La numeració i el càlcul a l'educació infantil: de la mecànica a la comprensió

Al nostre país, hi ha pràctiques d’aula encara molt arrelades en relació amb el procés d’ensenyament-aprenentatge de la numeració i el càlcul a l’educació infantil que cal qüestionar, perquè contribueixen de manera escassa o nul·la a ajudar a comprendre els continguts d’aquest bloc. Al present article, s’hi exposen diverses activitats implementades en contextos significatius d’aprenentatge, tant dins de l’aula com fora, que afavoreixen la comprensió de les quantitats discretes i les operacions aritmètiques elementals, el significat que tenen i les funcions que exerceixen, per poder usar aquests coneixements de manera eficaç en contextos diferents de la vida quotidiana

THE FORMAL AND THE FORMALIZED: THE CASES OF SYLLOGISTIC AND SUPPOSITION THEORY

As a discipline, logic is arguably constituted of two main sub-projects: formal theories of argument validity on the basis of a small number of patterns, and theories of how to reduce the multiplicity of arguments in non-logical, informal contexts to the small number of patterns whose validity is systematically studied (i.e. theories of formalization). Regrettably, we now tend to view logic 'proper' exclusively as what falls under the first sub-project, to the neglect of the second, equally important sub-project. In this paper, I discuss two historical theories of argument formalization: Aristotle's syllogistic theory as presented in the "Prior Analytics", and medieval theories of supposition. They both illustrate this two-fold nature of logic, containing in particular illuminating reflections on how to formalize arguments (i.e. the second sub-project). In both cases, the formal methods employed differ from the usual modern technique of translating an argument in ordinary language into a specially designed symbolism, a formal language. The upshot is thus a plea for a broader conceptualization of what it means to formalize.

Formal semantics for propositional attitudes

Contemporary logic is confined to a few paradigmatic attitudes such as belief, knowledge, desire and intention. My purpose is to present a general model-theoretical semantics of propositional attitudes of any cognitive or volitive mode. In my view, one can recursively define the set of all psychological modes of attitudes. As Descartes anticipated, the two primitive modes are those of belief and desire. Complex modes are obtained by adding to primitive modes special cognitive and volitive ways or special propositional content or preparatory conditions. According to standard logic of attitudes (Hintikka), human agents are either perfectly rational or totally irrational. I will proceed to a finer analysis of propositional attitudes that accounts for our imperfect but minimal rationality. For that purpose I will use a non standard predicative logic according to which propositions with the same truth conditions can have different cognitive values and I will explicate subjective in addition to objective possibilities. Next I will enumerate valid laws of my general logic of propositional attitudes. At the end I will state principles according to which minimally rational agents dynamically revise attitudes of any mode.

Uma nota sobre a lógica formal de Kant

O artigo apresenta um problema que surge da combinação da teoria kantiana dos juízos analíticos com a sua adesão oficial à silogística. Argumenta-se em seguida que o problema só pode ser inteiramente solucionado pelo reconhecimento de que a lógica com a qual Kant de fato operava não é consistente nem com a silogística, nem com a lógica clássica, consistindo, de fato, em uma espécie de lógica inclusiva.

HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS

Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.

PROLEGÓMENOS PARA UNA TEORÍA FORMAL DE ESTRUCTURAS (DESPUÉS DE N.DA COSTA)

Resumen El articulo tiene por objetivo la reconstrucción alternativa del concepto de estructura, motivado por los articulos (1) y (3), como una generalización abstracta de lo que es un objeto matemático. Primero, mostramos su construcción, que tiene que ver con la teoría de tipos y orden en lógica, dando a lugar a propiedades y varios ejemplos interesantes. Luego avanzamos hacia una semántica concreta, para su análisis, y para permitirnos operar sobre ellas, sabiendo de este modo, lo que es "lo verdadero en ella". Obtenido ello, mostraremos los resultados de reducción de orden y de individuos, pero vistos en este contexto, así formalizando completamente en nuestra teoría de tipos la discusión de (1) (Ver también (2) y (3)) sobre estos temas.

