Methodologies for investigating relationships between concept development and the development of problem solving abilities

This paper is the second in a pair that Lesh, English, and Fennewald will be presenting at ICME TSG 19 on Problem Solving in Mathematics Education. The first paper describes three shortcomings of past research on mathematical problem solving. The first shortcoming can be seen in the fact that knowledge has not accumulated – in fact it has atrophied significantly during the past decade. Unsuccessful theories continue to be recycled and embellished. One reason for this is that researchers generally have failed to develop research tools needed to reliably observe, document, and assess the development of concepts and abilities that they claim to be important. The second shortcoming is that existing theories and research have failed to make it clear how concept development (or the development of basic skills) is related to the development of problem solving abilities – especially when attention is shifted beyond word problems found in school to the kind of problems found outside of school, where the requisite skills and even the questions to be asked might not be known in advance. The third shortcoming has to do with inherent weaknesses in observational studies and teaching experiments – and the assumption that a single grand theory should be able to describe all of the conceptual systems, instructional systems, and assessment systems that strongly molded and shaped by the same theoretical perspectives that are being used to develop them. Therefore, this paper will describe theoretical perspectives and methodological tools that are proving to be effective to combat the preceding kinds or shortcomings. We refer to our theoretical framework as models & modeling perspectives (MMP) on problem solving (Lesh & Doerr, 2003), learning, and teaching. One of the main methodologies of MMP is called multi-tier design studies (MTD).

Tracking the defining moments of crisis process and practice

Crisis holds the potential for profound change in organizations and industries. The past 50 years of crisis management highlight key shifts in crisis practice, creating opportunities for multiple theories and research tracks. Defining crises such as Tylenol, Exxon Valdez, and September 11 terrorist attacks have influenced or challenged the principles of best practice of crisis communication in public relations. This study traces the development of crisis process and practice by identifying shifts in crisis research and models and mapping these against key management theories and practices. The findings define three crisis domains: crisis planning, building and testing predictive models, and mapping and measuring external environmental influences. These crisis domains mirror but lag the evolution of management theory, suggesting challenges for researchers to reshape the research agenda to close the gap and lead the next stage of development in the field of crisis communication for effective organizational outcomes.

Recommendations for the reporting of foot and ankle models

Multiple marker sets and models are currently available for assessing foot and ankle kinematics in gait. Despite the presence of such a wide variety of models, the reporting of methodological designs remains inconsistent and lacks clearly defined standards. This review highlights the variability found when reporting biomechanical model parameters, methodological design, and model reliability. Further, the review clearly demonstrates the need for a consensus of what methodological considerations to report in manuscripts, which focus on the topic of foot and ankle biomechanics. We propose five minimum reporting standards, that we believe will ensure the transparency of methods and begin to allow the community to move towards standard modelling practice. The strict adherence to these standards should ultimately improve the interpretation and clinical useability of foot and ankle marker sets and their corresponding models.

Mentor feedback : models, viewpoints and strategies

A mentor’s feedback can present professional insights to allow a mentee to reflect and develop practice. This paper positions two models for feedback that have emanated from empirical studies. It also demonstrates the diverse viewpoints of mentors and suggests strategies for providing quality feedback. In one qualitative study, 24 mentors observed a final-year preservice teacher through a professionally video-recorded lesson and wrote their observations towards giving feedback to the potential mentee. Tables illustrated in the paper, show that mentors’ positive feedback and constructive criticisms vary considerably on the same observed events. Data from this study were synthesised to posit a theoretical model for analysing mentor feedback in an interconnected, three-way Venn diagram, namely: visual, auditory and conceptual frames. Another study (n=28), which is a collection of mentor teachers’ work samples during the Mentoring for Effective Teaching (MET) program, provides strategies within six feedback practices, that is: (1) negotiated mentor-mentee expectations for providing feedback on practices, (2) reviewing teaching plans, (3) arranging for observations of practices, (4) providing oral feedback, (5) providing written feedback, and; (6) presenting opportunities for the mentee to evaluate teaching practices with consideration of the mentor’s feedback. For example, on the last mentioned practice (6) there were strategies such as “Plan a time for evaluation of practices (guided reflection)”, “Read the mentee’s reflection on practice and discuss how it aligns with your observations of their practices”, and “Highlight verbally and/or in writing where the mentee is perceptive about the reflection and how the reflection could be enhanced for future evaluations”. Developing a range of strategies that may assist the mentee in professional growth, include enlisting a community of mentors, ensuring mentors have a repertoire of strategies for articulating feedback, and using mentor feedback tools and models. This study has implications for the development of feedback models and strategies.

