Understanding complex Earth systems is challenging for scientists and students alike, because of the characteristics (e.g. bifurcations, self-organization, chaotic response) that are associated with these systems. This research integrates two research strands which contribute to the scientific and pedagogical understanding of complex Earth systems. In the first strand, a method that characterizes volatile organic compounds (VOCs) as ecological proxies of soil microbial ecosystems was validated. Unlike other measures of microbial community structure (e.g. Biolog and FAME), VOCs are advantageous because they are non-destructive and can provide temporal and spatial data. Additionally they are rich sources of information that describe the microbial metabolism, community structure, and organic carbon substrates utilized by soil microorganisms. Statistical results indicate that the detected and identified VOCs were significant (p < 0.05) indicators of microbial community composition shift in soil microcosm studies. Geographical information systems (GIS) illustrates that VOCs varied with space and time in south Texas soils. The second strand focuses on a geoscience education study exploring student conceptual model development of complex Earth systems. The efficacy of multiple representations and inquiry was tested as the pedagogical strategy in upper and lower level undergraduate courses to support students’ conceptual model development of complex Earth systems. Comparisons in student performance were based on prior knowledge (low and high) and on exposure to the implemented pedagogy (control and experimental groups). Results indicate that an inquiry-based learning model coupled with the use of multiple representations had significant positive performance impacts on students’ conceptual model development and content knowledge. This dissertation model integrates science and education research and is particularly useful for graduate students who intend to pursue a career in academia and envision teaching as part of their professional duties. It allows for synergy between teaching and research to be achieved where the classroom becomes a laboratory for research. Ultimately, the research conducted in the classroom informs pedagogy and enhances scholarship. Graduates learn to bridge the gap between education and science departments where they become leaders in science who conduct cutting-edge scientific research and also value making a broader impact on society through enhancing public education.

Computer Algebra Systems (CAS), a powerful mathematical software currently available on hand held calculators, is becoming increasingly available to assist secondary students learn school mathematics. This study investigates how two teachers taught introductory differential calculus to their Year 11 classes using multiple representations in a CAS-supported curriculum. This thesis aims to explore the impact of the teaching on students’ understanding of the concept of derivative. / Understanding of the concept of derivative was gauged using an innovative Differentiation Competency Framework that was developed to describe understanding of the concept of derivative. It consists of eighteen competencies for formulation and interpretation of derivatives with, and without, translation between different representations. It clarified the objectives of the curriculum, purpose for using particular CAS activities, and also guided the construction of individual test items on the Differentiation Competency Test that enabled individual and class learning about the concept of derivative to be identified. / The Framework also helped identify each teacher’s privileging characteristics and facilitated analysis of the learning in relation to the teaching. / This study found that using multiple representations was important in developing understanding of the concept of derivative but that the graphical and the symbolic representations were the most useful and important to emphasize and link. / Analysis of the teaching actions showed that the teachers used CAS in ways that were consistent with their teaching approach and preferred use of representations and that a conceptual teaching method and student-centred style supported understanding of the concept of derivative. / Teaching is directly linked to learning and each class developed a different understanding of the concept of derivative that related to the combined effect of their teacher’s privileging characteristics: calculus content, teaching approach, and use of CAS. This study also shows that if a CAS-supported curriculum is to be successfully implemented, it needs to acquire institutional status including a corresponding change in assessment to legitimize new teaching practices.