TOWARDS A PHILOSOPHICAL UNDERSTANDING OF THE LOGICS OF FORMAL INCONSISTENCY

Abstract In this paper we present a philosophical motivation for the logics of formal inconsistency , a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically justify paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we show that mbC , a logic of formal inconsistency based on classical logic, may be enhanced in order to express the basic ideas of an intuitive interpretation of contradictions as conflicting evidence.

Formal and informal mechanisms for knowledge protection and sharing

The most important knowledge in firms is mostly tacit and embedded in individuals within the organization. This background knowledge that firms possess is used for creation of new knowledge and innovations. As firms today greatly concentrate on their core competencies, they need external knowledge from various collaboration partners. Thus, collaborative relationship governance, as well as control (use of appropriability mechanisms) over background (the input from each firm in innovative activities) and foreground knowledge (the output of collaboration activities) is needed in order to successfully create and capture value from innovative activities without losing core knowledge and competitiveness. Even though research has concentrated on knowledge protection and knowledge sharing, studies that combine both of these views and examine the effects of sharing and protection on value creation and capture have been rather limited. Studies have mainly focused on the protection of the output of innovation while forgetting the protection of the input of innovation. On the other hand, as the research concentrating on the output of innovation tends to favor formal mechanisms, informal mechanisms have remained more unknown to researchers as well as managers. This research aims to combine the perspectives of knowledge sharing and knowledge protection and their relationship with value creation and value capture. The sharing and protection are viewed from two points of view: the use of appropriability mechanisms, as well as governance of the collaborative relationship. The study consists of two parts. The first part introduces the research topic and discusses the overall results. The second part comprises six complementary research publications. Both qualitative and quantitative research methods are used in the study. In terms of results, the findings enhance understanding of the combined use of formal and informal mechanisms for knowledge protection and sharing. Informal mechanisms appear to be emphasized in the protection of background knowledge, and thus are prerequisites for innovation, whereas formal mechanisms are relied on more for protecting the results of innovative activities. However, the simultaneous use of the formal and informal mechanisms that are relevant to the particular industry and innovation context is recommendedthroughout the collaborative innovation process. Further, the study adds to the current knowledge on HRM as an appropriability mechanism: on the firm level its uses include assessing and hedging against employee-related risks such as knowledge leaking and knowledge leaving. A further contribution is to the research on HRM protection and its interrelations with other appropriability mechanisms, its constituents, and its potential use in the area of knowledge protection.

Of pearls and pigs : a conceptual-semantic Tiernet approach to formal representation of structure and variation of phraseological units

"Helmiä sioille", pärlor för svin, säger man på finska om någonting bra och fint som tas emot av en mottagare som inte vill eller har ingen förmåga att förstå, uppskatta eller utnyttja hela den potential som finns hos det mottagna föremålet, är ointresserad av den eller gillar den inte. För sådana relativt stabila flerordiga uttryck, som är lagrade i språkbrukarnas minnen och som demonstrerar olika slags oregelbundna drag i sin struktur använder man inom lingvistiken bl.a. termerna "idiom" eller "fraseologiska enheter". Som en oregelbundenhet kan man t.ex. beskriva det faktum att betydelsen hos uttrycket inte är densamma som man skulle komma till ifall man betraktade det som en vanlig regelbunden fras. En annan oregelbundenhet, som idiomforskare har observerat, ligger i den begränsade förmågan att varieras i form och betydelse, som många idiom har jämfört med regelbundna fraser. Därför talas det ofta om "grundform" och "grundbetydelse" hos idiom och variationen avses som avvikelse från dessa. Men när man tittar på ett stort antal förekomstexempel av idiom i språkbruk, märker man att många av dem tillåter variation, t.o.m. i sådan utsträckning att gränserna mellan en variant och en "grundform" suddas ut, och istället för ett idiom råkar vi plötsligt på en "familj" av flera besläktade uttryck. Allt detta väcker frågan om hur dessa uttryck egentligen ska vara representerade i språket. I avhandlingen utförs en kritisk granskning av olika tidigare tillvägagångssätt att beskriva fraseologiska enheter i syfte att klargöra vilka svårigheter deras struktur och variation erbjuder för den lingvistiska teorin. Samtidigt presenteras ett alternativt sätt att beskriva dessa uttryck. En systematisk och formell modell som utvecklas i denna avhandling integrerar en beskrivning av idiom på många olika språkliga nivåer och skildrar deras variation i form av ett nätverk och som ett resultat av samspel mellan idiomets struktur och kontexter där det förekommer, samt av interaktion med andra fasta uttryck. Modellen bygger på en fördjupande, språkbrukbaserad analys av det finska idiomet "X HEITTÄÄ HELMIÄ SIOILLE" (X kastar pärlor för svin).

