Acompanha: O mundo nanométrico / A presente dissertação aborda a inserção de um tópico de Física Moderna e Contemporânea no Ensino Fundamental II, mais especificamente, a produção, caracterização e aplicação de nanopartículas, no contexto da Nanociência e Nanotecnologia (N&N). Foi utilizado o referencial da Transposição Didática, tendo em vista o processo que encadeia a ciência desenvolvida pelo cientista, o “saber sábio”, e o “saber ensinado”, aquele tratado educacionalmente em sala de aula. Este movimento também articula saberes interdisciplinares, envolvendo aspectos das ciências exatas e da natureza (física, química, biologia), saúde e ciências humanas. Deste modo, o trabalho consistiu em diversas etapas: 1- realizar uma investigação com respeito à presença da N&N em eventos da área de Ensino e revistas nacionais e internacionais; 2- analisar o tratamento dado para a N&N em livros didáticos do Ensino Médio e Fundamental II; 3- produzir um e-book interativo sobre N&N e 4- utilizar o material em sala de aula, incluindo realizar a avaliação das impressões causadas nos estudantes. Além da produção de um material didático inédito, os resultados obtidos revelam que a unidade didática despertou o interesse dos estudantes e mobilizou seu engajamento com o tema. Os resultados também mostram que os estudantes compreendem a natureza multidisciplinar da Nanociência e da Nanotecnologia, incluindo seu processo de constante construção de conteúdos científicos, bem como sua importância para o desenvolvimento tecnológico. / This thesis deals with the inclusion in Elementary Education of Modern and Contemporary Physics, more specifically, the production, characterization and application of nanoparticles, in the context of Nanoscience and Nanotechnology (N&N). Special attention is given to the importance of “didactic transposition” which refers to the transformations undertaken by a body of knowledge from “scholarly knowledge”, which is produced in academia, to “taught knowledge”, which is actually taught at schools, in real classrooms. In this process, Interdisciplinarity should be pointed out as an important element, considering the diverse aspects of science, including physics, chemistry, biology, health, and humanities, that are involved in and are related to N&N. Thus, our research comprises four steps: 1. an investigation on how N&N themes are presented in journals related to Physics/Science Education; 2- the analysis of didactic books used in Brazilian secondary education, regarding N&N; 3- the design and production of N&N teaching material (an interactive e-book); 4- classroom application of the developed e-book, including the assessment of students’ opinions about the educational resource. In summary, we have developed an open educational resource to address the didactic transposition of N&N. In addition, the results obtained reveal that the e-book was efficient to arouse student’s interest towards N&N, and mobilized their engagement with the topic. The results also show that students understand the multidisciplinary nature of N&N, including its importance to technological development.

Acompanha: Entendendo a radioatividade com a ajuda do Watchmen / Esta pesquisa utiliza as histórias em quadrinhos das séries “Watchmen” e “Before Watchmen - Dr. Manhattan” como base para ensinar física com enfoque CTS, levando em consideração a interdisciplinaridade da linguagem da arte sequencial. As revistas selecionadas inter-relacionam conteúdos referentes a física, história, sociologia, filosofia e arte em uma narrativa que gira em torno da física atômica, fazendo assim com que possam ser utilizadas como ferramenta para fazer um primeiro contato entre alunos e conteúdo e assim aumentar o engajamento. Esta pesquisa objetiva buscar informações para a elaboração de um material didático na forma de histórias em quadrinhos para o ensino de física, para isso utiliza-se de textos de diversos autores como Kakalios e Will Eisner, além de questionários e da matriz dialógica problematizadora. / This research uses the comics from the series “Watchmen” and “Before Watchmen Dr. Manhattan” as a base to teach physics with and enphasis on STS, considering the interdisciplinarity of the sequential arts, which on the selected comics interrelates subjects referring to physics, history, sociology, philosophy and art in a narrative that revolves around atomic physics, making it possible to use it as a tool for a first contact between the students and the subject as a way to increase the students engagement when studying physics with an enphasis on STS, specially on subjects concerning modern physcis. This research presents an history of the uses of comic books in teaching, historic reports concerning the dangers that a lack of information and the scarcity of a education focused on STS can cause when populations interact with radioactive technological artifacts.

