O erro produzido pelo aluno no contexto pedagógico: uma luz ou uma pedra no meio do caminho?

Student’s mistakes as viewed in a didactic and pedagogical perspective are a phenomenon inevitably observed in any context in which formal teaching-andlearning processes are taking place. Researchers have shown that such mistakes are viewed most of the times as undesirable and often as a consequence of lack of attention or poor commitment on the part of the student and rarely considered didactically useful. The object of our reflections in this work is exactly those mistakes, which are born in the entrails of the teaching-and-learning processes. It is our understanding that a mistake constitutes a tool which mediates knowledge and may therefore become a strong ally of the instructor’s actions in her/his teaching tasks and thus should be taken into the teacher’s best consideration. Understanding a mistake as so, we postulate that the teacher must face it as a possibility to be exploited rather than as a negative occurrence. Such an attitude on the part of the teacher would undoubtedly render profitable didactic situations. To deepen the understanding of our aim, we took a case study on the perception of senior college students in the program of Mathematics at UFRN in the year 2009, 2nd term. The reason of this choice is the fact that Mathematics is the field presenting traditionally the poorest records in terms of school grades. In this work we put forth data associated to ENEM1 , to the UFRN Vestibular2 and the undergraduate courses on Mathematics. The theoretical matrixes supporting our reflections in this thesis follow the ideas proposed by Castorina (1988); Davis e Espósito (1990); Aquino (1997); Luckesi (2006); Cury (1994; 2008); Pinto (2000); Torre (2007). To carry out the study, we applied a semi-structured questionnaire containing 14 questions, out of which 10 were open questions. The questions were methodologically based on the Thematic Analysis – One of the techniques for Content Analysis schemed by Bardin (1977) – and it was also used the computer program Modalisa 6.0 (A software designed by faculties the University of Paris VIII). The results indicate that most of the teachers training instructors in their pedagogical practice view the mistakes made by their students only as a guide for grading and, in this procedure, the student is frequently labeled as guilty. Conclusive analyses, therefore, signal to the necessity of orienting the teachers training instructors in the sense of building a new theoretical contemplation of the students’ mistakes and their pedagogical potentialities and so making those professionals perceive the importance of such mistakes, since they reveal gaps in the process of learning and provide valuable avenues for the teaching procedures.

As compreensões do construtivismo de Ernst Von Glasersfeld e John Fossa: intermediando um diálogo em busca de novas significações

The present thesis, orientated by a letter sent by Ernst von Glasersfeld to John Fossa, is the product of a theoretical investigation of radical constructivism. In this letter, von Glasersfeld made three observations about Fossa’s understanding of radical constructivism. However, we limited our study to the second of these considerations since it de als with some of the core issues of constructivism. Consequently, we investigated what issues are raised by von Glasersfeld’s observation and whether these issues are relevant to a better understanding of constructivism and its implications for the mathema tics classroom . In order to realize the investigation, it was necessary to characterize von Glasersfeld’s epistemological approach to constructivism, to identify which questions about radical constructivism are raised by von Glasersfeld’s observation, to i nvestigate whether these issues are relevant to a better understanding of constructivism and to analyze the implications of these issues for the mathematics classroom. Upon making a hermeneutic study of radical constructivism, we found that what is central to it is its radicalism, in the sense that it breaks with tradition by its absence of an ontology. Thus, we defend the thesis that the absence of an ontology, although it has advantages for radical constructivism, incurs serious problems not only for the theory itself, but also for its implications for the mathematics classroom. The advantages that we were able to identify include a change from the usual philosophical paths to a very different rational view of the world, an overcoming of a naive way of thi nking, an understanding of the subject as active in the construction of his/her experiential reality, an interpretation of cognition as an instrument of adaptation, a new concept of knowledge and a vision of knowledge as fallible (or provisional). The prob lems are associated with the impossibility of radical constructivism to explain adequately why the reality that we build up is regular, stable, non - arbitrary and publicly shared. With regard to the educational implications of radical constructivism, the ab sence of an ontology brings to the mathematics classroom not only certain relevant aspects (or favorable points) that make teaching a process of researching student learning, empowering the student to learn and changing the classroom design, but also certa in weaknesses or limitations. These weaknesses or limitations of constructivism in the classroom are due to its conception of knowledge as being essentially subjective. This requires it to work with one - on - one situations and, likewise, makes the success of teaching dependent on the teacher’s individual skills. Perhaps the most important weakness or limitation, in this sense, is that it makes teaching orientated by constructivist principles unable to reach the goal of the formation of a community. We conclud e that issues raised by von Glasersfeld’s observation are absolutely relevant to the context of a better understanding of radical constructivism and its implications for education, especially for Mathematics Education.