The role of design in the future of digital channels: Conceptual insights and future research directions

Purpose In the past channel literature has looked to other disciplines in developing and refining their theories, models and methods in order to evolve the field. This paper traces such history and highlights the substantial changes caused by the digital age. In light of this, the inclusion of design theory into future channel management is presented to overcome existing concerns. Design/methodology/approach A comprehensive review of literature on the history of channels, the emotional experience (people), limitations of digital innovation (technology) and the role of design (business) has been conducted to create a new approach, built upon the theory of the techno-economic innovation model. Findings The findings of this study propose design-led channel management as a new research area, providing novel research questions and future research directions. The inclusion of design and emotion theories indicates that the future of digital channel design requires a deeper understanding of customers and needs to go beyond technological advances. Theoretical implications The findings provide an opportunity to explore dynamic theories and methodologies within the field of design that will broaden the horizons and challenge existing notions in channel literature. Originality/value This paper is the first paper that introduces the theory of Emotionate, as the next evolution of channel literature. The value of Emotionate lies in providing a new design-led process of integrating emotion to provide advice to practitioners as well as identifies research areas for academia, thereby extending the reach and richness of this emerging research field.

Theory and Analysis of Classic Heavy Metal Harmony

This thesis explores melodic and harmonic features of heavy metal, and while doing so, explores various methods of music analysis; their applicability and limitations regarding the study of heavy metal music. The study is built on three general hypotheses according to which 1) acoustic characteristics play a significant role for chord constructing in heavy metal, 2) heavy metal has strong ties and similarities with other Western musical styles, and 3) theories and analytical methods of Western art music may be applied to heavy metal. It seems evident that in heavy metal some chord structures appear far more frequently than others. It is suggested here that the fundamental reason for this is the use of guitar distortion effect. Subsequently, theories as to how and under what principles heavy metal is constructed need to be put under discussion; analytical models regarding the classification of consonance and dissonance and chord categorization are here revised to meet the common practices of this music. It is evident that heavy metal is not an isolated style of music; it is seen here as a cultural fusion of various musical styles. Moreover, it is suggested that the theoretical background to the construction of Western music and its analysis can offer invaluable insights to heavy metal. However, the analytical methods need to be reformed to some extent to meet the characteristics of the music. This reformation includes an accommodation of linear and functional theories that has been found rather rarely in music theory and musicology.

Key ideas, research and challenges in early childhood education and care

The Australian government has recognised the importance of early childhood education and care (ECEC) in recent years. With over one million Australian children accessing early childhood education provision every day (Productivity Commission, 2014), today’s children are a generation who spend a large part of their early years in some form of out-of-home child care. Early chapters in this text have discussed a range of people, theories and approaches that inform the development of ECEC. Early childhood pedagogical practice is an eclectic mix of these ideas. This chapter begins with an overview of the ways young children learn in early childhood education, highlighting play-based learning as a pedagogical response to our understandings about children. Next the chapter outlines areas that have more recently influenced ECEC including international models of early childhood education, neuroscience, studies of young children, economic research and social justice principles. Drawing on the reflections of educators working in various ECEC contexts, the chapter then presents four topics encountered by educators as part of their everyday work with diverse communities. These topics include: • the educational program for children in the early years • relationships and partnerships with diverse families • professional accountabilities, and • changing constructions of childhood.

Sensor networks for geospatial event detection - theory and applications

This thesis presents theories, analyses, and algorithms for detecting and estimating parameters of geospatial events with today's large, noisy sensor networks. A geospatial event is initiated by a significant change in the state of points in a region in a 3-D space over an interval of time. After the event is initiated it may change the state of points over larger regions and longer periods of time. Networked sensing is a typical approach for geospatial event detection. In contrast to traditional sensor networks comprised of a small number of high quality (and expensive) sensors, trends in personal computing devices and consumer electronics have made it possible to build large, dense networks at a low cost. The changes in sensor capability, network composition, and system constraints call for new models and algorithms suited to the opportunities and challenges of the new generation of sensor networks. This thesis offers a single unifying model and a Bayesian framework for analyzing different types of geospatial events in such noisy sensor networks. It presents algorithms and theories for estimating the speed and accuracy of detecting geospatial events as a function of parameters from both the underlying geospatial system and the sensor network. Furthermore, the thesis addresses network scalability issues by presenting rigorous scalable algorithms for data aggregation for detection. These studies provide insights to the design of networked sensing systems for detecting geospatial events. In addition to providing an overarching framework, this thesis presents theories and experimental results for two very different geospatial problems: detecting earthquakes and hazardous radiation. The general framework is applied to these specific problems, and predictions based on the theories are validated against measurements of systems in the laboratory and in the field.

