The indicators of pupil opinion and teacher interactivity for inquiry-based science teaching

In order to establish those practices which underpin a science teaching performance that combines pupil enthusiasm and creative classrooms, it will be necessary to uncover evidence of inquiry-based learning experiences in science that can provide a warrant for theory and practice that will assist new science teachers in recognising and developing opportunities for investigative activity. Remaining aware, however, of the recurring theme in contemporary educational research which suggests that learning to teach has an important affective dimension associated with developing relationships and the formation of a teaching identity – a model of development which thus transcends atheoretical checklists of professional standards or pedagogical steps – the nature of that evidence will necessarily be in the area of the formative development of new teachers’ professional knowledge and understanding

On Vertically Global, Horizontally Local Models for Astrophysical Disks

Disks with a barotropic equilibrium structure, for which the pressure is only a function of the density, rotate on cylinders in the presence of a gravitational potential, so that the angular frequency of such a disk is independent of height. Such disks with barotropic equilibria can be approximately modeled using the shearing box framework, representing a small disk volume with height-independent angular frequency. If the disk is in baroclinic equilibrium, the angular frequency does generally depend on height, and it is thus necessary to go beyond the standard shearing box approach. In this paper, we show that given a global disk model, it is possible to develop approximate models that are local in horizontal planes without an expansion in height with shearing-periodic boundary conditions. We refer to the resulting framework as the vertically global shearing box (VGSB). These models can be non-axisymmetric for globally barotropic equilibria but should be axisymmetric for globally baroclinic equilibria. We provide explicit equations for this VGSB which can be implemented in standard magnetohydrodynamic codes by generalizing the shearing-periodic boundary conditions to allow for a height-dependent angular frequency and shear rate. We also discuss the limitations that result from the radial approximations that are needed in order to impose height-dependent shearing periodic boundary conditions. We illustrate the potential of this framework by studying a vertical shear instability and examining the modes associated with the magnetorotational instability.Comment: 24 pages, 8 figures, updated to match published versio

Becoming an effective science teacher at the Department of Curricular Studies, University of Strathclyde

In an article for the International section, Allan Blake, Colin Smith and Jim McNally from Strathclyde report on the start of a very important EU-funded project, involving 15 countries, which looks at how ‘inquiry-based science’ can be promoted in science teaching and the significance for teacher education. In their view, inquiry-based science is more about open-endedness and uncertainty of outcome than routine (prescribed) practical work. STE will keep track of this important project and we will report on its progress and outcomes in future issues

A Meshless Method for Magnetohydrodynamics and Applications to Protoplanetary Disks

This thesis presents an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. Local, third-order, least-squares, polynomial interpolations (Moving Least Squares interpolations) are calculated from the field values of neighboring particles to obtain field values and spatial derivatives at the particle position. Field values and particle positions are advanced in time with a second order predictor-corrector scheme. The particles move with the fluid, so the time step is not limited by the Eulerian Courant-Friedrichs-Lewy condition. Full spatial adaptivity is implemented to ensure the particles fill the computational volume, which gives the algorithm substantial flexibility and power. A target resolution is specified for each point in space, with particles being added and deleted as needed to meet this target. Particle addition and deletion is based on a local void and clump detection algorithm. Dynamic artificial viscosity fields provide stability to the integration. The resulting algorithm provides a robust solution for modeling flows that require Lagrangian or adaptive discretizations to resolve. The code has been parallelized by adapting the framework provided by Gadget-2. A set of standard test problems, including one part in a million amplitude linear MHD waves, magnetized shock tubes, and Kelvin-Helmholtz instabilities are presented. Finally we demonstrate good agreement with analytic predictions of linear growth rates for magnetorotational instability in a cylindrical geometry. We provide a rigorous methodology for verifying a numerical method on two dimensional Kelvin-Helmholtz instability. The test problem was run in the Pencil Code, Athena, Enzo, NDSPHMHD, and Phurbas. A strict comparison, judgment, or ranking, between codes is beyond the scope of this work, although this work provides the mathematical framework needed for such a study. Nonetheless, how the test is posed circumvents the issues raised by tests starting from a sharp contact discontinuity yet it still shows the poor performance of Smoothed Particle Hydrodynamics. We then comment on the connection between this behavior and the underlying lack of zeroth-order consistency in Smoothed Particle Hydrodynamics interpolation. In astrophysical magnetohydrodynamics (MHD) and electrodynamics simulations, numerically enforcing the divergence free constraint on the magnetic field has been difficult. We observe that for point-based discretization, as used in finite-difference type and pseudo-spectral methods, the divergence free constraint can be satisfied entirely by a choice of interpolation used to define the derivatives of the magnetic field. As an example we demonstrate a new class of finite-difference type derivative operators on a regular grid which has the divergence free property. This principle clarifies the nature of magnetic monopole errors. The principles and techniques demonstrated in this chapter are particularly useful for the magnetic field, but can be applied to any vector field. Finally, we examine global zoom-in simulations of turbulent magnetorotationally unstable flow. We extract and analyze the high-current regions produced in the turbulent flow. Basic parameters of these regions are abstracted, and we build one dimensional models including non-ideal MHD, and radiative transfer. For sufficiently high temperatures, an instability resulting from the temperature dependence of the Ohmic resistivity is found. This instability concentrates current sheets, resulting in the possibility of rapid heating from temperatures on the order of 600 Kelvin to 2000 Kelvin in magnetorotationally turbulent regions of protoplanetary disks. This is a possible local mechanism for the melting of chondrules and the formation of other high-temperature materials in protoplanetary disks

