A Historical Approach to Children s Physics Education : Modelling of DC-circuit Phenomena in a Small Group

This three-phase design research describes the modelling processes for DC-circuit phenomena. The first phase presents an analysis of the development of the DC-circuit historical models in the context of constructing Volta s pile at the turn of the 18th century. The second phase involves the designing of a teaching experiment for comprehensive school third graders. Among other considerations, the design work utilises the results of the first phase and research literature of pupils mental models for DC-circuit phenomena. The third phase of the research was concerned with the realisation of the planned teaching experiment. The aim of this phase was to study the development of the external representations of DC-circuit phenomena in a small group of third graders. The aim of the study has been to search for new ways to guide pupils to learn DC-circuit phenomena while emphasing understanding at the qualitative level. Thus, electricity, which has been perceived as a difficult and abstract subject, could be learnt more comprehensively. Especially, the research of younger pupils learning of electricity concepts has not been of great interest at the international level, although DC-circuit phenomena are also taught in the lower classes of comprehensive schools. The results of this study are important, because there has tended to be more teaching of natural sciences in the lower classes of comprehensive schools, and attempts are being made to develop this trend in Finland. In the theoretical part of the research an Experimental-centred representation approach, which emphasises the role of experimentalism in the development of pupil s representations, is created. According to this approach learning at the qualitative level consists of empirical operations like experimenting, observations, perception, and prequantification of nature phenomena, and modelling operations like explaining and reasoning. Besides planning teaching, the new approach can be used as an analysis tool in describing both historical modelling and the development of pupils representations. In the first phase of the study, the research question was: How did the historical models of DC-circuit phenomena develop in Volta s time? The analysis uncovered three qualitative historical models associated with the historical concept formation process. The models include conceptions of the electric circuit as a scene in the DC-circuit phenomena, the comparative electric-current phenomenon as a cause of different observable effect phenomena, and the strength of the battery as a cause of the electric-current phenomenon. These models describe the concept formation process and its phases in Volta s time. The models are portrayed in the analysis using fragments of the models, where observation-based fragments and theoretical fragements are distinguished from each other. The results emphasise the significance of the qualitative concept formation and the meaning of language in the historical modelling of DC-circuit phenomena. For this reason these viewpoints are stressed in planning the teaching experiment in the second phase of the research. In addition, the design process utilised the experimentation behind the historical models of DC-circuit phenomena In the third phase of the study the research question is as follows: How will the small group s external representations of DC-circuit phenomena develop during the teaching experiment? The main question is divided into the following two sub questions: What kind of talk exists in the small group s learning? What kinds of external representations for DC-circuit phenomena exist in the small group discourse during the teaching experiment? The analysis revealed that the teaching experiment of the small group succeeded in its aim to activate talk in the small group. The designed connection cards proved especially successful in activating talk. The connection cards are cards that represent the components of the electric circuit. In the teaching experiment the pupils constructed different connections with the connection cards and discussed, what kinds of DC-circuit phenomena would take place in the corresponding real connections. The talk of the small group was analysed by comparing two situations, firstly, when the small group discussed using connections made with the connection cards and secondly with the same connections using real components. According to the results the talk of the small group included more higher-order thinking when using the connection cards than with similar real components. In order to answer the second sub question concerning the small group s external representations that appeared in the talk during the teaching experiment; student talk was visualised by the fragment maps which incorporate the electric circuit, the electric current and the source voltage. The fragment maps represent the gradual development of the external representations of DC-circuit phenomena in the small group during the teaching experiment. The results of the study challenge the results of previous research into the abstractness and difficulty of electricity concepts. According to this research, the external representations of DC-circuit phenomena clearly developed in the small group of third graders. Furthermore, the fragment maps uncover that although the theoretical explanations of DC-circuit phenomena, which have been obtained as results of typical mental model studies, remain undeveloped, learning at the qualitative level of understanding does take place.

Stability of multi-cluster synchronization

A system of many coupled oscillators on a network can show multicluster synchronization. We obtain existence conditions and stability bounds for such a multicluster synchronization. When the oscillators are identical, we obtain the interesting result that network structure alone can cause multicluster synchronization to emerge even when all the other parameters are the same. We also study occurrence of multicluster synchronization when two different types of oscillators are coupled.

From Bathymetry to Bioshields: A Review of Post-Tsunami Ecological Research in India and its Implications for Policy

More than half a decade has passed since the December 26th 2004 tsunami hit the Indian coast leaving a trail of ecological, economic and human destruction in its wake. We reviewed the coastal ecological research carried out in India in the light of the tsunami. In addition, we also briefly reviewed the ecological research in other tsunami affected countries in Asia namely Sri Lanka, Indonesia, Thailand and Maldives in order to provide a broader perspective of ecological research after tsunami. A basic search in ISI Web of Knowledge using keywords ``tsunami'' and ``India'' resulted in 127 peer reviewed journal articles, of which 39 articles were pertaining to ecological sciences. In comparison, Sri Lanka, Indonesia, Thailand and Maldives had, respectively, eight, four, 21 and two articles pertaining to ecology. In India, bioshields received the major share of scientific interest (14 out of 39) while only one study (each) was dedicated to corals, seagrasses, seaweeds and meiofauna, pointing to the paucity of research attention dedicated to these critical ecosystems. We noted that very few interdisciplinary studies looked at linkages between pure/applied sciences and the social sciences in India. In addition, there appears to be little correlation between the limited research that was done and its influence on policy in India. This review points to gap areas in ecological research in India and highlights the lessons learnt from research in other tsunami-affected countries. It also provides guidance on the links between science and policy that are required for effective coastal zone management.

On the integrability and chaotic behavior of an ecological model

A three-species food chain model is studied analytically as well as numerically. Integrability of the model is studied using Painleve analysis while chaotic behavior is studied using numerical techniques, such as calculation of Lyapunov exponents, plotting the bifurcation diagram and phase plots. We correct and critically comment on the wrong results reported recently on this ecological model, in a paper by Rai [1995].

Spatial Decision Support System for Assessing Micro, Mini and Small Hydel Potential

This study describes the design and implementation of DSS for assessment of Mini, Micro and Small Schemes. The design links a set of modelling, manipulation, spatial analyses and display tools to a structured database that has the facility to store both observed and simulated data. The main hypothesis is that this tool can be used to form a core of practical methodology that will result in more resilient in less time and can be used by decision-making bodies to assess the impacts of various scenarios (e.g.: changes in land use pattern) and to review, cost and benefits of decisions to be made. It also offers means of entering, accessing and interpreting the information for the purpose of sound decision making. Thus, the overall objective of this DSS is the development of set of tools aimed at transforming data into information and aid decisions at different scales.

Generalized eigenvalue decomposition of the field autocorrelation in correlation diffusion of photons in turbid media

We propose a novel numerical method based on a generalized eigenvalue decomposition for solving the diffusion equation governing the correlation diffusion of photons in turbid media. Medical imaging modalities such as diffuse correlation tomography and ultrasound-modulated optical tomography have the (elliptic) diffusion equation parameterized by a time variable as the forward model. Hitherto, for the computation of the correlation function, the diffusion equation is solved repeatedly over the time parameter. We show that the use of a certain time-independent generalized eigenfunction basis results in the decoupling of the spatial and time dependence of the correlation function, thus allowing greater computational efficiency in arriving at the forward solution. Besides presenting the mathematical analysis of the generalized eigenvalue problem on the basis of spectral theory, we put forth the numerical results that compare the proposed numerical method with the standard technique for solving the diffusion equation.