A conservação do papagaio-da-cara-roxa (Amazona brasiliensis) no estado do Paraná: uma experiência de Educação Ambiental no ensino formal

No presente trabalho, avaliou-se a experiência de Educação Ambiental do "Projeto de Conservação do Papagaio-da-Cara-Roxa (Amazona brasiliensis)", no ensinoformal, realizado pela Sociedade de Pesquisa em Vida Selvagem e Educação Ambiental (SPVS), no litoral norte do Estado do Paraná. A experiência teve o intuito de fomentar, tanto no corpo docente quando no corpo discente, a discussão sobre valores e princípios que norteiam as relações homem/natureza, desenvolvendo-se, assim, uma interação mais responsável com o meio ambiente. Foram desenvolvidos módulos-educativos sobre o papagaio-da-cara-roxa e seu ambiente, direcionados a 795 estudantes do ensino fundamental, nos Municípios de Paranaguá e Guaraqueçaba. Para analisar a eficácia das atividades, os estudantes responderam a testes antes e depois do processo educativo que mediram mudanças obtidas com relação ao incremento de conhecimento, postura e valorização do papagaio-da-cara-roxa e de seu ambiente. Os resultados indicaram que a utilização do exemplo de uma espécie, ameaçada de extinção e que ocorre próximo às comunidades envolvidas no processo de conservação, serviu de base para a associação do tema específico para com uma realidade ambiental mais ampla e contextualizada localmente.

Making Sense of Shared Leadership. A case study of leadership processes and practices without formal leadership structure in the team context

Leadership is essential for the effectiveness of the teams and organizations they are part of. The challenges facing organizations today require an exhaustive review of the strategic role of leadership. In this context, it is necessary to explore new types of leadership capable of providing an effective response to new needs. The presentday situations, characterized by complexity and ambiguity, make it difficult for an external leader to perform all leadership functions successfully. Likewise, knowledge-based work requires providing professional groups with sufficient autonomy to perform leadership functions. This study focuses on shared leadership in the team context. Shared leadership is seen as an emergent team property resulting from the distribution of leadership influence across multiple team members. Shared leadership entails sharing power and influence broadly among the team members rather than centralizing it in the hands of a single individual who acts in the clear role of a leader. By identifying the team itself as a key source of influence, this study points to the relational nature of leadership as a social construct where leadership is seen as social process of relating processes that are co-constructed by several team members. Based on recent theoretical developments concerned with relational, practice-based and constructionist approaches to the study of leadership processes, this thesis proposes the study of leadership interactions, working processes and practices to focus on the construction of direction, alignment and commitment. During the research process, critical events, activities, working processes and practices of a case team have been examined and analyzed with the grounded theory –approach in the terms of shared leadership. There are a variety of components to this complex process and a multitude of factors that may influence the development of shared leadership. The study suggests that the development process of shared leadership is a common sense -making process and consists of four overlapping dimensions (individual, social, structural, and developmental) to work with as a team. For shared leadership to emerge, the members of the team must offer leadership services, and the team as a whole must be willing to rely on leadership by multiple team members. For these individual and collective behaviors to occur, the team members must believe that offering influence to and accepting it from fellow team members are welcome and constructive actions. Leadership emerges when people with differing world views use dialogue and collaborative learning to create spaces where a shared common purpose can be achieved while a diversity of perspectives is preserved and valued. This study also suggests that this process can be supported by different kinds of meaning-making and process tools. Leadership, then, does not reside in a person or in a role, but in the social system. The built framework integrates the different dimensions of shared leadership and describes their relationships. This way, the findings of this study can be seen as a contribution to the understanding of what constitutes essential aspects of shared leadership in the team context that can be of theoretical value in terms of advancing the adoption and development process of shared leadership. In the real world, teams and organizations can create conditions to foster and facilitate the process. We should encourage leaders and team members to approach leadership as a collective effort that the team can be prepared for, so that the response is rapid and efficient.