Making it real of sustaining a fantasy? Personal budgets for older people

The restructuring of English social care services in the last three decades, as services are provided through a shifting collage of state, for-profit and non-profit organisations, exemplifies many of the themes of governance (Bevir, 2013). As well as institutional changes, there have been a new set of elite narratives about citizen behaviours and contributions, undergirded by modernist social science insights into the wellbeing benefits of ‘self-management’ (Mol, 2008). In this article, we particularly focus on the ways in which a narrative of personalisation has been deployed in older people’s social care services. Personalisation is based on an espoused aspiration of empowerment and autonomy through universal implementation to all users of social care (encapsulated in the Making it Real campaign [Think Local, Act Personal (TLAP), no date)], which leaves unproblematised the ever increasing residualisation of older adult social care and the abjection of the frail (Higgs and Gilleard, 2015). In this narrative of universal personalisation, older people are paradoxically positioned as ‘the unexceptional exception’; ‘unexceptional’ in the sense that, as the majority user group, they are rhetorically included in this promised transformation of adult social care; but ‘the exception’ in the sense that frail older adults are persistently placed beyond its reach. It is this paradoxical positioning of older adult social care users as the unexceptional exception and its ideological function that we seek to explain in this article.

THE EFFECT OF PURPOSEFUL MATHEMATICS DISCOURSE IN THE CLASSROOM ON STUDENTS’ MATHEMATICS LANGUAGE IN THE CONTEXT OF PROBLEM SOLVING

This study examines how one secondary school teacher’s use of purposeful oral mathematics language impacted her students’ language use and overall communication in written solutions while working with word problems in a grade nine academic mathematics class. Mathematics is often described as a distinct language. As with all languages, students must develop a sense for oral language before developing social practices such as listening, respecting others ideas, and writing. Effective writing is often seen by students that have strong oral language skills. Classroom observations, teacher and student interviews, and collected student work served as evidence to demonstrate the nature of both the teacher’s and the students’ use of oral mathematical language in the classroom, as well as the effect the discourse and language use had on students’ individual written solutions while working on word problems. Inductive coding for themes revealed that the teacher’s purposeful use of oral mathematical language had a positive impact on students’ written solutions. The teacher’s development of a mathematical discourse community created a space for the students to explore mathematical language and concepts that facilitated a deeper level of conceptual understanding of the learned material. The teacher’s oral language appeared to transfer into students written work albeit not with the same complexity of use of the teacher’s oral expression of the mathematical register. Students that learn mathematical language and concepts better appear to have a growth mindset, feel they have ownership over their learning, use reorganizational strategies, and help develop a discourse community.

The making of professionals: Embedded civil society development in a transition country