Orientador: Ariane Luzia dos Santos / Resumo: Este texto tem como objetivo, reconhecendo a devida importância do tema Funções, apresentar uma proposta de atividades apoiadas pelo software Geogebra como forma de potencializar a aprendizagem da matemática, onde enfatizamos o conceito de função, as particularidades de suas representações e as propriedades, nos utilizando da transição entre elas como sugestão para sanar as dificuldades encontradas pelos alunos na compreensão desse tema. Também incluímos uma noção dos conceitos de limite e continuidade entendendo que a abordagem de alguns tópicos do cálculo no Ensino Médio seria de grande valia para auxiliá-los nessa tarefa, ressaltando que utilizamos a tecnologia em conjunto com os atores tradicionais (oralidade e escrita) através de aulas expositivas dialogadas. / Abstract: This paper aims, recognizing the importance of the theme Functions, to present a proposal of activities supported by Geogebra software as a way to enhance the learning of mathematics, where we emphasize the concept of function, the particularities of its representations and the properties, using of the transition between them as a suggestion to remedy the di culties encountered by students in understanding this theme. We also included a notion of the concepts of limit and continuity, understanding that the approach to some topics of calculus in High School would be of great value to assist them in this task, emphasizing that we use technology with traditional actors (oral and written) through dialogic expositive classes. / Mestre

Submitted by Wagner Junior (wagner.junior@unioeste.br) on 2018-09-20T20:52:59Z No. of bitstreams: 2 Leide_Katia_Giehl_2018.pdf: 2495458 bytes, checksum: dbccdad065933b748a8722866c131fd6 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-09-20T20:52:59Z (GMT). No. of bitstreams: 2 Leide_Katia_Giehl_2018.pdf: 2495458 bytes, checksum: dbccdad065933b748a8722866c131fd6 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-03-23 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work explores the didactic potential of the multi-mode and multiple representations (MMR) as a teaching strategy for the teaching the theme Semiconductors and its applications in technology devices. The teaching strategy is conducted through the construction and application of a didactic workshop composed of four meeting addressing the content of Modern and Contemporary Physics - Semiconductors applied to technology. The MMR teaching strategy aims to provide students with a range of opportunities to construct, refine and deepen scientific knowledge. So that if a student can not understand a concept in relation to a particular representation, another representation may be more effective and engaging. The main goal of this work is to evaluate the potential of the teaching strategy of the MMR for the teaching of Modern and Contemporary Physics. In order to reach this goal, it was investigated how the conceptual evolution of the students takes place under the multirepresentational activities by means of some diagnostic evaluations. In order to find elements that fulfill our objectives, we have opted for the data analysis divided into two parts. First we observe if there is some conceptual evolution of the students about the main physical concepts, and then analyze how this conceptual evolution takes palce during the workshop period. Data analysis was develope using content analysis technique and interpreted under the conceptual change model. The data analysis provided us with indications that there was a conceptual evolution of the students who participated of the workshop, being this evolution the result of the variety of multirepresentational activities that, taked together, contributed to the didatic functions of the MMR. / Neste trabalho, explora-se o potencial didático da estratégia de ensino baseada nos multimodos e múltiplas representações (MMR) para o ensino de Semicondutores e suas aplicações na tecnologia. A estratégia de ensino é proposta a partir da construção e aplicação de uma oficina didática dividida em quatro encontros, desenvolvida com um grupo de alunos da terceira série do ensino médio com abordagem do conteúdo de Física Moderna e Contemporânea (FMC) – Os semicondutores aplicados à tecnologia. A estratégia de ensino dos MMR tem por objetivo proporcionar aos alunos uma gama de oportunidades para construir, refinar e aprofundar o conhecimento científico de forma que, se um aluno não consegue entender um conceito em relação a uma representação particular, outra representação pode ser mais eficaz e envolvente. O trabalho tem por objetivo avaliar as potencialidades da estratégia de ensino dos MMR para o ensino da FMC. Ao longo da oficina, é investigado como se dá a evolução conceitual dos estudantes a partir das atividades multirrepresentacionais e das avaliações diagnósticas propostas. Para buscar elementos que cumpram os objetivos propostos, optou-se por fazer a análise de dados dividida em duas partes. Primeiramente observamos se houve evolução conceitual dos estudantes, para então analisar como ocorreu esta evolução no decorrer da oficina. A análise de dados foi desenvolvida através da técnica de análise de conteúdo e interpretada através do modelo de mudança conceitual. A análise de dados no trouxe indícios de que houve evolução conceitual dos estudantes participantes da oficina, a qual é fruto da variedade de atividades multirrepresentacionais desenvolvidas que, em conjunto, contribuíram com as funções didáticas dos MMR.