Proactive and Preventive Student Welfare Activities in Finnish Preschool and Elementary School: Handling of Transition to Formal Schooling and a National Anti-Bullying Program as Examples

Prerequisites and effects of proactive and preventive psycho-social student welfare activities in Finnish preschool and elementary school were of interest in the present thesis. So far, Finnish student welfare work has mainly focused on interventions and individuals, and the voluminous possibilities to enhance well-being of all students as a part of everyday school work have not been fully exploited. Consequently, in this thesis three goals were set: (1) To present concrete examples of proactive and preventive psycho-social student welfare activities in Finnish basic education; (2) To investigate measurable positive effects of proactive and preventive activities; and (3) To investigate implementation of proactive and preventive activities in ecological contexts. Two prominent phenomena in preschool and elementary school years—transition to formal schooling and school bullying—were chosen as examples of critical situations that are appropriate targets for proactive and preventive psycho-social student welfare activities. Until lately, the procedures concerning both school transitions and school bullying have been rather problem-focused and reactive in nature. Theoretically, we lean on the bioecological model of development by Bronfenbrenner and Morris with concentric micro-, meso-, exo- and macrosystems. Data were drawn from two large-scale research projects, the longitudinal First Steps Study: Interactive Learning in the Child–Parent– Teacher Triangle, and the Evaluation Study of the National Antibullying Program KiVa. In Study I, we found that the academic skills of children from preschool–elementary school pairs that implemented several supportive activities during the preschool year developed more quickly from preschool to Grade 1 compared with the skills of children from pairs that used fewer practices. In Study II, we focused on possible effects of proactive and preventive actions on teachers and found that participation in the KiVa antibullying program influenced teachers‘ self-evaluated competence to tackle bullying. In Studies III and IV, we investigated factors that affect implementation rate of these proactive and preventive actions. In Study III, we found that principal‘s commitment and support for antibullying work has a clear-cut positive effect on implementation adherence of student lessons of the KiVa antibullying program. The more teachers experience support for and commitment to anti-bullying work from their principal, the more they report having covered KiVa student lessons and topics. In Study IV, we wanted to find out why some schools implement several useful and inexpensive transition practices, whereas other schools use only a few of them. We were interested in broadening the scope and looking at local-level (exosystem) qualities, and, in fact, the local-level activities and guidelines, along with teacherreported importance of the transition practices, were the only factors significantly associated with the implementation rate of transition practices between elementary schools and partner preschools. Teacher- and school-level factors available in this study turned out to be mostly not significant. To summarize, the results confirm that school-based promotion and prevention activities may have beneficial effects not only on students but also on teachers. Second, various top-down processes, such as engagement at the level of elementary school principals or local administration may enhance implementation of these beneficial activities. The main message is that when aiming to support the lives of children the primary focus should be on adults. In future, promotion of psychosocial well-being and the intrinsic value of inter- and intrapersonal skills need to be strengthened in the Finnish educational systems. Future research efforts in student welfare and school psychology, as well as focused training for psychologists in educational contexts, should be encouraged in the departments of psychology and education in Finnish universities. Moreover, a specific research centre for school health and well-being should be established.