For the development of this work, in the introduction we present a few topics which motivated it, as well as the research problem and its reason. The main objective of this dissertation is to research on the possible reasons for the hierarchy of the four mathematical operations. With this purpose, we attempted to verify if there were some explanations for such hierarchy. Thus, we researched on national and international sites. On this search, we found two articles of interest, namely: “the order of operation in elementary arithmetic” and the thesis “the school mathematics knowledge: operations with the natural numbers in the grade and middle school”, which were formulated comments about them. This research is classified as qualitative and bibliographical descriptive. In the chapter about the theory we presented how the subject numerical expression is explained in some official documents, as well as in textbooks of the Middle School. Since we have not found any reasonable and plausible explanation for such hierarchy, we included a chapter about a historical retrospective on the order of operations and the use of the parenthesis which, in turn, prepared the way for the chapter on a proposal to justify the why of the hierarchy for the four mathematical operations. / Para o desenvolvimento deste trabalho apresentamos na introdução alguns tópicos motivadores da pesquisa, bem como a sua problemática e justificativa. Esta dissertação tem como objetivo principal pesquisar as possíveis justificativas para a hierarquia das quatro operações aritméticas nas expressões numéricas. Para isso buscamos verificar se existia alguma proposta para a justificativa da hierarquia das operações na resolução de expressões numéricas. Assim, realizamos buscas tanto em sites nacionais, como também internacionais. Nessas buscas os trabalhos de interesse que encontramos foram: o artigo Order of operations in elementar arithmetic e a tese “O conhecimento matemático escolar: operações com números naturais (e adjacências) no Ensino Fundamental” os quais foram realizadas descrição e comentários cabíveis a respeito. O tipo de pesquisa é qualitativa, bibliográfica descritiva e, de certa forma, também explicativa. No referencial teórico apresentamos como o conteúdo expressão numérica é colocado em alguns documentos oficiais e livros didáticos do Ensino Fundamental. Como não foi encontrada nenhuma justificativa plausível e completa para a hierarquia das quatro operações nas expressões numéricas, realizamos um capítulo denominado retrospectiva histórica do uso das quatro operações e dos parênteses, neste capítulo descrevemos sobre as quatro operações, e sobre os parênteses que servirá para embasar o próximo capítulo denominado: hierarquia das quatro operações, buscando uma justificativa.

Orientador: Eleutério Fernando da Silva Prado / Banca: Eduardo Strachman / Banca: Ramón Vicente Garcia Fernández / Resumo: O presente estudo realiza uma avaliação das diferentes abordagens da racionalidade e suas implicações sobre a compreensão dos fenômenos econômicos. Neste sentido, utilizar-se-á um referencial teórico abrangente, pois a adequada compreensão desse tema exige aproximações teóricas de varias matrizes potencialmente complementares. Isso será feito com o intuito de oferecer um retrato não estilizado da racionalidade, seja na abordagem neoclássica, seja na abordagem de Herbert Simon. A concepção neoclássica se expressa através de postulados, que possuem baixa correspondência com a realidade, sobretudo, por pressupor processos cognitivos de maneira idealizada e incerteza na forma probabilística. Consequentemente, essa representação altera características importantes dos agentes e do ambiente. A concepção de racionalidade limita de Herbert Simon gera avanços nos campos explicativos e descritivos, principalmente para cenários bem estabelecidos. Em especial, permite conhecer como os agentes interpretam e representam diferentes problemas, além disso, contribui para elucidar qual o processo e as ações que ligam o objetivo ao resultado. Por conseguinte, gera avanços significativos em relação à compreensão ofertada pela teoria neoclássica, ademais essas pesquisas produziram como subproduto uma noção de complexidade, pois a racionalidade é limitada em virtude dos processos complexos que caracterizam o ambiente. Neste sentido, a utilização desse conceito em situações instáveis gerou avanços no conhecimento. Entretanto, é necessário aprofundar essa relação para se obter respostas para condições de incerteza forte, questão não restrita ao conhecimento econômico, já que se relaciona com o avanço da filosofia e métodos da ciência / Abstract: This dissertation makes an evaluation of different approaches of rationality and its implications about the understanding of economical phenomena. For that, it will be adopted a wide-ranging theoretical references, because