The crucial role of representation in mathematical and statistical modeling and problem solving as evident in learners' arrangement and representation of statistical data were investigated with focus points data arrangement, data representation and statistical thinking levels. The representation tasks required learners to arrange and represent data through modeling, focusing on spontaneous representations. Successful transnumeration determine the ultimate success of a representation and the ability to organise data is regarded as critical. Arrangement types increased in sophistication with increased grade level and the hierarchical nature of arrangement types became apparent when regarded in the context of an adapted SOLO Taxonomy framework. A higher level arrangement strategy pointed to a higher SOLO level of statistical thinking. Learners in the two tasks produced a rich variety of representations which included idiosyncratic, unsophisticated responses as well as standard statistical representations. The context of the two tasks, the quantitative versus qualitative nature of the data in the tasks, and the statistical tools or representational skills learners have at their disposal, played an important role in their representations. Well-planned data handling activities develop representational and higher order thinking skills. The variety of responses and different response levels elicited in the two tasks indicate that the nature of the tasks rather than the size of the data set play a conclusive role in data tasks. Multiple representations by an individual were an indication of successful modeling, are effective in problem solving and are associated with good performance. The SOLO model which incorporates a structural approach as well as a multimodal component proved valuable in the analysis of responses. Using this model with accompanying acknowledgement of different problem solving paths and the contribution of ikonic support in the concrete symbolic mode, promote the in-depth analysis of responses. This study contributes to the research in the field of data representation and statistical thinking. The analysis and results led to an integrated picture of Grade 4-7 learners' representation of statistical data and of the statistical thinking levels evident in their representations. / Educational Studies / D. Ed. (Didactics)

Essa pesquisa inicia-se pela consideração na literatura da área, de ensino de física, sobre as perspectivas dadas a algumas formas de representações, no contexto da construção do conhecimento científico, realizada no campo dos especialistas e nas pesquisas que relatam a sala de aula. As representações visuais distinguíveis nesta pesquisa são as esboçadas pelos alunos, as que se notam na simulação computacional e as gestuais: os gestos além das representações gestuais icônicas possibilitam mediações com outras representações empregadas em aula, por isso, serão considerados os gestos dêiticos, os movimentos ergóticos e epistêmicos; outra forma observada de mediação para a construção de conhecimento serão as analogias empregadas. Entre as hipóteses desta pesquisa está, que a sala de aula em que se propicia um ensino, onde mais se evidencia tanto a construção de conhecimento, quanto um caráter multimodal de representações será aquela cuja metodologia empregada é de \"ensino por investigação\". Em face disso, definem-se as características desse ensino, desde suas concepções históricas iniciais quando compreendidas como a aplicação do método científico, com problema, hipóteses, teste das hipóteses e conclusão, até as concepções contemporâneas em que se consideram aspectos da natureza da ciência, além da argumentação, a multimodalidade e as relações CTS. Para a representação verbal, expressando tanto o conhecimento construído quanto as reflexões sobre o processo de construção, considerou-se se a fala dos alunos se enquadra no padrão hipotético-dedutivo apresentado por Lawson (2002; 2004). Os dados para a realização desta pesquisa provêm da observação e de materiais produzidos em sala de aula bem como das transcrições do registro audiovisual dessas aulas. Categorizadas as representações e classificadas quanto à sua posição junto a elementos dos padrões de argumentação hipotético-dedutivo, apresentar-se-á uma solução para o problema \"Como múltiplas representações atuam na construção do conhecimento científico em sala de aula.\" Múltiplas representações e interações foram usadas principalmente na proposição da hipótese e no planejamento e execução dos testes; o emprego de atividade favorecendo o uso de várias representações não qualifica um ensino como investigativo; se colocado à disposição, os alunos utilizam em suas atividades, principalmente nas construções de conhecimento; as transições entre as formas de mediação e de representações obedecem a um padrão de continuidade e de uniformidade. / This research begins by considering the literature in the field of physical education on prospects given to some forms of representations in the context of construction of scientific knowledge, carried out in the field and experts in research that reports the classroom. The distinguishable visual representations in this research are the pictorial outlined by the students, the visually represented in computer simulation and sign iconic representations; gestures beyond the iconic gestural representation possible mediations with other representations used in class, so they are considered the deictic gestures, ergot and epistemic movements; other form of mediation for the construction of knowledge will be the use of analogies. Among the hypotheses of this research is that the classroom that provides an education, where the evidence of both the construction of knowledge, as a multimodal character representations will be the one whose methodology is \"learning by inquiry\". So let\'s define the characteristics of this teaching, from their initial historical conceptions when understood as the application of the scientific method, problem, hypothesis, testing of hypotheses and conclusion, to contemporary conceptions that also consider aspects of science nature beyond argument, multimodality and CTS relations. For verbal representation, expressing both knowledge built as reflections on the construction process, we consider how the speech of students falls within the hypothetical-deductive pattern presented by Lawson (2002 and 2004). Data for this survey out of observation and materials produced in the classroom, in addition to transcripts of audio-visual record of these classes. Categorized representations and classified according to their position along the elements of the hypothetical-deductive reasoning patterns, we present a solution to the problem \"How multiple representations work in the construction of scientific knowledge in the classroom\".