Promoting inquiry skills in Curriculum for Excellence in Science: conceptualising inquiry to improve practice

This paper describes a Scottish initiative (arising out of a EU funded development project) involving university researchers, a local authority curriculum development officer and a group of teachers interested in developing more inquiry based approaches in science education. The project is not one in which the researchers bring prescriptions from research. Rather, it is seen as a joint effort aimed at solving practitioners' conceptual and practice issues. The overall question for the teachers was, How do I (we) make our practice more inquiry based? The question for the researchers was, How do we help you (the interested science teachers) to make your practice more inquiry based? This has two sub-questions: How do we help you to conceptualise the issues? How do we help you to solve the practice problems? As it turned out, the particular group of teachers we worked with did not ask for help with practice issues, so we have not made much progress in answering the second question. Therefore, this paper will focus on the first. We seem to have been successful in helping the teachers to acquire some useful conceptual tools for thinking about and changing their practice in ways that they valued for themselves. Perhaps the answer to the second question is that researchers can help teachers to solve their practice problems by helping them to conceptualise the issues

Promoting Inquiry in Science Classrooms in European Schools : a Handbook for Tutors

In Scotland, PISCES stands for Promoting Inquiry Skills for a Curriculum for Excellence in Science. It is a CPD module for teachers of science, which has been developed in Scotland with the support of the S-TEAM project. However, this Handbook uses our international acronym in which PISCES stands for Promoting Inquiry in Science Classrooms in European Schools . It is, we believe, potentially equally as successful across Europe as it was designed around the idea of empowering teachers to think for themselves how to make their practice more-inquiry based, wherever they are. It is recognised that some school, social, policy and cultural environments may be more supportive of the idea of ‘more inquiry-based practice’ than others. PISCES empowers teachers to make small or large changes to their practice, according to those sorts of contextual factors, their own aims and how they perceive the needs of their pupils. You will note that we have been careful to use the word ‘more’ in ‘more inquiry-based.’ As befits the idea of empowerment to adapt to one’s own context, there is no single model of inquiry being ‘pushed’ here. Indeed, we count it as a measure of success of PISCES that the teachers who have participated did very different things in making their practice more inquiry-based. Strathclyde University is a leading partner in S-TEAM. Members of Strathclyde University, along with the Development Officer for Curriculum for Excellence for East Lothian, successfully developed and delivered a pilot version of PISCES as a module to a group of East Lothian teachers, in 2010/11. The module resulted in successful ‘experiments in practice’ and increased awareness of the benefits of inquiry-based teaching and learning. The same group of teachers have also taken part in a follow-up course (ARIES: Advanced Resources for Inquiry and Evaluation in Science). PISCES is a high quality CPD programme, valued by teachers and supportive of their professional self-development. It can be applied to both primary and secondary teaching, in all science subjects. Pupils benefit from learning experiences, which develop scientific inquiry skills. Feedback from participating teachers has been consistently positive