The paper addresses the development of non-governmental organisations (NGOs) in transition settings. Caught in the balance of knowledge exchange and translation of ideas from abroad, organisations in turbulent setting legitimise their existence by learning through professional networks. By association, organisational actors gain acknowledgement by their sector by traversing the corridors of influence provided by international partnerships. What they learn is how to conduct themselves as agents of change in society, and how to deliver on stated missions and goals, therefore, legitimising their presence in a budding civil society at home. The paper presents a knowledge production and learning practices framework which indicates a presence of dual identity of NGOs - their “embeddedness” locally and internationally. Selected framework dimensions and qualitative case study themes are discussed with respect to the level of independence of organisational actors in the East from their partners in the West in a post-socialist context. A professional global civil society as organisations are increasingly managed in similar, professional ways (Anheier & Themudo 2002). Here knowledge “handling” and knowledge “translation” take place through partnership exchanges fostering capable and/or competitive change-inducing institutions (Czarniawska & Sevon 2005; Hwang & Suarez 2005). How professional identity presents itself in the third sector, as well as the sector’s claim to expertise, need further attention, adding to ongoing discussions on professions in institutional theory (Hwang & Powell 2005; Scott 2008; Noordegraaf 2011). A conceptual framework on the dynamic involved for the construction professional fields follows: • Multiple case analysis provides a taxonomy for understanding what is happening in knowledge transition, adaptation, and organisational learning capacity for NGOs with respect to their role in a networked civil society. With the model we can observe the types of knowledge produced and learning employed by organisations. • There are elements of professionalisation in third sector work organisational activity with respect to its accreditation, sources and routines of learning, knowledge claims, interaction with the statutory sector, recognition in cross-sector partnerships etc. • It signals that there is a dual embeddedness in the development of the sector at the core to the shaping the sector’s professional status. This is instrumental in the NGOs’ goal to gain influence as institutions, as they are only one part of a cross-sector mission to address complex societal problems The case study material highlights nuances of knowledge production and learning practices in partnerships, with dual embeddedness a main feature of the findings. This provides some clues to how professionalisation as expert-making takes shape in organisations: • Depending on the type of organisations’ purpose, over its course of development there is an increase in participation in multiple networks, as opposed to reliance on a single strategic partner for knowledge artefacts and practices; • Some types of organisations are better connected within international and national networks than others and there seem to be preferences for each depending on the area of work; • The level of interpretation or adaptation of the knowledge artefacts is related to an organisation’s embeddedness locally, in turn giving it more influence within the network of key institutions; An overreaching theme across taxonomy categories (Table 1)is “professionalisation” or developing organisational “expertise”, embodied at the individual, organisational, and sector levels. Questions relevant to the exercise of power arise: Is competence in managing a dual embeddedness signals the development of a dual identity in professionalisation? Is professionalisation in this sense a sign of organisations maturing into more capable partners to the arguably more experienced (Western) institutions, shifting the power balance? Or is becoming more professional a sign of domestication to the agenda of certain powerful stakeholders, who define the boundaries of the profession? Which dominant dynamics can be observed in a broadly-defined transition country civil society, where individual participation in the form of activism may be overtaking the traditional forms of organised development work, especially with the spread of social media?

Design and Implementation of a Low Cost Virtual Rugby Decision Making Interactive

The paper describes the design and implementation of a novel low cost virtual rugby decision making interactive for use in a visitor centre. Original laboratory-based experimental work in decision making in rugby, using a virtual reality headset [1] is adapted for use in a public visitor centre, with consideration given to usability, costs, practicality and health and safety. Movement of professional rugby players was captured and animated within a virtually recreated stadium. Users then interact with these virtual representations via use of a lowcost sensor (Microsoft Kinect) to attempt to block them. Retaining the principles of perception and action, egocentric viewpoint, immersion, sense of presence, representative design and game design the system delivers an engaging and effective interactive to illustrate the underlying scientific principles of deceptive movement. User testing highlighted the need for usability, system robustness, fair and accurate scoring, appropriate level of difficulty and enjoyment.

Audiovisual Storytelling and Ideological Horizons : Audiences, Cultural Contexts and Extra-textual Meaning Making