Distributed Control and Optimization for Communication and Power Systems

We are at the cusp of a historic transformation of both communication system and electricity system. This creates challenges as well as opportunities for the study of networked systems. Problems of these systems typically involve a huge number of end points that require intelligent coordination in a distributed manner. In this thesis, we develop models, theories, and scalable distributed optimization and control algorithms to overcome these challenges.

This thesis focuses on two specific areas: multi-path TCP (Transmission Control Protocol) and electricity distribution system operation and control. Multi-path TCP (MP-TCP) is a TCP extension that allows a single data stream to be split across multiple paths. MP-TCP has the potential to greatly improve reliability as well as efficiency of communication devices. We propose a fluid model for a large class of MP-TCP algorithms and identify design criteria that guarantee the existence, uniqueness, and stability of system equilibrium. We clarify how algorithm parameters impact TCP-friendliness, responsiveness, and window oscillation and demonstrate an inevitable tradeoff among these properties. We discuss the implications of these properties on the behavior of existing algorithms and motivate a new algorithm Balia (balanced linked adaptation) which generalizes existing algorithms and strikes a good balance among TCP-friendliness, responsiveness, and window oscillation. We have implemented Balia in the Linux kernel. We use our prototype to compare the new proposed algorithm Balia with existing MP-TCP algorithms.

Our second focus is on designing computationally efficient algorithms for electricity distribution system operation and control. First, we develop efficient algorithms for feeder reconfiguration in distribution networks. The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as power loss. It is a mixed integer nonlinear program and hence hard to solve. We propose a heuristic algorithm that is based on the recently developed convex relaxation of the optimal power flow problem. The algorithm is efficient and can successfully computes an optimal configuration on all networks that we have tested. Moreover we prove that the algorithm solves the feeder reconfiguration problem optimally under certain conditions. We also propose a more efficient algorithm and it incurs a loss in optimality of less than 3% on the test networks.

Second, we develop efficient distributed algorithms that solve the optimal power flow (OPF) problem on distribution networks. The OPF problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. Traditionally OPF is solved in a centralized manner. With increasing penetration of volatile renewable energy resources in distribution systems, we need faster and distributed solutions for real-time feedback control. This is difficult because power flow equations are nonlinear and kirchhoff's law is global. We propose solutions for both balanced and unbalanced radial distribution networks. They exploit recent results that suggest solving for a globally optimal solution of OPF over a radial network through a second-order cone program (SOCP) or semi-definite program (SDP) relaxation. Our distributed algorithms are based on the alternating direction method of multiplier (ADMM), but unlike standard ADMM-based distributed OPF algorithms that require solving optimization subproblems using iterative methods, the proposed solutions exploit the problem structure that greatly reduce the computation time. Specifically, for balanced networks, our decomposition allows us to derive closed form solutions for these subproblems and it speeds up the convergence by 1000x times in simulations. For unbalanced networks, the subproblems reduce to either closed form solutions or eigenvalue problems whose size remains constant as the network scales up and computation time is reduced by 100x compared with iterative methods.

Measurement errors in body size of sea scallops (Placopecten magellanicus) and their effect on stock assessment models

Body-size measurement errors are usually ignored in stock assessments, but may be important when body-size data (e.g., from visual sur veys) are imprecise. We used experiments and models to quantify measurement errors and their effects on assessment models for sea scallops (Placopecten magellanicus). Errors in size data obscured modes from strong year classes and increased frequency and size of the largest and smallest sizes, potentially biasing growth, mortality, and biomass estimates. Modeling techniques for errors in age data proved useful for errors in size data. In terms of a goodness of model fit to the assessment data, it was more important to accommodate variance than bias. Models that accommodated size errors fitted size data substantially better. We recommend experimental quantification of errors along with a modeling approach that accommodates measurement errors because a direct algebraic approach was not robust and because error parameters were diff icult to estimate in our assessment model. The importance of measurement errors depends on many factors and should be evaluated on a case by case basis.