Acompanha: Ciência e arte na sala de aula e atividades / Este trabalho se propôs a repensar o ensino de alguns tópicos da óptica a partir das relações entre ciência e arte, entendidas como expressões humanas inseparáveis e instrumentos de compreensão do mundo. O referencial teórico possibilitou reflexões sobre o processo ensino-aprendizagem, sobre as relações entre Ciência a Arte como áreas do conhecimento humano construídas sócio historicamente e sobre o papel da criatividade e da imaginação no ensino de ciências. Baseando-se nestas relações, foi desenvolvida uma unidade didática alternativa para transposição de conceitos da óptica geométrica no ensino médio. A intervenção teve como concepção norteadora a pedagogia dialógico-problematizadora de Paulo Freire e se utilizou dos três momentos pedagógicos Estudo da Realidade, Organização do Conhecimento e Aplicação do Conhecimento, que são proposição dos pesquisadores J.A. Angotti e D. Delizoicov. Foi desenvolvida em três etapas e envolveu seis turmas de três colégios estaduais em Curitiba. O tema gerador foi a Arte Urbana (especialmente o grafite), presente no universo dos nossos educandos. A discussão gerada abordou o conceito de Ciência e a problematização foi feita utilizando-se a tela “An Experiment on a Bird in the Air Pump” (1766), de Joseph Wright of Derby. A estratégia de pesquisa foi do tipo observação participante e o tratamento de dados pelo método comparativo constante. Os dados foram obtidos no estilo cooperativo e a categoria geral definida para análise foi a das “Perspectivas tidas pelos sujeitos”, pois esta é consoante com a concepção freiriana de educação centrada nos sujeitos envolvidos e suas vivências. A pesquisa possibilitou concluir que são promissoras as possibilidades de incrementar o ensino de Física numa abordagem que busque reflexão sobre o papel da Ciência na construção coletiva e histórica do conhecimento, enriquecida pelas suas relações com a Arte; tanto na dimensão pedagógica quanto na acadêmica de pesquisa. / A summary of the stages of a qualitative research on Education, developed at UTFPR, Brazil, is presented. The purpose of this work is to rethink Education on some topics of Optics, on the basis of the relationship between Science and Art, which are understood here as inseparable human expressions and representations of the world. Based on this relationship, an alternative didactic unit was developed, aiming the transposition of concepts on Geometrical Optics in high school. The intervention was based on the dialogical and problem-posing approach due to Paulo Freire, and it was applied to six classes at three State high schools in Curitiba. The generative theme was Street Art, ubiquitous in the universe of students. The generated discussion involved the concept of Science and questioning was made using the painting “An Experiment on a Bird in the Air Pump”, by Joseph Wright of Derby (1766). The research strategy was participant observation, and data were processed by constant comparative method. The data were obtained from the cooperative style and the general category set for analysis was that of “Perspectives taken by subject”, since this is consonant with the Freirian conception for education centered on the involved subjects and their experiences. The research made it possible to conclude that the possibilities are promising to increase the teaching of Physics in an approach that aims to reflect on the role of science in building collective and historic knowledge, enriched by their relationships with art; both in pedagogical and academic research.

Acompanha: Procedimento para o uso do Tracker como objeto de ensino, suas potencialidades e dificuldades para aprendizagem de física no ensino médio / Nessa dissertação investiga-se o processo de ensino-aprendizagem empregando um objeto de ensino, o aplicativo conhecido como Tracker, que utiliza recursos tecnológicos, através do vídeo análise, a fim de favorecer a interação entre os experimentos de laboratório de física com recursos de imagens e vídeo. Esta pesquisa fundamentou-se em autores como David Ausubel, Carl Rogers, Marco Antônio Moreira, Pozo e Crespo. Esta pesquisa teve como objetivo verificar a importância das atividades utilizando os recursos do aplicativo e a mediação na aplicação das atividades desenvolvidas com os alunos da primeira série do ensino médio. Participaram deste trabalho professores do ensino médio e alunos da primeira série do ensino médio da escola Marista Santa Maria. No intuito de verificar se houve indícios de aprendizagem significativa no conteúdo relacionado ao lançamento horizontal de projétil, aplicou-se uma avaliação sobre as propriedades envolvidas neste conteúdo antes e após o uso do Tracker. A partir dos resultados obtidos, fez-se uma comparação entre o conhecimento que os estudantes tinham antes e o conhecimento adquirido após o seu uso, verificando então, que através das atividades desenvolvidas, podemos perceber indícios de aprendizagem significativa em relação ao conteúdo descrito. Nessa pesquisa observamos que a mediação do professor no processo de aplicação do Tracker foi fundamental para o resultado obtido. / This dissertation investigates the process of teaching and learning using a teaching object, the application called Tracker, which uses technological resources, through video analysis, in order to facilitate the interaction between physics laboratory experiments with imaging capabilities and video. This research was based on authors such as David Ausubel, Carl Rogers, Marco Antonio Moreira, and Pozo Crespo. This research aimed to evaluate the importance of activities using the application's features and mediation in the implementation of activities with the students of the first year of high school. In this work high school teachers and students of the first grade of high school of the Marist Santa Maria school. In order to verify if there was significant evidence on learning content related to horizontal launch projectile, an evaluation was applied on the properties involved in this content before and after using the Tracker. From the results obtained, there was a comparison of the knowledge that students had before and the knowledge gained after use, checking so that through the activities developed, we can see significant learning signs regarding the described content. In this research we observed that the mediation of the teacher in the Tracker application was fundamental to the result obtained.