Abstract: Audiovisual Storytelling and Ideological Horizons: Audiences, Cultural Contexts and Extra-textual Meaning Making In a society characterized by mediatization people are to an increasing degree dependent on mediated narratives as a primary means by which we make sense of our experience through time and our place in society (Hoover 2006, Lynch 2007, Hjarvard 2008, Hjarvard & Lövheim 2012). American media scholar Stewart Hoover points to symbols and scripts available in the media environment, what he call the “symbolic inventory” out of which individuals make religious or spiritual meaning (Hoover 2006: 55). Vernacular meaning-making embedded in everyday life among viewers’ dealing with fiction narratives in films and tv-series highlight a need for a more nuanced understanding of complex audiovisual storytelling. Moving images provide individuals with stories by which reality is maintained and by which humans construct ordered micro-universes for themselves using film as a resource for moral assessment and ideological judgments about life (Plantinga 2009, Johnston 2010, Axelson 2015). Important in this theoretical context are perspectives on viewers’ moral frameworks (Zillman 2005, Andersson & Andersson 2005, Frampton 2006, Avila 2007).This paper presentation will focus on ideological contested meaning making where audiences of different cultural background engage emotionally with filmic narratives, possibly eliciting ideological and spiritual meaning-making related to viewers’ personal world views. Through the example of the Homeland tv-series I want to discuss how spectators’ cultural, religious, political and ideological identities could be understood playing a role in the interpretative process of decoding content. Is it possible to trace patterns of different receptions of the multilayered and ambiguous story depicted in Homeland by religiously engaged Christians and Moslems as well as non-believers, in America, Europe and Middle East? How is the fiction narrative dealt with by spectators in the audience in different cultural contexts and how is it interpreted through the process of extra-text evaluation and real world2understanding in a global era preoccupied with war on terror? The presentation will also discuss methodological considerations about how to reach out to audiences anchored in different cultural context.

The Search for the Operatic: Bridging the Gap Between the Spectatorial and Performer Positions Through Sketch-making and Embodiment Techniques

The exhibition was of sketches and a photograph from my PhD practice research. The practice-research was comprised of observing opera singers in rehearsal and sketching them as they moved. As well as records of body position, and to some degree dynamic flow, the exhibited sketches were regarded as kinaesthetic responses in and of themselves – responses to the environment of the rehearsal, in particular responding to the sounds of the orchestra. These sketches were, in part, generated through an embodiment of the music, which was occurring in the same moment as the singer was engaged in embodying the music. These sketches were then used as tools that therefore contained kinaesthetic information which could be unlocked through a process of Butoh derived embodiment techniques alongside reference to the sketched image. This ultimately allowed me to move from a spectatorial position to a performance maker position, bringing a sense of the operatic into the non-singing body, whether that was my own or the bodies of other performers. In this way, and combined with rigorous observation of the corporeal restrictions of singing operatically, choreographies were created that employed operatic ways of moving in non-singing bodies and the operatic was extracted from opera and employed in movement based practice. The aspect of the practice-research exhibited is the correspondence between sketched documentation of the singers in rehearsal and photographic documentation of the dancer (researcher) in performance.

Analysis on the connotation of probability in the artificial intelligence algorithm for economic decision making.

This paper analyzes the inner relations between classical sub-scheme probability and statistic probability, subjective probability and objective probability, prior probability and posterior probability, transition probability and probability of utility, and further analysis the goal, method, and its practical economic purpose which represent by these various probability from the perspective of mathematics, so as to deeply understand there connotation and its relation with economic decision making, thus will pave the route for scientific predication and decision making.

Exploring the Process of Meaning-making after Partner Suicide

Meaning-making is increasingly recognized as a fundamental aspect of the grief experience. This study investigated the process of meaning-making in the narratives of individuals whose partners died by suicide, exploring their meaning reconstruction in response to this form of loss. The narratives of users of a public online grief support forum (n = 50) were analyzed using the Meaning of Loss Codebook (Gillies, Neimeyer, & Milman, 2014), which consists of core categories of meaning of loss in response to the death of a loved one. The results indicated that these individuals predominantly experienced negative affect, a lack of understanding associated with the loss, and a longing for their partners. The grief experience of participants in this study was marked by substantial psychological distress and an ongoing struggle to make sense of and find meaning in this type of loss. It is clear that grieving the loss of a partner as a result of suicide presents unique challenges to meaning-making in comparison to other types of loss. Given the importance of this aspect of adjustment to loss, these findings deepen the understanding of this component of grief and inform the provision of support for those grieving a loved one who died by suicide.

Influência da tecnologia no desenvolvimento do pensamento algébrico : um estudo no 1º CEB

Relatório de Estágio apresentado à Escola Superior de Educação do Instituto Politécnico de Castelo Branco para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Educação Pré-Escolar e Ensino do 1º Ciclo do Ensino Básico.