Models for magnetohydrodynamics of aluminium electrolysis cells

The electric current and the associated magnetic field in aluminium electrolysis cells create effects limiting the cell productivity and possibly cause instabilities: surface waving, ‘anode effects’, erosion of pot lining, feed material sedimentation, etc. The instructive analysis is presented via a step by step inclusion of different physical coupling factors affecting the magnetic field, electric current, velocity and wave development in the electrolysis cells. The full time dependent model couples the nonlinear turbulent fluid dynamics and the extended electromagnetic field in the cell, and the whole bus bar circuit with the ferromagnetic effects. Animated examples for the high amperage cells are presented. The theory and numerical model of the electrolysis cell is extended to the cases of variable cell bottom of aluminium layer and the variable thickness of the electrolyte due to the anode non-uniform burn-out process and the presence of the anode channels. The problem of the channel importance is well known Moreau-Evans model) for the stationary interface and the velocity field, and was validated against measurements in commercial cells, particularly with the recently published ‘benchmark’ test for the MHD models of aluminium cells [1]. The presence of electrolyte channels requires also to reconsider the previous magnetohydrodynamic instability theories and the dynamic wave development models. The results indicate the importance of a ‘sloshing’ parametrically excited MHD wave development in the aluminium production cells.

Global assessment of ocean carbon export by combining satellite observations and food-web models

The export of organic carbon from the surface ocean by sinking particles is an important, yet highly uncertain, component of the global carbon cycle. Here we introduce a mechanistic assessment of the global ocean carbon export using satellite observations, including determinations of net primary production and the slope of the particle size spectrum, to drive a food-web model that estimates the production of sinking zooplankton feces and algal aggregates comprising the sinking particle flux at the base of the euphotic zone. The synthesis of observations and models reveals fundamentally different and ecologically consistent regional-scale patterns in export and export efficiency not found in previous global carbon export assessments. The model reproduces regional-scale particle export field observations and predicts a climatological mean global carbon export from the euphotic zone of ~6 Pg C yr−1. Global export estimates show small variation (typically < 10%) to factor of 2 changes in model parameter values. The model is also robust to the choices of the satellite data products used and enables interannual changes to be quantified. The present synthesis of observations and models provides a path for quantifying the ocean's biological pump.

Three-dimensional pure deflagration models with nucleosynthesis and synthetic observables for type ia supernovae

We investigate whether pure deflagration models ofChandrasekhar-mass carbon-oxygen white dwarf stars can account for one or more subclass of the observed population of Type Ia supernova (SN Ia) explosions. We compute a set of 3D full-star hydrodynamic explosion models, in which the deflagration strength is parametrized using the multispot ignition approach. For each model, we calculate detailed nucleosynthesis yields in a post-processing step with a 384 nuclide nuclear network. We also compute synthetic observables with our 3D Monte Carlo radiative transfer code for comparison with observations. For weak and intermediate deflagration strengths (energy release E {less-than or approximate} 1.1 × 10 erg), we find that the explosion leaves behind a bound remnant enriched with 3 to 10 per cent (by mass) of deflagration ashes. However, we do not obtain the large kick velocities recently reported in the literature. We find that weak deflagrations with E ~ 0.5 × 10 erg fit well both the light curves and spectra of 2002cx-like SNe Ia, and models with even lower explosion energies could explain some of the fainter members of this subclass. By comparing our synthetic observables with the properties of SNe Ia, we can exclude the brightest, most vigorously ignited models as candidates for any observed class of SN Ia: their B-V colours deviate significantly from both normal and 2002cx-like SNe Ia and they are too bright to be candidates for other subclasses.

An Architecture of a Multi-Agent System for SCADA - Dealing With Uncertainty, Plans and Actions

This paper presents a multi-agent system approach to address the difficulties encountered in traditional SCADA systems deployed in critical environments such as electrical power generation, transmission and distribution. The approach models uncertainty and combines multiple sources of uncertain information to deliver robust plan selection. We examine the approach in the context of a simplified power supply/demand scenario using a residential grid connected solar system and consider the challenges of modelling and reasoning with
uncertain sensor information in this environment. We discuss examples of plans and actions required for sensing, establish and discuss the effect of uncertainty on such systems and investigate different uncertainty theories and how they can fuse uncertain information from multiple sources for effective decision making in
such a complex system.