Acompanha: Raciocinal e empírico: caderno pedagógico / Este trabalho trata de uma pesquisa qualitativa sobre a mediação de roteiros no ensino-aprendizagem do experimento da segunda lei de Newton. Iniciamos a pesquisa com uma análise documental sobre a demanda histórica, procurando diagnosticar a produção de roteiros da segunda lei nos últimos 50 anos, baseados nos arquivos históricos do Colégio Estadual do Paraná, os resultados da investigação bibliográfica mostraram que não existiu evolução didático-metodológica em relação as orientações para a execução das práticas experimentais em torno da segunda lei de Newton. Mesmo com a evolução tecnológica e instrumental dos laboratórios já interfaceados com fotogates e computadores, os roteiros ainda privilegiam uma concepção de ensino tradicional de ciência altamente reprodutivista. Concluímos que desde os projetos como o PSSC (MIT), o de Harvard e outros que tinham uma base tecnicista e que propunham o aprendizado de Física tornando os estudantes pequenos cientistas, e que proporcionou aos estudantes muita habilidade motora e uma aprendizagem automatizada e, acabou negligenciando a parte cognitiva presente no processo entre observações e fatos, ao nosso ver isso corrobora com uma concepção de ensino de divulgação de ciência no estilo panfleto. Para nos auxiliar neste problema buscamos principalmente os estudos de Gaston Bachelard, Paulo Freire, Thomas S. Kuhn, Ian Hacking, Neill Postman e Kim Vicente. Problema delimitado propomos uma possível modificação do roteiro da segunda lei de Newton com uma sequência de atividades experimentais com plano de fundo de uma lei ou teoria associado à ciência normal no sentido de Kuhn, no qual os estudantes são provocados em resolver quebra-cabeças, propostos na problematização do roteiro promovendo uma possibilidade de entrelaçamento entre teoria e a prática, valorizando aspectos racionais e empíricos, de forma de aproximação, de tensão conciliadora e de retroalimentação. No método experimental artesanal e tecnológico associado a contextos e problematizações, apostamos na especulação complexa do aparelho experimental e das entidades da física relacionadas com a lei fundamental dos movimentos, com a intencionalidade da especialização na utilização dos aparelhos e do aumento do realismo científico das entidades manipuladas pelos estudantes. Como principais resultados que verificamos pela comparação de representações dos estudantes em questionários aplicados antes e depois da sequência de atividades, apontamos aspectos de uma evolução em maior ou menor grau do gênero de raciocínio associado à cultura do laboratório, com indícios de uma possível evolução do perfil epistemológico dos estudantes em relação as entidades da física manipuladas, através do aparelho experimental e dos elementos articuladores, entre eles o cálculo, no manuseio da linguagem físico matemática. / This assignment is a qualitative research on mediation scripts in the teaching- learning experiment of Newton's second law. We started the research with documentary analysis of the historical demand, looking diagnose the production of script about second law on last fifty years, based on the historical archives of the Colégio Estadual do Paraná. The results of the literature search showed that there was not didactic-methodological, development in relation the guidelines for execution of experimental practices around Newton's second law. Even with the technological and instrumental development of laboratories already interfaced with photogates and computers, the scripts still prefer a traditional school design highly reproductivist science. We conclude from since the projects as the PSSC (MIT), of the Harvard and others, who had a technical basis and that the proposed Physical learning becoming the students in little scientists. And which provided students with a lot of motor skills and an automated learning and, finishes up neglecting the cognitive part of this process between observations and facts, in our view this confirms a science of dissemination of teaching design in the pamphlet style. To help us in this problem we sought studies of Gaston Bachelard, Paulo Freire, Thomas S. Kuhn, Ian Hacking, Neill Postman and Kim Vicente. With the delimited problem, we propose a possible modification of the script of Newton's second law, with a series of experimental activities with the background plan of a law or theory associated with normal science in Kuhn's sense, in which students are challenged to solve puzzles. Problematized in script with a chance of entanglement between theory and practice, valuing rational and empirical aspects, promoting his approach, tension and feedback. In experimental method associated with contexts and problematizations, handmade and with technology, we bet on complex speculation, of the experimental apparatus and of the physical entities related to the fundamental law of motion, with the intentionality of the specialization in the use of equipment and the increase of the realism scientific of the manipulated entities by students. The main results that we see by comparing representations of students in questionnaires before and after the sequence of activities. We point out aspects of an evolution to a greater or lesser degree, gender of reasoning associated with the laboratory culture, with indications of a possible evolution of the profile epistemological of students regarding the physical entities manipulated by the experimental apparatus and the joint by calculation with the handling of physical mathematical language.