the appropriate understanding of this subject demands theoretical approximation of various matrices with potential overlapping. This will be done in order to offer a non stylized portrait of rationality, either in a neoclassical approach or the Hebert Simon approach. The neoclassical notion is expressed through assumptions, which are fairly different from reality, due to the fact that presumes the cognitive process in an idealized way and also to associate uncertainty and probabilities. Consequently, this representation changes important characteristics of the agents and environment. The notion of bounded rationality of Hebert Simon generates improvement in the explanatory and descriptive fields, mainly for well-established scenarios. Especially, it allows knowing how the agents interpret and show different problems. Besides that, it contributes to elucidate which process and actions link the object to the result. In consequence, creates remarkable improvements in relation to the understanding offered by the neoclassic theory, moreover, these researches produce as a sub-product a notion of complexity, because rationality is bounded due to complex process that characterized the environment. For this reason, the use of this concept in unstable situations generates improvement of knowledge. Nevertheless, it is necessary to get deep into this relationship to obtain answers in circumstances of strong uncertainty, a matter not exclusive to economics knowledge because it is already related to the advance of philosophy and science methods / Mestre

Esta pesquisa tem o intuito de estudar as concepções dos mediadores do museu de ciências - Catavento Cultural e Educacional - acerca do que é a mediação. Nosso interesse se resume em conhecer essas concepções e analisar seus fundamentos. Com isso esperamos apontar possíveis rumos para o processo de formação dos mediadores e de divulgação da ciência com subsídios trazidos por esta pesquisa empírica. Esta investigação foi desenvolvida sob a luz da teoria da Biologia do Conhecer de Humberto Maturana e Francisco Varela a qual considera a explicação como um fenômeno humano e biológico e que só existe quando é aceito pelo observador. Os dados que serviram para análise neste trabalho foram obtidos durante a realização de entrevistas semiestruturadas com os mediadores do museu investigado. Após a coleta dos dados transcrevemos as entrevistas e elaboramos quatro mapas conceituais correspondentes a cada uma delas. Em seguida pedimos para que os entrevistados reconhecessem seu mapa e elaborassem de forma colaborativa um mapa conceitual com a mesma questão focal dos mapas individuais: o que é a mediação no museu de ciências? A partir disso, com ajuda do nosso referencial teórico e dos mapas conceituais, construímos nossas categorias e analisamos as concepções dos mediadores. Os resultados dessa análise revelaram que suas explicações sobre a mediação no museu de ciências possuem uma predominância de concepções embasadas na experiência do viver dentro do espaço museal. Suas distinções sobre o assunto não se valeram de reflexões teóricas, principalmente, daquelas que tratam da comunicação e do ensino nesses espaços, pois a formação acadêmica e a oferecida no museu foram insuficientes. / This research aims to study the conceptions of mediators of the Science museum - Catavento Cultural e Educacional - about what is mediation. Our interest boils down to knowing these views and analyze its foundations. With this we hope to identify possible directions for the process of training of mediators and the dissemination of science with subsidies brought by this empirical research. This research was developed in the light of the theory of Biology of Cognition Humberto Maturana and Francisco Varela which considers the explanation as a human and biological phenomenon that exists only when it is accepted by the observer. The data used for analysis in this study were obtained during the performance of semi-structured interviews with the mediators of the museum investigated. After collecting the data, transcribed the interviews and prepare four concept maps corresponding to each of them. Then we ask that respondents recognize your map and draw up collaboratively a single concept map with the same focal issue of individual maps: what is mediation in the science museum? From this, with the help of our theoretical framework and conceptual maps, build our categories and analyzes the concepts of mediators. The results of this analysis revealed that his explanations of mediation in the science museum have a predominance of informed views on the experience of living within the museum space. His distinctions about it not relied on theoretical reflections, mainly those dealing with communication and education in these areas, because the academic and the one offered in the museum were insufficient.