Este trabalho apresenta uma reflexão sobre o papel do princípio de Le Chatelier desde a sua criação e algumas implicações no ensino de química. Foram levantados aspectos históricos da evolução do princípio com o objetivo de discutir características como, por exemplo: o caráter universal do mesmo, problemas e limitações quanto à sua aplicação e possíveis alternativas ao uso do princípio. Também foram analisados como os livros didáticos de química no nível médio tratam muitos destes aspectos. Além disto, é realizada uma discussão nestes textos didáticos a respeito das variáveis que influenciam no estado de equilíbrio tais como: concentração, pressão, catalisador e temperatura. Um aspecto presente na análise destas variáveis foi o levantamento de ilustrações presentes nos livros baseando-se nos níveis de representação presentes no triângulo de Johnstone. Os principais resultados mostraram que os autores de livros de Química do Ensino Médio apresentam o conceito do princípio de Le Chatelier marcado por um caráter indutivo, vago, ambíguo, e sem apresentar uma fundamentação teórica e suas limitações, enfatizando-o como um princípio infalível ou uma verdade absoluta. Perpetuou-se no ensino de química, ao longo do tempo, a formulação mais simples e popular criada por Le Chatelier, no ano de 1888. Outra conclusão importante refere-se ao fato de a maioria das figuras presentes nos livros didáticos estar relacionada ao nível macroscópico e a concentração é a alteração mais discutida. Poucas são as figuras que interligam os três vértices do triângulo. Resta ao professor o desafio de incluir as ilustrações faltantes, principalmente as microscópicas pois estas têm o objetivo de explicar aos estudantes o que ocorre do ponto de vista molecular quando se altera o estado de equilíbrio químico. Portanto, este tratamento superficial do princípio pode favorecer processos de ensino-aprendizagem baseados na memorização, repetição e na sua utilização sem a compreensão exata dos fenômenos envolvidos. / This work presents a reflection on the role of the Le Chatelier\"s principle concerned by its creation and some implications in the teaching of chemistry. The main purpose was to analyze as high school chemical textbooks approach with this subject. For this, historical aspects of the evolution of the principle were studied with the objective of discussing important characteristics, for example: the universal character of the principle, his problems and limitations regarding their applications to previse changes in chemical equilibrium systems and the possible alternatives to the use of the principle. It was found that the principle formulations were similar to that more simple and popular wrote by Le Chatelier, in the year of 1888. It was also made an analysis of how the textbooks address the issue of variables that influence in the state of equilibrium such as: concentration, pressure, catalyst and temperature. Also was analyzed the illustrations present in these books with the objective of address the equilibrium change based in the of Johnstone\"s triangle (that explicitly shows the macroscopic, microscopic and representational levels of chemical knowledge). The main results showed that the majority of the figures in textbooks refers only to macroscopic level and the effects done by of the equilibrium reactants concentration change. There are few figures which are related the three levels represented in the Johnstone\"s triangle. Is very important that teachers include the illustrations missing, mainly the microscopic level, once that this level is essential to correct understand of chemical equilibrium change in the molecular level. In general, the authors of chemical textbooks present the Le Chatelier\"s principle in an inductive manner, vague and ambiguous. They never present theoretical aspects and limitations in the application of the principle. This stresses the infallible character of Le Chatelier\"s principle and transmits the idea that it is an absolute truth. This superficial treatment of the principle can encourage processes of teaching-learning based on memorization and the students can correctly use the principle in the problems solutions without have an exact understanding the phenomena.

