Neste trabalho apresentamos o conceito de desenvolvimento atípico; um texto de referência para o ensino de funções voltado para o 9ª ano, dois modelos didáticos de avaliação formativa, levando em consideração a diversidade do educando e uma palestra motivacional e instrutiva sobre educação inclusiva. Atualmente o ensino da Matemática está voltado para uma apresentação estritamente formal, sem levar em consideração o desenvolvimento do aluno no processo de ensino aprendizagem, quantizando o aprendizado segundo padrões. Nosso objetivo é promover uma aprendizagem significativa pelo aluno, abandonando o uso de fórmulas decoradas, prezando o raciocínio lógico e analisar se o uso de estratégias diferenciadas como: jogos, listas personalizadas, laboratório de matemática são capazes de motivar o aluno, em especial os casos de desenvolvimento atípico, a desejar ser parte da turma e trabalhar em função do seu progresso. / In this work we present the concept of atypical development; a reference text for teaching towards facing the 9th grade, two educational models of formative assessment, taking into consideration the student\'s diversity and motivational and instructive lecture on inclusive education. Currently teaching mathematics is aimed at a strict presentation, regardless of the student\'s development in the teaching and learning process, quantizing the standard learning. Our goal is to promote meaningful learning by the student, abandoning the use of decorated formulas, valuing logical reasoning and examine whether the use of different strategies as games, custom lists, math lab are able to motivate the student with special cases of atypical development, to wish to be part of the class and work according to their progress.

The concept of function is one of the essential topics in the teaching and learning of secondary mathematics because of the central and unifying role it plays within secondary and college level mathematics. Organizations, such as the National Council of Teachers of Mathematics, suggest students should be able to make connections across multiple representations of mathematical functions by the time they complete high school. Despite the prominent role functions play in secondary mathematics curriculum, students continue to struggle with the complex notion of functions and especially have difficulty using the different representations that are inherent to functions (algebraic, graphical and tabular). Technology is often considered an effective tool in raising student achievement, especially in learning functions where the different representations of a graphing calculator are analogous to the different representations of a function. Opportunity to learn is another important consideration when examining achievement and is generally considered one of, if not the most important, factor in student achievement. Opportunity to learn, or the measure of to what extent students have had an opportunity to learn or review a concept, is often measured with self-reports of content coverage. This study examined the relationship between opportunity to learn, students'; use of graphing calculators, and achievement within a curriculum that supports integrated use of technology and focuses on conceptual understanding of mathematical concepts. The research questions focused on what opportunities students had to learn functions from the enacted curriculum, what calculator strategies students used when solving function problems, how both opportunity to learn and calculator strategies influenced student achievement, and what relationships exist between opportunity to learn, use of calculator strategies, and student achievement. This study is an in-depth secondary analysis of a portion of data collected as part of the evaluation study of Precalculus and Discrete Mathematics (Third Edition, Field-Trial Version) developed by the University of Chicago School Mathematics Project. Participants in this study (n = 271) came from six schools, seven teachers, and 14 classes. Instruments in this study include two pretests (one with technology and one without) and three posttests (two with technology and one without) and a calculator usage survey for one posttest. In addition to five student assessments, teachers completed opportunity-to-learn surveys for the posttests and chapter evaluations forms on which they indicated the lessons taught and the homework problems assigned from the textbook. Some students (n = 151) had access to graphing calculators equipped with computer algebra systems (CAS) while others (n = 120) had access to graphing calculators. Students had multiple opportunities to learn functions as measured by lessons taught, homework assigned, and posttest items teachers reported as having taught or reviewed the content necessary for students to correctly answer the items. Overall, students showed a positive increase in achievement between the pretests and posttests. In general, achievement was positively correlated to OTL Lessons, negatively correlated to OTL Homework, and had no correlation to OTL Posttests when controlling for prior knowledge. Results indicate students appear to be, for the most part, making wise choices about when and how to use graphing calculators to solve function items. Students prefer the graphical representation and are rarely using CAS features or tables, even when they are the best choices for solving a problem. Results from hierarchical linear models (HLM) show use of strategies (beta = 0.96), access to CAS (beta = 5.12), and OTL lessons (beta = 0.75) all had significant and positive impacts on student achievement for one of the posttests, when controlling for prior knowledge. Results from path analyses also indicated use of strategies had a direct and positive effect (beta =0 .14) on student achievement but showed access to CAS had a negative indirect effect (beta = -0.64) on student achievement for the same posttest mitigated through OTL Lessons (beta = 0.30). The results of this study have implications for both researchers and mathematics educators who seek to understand ways in which teachers can increase students'; understanding of functions and student achievement. The relationship between the use of technology and student achievement in relation to opportunity to learn is complex, but use of calculator strategies appears to have a positive effect on students' opportunity to learn functions and student achievement when used in a curriculum that focuses on conceptual understanding and integrates technology.