O presente trabalho tem por objetivo analisar o papel das ações interdisciplinares na formação do conceito de escala do estudante. Para isso, investigou-se, a literatura e os livros-texto sobre o assunto, assim como a posição dos docentes e a legislação estabelecida pelos Parâmetros Curriculares Nacionais sobre o tema. A pesquisa insere-se na linha de Epistemologia e Linguagem, do Programa de Pós-Graduação em Educação da Universidade de Caxias do Sul, coordenado pelo Professor Doutor Jayme Paviani e orientada pelo Professor Doutor Francisco Catelli que trabalha na investigação de abordagens alternativas no ensino de ciências. No primeiro capítulo é feita uma análise do objeto de pesquisa, "escala", buscando-se elementos na história da Matemática e da Física e relacionando-os com a Educação, especialmente com a construção do conhecimento. No segundo capítulo é realizada uma investigação na literatura sobre o conceito de interdisciplinaridade, consultando principalmente autores como Jayme Paviani e Olga Pombo, a fim de examinar a presença da noção de interdisciplinaridade no processo de construção do conhecimento. No terceiro capítulo procura-se identificar o processo de construção, leitura e interpretação do objeto escala na perspectiva dos professores de matemática e de física do ensino médio, verificando suas concepções sobre esse objeto e em que ele contribui para a formação do aluno. Observou-se, antes mesmo do início desta pesquisa, que o objeto escala não estava suficientemente esclarecido ao aluno de Ensino Médio que, frequentemente, apresenta dificuldades em construí-la e interpretá-la. Procura-se então responder à pergunta: "Que argumentos ajudam a sustentar o encaminhamento de ações interdisciplinares no ensino de escalas e medidas no Ensino Médio?" Buscando compreender a forma com que o objeto escala está sendo desenvolvido, foi feita uma análise de alguns livros didáticos de matemática e física distribuídos aos professores e alunos das escolas públicas de Ensino Médio pelo Programa Nacional do Livro Didático. Para conhecer o posicionamento dos professores sobre a forma com que o conceito de escala é trabalhado, foi feita uma entrevista semi-estruturada com um grupo de docentes que trabalha rotineiramente com esses livros. A partir da análise das respostas procurou-se verificar como eles acreditam que o aluno aprende, não apenas esse conceito, mas as definições fundamentais para a formação do estudante, e, se acreditam que ações interdisciplinares possam promover a melhoria na apreensão de conceitos. Através desta pesquisa foi possível perceber que os conceitos de escala e de medida são vistos, muitas vezes, apenas como ferramentas e não como formas de comunicação e representação. Esses conceitos não pertencem a uma disciplina somente, justificando a necessidade da presença da interdisciplinaridade, conceito pouco desenvolvido no contexto escolar atual. O presente trabalho tem como relevância científica a percepção da necessidade de se ampliar o campo de visão da ciência, extrapolando o conhecimento de apenas uma disciplina e interagindo com outras áreas. Além disso, esta investigação é relevante pedagogicamente na medida em que pretende contribuir para o preenchimento de uma importante lacuna existente no processo de ensino-aprendizagem de Matemática e de Física, a saber, a consciência limitada, por parte de alunos e professores, do caráter inerentemente interdisciplinar dos conceitos de escala e de medida, caráter esse que dá a elas a devida amplitude. / The current paper aims to analyze the role of disciplinary actions in shaping the formaction of the concept of the scale of the student. In order to do so, the literature, didactics about the subject, the position of the docents who work in the areas and the legislation established by the National Curricula Parameters were investigated. The research is held in the line of Epistemology and Language, of the Post Graduation Program in Education at the University of Caxias do Sul, coordinated by Professor Doctor Jayme Paviani and monitored by Professor Doctor Francisco Catelli who works in the investigation of alternative approaches in the teaching of sciences. In the first chapter an analysis of the research object, "Scale", is made in order to search for elements in the history of Mathematics and Physics and relate them with Education, especially concerning the of knowledge building. In the second chapter an investigation on the literature about interdisciplinarity is held, consulting mainly to authors Jayme