Made available in DSpace on 2015-09-25T12:23:18Z (GMT). No. of bitstreams: 1 PDF - Jefferson Dagmar Pessoa Brandao.pdf: 2577674 bytes, checksum: d068a60e592b29eb2c4f8ceed3659e4c (MD5) Previous issue date: 2014-09-29 / This paper analyzes the difficulties and possibilities of mathematics teaching and learning through problem solving, coupled with multiple representations, viewing the formation of the function concept in the classroom. It becomes the basis of the five big essential ideas for the development of the concept of function proposed by Cooney, Beckmann and Lloyd (2010), namely, the concept of function, covariation and rate of change, family of functions, combination and transformation of functions and representations of functions. Also becomes a literature review of some Brazilian research that addressed the concept of function, whose gaze turned to those who have correlation with our research in order to understand what these investigations deal on it. We opted for the work in the classroom by using the problem solving, posing and exploration, which is why we devote a few pages to discuss it. The research methodology is a qualitative approach in the form of teacher research in which the teacher researcher tries to look his own practice in the classroom. The survey was conducted in a public school in the Lagoa Seca city, Paraíba State, Brazil, with a high school first year classroom. Among the detected working with function different representations was realized that the students were able to see more details of the concept of function allowing a more consistent understanding this, it was also observed that the use of problem solving, posing and exploration methodology allowed the students to get involved with the classroom activities and feel more motivated to study the contents. / O presente trabalho analisa as dificuldades e possibilidades da metodologia de ensino aprendizagem de Matemática através da resolução de problemas, aliada ao trabalho com as representações múltiplas, visando à formação do conceito de função em sala de aula. Toma-se com base as cinco grandes ideias essenciais para o desenvolvimento do conceito de função propostas por Cooney, Beckmann e Lloyd (2010), a saber: o conceito de função; covariação e taxa de variação; família de funções; combinação e transformação de funções e representações de funções. Faz-se, também, uma revisão bibliográfica de algumas pesquisas nacionais que abordaram, como tema, o conceito de função, cujo olhar se voltou para aquelas que possuem correlação com a nossa pesquisa a fim de compreender o que essas investigações tratam sobre o tema função, consequentemente, fazendo um aprofundamento. Optou-se pelo trabalho em sala de aula por utilizar a resolução, proposição e exploração de problemas, razão por que dedicamos algumas páginas para discutir seus aspectos. A metodologia de pesquisa é de cunho qualitativo na modalidade de pesquisa pedagógica na qual o professor pesquisa sua própria prática em sala de aula. A pesquisa foi aplicada em uma escola Pública da cidade de Lagoa Seca, PB, com uma turma de primeiro ano do Ensino Médio. Dentre os resultados detectados, o trabalho com as diferentes representações de funções fez com que os alunos conseguissem ver mais detalhes do conceito de função permitindo uma compreensão mais consistente; observou-se que o uso da metodologia de resolução de problemas permitiu que os alunos se envolvessem com as atividades e se sentissem mais motivados a estudar o conteúdo.