Mineral Processing by Short Circuits in Protoplanetary Disks

Meteoritic chondrules were formed in the early solar system by brief heating of silicate dust to melting temperatures. Some highly refractory grains (Type B calcium-aluminum-rich inclusions, CAIs) also show signs of transient heating. A similar process may occur in other protoplanetary disks, as evidenced by observations of spectra characteristic of crystalline silicates. One possible environment for this process is the turbulent magnetohydrodynamic flow thought to drive accretion in these disks. Such flows generally form thin current sheets, which are sites of magnetic reconnection, and dissipate the magnetic fields amplified by a disk dynamo. We suggest that it is possible to heat precursor grains for chondrules and other high-temperature minerals in current sheets that have been concentrated by our recently described short-circuit instability. We extend our work on this process by including the effects of radiative cooling, taking into account the temperature dependence of the opacity; and by examining current sheet geometry in three-dimensional, global models of magnetorotational instability. We find that temperatures above 1600 K can be reached for favorable parameters that match the ideal global models. This mechanism could provide an efficient means of tapping the gravitational potential energy of the protoplanetary disk to heat grains strongly enough to form high-temperature minerals. The volume-filling nature of turbulent magnetic reconnection is compatible with constraints from chondrule-matrix complementarity, chondrule-chondrule complementarity, the occurrence of igneous rims, and compound chondrules. The same short-circuit mechanism may perform other high-temperature mineral processing in protoplanetary disks such as the production of crystalline silicates and CAIs.Comment: 6 pages, 3 figures, ApJL published versio

'Science isn’t my favourite subject' : pupil opinion in the professional learning of science teachers

The S-TEAM Project has found that inquiry-based science teaching is welcomed by the science teaching community, but that there are constraints on its effectiveness. For example, though many teachers do support inquiry based activity, existing teacher professional development systems across Europe tend not to provide the skills or confidence that this more innovative practice requires, nor the space for related self-reflection or evaluation. This chapter describes the development of the Science Classroom Environment Pupil Satisfaction & Achievement Instrument (scepsati). Based on research which reveals that becoming a teacher is an affective transition in which relationships with pupils are crucial – in which there is little mention by new teachers of pupils’ achievement or performance in tests, but more discussion about getting to know and interacting with them in fairly fundamental and productive ways – the chapter explores the use of pupil opinion as a formative instrument for professional learning. Providing evidence for a correlation between positive emotional engagement and more open ended thinking, the discussion will further conceptualise the ‘added value’ in the advanced methods that S-TEAM seeks to promote, to thus exemplify inquiry more clearly as a metacognitive goal of teaching and learning in the science classroom

Short Circuits in Thermally Ionized Plasmas: A Mechanism for Intermittent Heating of Protoplanetary Disks

Many astrophysical systems of interest, including protoplanetary accretion disks, are made of turbu- lent magnetized gas with near solar metallicity. Thermal ionization of alkali metals in such gas exceeds non-thermal ionization when temperatures climb above roughly 1000 K. As a result, the conductiv- ity, proportional to the ionization fraction, gains a strong, positive dependence on temperature. In this paper, we demonstrate that this relation between the temperature and the conductivity triggers an exponential instability that acts similarly to an electrical short, where the increased conductivity concentrates the current and locally increases the Ohmic heating. This contrasts with the resistiv- ity increase expected in an ideal magnetic reconnection region. The instability acts to focus narrow current sheets into even narrower sheets with far higher currents and temparatures. We lay out the basic principles of this behavior in this paper using protoplanetary disks as our example host system, motivated by observations of chondritic meteorites and their ancestors, dust grains in protoplanetary disks, that reveal the existence of strong, frequent heating events that this instability could explain.Comment: 9 pages, 6 figures, 1 table Accepted, Ap