Deveria ser esperado que a população fosse ciente de como a ciência, e principalmente, seus conhecimentos e aplicações, chegam até ela e, para isso, tivesse esclarecimento e discernimento suficientes para perceber, entender e julgar as novidades científico-tecnológicas a que tem acesso no que poderíamos chamar de Alfabetização Científica (AC). Sasseron (2008) define a AC como um processo de inserção dos indivíduos dentro da cultura científica. Sasseron e Carvalho (2008), a partir de eixos estruturantes da AC, propõem indicadores que servem como parâmetros que permitam identificar que a AC está em processo. Osborne e Patterson publicam, em 2011, um polêmico trabalho com o intuito de distinguir Argumentos de Explicações, alegando que a falta de distinção entre estes dois conceitos representa uma fraqueza no campo de pesquisa em ensino de Ciências. Tomando a AC como norte para o ensino de ciência, Argumentos e Explicações se valorizam, já que pertencem às práticas da ciência e podem ser um meio de atingir metas cognitivas, epistêmicas e sociais da aprendizagem em Ciências. Os objetivos deste trabalho: a) a partir de apoios da literatura, desenvolver recursos metodológicos para caracterizar e diferenciar argumentos e explicações; b) identificar e analisar argumentos e explicações presentes nas produções escritas de alunos; c) identificar e analisar indicadores de AC presentes nas produções escritas dos alunos. Nossa análise se deu sobre uma das atividades realizadas dentro do contexto de uma sequência de ensino investigativo (SEI), a qual aborda a temática \"Dinâmica Populacional\", aplicada em duas turmas do 1° ano do Ensino Médio da Escola de Aplicação da Faculdade de Educação da Universidade de São Paulo (EAFEUSP) em 2012 e 2013. Os alunos realizaram um experimento sobre a capacidade suporte de um ambiente para a população de Lemna sp (uma planta aquática de pequeno porte que apresenta alta taxa de reprodução por brotamento). Após a realização desse experimento, os alunos produziram relatórios coletivamente com conclusões individuais. Analisamos cada trecho (o qual poderia se constituir de um parágrafo, tabela, gráfico ou figura) de um conjunto de 29 relatórios em busca dos indicadores da AC e de Explicações e Argumentos. Foram encontrados 571 indicadores de AC nos relatórios e 367 nas conclusões individuais, e isso nos permite considerar que a AC está em processo. Também podemos considerar que os alunos envolveram-se com as investigações e as discussões propostas. A proposição de uma metodologia de desambiguação é tanto metodologia como resultado, e a aplicação desta nos permitiu identificar 35 Explicações e 22 Argumentos nos relatórios e respectivamente 21 e 40 nas 52 conclusões individuais que foram produzidas apenas no ano de 2013. No tocante aos objetivos desta pesquisa, acreditamos tê-los respondido na medida em que desenvolvemos uma metodologia que nos permitiu distinguir Argumentos e Explicações em produções escritas de alunos e identificamos os indicadores de Alfabetização Científica presentes nessas produções. Essa última tarefa culminou na proposição de dois novos indicadores em acréscimo aos que usamos como referência (SASSERON 2008; SASSERON e CARVALHO 2008): um deles é o próprio Argumento, e outro, a Listagem de materiais. / Should be expected that the population is aware of how science, especially their knowledge and reach, comes to her and, therefore, had sufficient enlightenment and discernment to perceive, understand and judge the scientific and technological innovations that give access to what may be called the Scientific Literacy (SL). Sasseron (2008) defines the SL as a process of integration of individuals within the scientific culture. Sasseron and Carvalho (2008) from the structural axis of SL propose indicators that serve as parameters that identify that the SL is in process. Osborne and Patterson published a controversial study in 2011 in order to distinguish Arguments from Explanations, claiming that the lack of distinction between these concepts is a weakness in the field of research in science teaching. Taking the SL as north to the teaching of science, Arguments and Explanations are valued, since they belong to the practices of science and can be a way to achieve cognitive, epistemic and social goals of learning in science. The aims of this work: a) supported from the literature, develop methodological tools to characterize and differentiate Arguments and Explanations; b) identify and analyze Arguments and Explanations present in the written production of students; c) identify and analyze indicators of SL present in the students\' written productions. Our analysis was based on one of the activities carried out within the context of a sequence of investigative teaching (SEI), which deals with the \"Population Dynamics\" theme, applied to two classes of the 1st year of high school at the Escola de Aplicação from the Faculdade de Educação from University of São