The crucial role of representation in mathematical and statistical modeling and problem solving as evident in learners' arrangement and representation of statistical data were investigated with focus points data arrangement, data representation and statistical thinking levels. The representation tasks required learners to arrange and represent data through modeling, focusing on spontaneous representations. Successful transnumeration determine the ultimate success of a representation and the ability to organise data is regarded as critical. Arrangement types increased in sophistication with increased grade level and the hierarchical nature of arrangement types became apparent when regarded in the context of an adapted SOLO Taxonomy framework. A higher level arrangement strategy pointed to a higher SOLO level of statistical thinking. Learners in the two tasks produced a rich variety of representations which included idiosyncratic, unsophisticated responses as well as standard statistical representations. The context of the two tasks, the quantitative versus qualitative nature of the data in the tasks, and the statistical tools or representational skills learners have at their disposal, played an important role in their representations. Well-planned data handling activities develop representational and higher order thinking skills. The variety of responses and different response levels elicited in the two tasks indicate that the nature of the tasks rather than the size of the data set play a conclusive role in data tasks. Multiple representations by an individual were an indication of successful modeling, are effective in problem solving and are associated with good performance. The SOLO model which incorporates a structural approach as well as a multimodal component proved valuable in the analysis of responses. Using this model with accompanying acknowledgement of different problem solving paths and the contribution of ikonic support in the concrete symbolic mode, promote the in-depth analysis of responses. This study contributes to the research in the field of data representation and statistical thinking. The analysis and results led to an integrated picture of Grade 4-7 learners' representation of statistical data and of the statistical thinking levels evident in their representations. / Educational Studies / D. Ed. (Didactics)

Essa pesquisa inicia-se pela consideração na literatura da área, de ensino de física, sobre as perspectivas dadas a algumas formas de representações, no contexto da construção do conhecimento científico, realizada no campo dos especialistas e nas pesquisas que relatam a sala de aula. As representações visuais distinguíveis nesta pesquisa são as esboçadas pelos alunos, as que se notam na simulação computacional e as gestuais: os gestos além das representações gestuais icônicas possibilitam mediações com outras representações empregadas em aula, por isso, serão considerados os gestos dêiticos, os movimentos ergóticos e epistêmicos; outra forma observada de mediação para a construção de conhecimento serão as analogias empregadas. Entre as hipóteses desta pesquisa está, que a sala de aula em que se propicia um ensino, onde mais se evidencia tanto a construção de conhecimento, quanto um caráter multimodal de representações será aquela cuja metodologia empregada é de \"ensino por investigação\". Em face disso, definem-se as características desse ensino, desde suas concepções históricas iniciais quando compreendidas como a aplicação do método científico, com problema, hipóteses, teste das hipóteses e conclusão, até as concepções contemporâneas em que se consideram aspectos da natureza da ciência, além da argumentação, a multimodalidade e as relações CTS. Para a representação verbal, expressando tanto o conhecimento construído quanto as reflexões sobre o processo de construção, considerou-se se a fala dos alunos se enquadra no padrão hipotético-dedutivo apresentado por Lawson (2002; 2004). Os dados para a realização desta pesquisa provêm da observação e de materiais produzidos em sala de aula bem como das transcrições do registro audiovisual dessas aulas. Categorizadas as representações e classificadas quanto à sua posição junto a elementos dos padrões de argumentação hipotético-dedutivo, apresentar-se-á uma solução para o problema \"Como múltiplas representações atuam na construção do conhecimento científico em sala de aula.\" Múltiplas representações e interações foram usadas principalmente na proposição da hipótese e no planejamento e execução dos testes; o emprego de atividade favorecendo o uso de várias representações não qualifica um ensino como investigativo; se colocado à disposição, os alunos utilizam em suas atividades, principalmente nas construções de conhecimento; as transições entre as formas de mediação e de representações obedecem a um padrão de continuidade e de uniformidade. / This research begins by considering the literature in the field of physical education on prospects given to some forms of representations in the context of construction of scientific knowledge, carried out in the field and experts in research that reports the classroom. The distinguishable visual representations in this research are the pictorial outlined by the students, the visually represented in computer simulation and sign iconic representations; gestures beyond the iconic gestural representation possible mediations with other representations used in class, so they are considered the deictic gestures, ergot and epistemic movements; other form of mediation for the construction of knowledge will be the use of analogies. Among the hypotheses of this research is that the classroom that provides an education, where the evidence of both the construction of knowledge, as a multimodal character representations will be the one whose methodology is \"learning by inquiry\". So let\'s define the characteristics of this teaching, from their initial historical conceptions when understood as the application of the scientific method, problem, hypothesis, testing of hypotheses and conclusion, to contemporary conceptions that also consider aspects of science nature beyond argument, multimodality and CTS relations. For verbal representation, expressing both knowledge built as reflections on the construction process, we consider how the speech of students falls within the hypothetical-deductive pattern presented by Lawson (2002 and 2004). Data for this survey out of observation and materials produced in the classroom, in addition to transcripts of audio-visual record of these classes. Categorized representations and classified according to their position along the elements of the hypothetical-deductive reasoning patterns, we present a solution to the problem \"How multiple representations work in the construction of scientific knowledge in the classroom\".