This paper presents part of a study that aimed to make more explicit the pragmatic theories that inform the design of professional development programs with an emphasis on the integration of digital technologies in the practices of mathematics teachers. The analysis carried out was based on a set of projects considered representative and implemented in four countries – Colombia, Italy, Mexico and Portugal. Based on this analysis, we identify relevant elements (e.g., similarities and differences, barriers and opportunities) and develop recommendations to be taken into account in the design of future professional development programs. In this process, we identified a set of aspects and sub-aspects, as well as several interconnections between them, which emerged in relation to five main themes and allowed us to reveal our pragmatic theories. Thus, this work provides a framework to support the design of future projects for the professional development of mathematics teachers regarding the use of digital technology.

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Portugal has been referred as one example of lower levels of integration of social partners in the governance of education and training systems (Sanz de Miguel, 2017). There is lack of research about the effectiveness of the governance of the only program close to the Dual VET concept: the Apprenticeship system. A pilot project of Dual VET ran from 2012 and terminated in 2016 without substantial evaluation. The objective of this paper is to provide an overview of the role social partners have in the governance of the existing Portuguese Apprenticeship system. We carried out extensive review of the scientific and grey literature about Dual VET for youngsters in Portugal, as well as database queries to official statistical sources. Our research reveals a complex formal role: The employment agency IEFP provides funding for Apprenticeship and negotiates with the main social partners the allocation of the Single Social Tax for its regional centres. Indirectly, many social partners are formally involved in the general VET governance participating in various coordination and monitoring structures of the National System of Qualifications and other regulatory agencies (IEFP and ANQEP). In this article we also discuss possible causes for the failure of the pilot Dual VET, which took effect within the scope of a curricular review of the primary and secondary education.

Since the 1970s, the application of microprocessor in industrial machinery and the development of computer systems have transformed the manufacturing landscape. The rapid integration and automation of production systems have outpaced the development of suitable human design criteria, creating a deepening gap between humans and systems in which human was seen as an important source of errors and disruptions. Today, the situation seems different: the scientific and public debate about the concept of Industry 4.0 has raised awareness about the central role humans have to play in manufacturing systems, the design of which must be considered from the very beginning. The future of industrial systems, as represented by Industry 4.0, will rely on the convergence of several research fields such as Intelligent Manufacturing Systems (IMS), Cyber-Physical Systems (CPS), Internet of Things (IoT), but also socio-technical fields such as social approaches within technical systems. This article deals with different human social dimensions associated with CPS and IoT and focuses on their conceptual evolution regarding automated production systems’ sociability, notably by bringing humans back in the loop. Hereby, this paper aims to take stock of current research trends to show the importance of integrating human operators as a part of a socio-technical system based autonomous and intelligent products or resources. Consequently, different models of sociability as a way to integrate humans in the broad sense and/or the develop future automated production systems have been identified from the literature and analysed.

Regime switching diffusion processes with one or two thresholds and regime switching occurring by a change in the diffusion drift and/or volatility functions parameters of a stochastic differential equation, whose solution defines a continuous time diffusion process, were defined in previous works; the change in regime occurring whenever the trajectory of the process crosses a threshold, possibly with some delay. In this paper we generalise the previous
results by allowing the underlying diffusion process to change from one family of diffusions in one regime to an entirely different one in the other regime; these families of diffusions are characterised by specific functional forms for drift and volatility coefficients depending on parameters. We propose an estimation procedure for all the parameters, namely the thresholds, the delay and, for both regimes, diffusion’s parameters and we apply the introduced estimation procedure to both simulated and real data.

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Teacher education is central to promote the development of the professional knowledge of teachers, and
to help them achieve an appropriate integration of digital technologies, an issue that has proved to be a
difficult one. Several authors refer difficulties in the integration of the technology, emphasizing the central
role played by the teachers’ knowledge in classroom use. In this paper we discuss three models (TPACK
– Technological Pedagogical and Content Knowledge, KTMT – Knowledge for Teaching Mathematics with
Technology, PTK / MPTK - Mathematical Pedagogical Technology Knowledge), intending to identify the
main contributions of each model to a deeper understanding of how to promote the teachers’ integration
of technology in the teaching of Mathematics. The study is based on a literature review and on an analysis
of the similarities and differences among the models and its use. On this analysis we identify common
influences among the models as well as influences from other research areas. The main conclusions
achieved point to a common base to all the models considered, but also to several differences among
them, being that some of the models emphasize the role of technology and its impact on Mathematics
learning, but others go further, intending to integrate in the model elements based on the research on
technology or even other theories such as the one on instrumental genesis.

