Mathematics Education & Digital Technologies: Facing the Challenge of Networking European Research Teams

This paper introduces the IJCML Special Issue dedicated to digital technologies and mathematics education and, in particular, to the work performed by the European Research Team TELMA (Technology Enhanced Learning in Mathematics). TELMA was one of the initiatives of the Kaleidoscope Network of Excellence established by the European Community (IST-507838—2003–2007) to promote the joint elaboration of concepts and methods for exploring the future of learning with digital technologies. TELMA addressed the problem of fragmentation of theoretical frameworks in the research field of mathematics education with digital technologies and developed a methodology based on the in field cross-experimentation of educational digital environments for maths. Six European research teams engaged in cross-experimentation in classrooms as a means to begin to develop a common language and to analyse the intertwined influence played, both explicitly and implicitly, by different contextual characteristics and theoretical frames assumed as reference by the diverse teams participating in the initiative.     

Comparing theoretical frameworks enacted in experimental research: TELMA experience

In the context of the Kaleidoscope Network of Excellence, six European research teams developed a methodology for integrating their research approaches. In this paper, we present the methodology based on a cross-experimentation, showing how it gave insight to the understanding of each team’s research and on the relationship between theoretical frameworks and experimental research.     

A basic course on compiler principles

An attempt to devise a methodology of compiler design is described, and an outline is given for a possible course on this subject. The theoretical basis is formed by the concepts of phrase-structure language, finite-state- and stack-acceptor, and transducer. As their extension capable of processing context-dependent elements of languages, a so-called Table-Transducer is postulated, and it serves as the core-algorithm upon which compilers are based. The developed theory and method of compiler construction is applied to an example of a simple programming language.     

Strategic planning decisions in an R & D setting

Strategic planning, by nature, is concerned with the organization's interaction with its environment and is normative because it deals with organizational motives and self image. The salient problem confronting strategic planning is to reflect the abstract and implicit value system held by management within a disciplined and informed analytical methodology.The Gas Research Institute has developed a strategic planning process, centered upon the annual development of a projection of the U.S. energy/economic situation. The process, which requires collaboration of top management and analytical staff, brings current environmental data and sophisticated methodology to bear on the outlook for the gas industry and gas-related technologies, but it ensures that analytical judgements will be influenced and, if necessary, overriden by current management values. Contradictions between managament perceptions and objective analysis are raised and resolved in an explicit process.     

Sample-Based Optimal Transport and Barycenter Problems

A methodology is developed for the numerical solution to the sample-based optimal transport and Wasserstein barycenter problems. The procedure is based on a characterization of the barycenter and of the McCann interpolants that permits the decomposition of the global problem under consideration into various local problems where the distance among successive distributions is small. These local problems can be formulated in terms of feature functions and shown to have a unique minimizer that solves a nonlinear system of equations. Both the theoretical underpinnings of the methodology and its practical implementation are developed, and illustrated with synthetic and real data sets. © 2019 Wiley Periodicals, Inc.     

Solution of general ordinary differential equations using the algebraic theory approach

The algebraic theory for numerical methods, as developed by Herrera [3–7], provides a broad theoretical framework for the development and analysis of numerical approximations. To this point, the technique has only been applied to ordinary differential equations with constant coefficients. The present work extends the theory by developing a methodology for equations with variable coefficients. Approximation of the coefficients by piecewise polynomials forms the foundation of the approach. Analysis of the method provides firm error estimates. Furthermore, the analysis points to particular procedures that produce optimal accuracy. Example calculations illustrate the computational procedure and verify the theoretical convergence rates.     

Mathematical modeling of catalytic wet oxidation in trickle-bed reactors by a diffusion–convection–reaction approach embedded with an interstitial CFD framework

In this work, we propose a diffusion–convection–reaction methodology to gain further insights into the heterogeneous multiphase flow of trickle beds. Our case-study encompasses a multi-fluid model embedded within an interstitial framework on the numerical simulation of continuous catalytic wet oxidation of hazardous compounds. First, with the proviso that phase holdup, pressure drop, and liquid distribution are fundamental criteria for the efficient design of trickle beds, the multiphase flow constitutive equations have been developed and solved by the conservative unstructured finite volume method. Second, several numerical variables were parametrically optimized based on the application of different under-relaxation parameters, mesh densities, and time stepping strategies. The segregated solver has been found to reveal good properties in terms of convergence and stability criteria, which endorsed the further corroboration. Finally, this theoretical probing-sensing scheme enabled the characterization of liquid flow texture accomplished by three-dimensional flow patterns exposing their deviation from ideal plug flow. The diffusion–convection–reaction framework coupled within a CFD model can then be further exploited on the simulation of complex multiphase reactive flows with adjustable parameters.     