Paviani and Olga Pombo, to examine the presence of the concept of interdisciplinarity in the construction of knowledge. In the third chapter the aim is to identify the process of building, reading and interpretation of the scale object in the perspective of mathematics and physics teachers of high school, verifying their conceptions about this object, and in what it contributes on the pupils´ formation. It was observed even before the beginning of this research that the scale object was not clear enough for the High School student who often has difficulty in building it and interpreting it. It was then necessary to answer the question: "What arguments give support of implementation of actions interdisciplinary teaching of scales and measures in high school?" In order to understand the way in which the scale object is being developed, an analysis of didactic materials was made, having books of Math and Physical aproved in the National Program of Didactic Book, and delivered for teachers and students of public high schools selected as samples.So that we could find out the positioning of the docents about the way the concept of scale is worked, a semi-structured interview was conducted with a group of mathematics and physics teachers who work with these books every day. From the analysis of their answers it was verified how they believe their pupils learn, not only this concept, but the fundamental definitions of the student´s formation, and, if they believe that interdisciplinary actions can foster the improvement in grasping concepts. Through this research it was possible to notice that the concepts of scale and of measure are often seen only as tools and not as ways of communication or representations. These concepts do not belong to a unique subject, that is why the interdisciplinarity is needed, a concept which is not enough developed in the school context. The realization of the need to broaden the view camp of science gives scientific relevance to the research, going beyond the knowledge of only one subject and interacting with other areas. Furthermore, this investigation is pedagogically relevant as it intends to contribute for the bridging of an important gap existing in the process of teaching-learning of Mathematics and Physics, the limited awareness of teachers and pupils of the inherent character of the concepts of scale and measure, a character that gives them the due extension.

Mathematics plays a pertinent role in physics. Students' understanding of this role has significant implications in their understanding of physics. Studies have shown that some students prefer the use of mathematics in learning physics. Other studies show mathematics as a barrier in students' learning of physics. In this study the role of mathematics in students' understanding of electricity problems was examined. The study undertakes a qualitative approach, and is based on an intepretivist research paradigm. A survey administered to students was used to establish students' expectations on the use of mathematics in physics. Focus group interviews were conducted with the students to further corroborate their views on the use of mathematics in physics. Copies of students' test scripts were made for analysis on students' actual work, applying mathematics as they were solving electricity problems. Analysis of the survey and interview data showed students' views being categorised into what they think it takes to learn physics, and what they think about the use of mathematics in physics. An emergent response was that students think that, problem solving in physics means finding the right equation to use. Students indicated that they sometimes get mathematical answers whose meaning they do not understand, while others maintained that they think that mathematics and physics are inseparable. Application of a tailor-made conceptual framework (MATHRICITY) on students work as they were solving electricity problems, showed activation of all the original four mathematical resources (intuitive knowledge, reasoning primitives, symbolic forms and interpretive devices). Two new mathematical resources were identified as retrieval cues and sense of instructional correctness. In general, students were found to be more inclined to activate formal mathematical rules, even when the use of basic or everyday day mathematics that require activation of intuitive knowledge elements and reasoning primitives, would be more efficient. Students' awareness of the domains of knowledge, which was a measure of their understanding, was done through the Extended Semantic Model. Students' awareness of the four domains (concrete, model, abstract, and symbolic) was evident as they were solving the electricity questions. The symbolic domain, which indicated students' awareness of the use of symbols to represent a problem, was the most prevalent. / Science and Technology Education / D. Phil. (Mathematics, Science and Technology Education (Physics Education))