Submitted by Aelson Maciera (aelsoncm@terra.com.br) on 2017-06-14T17:55:05Z No. of bitstreams: 1 DissGABF.pdf: 7214889 bytes, checksum: 6de3fc0b60e1ff02be332fb45551e261 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-06-22T13:08:18Z (GMT) No. of bitstreams: 1 DissGABF.pdf: 7214889 bytes, checksum: 6de3fc0b60e1ff02be332fb45551e261 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-06-22T13:08:28Z (GMT) No. of bitstreams: 1 DissGABF.pdf: 7214889 bytes, checksum: 6de3fc0b60e1ff02be332fb45551e261 (MD5) / Made available in DSpace on 2017-06-22T13:18:47Z (GMT). No. of bitstreams: 1 DissGABF.pdf: 7214889 bytes, checksum: 6de3fc0b60e1ff02be332fb45551e261 (MD5) Previous issue date: 2017-02-17 / Não recebi financiamento / This research project refers to an experience applied to study groups for high school students in order to provide them with an improvement of Mathematics contents, as well as an improvement in the practice of their studies, using the approach proposed and systematized by George Pólya, which is the method of solving problems in Mathematics. Some topics involving functions were explored, through problem solving, mathematical language, collective discussions and applications. The actions implemented in this project also aim to improve the teaching practice, provided by the methodology, to be developed at other times in the classroom, as an important teaching tool. / Este projeto de pesquisa se refere a uma experiência aplicada a grupos de estudos para estudantes do ensino médio com o objetivo de proporcionar-lhes um aprimoramento dos conteúdos de Matemática, bem como um aperfeiçoamento na prática de seus estudos, utilizando-se para isso a abordagem proposta e sistematizada por George Pólya, que é o método de resolução de problemas em Matemática. Foram selecionados alguns tópicos envolvendo funções e explorados, através da resolução de problemas, a linguagem matemática, discussões coletivas e aplicações. As ações implantadas neste projeto visam também aprimorar a prática docente, proporcionada pela metodologia, a ser desenvolvida em outros momentos na sala de aula, como uma importante ferramenta de ensino.

Neste trabalho apresentamos o conceito de desenvolvimento atípico; um texto de referência para o ensino de funções voltado para o 9ª ano, dois modelos didáticos de avaliação formativa, levando em consideração a diversidade do educando e uma palestra motivacional e instrutiva sobre educação inclusiva. Atualmente o ensino da Matemática está voltado para uma apresentação estritamente formal, sem levar em consideração o desenvolvimento do aluno no processo de ensino aprendizagem, quantizando o aprendizado segundo padrões. Nosso objetivo é promover uma aprendizagem significativa pelo aluno, abandonando o uso de fórmulas decoradas, prezando o raciocínio lógico e analisar se o uso de estratégias diferenciadas como: jogos, listas personalizadas, laboratório de matemática são capazes de motivar o aluno, em especial os casos de desenvolvimento atípico, a desejar ser parte da turma e trabalhar em função do seu progresso. / In this work we present the concept of atypical development; a reference text for teaching towards facing the 9th grade, two educational models of formative assessment, taking into consideration the student\'s diversity and motivational and instructive lecture on inclusive education. Currently teaching mathematics is aimed at a strict presentation, regardless of the student\'s development in the teaching and learning process, quantizing the standard learning. Our goal is to promote meaningful learning by the student, abandoning the use of decorated formulas, valuing logical reasoning and examine whether the use of different strategies as games, custom lists, math lab are able to motivate the student with special cases of atypical development, to wish to be part of the class and work according to their progress.

Teaching and learning mathematical functions and graphs pose significant challenges for teachers and students. Students often have difficulty in understanding a functional relationship between two quantities such as distance and time, temperature and precipitation, and gas price and number of gallons. Teaching students to have quantitative thinking about functions can help them understand the rate of change for complicated functions and later succeed in learning Calculus. Traditional educational methods such as static graph images and some learning tools usually have some limitations. Teaching students the dynamic changes of quantities within the static picture has serious difficulties. Compared to the learning tools, the game-based learning increases interest when students are learning complicated functions. This thesis presents a game-based learning application called Functions Fun, which runs on iPad tablet computers. The game is created to teach / learn the following functions: Linear, Quadratic, Exponential, Logarithmic, Trigonometric, and Polynomial with degrees over four. Each function is covered under a game level. The game setting is a jungle environment. Each game level has its own scene, challenging the player to take an action while teaching a function and its graphical representation. Functions Fun enables students to play and learn functions and graphs in a more effective and entertaining manner. / Master of Science / Teaching functions and graphs plays an important role in mathematics education. Teachers and researchers emphasize the need for students to form the quantitative thinking habits when they are learning different function graphs. This thesis presents Functions Fun, an iPad educational game that aims to help secondary students to understand function graphs by varying two quantities x and y such as distance and time, temperature and precipitation, and gas price and number of gallons. Adventure game is chosen as the game genre and six real-life models related to the following six functions are created: Linear, Quadratic, Exponential, Logarithmic, Trigonometric, and Polynomial with degrees over four. Each function is covered under a game level. The game setting is a jungle environment. Players are rewarded for their accomplishments. Through game effects and animations, students can have a better understanding of how the value changes of variables x and y influence the shape of graphs.