The bounded proof property via step algebras and step frames

The paper introduces semantic and algorithmic methods for establishing a variant of the analytic subformula property (called ‘the bounded proof property’, bpp) for modal propositional logics. The bpp is much weaker property than full cut-elimination, but it is nevertheless sufficient for establishing decidability results. Our methodology originated from tools and techniques developed on one side within the algebraic/coalgebraic literature dealing with free algebra constructions and on the other side from classical correspondence theory in modal logic. As such, our approach is orthogonal to recent literature based on proof-theoretic methods and, in a way, complements it.     

Comparing the adaptive control methodology (ACM) to the financial planning practice of a large international group

The present paper is a contribution to the validation of the newly developed methodological framework called “adaptive control methodology” (ACM) introduced in a previous paper. ACM is a tool for planning and on-line control of complex socio-economic processes. It combines the techniques of adaptive control theory with system dynamics (SD) and group multicriteria decision aid (GMCDA). In the following, the usefulness and practical use of this framework are set in perspective by comparing it with recurrent planning and control of financial processes in the BSN/DANONE group. As a result of this comparison, some lessons drawn on the way of practical implementation of the theoretical framework can be eased. As by-product recommendations are made on how to influence in a constructive way common planning processes in the real world.     

An application of Soft Systems Dynamics Methodology (SSDM)

The paper argues that by combining some of systems dynamics (SD) and soft systems methodology (SSM) stages, within the intellectual framework proposed by soft systems dynamics methodology (SSDM), a systemic methodology developed by Rodriguez-Ulloa, much can be gained in a systemic intervention when tackling complex social problematic situations. A framework for comparing the ontological, epistemological and methodological principles of SD, SSM and SSDM is proposed and the synthesizing role of SSDM is advanced. SSDM ten stages are briefly outlined and a full account of an application on a small Peruvian enterprise is presented. A reflection on SSDM as a systemic intellectual tool is proposed and conclusions together with points for further research are suggested.     

Using OR for diagnosis and facilitation in change programmes: a university application

In this paper, a methodology for the ongoing diagnosis and facilitation (when required) of organizational change management programmes in an Australian University is described. The application of this methodology on an annual basis requires the assessment of research attitudes and behaviour, areas that have assumed considerable importance within universities around the world in the last decade. This increasing importance associated with research stems in part (a significant part) from the linkage of research quantum (output) of universities to their funding from government. The methodology developed in this paper embraces a wide range of OR-type techniques as well as a range of change management tools from human resources management. These two sets of techniques and tools work together as tools in their own right as well as providing the infrastructure to achieve the objectives. The developed methodology is an interesting blend of hard techniques and ‘soft’ approaches implemented through a soft heuristic, indeed this application is an example of mixed-mode modelling. The OR techniques (conventional in both their nature and application) are comprised of social judgement theory (for bench-marking research attitudes) and integer linear programming (for setting research targets). The results of the application of the developed methodology are discussed in terms of the effect on research quantum over a 5-year period. A similar methodology could be developed for a change process covering aspects of an organization other than research output in a number of countries.     

Path planning,modeling and simulation of an autonomous articulated heavy construction machine performing a loading cycle

This research presents path planning and tracking for an articulated large wheel loader during the travel portion of a loading cycle. The study proposes a methodology for path planning, modeling, simulation and control of such vehicles; the analysis focuses on all of these components together and explains the relation among them. The developed methodology for path planning takes into account the dynamics and the performance characteristics of the heavy construction articulated vehicles, it also takes into account the construction working site constraints. The path optimization criterion is based on distance and cusp minimization without neglecting the constraints imposed by the size of the vehicle and its stable turning radius. The proposed path planning methodology is an extension and an improvement for Reeds and Shepp algorithm for a point shortest path calculation. The optimal path is consisted of circular arcs and straight segments, the radius is constant and identical for each arc in the desired path, the radius assumed to be similar to the minimum turning radius of the machine. When optimizing articulated machine path; to best account for machine size and articulation; more than one approach are discussed and compared. The machine is modeled and simulated during tracing the pre-defined planned path. The machine model includes the main frames, tires and a steering controller. The developed PID controller is used to keep machine lateral position within the pre-defined path while traveling with constant speed. The results showed an acceptable optimized path which the machine is able to track closely.     

