representing a set of closely-related or synonymous terms. The lexicons by 14 pre-service teachers reveal remarkable variation and differences, and are strongly context-dependent. We also analyzed lexicons corresponding to two didactically-oriented research articles on the same topic and found that they also differ. Lexicons paralleling both texts are found among the pre-service teachers’ lexicons. However, only some of the pre-service teachers use such rich vocabulary as would indicate multi-faceted understanding of quantum entities

Discussion of a physical optics method and its application to absorbing smooth and slightly rough hexagonal prisms

Three different mathematical solutions of a physical optics model for far field diffraction by an aperture due to Karczewski and Wolf are discussed. Only one of them properly describes diffraction by an aperture and can, by applying Babinet's principle, be used to model diffraction by the corresponding plane obstacle, and by further approximation, diffraction by a particle. Studying absorbing scatterers allows a closer investigation of the external diffraction component because transmission is negligible. The physical optics model has been improved on two aspects: (i) To apply the diffraction model based on two-dimensional apertures more accurately to three-dimensional objects, a size parameter dependent volume obliquity factor is introduced, thus reducing the slightly overestimated side scattering computed for three-dimensional objects. (ii) To compensate simplifications in the underlying physical optics diffraction model for two-dimensional apertures [26] a size parameter dependent cross polarisation factor is implemented. It improves cross polarisation for diffraction and reflection by small particle facets. 2D patterns of P 11, –P 12/P 11 and P 22/P 11 and their azimuthal averages for slightly rough absorbing hexagonal prisms in fixed orientation are obtained and compared with results from the discrete dipole approximation. For particle orientations where shadowing is not negligible, improved phase functions are obtained by using a new method where the incident beam is divided into sub-beams with small triangular cross sections. The intersection points of the three sub-beam edges with the prism define the vertices of a triangle, which is treated by the beam tracer as an incidence-facing facet. This ensures that incident facing but shadowed crystal facets or regions thereof do not contribute to the phase functions. The method captures much of the fine detail contained in 2D scattering patterns obtained with DDA. This is important as speckle can be used for characterizing the size and roughness of small particles such as ice crystals.Peer reviewedFinal Accepted Versio

Models for integrated and differential scattering optical properties of encapsulated light absorbing carbon aggregates

Optical properties of light absorbing carbon (LAC) aggregates encapsulated in a shell of sulfate are computed for realistic model geometries based on field measurements. Computations are performed for wavelengths from the UV-C to the mid-IR. Both climate- and remote sensing-relevant optical properties are considered. The results are compared to commonly used simplified model geometries, none of which gives a realistic representation of the distribution of the LAC mass within the host material and, as a consequence, fail to predict the optical properties accurately. A new core-gray shell model is introduced, which accurately reproduces the size- and wavelength dependence of the integrated and differential optical properties

Modelling light scattering by absorbing smooth and slightly rough facetted particles

A method for approximating light scattering properties of strongly absorbing facetted particles which are large compared to the wavelength is presented. It consists in adding the approximated external diffraction and reflection far fields and is demonstrated for a smooth hexagonal prism. This computationally fast method is extended towards prisms with slightly rough surfaces by introducing a surface scaling factor in order to account for edge effects on subfacets forming the rough surface. These effects become more pronounced with decreasing subfacet dimension to wavelength ratio. Azimuthally resolved light scattering patterns, phase functions and degree of linear polarisation obtained by this method and by the Discrete Dipole Approximation are compared for hexagonal prisms with smooth and slightly rough surfaces, respectively.Peer reviewedSubmitted Versio