Humor in mathematics teaching

HUMOR: OUR VIEW FOR MATHEMATICS TEACHING Our assumptions and context. Process humor and be able to produce is clearly a sign of intelligence, revealing, when done well, complex reasoning. Humor has an important social role, assuming as a cognitive experience that as well as creating a sense of well-being, predisposes people to work and can improve the productivity of that work. Mathematics is a discipline in which the reasoning occupies a very prominent place, both as a science as a school area. At the same time, students' interest for mathematics is not always the same and some have initially not very favorable feelings (Toh, 2009; Wanzer, Frymier & Irwin, 2010). Recent curriculum changes to the teaching of mathematics have been, in most countries of the world, showing the need for students to develop skills of critical nature, such as communication, thinking and problem solving along with the acquisition of mathematical knowledge. Also in Portugal, it is claimed the importance of promoting learning that combine the construction of mathematical knowledge with its use, when performing mathematical tasks and communicating mathematical ideas and mathematical reasoning. In the early years of schooling, corresponding to primary education in many countries, the use of texts such as short stories or comics, from which we can develop challenging mathematical tasks, is reported in the literature as having potential to promote learning specified in curricular documents (Wanzer, Frymier., & Irwin, 2010). In particular, some texts focus on mathematical topics in a humorous way and to be understood, students must develop their mathematical competence. The development of mathematical tasks from stories and other humorous presents big challenges to teachers (Flores & Moreno, 2011). Our questions. In this context, we put some questions: Primary teachers use in their classes tasks or situations that present, in a humorous way, mathematical ideas? What resources do they use? Also: How to select, adapt or build texts and tasks which have, in a humorous way, mathematical ideas with didactic potential for education in the early years of schooling? If the resources for this purpose have been produced and if teachers have been sensitized for their use, are they able to integrate them in their classes? Our intentions. This research project seeks to address these questions, focused on: (i ) assessment of teachers’ practices and underlying knowledge, resources available for the use of texts with mathematical ideas presented in a humorous way; (ii) selection, adaptation and construction of mathematical tasks from texts that present, in a humorous way, mathematical ideas with didactic potential in education for the early years of schooling; and ( iii ) integration and use, by primary school teachers, of texts that present , in a humorous way, contexts for the teaching of mathematics. So, the project is organized into three tasks and as a methodological design that combines qualitative elements with quantitative elements, the first one prevailing.

Computational approaches to emotional decision making

Findings on the role that emotion plays in human behavior have transformed Artificial Intelligence computations. Modern research explores how to simulate more intelligent and flexible systems. Several studies focus on the role that emotion has in order to establish values for alternative decision and decision outcomes. For instance, Busemeyer et al. (2007) argued that emotional state affects the subjectivity value of alternative choice. However, emotional concepts in these theories are generally not defined formally and it is difficult to describe in systematic detail how processes work. In this sense, structures and processes cannot be explicitly implemented. Some attempts have been incorporated into larger computational systems that try to model how emotion affects human mental processes and behavior (Becker-Asano & Wachsmuth, 2008; Marinier, Laird & Lewis, 2009; Marsella & Gratch, 2009; Parkinson, 2009; Sander, Grandjean & Scherer, 2005). As we will see, some tutoring systems have explored this potential to inform user models. Likewise, dialogue systems, mixed-initiative planning systems, or systems that learn from observation could also benefit from such an approach (Dickinson, Brew & Meurers, 2013; Jurafsky & Martin, 2009). That is, considering emotion as interaction can be relevant in order to explain the dynamic role it plays in action and cognition (see Boehner et al., 2007).

The development of an eBook for teaching and learning mathematics

Mobile devices, smartphones, phablets and tablets, are widely avail‐ able. This is a generation of digital natives. We cannot ignore that they are no longer the same students for which the education system was designed tradition‐ ally. Studying math is many times a cumbersome task. But this can be changed if the teacher takes advantage of the technology that is currently available. We are working in the use of different tools to extend the classroom in a blended learning model. In this paper, it is presented the development of an eBook for teaching mathematics to secondary students. It is developed with the free and open standard EPUB 3 that is available for Android and iOS platforms. This specification supports video embedded in the eBook. In this paper it is shown how to take advantage of this feature, making videos available about lectures and problems resolutions, which is especially interesting for learning mathematics.