Due to the innovative possibilities of digital technologies, the issue of increasing automation is once again on the agenda – and not only in the industry, but also in other branches and sectors of contemporary societies. Although public and scientific discussions about automation seem to raise relevant questions of the “old” debate, such as the replacement of human labor by introducing new technologies, the authors focus here on the new contextual quality of these questions. The debate should rethink the relationship between technology and work with regard to quantitative and qualitative changes in work. In this article, our example will be the introduction of automation in industry, which has been reflected in the widely recognized study by Frey and Osborne in 2013. They estimated the expected impacts of future computerization on US labor market outcomes as very high, specifically regarding the number of jobs at risk. Surprisingly, this study was the starting point of an intensive international debate on the impact of technologies on the future of work and the role of technological change in working environments. Thus, according to the authors, “old” questions remain important, but they should be reinterpreted for “new” societal demands and expectations of future models of work.

This paper intended to provide a vision on the potential consequences of the introduction of emerging air transportation system which was based on a section of the thesis to contribute to the forming of public and policy opinion.Especially this paper tried to understand whether there were enough positive social and environmental impacts in terms of potential benefits to continue the efforts.The negative impacts are beyond the scope of this paper. Limitations of the current ground and airline transportation systems, increasing congestion, poor block speed, combined with expanding population and demand for affordable on-demand mobility are driving the development of future transportation technology and policy. The third wave of aeronautic,e VTOL (Vertical Takeoff and landing) Air Transportation System, is envisioned as the next logical step in the natural progression and could bring about great new capabilities for society that would bring aviation into a new age of being relevant in daily lives. Considering door to door block time, e VTOL Air Transportation System has the potential to achieve anotherfive-fold increase over the auto today as the auto provided ten-fold increase over the horse, and a daily mobility reach of 125 to 250 miles.The main benefits will be on-demand, point-to-point,safe travel, further and anywhere in less travel time with almost zero environmental impact for general people. Besides, a successful implementation and sustainable transition will depend on overcoming technological hurdles, regulatory frameworks, operational safety, cost competitiveness, and sensibilities of the affected communities.

Perante as conhecidas dificuldades em alcançar uma adequada integração da tecnologia no processo de ensino e aprendizagem da Matemática, este estudo pretende, apoiando-se na formação ao nível da tecnologia ministrada em duas instituições europeias, identificar aspetos com potencial para promover a formação inicial, no âmbito da tecnologia, de professores de Matemática. Adota-se uma metodologia de índole qualitativa e interpretativa, sendo os dados recolhidos de natureza documental ou relativos a trabalhos de análise e reflexão crítica realizados por dois futuros professores (um de cada instituição). As principais conclusões alcançadas apontam para grandes diferenças entre os contextos de formação, com uma das instituições a valorizar de forma mais significativa a formação na área. Ainda assim, os futuros professores de ambas as instituições mostram alguma tendência para escolher tarefas onde a exploração que é feita da tecnologia fica aquém do seu potencial, onde o recurso ao papel e lápis está sempre presente, e onde a reflexão em torno das características das tarefas e da sua implementação parece ser algo superficial. Apesar da complexidade do processo de integração da tecnologia nas práticas, os aspetos referidos parecem-nos ser dignos de atenção em qualquer programa de formação inicial de professores de Matemática.

This chapter aims to make more explicit the grounded or ‘pragmatic theories’ that inform the design of mathematics teachers’ professional development (PD) to exploit technological affordances. It uses aspects of some representative projects that took place in four countries (Colombia, Italy, Mexico, and Portugal) to illustrate lessons learned (e.g., similarities and differences, barriers and opportunities) and provide important insights to inform future PD implementations. To do this, we have identified a set of aspects (and sub-aspects) that emerged in relation to five major themes and reveal our ‘pragmatic theories’ alongside a consideration of the interconnections between these aspects. Our contribution offers a methodological frame to support future PD designs for teachers of mathematics concerning digital technology uses.

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In this short note we construct an extension of the Vagner-Preston representation for block-groups and show that its kernel is the largest congruence that separates regular elements.

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