Social indicators and policy selection: An experiment in constructing a social objective function

A small scale experiment is described, the main purpose of which is to evaluate methodology for evaluating within group and between group differences in attitude to a range of scenarios constructed from a number of social and economic indicators. Three countries featured in the study, Greece, Holland, and the U.K. The tool employed in the multidimensional analysis of preference judgements was the suite of linear programming techniques (linmap) developed during the 1970's by Srinivasan and Shocker. It is concluded that the methodology is feasible and could have more general application.     

Developing a visioning methodology: Visioning Choices for the future of operational research

This paper describes the development of a participative visioning methodology, Visioning Choices, which is placed within the family of problem structuring methods, due to a range of characteristics and attributes that are discussed. The Visioning Choices methodology was developed in an action research paradigm, and consists of a number of stages. The case study presented describes an application of the methodology to the issue of the future of operational research (OR). More than 200 individuals participated in workshops to outline a desirable future for OR. Earlier work has shown that while the majority of organizations claim to have visions, and that visions are perceived to have an important role in contributing to organizational success, visions are usually developed using informal small group processes, rather than existing formal visioning methodologies. The paper uses coherence and correspondence arguments to reflect on the methodology described, and possible future developments to address issues such facilitation style and participant numbers.     

The greater whole: Towards a synthesis of system dynamics and soft systems methodology

This paper makes a theoretical case for using these two systems approaches together. The theoretical and methodological assumptions of system dynamics (SD) and soft system methodology (SSM) are briefly described and a partial critique is presented. SSM generates and represents diverse perspectives on a problem situation and addresses the socio-political elements of an intervention. However, it is weak in ensuring `dynamic coherence'. consistency between the intuitive behaviour resulting from proposed changes and behaviour deduced from ideas on causal structure. Conversely, SD examines causal structures and dynamic behaviours. However, whilst emphasising the need for a clear issue focus, it has little theory for generating and representing diverse issues. Also, there is no theory for facilitating sensitivity to socio-political elements. A synthesis of the two called ‘Holon Dynamics' is proposed. After an SSM intervention, a second stage continues the socio-political analysis and also operates within a new perspective which values dynamic coherence of the mental construct - the holon - which is capable of expressing the proposed changes. A model of this holon is constructed using SD and the changes are thus rendered `systemically desirable' in the additional sense that dynamic consistency has been confirmed. The paper closes with reflections on the proposal and the need for theoretical consistency when mixing tools is emphasised.     

Multivariate nonlinear least squares: robustness and efficiency of standard versus Beauchamp and Cornell methodologies

Simultaneous estimation in nonlinear multivariate regression contexts is a complex problem in inference. In this paper, we compare the methodology suggested in the literature for an unknown covariance matrix among response components, the methodology by Beauchamp and Cornell (B&C), with the standard nonlinear least squares approach (NLS). In the first part of the paper, we contrast B&C and the standard NLS, pointing out, from the theoretical point of view, how a model specification error could affect the estimation. A comprehensive simulation study is also performed to evaluate the effectiveness of B&C versus standard NLS under both correct and misspecified models. Several alternative models are considered to highlight the consequences of different types of specification error. An application to a real dataset within the context of quantitative marketing is presented.     

A web-based methodology for product design evaluation and optimisation

The authors have developed a methodology that takes advantages of the World Wide Web to analyse and develop optimal new product designs. This paper describes the methodology and illustrates its application to a case study involving the design of an actual Web site where music CDs are sold. The proposed methodology has the following features: (a) it is based on a design inspired by conjoint analysis; (b) it involves unobtrusive electronic measurement of the actual behavior of Web users who remain undisturbed by experimental factors; and (c) it utilises an integer programming approach to seek optimal Web site configurations. The methodology uses limited dependent variable methods to develop response models that provide the basis for the development of objective functions for an optimisation model. The optimisation model can consider either single or multiple objective functions by using a Pareto optimum approach.     

The Superior Commander: A Methodology for the Control of Crisis Games

The Superior Commander is a new methodology for the design and control of experimental games in which the players may be exposed to crisis or stress. It satisfies three important requirements: the player in the game believes that he is an active decision maker; the game contains sufficient complexity and detail to be accepted by the player as realistic; and the experimenter is able to control the game so that he can replicate it exactly with different players. One implementation of the methodology, the Organisational Control Game, is described in detail, and the principles of the Superior Commander are demonstrated.The Superior Commander was developed to overcome some of the limitations of other gaming approaches to the study of decision making in crises, but it is also a general methodology for research games, and can be used for a range of purposes for which both realism and good experimental control are required.