Studiens syftar till att utveckla förståelse för idrottslärares friluftslivsundervisning inom idrott och hälsa. Studiens utgår från Biestas tre undervisningsfunktioner om kvalificering, socialisering och subjektifiering. Det bidrar med att undersöka vilket kunnande som idrottslärare vill förmedla till sina elever samt vilka värden, normer och attityder som idrottslärare också vill förmedla till sina elever. Intervjuer har genomförts med idrottslärare för att undersöka hur de uttrycker sig om kunnande, värden, normer och attityder gällande friluftslivsundervisningen. Sex idrottslärare deltog i studien och deras svar har sedan analyserat med hjälp av en tematisk analys för att få fram resultatet i studien. Resultatet visade att idrottslärare prioriterade att förmedla vidare värden, normer och attityder till sina elever i friluftslivsundervisningen. De förmedlade även kunnande som de ansåg som viktigt till sina elever men det var inte kunnandet som ansågs ha det största fokuset utifrån hur idrottslärarna uttryckte sig om deras friluftslivsundervisning. / The study’s aim is to develop an understanding of physical education teachers friluftsliv education in physical education. The study is based in Biesta´s three teaching functions of qualification, socialization, and subjectification. It contributes to investigating what knowledge physical education teachers want to convey to their students and what values, norms and attitudes physical education teachers also want to convey to their students. Interviews have been conducted with physical education teachers to investigate how they express themselves about knowledge, values, norms, and attitudes regarding friluftsliv education. Six physical education teachers participated in the study and their responses were then analyzed using a thematic analysis to produce the results of the study. The results showed that physical education teachers prioritized passing on the values, norms, and attitudes to their students in friluftsliv education. They also imparted knowledge that they considered important to their students, but it was not the knowledge that was considered to have the biggest focus based on how the physical education teachers expressed themselves about their outdoor education.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The present work aims to present a proposal for the introduction and exploration of the main concepts in the study of affine and quadratic functions. This proposal was developed from the realization, through preliminary studies, the existence of difficulties in relation to learning and understanding of concepts related to this topic. Considering the importance of the study of functions in the school curriculum and understanding of phenomena related to different areas of knowledge, the activities that make up this proposal are based on the ideas that learning occurs through a process of knowledge construction and social interaction. Furthermore, believing that contextualization of content and interdisciplinarity to corroborate the significant learning of mathematics, our work proposes a sequence of activities from, real problems will explore the main concepts in the study of affine and quadratic functions. To assist students in solving problems and exploring these concepts and use the learning objects, more specifically, softwares Tracker and GeoGebra. We believe that this proposal will contribute to improving the quality of mathematics teaching and more specifically for teaching functions. Moreover, this work could serve as inspiration for math teachers to create new teaching methodologies. / O presente trabalho tem como objetivo apresentar uma proposta para a introdução e exploração dos principais conceitos presentes no estudo de funções afins e quadráticas. Esta proposta foi elaborada a partir da constatação, através de estudos preliminares, da existência de dificuldades em relação à compreensão e aprendizagem dos conceitos relacionados a este tema. Considerando a importância do estudo de funções no currículo escolar e na compreensão de fenômenos relacionados a diversas áreas do conhecimento, as atividades que compõem esta proposta estão fundamentadas nas ideias de que a aprendizagem se dá através de um processo de construção do conhecimento e pela interação social. Além disso, acreditando que a contextualização dos conteúdos e a interdisciplinaridade corroboram para a aprendizagem significativa da matemática, nosso trabalho propõe uma sequência de atividades que, a partir de problemas reais, pretende explorar os principais conceitos presentes no estudo de funções afins e quadráticas. Para auxiliar os alunos na resolução dos problemas e na exploração destes conceitos, utilizamos os objetos de aprendizagem, mais especificamente, os softwares Tracker e GeoGebra. Acreditamos que esta proposta poderá contribuir para a melhoria da qualidade do ensino da matemática e mais especificamente para o ensino de funções. Além disso, este trabalho poderá servir como inspiração aos professores de matemática para a criação de novas metodologias de ensino.