Paulo (EAFEUSP) in 2012 e 2013. Students conducted an experiment on the carrying capacity of an environment for the population of Lemna sp (an aquatic plant that features small high rate of reproduction by budding). After performing this experiment, students collectively produced reports with individual conclusions. We analyzed each passage (which could be a paragraph, table, graph or diagram) of a set of 29 reports in search of indicators of the AC, the explanations and arguments. We found 571 indicators of SL in the reports and the 367 in the individual conclusions, and this allows us to consider that the SL is in progress. We can also consider that the students were involved with the investigation and the proposed discussions. The proposition of a methodology for the disambiguation is both method and result. Applying this methodology allowed us to identify 35 Explanations and 22 Arguments in the reports. We found respectively 21 and 40 in 52 individual conclusions that were produced in 2013 only. Concerning the aims of this study, we believe having them answered, as we developed a methodology that allowed us to distinguish Arguments and Explanations in written production of students, and identify indicators of Scientific Literacy on those productions. This last task culminated in the proposal of two new indicators in addition to those we used as reference (SASSERON 2008; SASSERON e CARVALHO 2008): one is the Argument itself, and another, the Listing of Materials.

Orientador: Lucas Angioni / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas / Made available in DSpace on 2018-08-10T07:52:29Z (GMT). No. of bitstreams: 1 Ferreira_MateusRicardoFernandes_M.pdf: 743977 bytes, checksum: 14ea5ca680f81291864123f42bb14c9b (MD5) Previous issue date: 2008 / Resumo: Essa dissertação analisa as discussões de Aristóteles sobre a unidade da substância em Metafísica Z e como essas discussões pressupõem comprometimentos do autor, já enunciados nos Segundos Analíticos, sobre essencialismo, necessidade e unidade dos tipos naturais. Aristóteles não concebe a unidade da substância como um fato elementar, mas julga assegurá-la pela existência de uma causa capaz de unificar os elementos que a constituem. No entanto, para satisfazer o critério (que a própria distinção entre substância e concomitante estabelece) de que entre os constituintes de uma substância não pode haver heterogeneidade, Aristóteles depende fundamentalmente da existência de tipos controversos de causa: as formais e as teleológicas / Abstract: This thesis analyses Aristotle¿s discussion about the unity of substance in Metaphysics Z and how it presupposes his commitments on essentialism, necessity and unity of natural kinds stated in the Posterior Analytics. Aristotle does not consider the unity of substance as a basic fact, but he claims to explain it by means of a cause that unifies the constituent elements of a substance. However, in order to satisfy the criterion that those constituents should not be extrinsic to each other (a criterion which the distinction between substance and accidents establishes), Aristotle critically depends on controversial kinds of cause: the formal and teleological causes / Mestrado / Mestre em Filosofia

Si les scores psychotechniques ne sont pas des mesures, leur utilisation par les chercheurs an neuropsychologie pour tester des hypothèses de recherche et par les neuropsychologues pour effectuer des bilans mémoire manque de légitimité scientifique. Le chercheur en neuropsychologie qui, à l'aide d'une étude de cas, veut départager deux approches théoriques concurrentes, doit plutôt se demander si les théories prédisent des probabilités de réussite aux items des tests appartenant à des intervalles de valeurs disjoints. Cela suppose que la notion de probabilité de réussite d'un item par le patient soit empiriquement fondée (absence d'apprentissage). Si l'apprentissage a lieu, en particulier chez un patient cérébrolésé, le problème scientifique est différent : il s'agit de découvrir ce qui permet cet apprentissage. Le clinicien, praticien des tests neuropsychologiques, participe quant à lui à une institution diagnostique, contrainte à opérer une sélection des patients qui pourront bénéficier d'examens plus approfondis de leur cerveau. Dans cette perspective, les scores psychotechniques nourrissent un dispositif sociotechnique dont la légitimation ne devrait pas être seulement scientifique mais aussi politique. Le scientisme qui détermine les conditions actuelles de validation des tests non seulement masque la dimension politique de ce dispositif, mais encore empêche les chercheurs de réfléchir à ce que mesurer signifie (le scorage d'une performance n'est pas équivalent au mesurage d'une quantité théorique). La méthodologie de cette réflexion s'appuie (I) sur une série de travaux standards (validation de test, étude de cas) et (II) sur une analyse approfondie de la notion de testabilité des hypothèses de recherche