A combination of theoretical perspectives is used to create a rich description of student reasoning when facing a highly-geometric electricity and magnetism problem in an upper-division active-engagement physics classroom at Oregon State University. Geometric reasoning as students encounter problem situations ranging from familiar to novel is described using van Zee and Manogue's (2010) ethnography of communication. Bing's (2008) epistemic framing model is used to illuminate how students are framing what they are doing and whether or not they see the problem as geometric. Kuo, Hull, Gupta, and Elby's (2010) blending model and Krutetskii's (1976) model of harmonic reasoning are used to illuminate ways students show problem-solving expertise. Sayer and Wittmann's (2008) model is used to show how resource plasticity impacts students' geometric reasoning and the degree to which students accept incorrect results. / Graduation date: 2013

This study investigated whether girls achieve better results in Physical Science in single sex environments or in co-educational classes. Thirteen independent South African schools where children were of similar socio-economic background were considered. Grade 12 Matriculation Physical Science examination results for 1999 to 2003 were analysed using Bonferroni (Dunn) t-Tests and Scheffe's Tests. Questionnaires were completed by a small number of students in order to compare their attitudes towards Physical Science and examined qualitatively. There were significant differences found by the administration of the Bonferroni (Dunn) t-Tests and Scheffe's Tests in 2000, 2001 and 2002 to indicate that girls in single sex schools achieved better results in Science than the co-educational schools. However, in 1999 and 2003 there was no significant difference in the results achieved, and so there may be other factors that are more important predictors of achievement than whether the schools are mixed or single sex. / Educational Studies / M.Ed. (Natural Science Teaching)

Not only is Quantum Mechanics (QM) conceptually rich, it is also a theory that physics students have found abstract and technically formidable. Nevertheless, compared to other classical topics of physics, university students’ understanding of QM has received minimal attention in the physics education literature. The principal purpose of this study was to characterize the variation in the ways that undergraduate physics students depict the basic concepts of QM and to extrapolate the results to scaffold possible changes to instructional practices at the university that provided the context for the study. In so doing, an adaptation of a developmental phenomenographic perspective was chosen. Empirically, the study was approached through in-depth interviews with 35 physics students from two Ethiopian governmental universities after they had been exposed to the traditional QM course for one-third of a semester. Interview responses were analyzed using phenomenographic approach where a picture of students’ depictions was established for each quantum concept by expounding the given responses. For each basic quantum concept addressed, the structure of the description categories was separately constructed, and overall, it was found that naive, quasi-classical ontology and/or variants of classical ways of visualization are dominant in students’ responses. For example, it was found that students’ depictions of the photon concept could be described with three distinct categories of description, which are (a) classical intuitive description, (b) mixed model description and (c) quasi-quantum model description. Similarly, the findings revealed that it is possible to establish three qualitatively different categories of description to picture students’ depictions of matter waves, namely, (a) classical and trajectory-based description, (b) an intricate blend of classical and quantum description and (c) incipient quantum model description. Likewise, it was found that students’ depictions of uncertainty principle can be described as: (a) uncertainty as classical ignorance, (b) uncertainty as measurement disturbance and (c) uncertainty as a quasi-quantum principle. With regard to learning QM, the categories of description made clear several issues: most students did not have enough knowledge to depict the basic concepts of QM properly; they were influenced by the perspective of classical physics and their perceptions in making explanations about QM; and they also applied mixed ideas, one based on their classical model and the other from newly introduced QM. These results are also supported by the findings of previous studies in similar domains. Findings from the study were used to guide the design of multiple representations-based instructions and interactive learning tutorials on the conceptual aspects of QM that has been shown to address specific difficulties identified in the study. Theoretical and practical implications of the study, as well as potential future considerations are drawn. / Mathematics, Science and Technology Education / D. Phil. (Mathematics, Science and Technology Education)