utilisées par les chercheurs en neuropsychologie, ainsi que des hypothèses qui sous-tendent la mesurabilité d'une grandeur théorique. / The use of psycho-technical scores by neuropsychology researchers to test research hypotheses and neuropsychologists to perform memory assessments lacks scientific legitimacy if these scores are not measurements. A neuropsychology researcher who wants to decide between two competing theoretical approaches, by means of a case study, rather should consider whether the theories predict the probability of success in test items belonging to disjoint ranges. This implies that the notion of probability of success of an item by the patient is empirically based (absence of any learning). If learning takes place, especially in a patient with brain-injury, the scientific problem is different since it is to discover what make learning possible. The clinician, the practitioner of neuropsychological tests, participates in his turn to a diagnostic institution obliges to make a selection of patients who will benefit from further examination of their brains. In this perspective, the psycho-technical scores feed a socio-technical system whose legitimacy not expected to be merely scientific but also political. Scientism determining the current conditions of test validation not only masks the political aspect of this system, but also prevents researchers to think about what measuring means (the scoring of a performance is not equivalent to measuring a theoretical quantity). The methodology for this reflection is based on (i) a series of standard studies (validation testing, case study) and (ii) a thorough analysis of the notion of testability of research hypotheses used by neuropsychology researchers, and assumptions underlying measurability of a theoretical quantity.

Many critics of rational choice theory aim at unrealistic psychological assumption of this theory. To what extent is this kind of critic relevant? If we analyze the formalized scheme of choice than we will find difficult to interpret this scheme as psychological theory that develops intentional explanations. We should rather understand this theory as a theory developing causal explanations that are generated by the structure of surrounding. Intencionality in this theory is only a auxiliary tool and the explanation is made in terms of structure, not in terms of mental states. From this perspective most of the critic aim at wrong target.

Recent calls in education have emphasized the critical need for curricula in the sciences to support student development of the general and disciplinary-specific practices that are relevant to modern scientific research and careers, as well as foundational scientific knowledge that reflects recent advances. In this regard, the life sciences, including biochemistry, have been under pressure to develop curricula that reflect current research knowledge and practices, and that develop student competence in areas such as experimentation and visualization. In contrast to these calls, biochemistry textbooks, and instruction based on them, seldom discuss how disciplinary knowledge is combined with experimental work or other disciplinary resources to investigate and communicate about biochemical phenomena. This is of great concern given that graduates entering life science careers must be able to reason with relevant disciplinary knowledge, utilize experimental research methods, and navigate data representations in order to solve research problems. It is therefore crucial for biochemistry instruction to expose students to the ways in which expert scientists navigate and reason with disciplinary resources in cutting-edge scientific research on topics such as protein folding and dynamics, the focus of this project. Thus, this dissertation aims to fill a gap in our understanding of how expert research scientists explain protein-folding and dynamics research, and how that research knowledge can be used to inform the development of instructional materials in this crucially important area of biochemistry. To address this goal, we explore three overarching research questions: How can we model experts’ explanations of their research related to protein folding and dynamics? (RQ1); How do experts use representations to explain their protein-folding and dynamics research? (RQ2); and How can we use expert research to inform the design and implementation of instructional materials aimed at developing biochemistry students’ understanding of protein-folding and dynamics? (RQ3). To address these research questions, we first collected and analyzed interview data from four experts to explore the nature of their research explanations. This data was used to develop a model (i.e. the MAtCH model) of how experts integrate theoretical knowledge with their research context, methods, and analogies when explaining how phenomena operate (RQ1). In doing so, we also established how the experts use and combine explanatory models depending on the phenomena discussed and their explanatory aims, as well as how they explain thermodynamic and kinetic concepts relevant to protein folding in ways that align with their experimental research methods. We then examined selected representations from the expert interviews to explore how experts use language and representations to create meaning when explaining their research (RQ2). In comparing these to representations from biochemistry textbooks, analysis of the data indicated that textbooks generally explain ‘what is known’ but seldom explain ‘how it is known,’ whereas the experts use a combination of language, multiple representations, and gestures to explain how experimental research methods can provide evidence for phenomena. From this analysis, suggestions were made regarding the design of instructional materials to support discussion of experimental research methods and student interpretation of representations in classroom activities. In the final study, these suggestions were used in combination with additional analysis of expert research to inform the development anticipated learning outcomes (ALOs) and the design of instructional materials aimed at developing biochemistry students’ understanding of protein folding and dynamics (RQ3). The materials focus on the use of hydrogen-deuterium exchange mass spectrometry (HDX-MS) to study changes in protein structure due to denaturation and interactions with other molecules. The instructional materials were piloted in an undergraduate biochemistry course for the health sciences, and the nature of students’ understandings were explored. Our findings suggest that research practice – including research context, experimental methods, and representations – influences reasoning and explanation, providing additional evidence of the importance of developing discursive literacy in science students. To that end, a major implication of this work is that student knowledge of experimentation and representation may be a critical component of developing functional scientific understanding. Each of the studies contained in this dissertation therefore suggests ways in which practitioners may use our findings to modify instruction and instructional materials so that they are more aligned with expert practices. In order to teach students how scientific research underpins factual knowledge in biochemistry, future research should continue to explore experts’ use of disciplinary resources and ways of thinking in order to inform teaching and learning strategies and materials that can support the development of students’ disciplinary literacy.

In this paper, the psychological aspects of clearness in teaching mathematics are considered and some suggestions for the achieve the clearness are given.

I föreliggande studie undersöks relationen mellan ”förklaringar” och musikalisk interpretation. Mer specifikt frågan varför jag spelar Prokofievs 6:e pianosonat på ett visst sätt. Alla interpreter gör olika val vid förberedelsen och framförandet av ett musikaliskt verk. Många av de valen handlar om tempo, dynamik, frasering men även andra musikaliska parametrar. Denna studie undersöker till vilken grad sådana val går att basera på analytiska ”förklaringar” rörande musikens struktur. Med hjälp av teoretiska perspektiv från Leonard Meyer och Karl Popper undersöker jag ett antal passager som delvis blivit valda för att belysa hur varierat de brukar tolkas. Framförallt försöker studien att undersöka den ”tysta kunskapen” som ligger bakom specifika interpretationer — och i processen göra den kunskapen artikulerad. På grund av detta kan resultatet vara värdefullt både för teoretiker men också för praktiken inom intepretation. Projektet kulminerade i ett liveframförande av sonaten som spelades in. Det framförandet var influerat av min analys av musiken. / The present study investigates the relationship between “explanations” and musical interpretation. More specifically the question why do I play Prokofievs 6th piano sonata in a particular way? Every interpreter makes choices when preparing and performing a musical work. Many such choices involve tempo, dynamics, or phrasing, as well as other musical parameters. This study explores the degree to which these choices may be based on analytic “explanations" of the structure of the music. Building upon the theoretical work of Leonard Meyer and Karl Popper, I identify certain passages which highlight the diversity of interpretation, examining the differences through structural and interpretive analyses. Above all, the study seeks to understand the “tacit knowledge” embodied in certain approaches to musical interpretation — and, in the process, to make it explicit. Therefore, the results are of potential value not only in performance analysis, but in the training of performers. The project culminated in a performance and live recording of the sonata which were influenced by my analysis of the music.