The purpose of this study was to identify relationships between selected academic variables and student achievement and time of matriculation for students enrolled full-time at two Virginia community colleges; and to ascertain from those relationships the potential for predicting community college achievement. Data were collected, with permission from the VCCS Office of Research and Planning, on students (N = 287) enrolled at either Central Virginia Community College in Lynchburg, Virginia, or Southside Virginia Community College in Alberta and Keysville, Virginia, from the fall semester of 1988 through the summer semester of 1995. Persons were enrolled in either drafting and design technology, electronics technology, or engineering technology. The dependent variables used in this study were: (a) achievement in college level mathematics courses, (b) overall occupational/technical program achievement, and (c) time required to finish an occupational/technical AAS degree. Independent variables were: (a) high school curriculum (i.e., general or academic), and = (b) high school program participation (i.e., traditional articulation, dual enrollment, or no participation in either). The covariates were: (a) high school GPA, (b) scores on math portion of entrance placement test, (c) algebra I GPA, (d) geometry GPA, and (e) algebra II/trigonometry GPA. The analysis used in this study was developed in several stages. Tests of assumptions were conducted to assure normality and homogeneity of data as well as the elimination of any possibility of multicollinearity between math achievement and overall program achievement. All tests were satisfied and no significance was found at the p < .05 alpha level between math and program achievement. A 2X3 MANCOVA was conducted to ascertain any statistical relationship between the dependent variables and the independent variables. Because only persons participating in an academic high school curriculum (n = 88) had all three math prerequisites, a one way MANCOVA was then conducted to determine statistical significance, regression models were developed for the purpose of predicting community college math achievement, overall program achievement, and time required to finish an AAS degree. The study concluded that the significant predictor of time was high school GPA. The significant predictors of college math achievement were high school GPA, placement test scores, and algebra I. Significant predictors of college program achievement were high school GPA, algebra I, participation in traditional articulation and dual enrollment. / Ed. D.

It is the purpose of this study to review in brief the changes that have taken place since the turn of the century in content of mathematical studies in the high school and to examine theoretically the significance of such changes.

This dissertation study explored: 1) instructors’ use of discussion strategies that enhance meaningful learner interactions in online discussions and student performance, and 2) learners’ interaction patterns in online discussions that lead to better student performance in online introductory mathematics courses. In particular, the study applied a set of data mining techniques to a large-scale dataset automatically collected by the Canvas Learning Management System (LMS) for five consecutive years at a public university in the U.S., which included 2,869 students enrolled in 72 courses. First, the study found that the courses that posted more open-ended prompts, evaluated students’ discussion messages posted by students, used focused discussion settings (i.e., allowing a single response and replies to that response), and provided more elaborated feedback had higher students final grades than those which did not. Second, the results showed the instructors’ use of discussion strategies (discussion structures) influenced the quantity (volume of discussion), the breadth (distribution of participation throughout the discussion), and the quality of learner interactions (levels of knowledge construction) in online discussions. Lastly, the results also revealed that the students’ messages related to allocentric elaboration (i.e., taking other peers’ contributions in argumentive or evaluative ways) and application (i.e., application of new knowledge) showed the highest predictive value for their course performance. The findings from this study suggest that it is important to provide opportunities for learners to freely discuss course content, rather than creating a discussion task related to producing a correct answer, in introductory mathematics courses. Other findings reported in the study can also serve as guidance for instructors or instructional designers on how to design better online mathematics courses.

The purpose of the study is to find answers to the following questions. 1. Is there a significant difference in any of the three simple pair-wise comparisons of the attitudes of the three groups of mathematics instructors of college preparatory courses toward teaching those courses? 2. Is there a significant difference in any of the three simple pair-wise comparisons of the attitudes of the three groups of mathematics instructors of college preparatory courses toward the MAA-NCTM recommendations? 3. Is there a significant correlation between the attitudes toward the MAA-NCTM recommendations and the attitudes toward teaching the college preparatory mathematics courses held by the mathematics instructors in each of the three groups? The data led to the conclusion that all three groups held the same favorable attitude toward teaching college preparatory mathematics courses. Also, there were no significant differences among the three groups' attitudes toward the MAA-NCTM recommendations. However, while no significant correlation was found for the high school instructors, there did exist a significant positive correlation between the two attitudes for each of the other two groups studied.

Made available in DSpace on 2016-07-27T13:53:53Z (GMT). No. of bitstreams: 1 Dagmar Junqueira Guimaraes Silva.pdf: 2252546 bytes, checksum: cb79edb0c7d07381df8bc9ae0232f448 (MD5) Previous issue date: 2003-10-20 / The aim of this research was to understand and analyze the process of the setting up and consolidation of the Mathematics courses at the Catholic University of Goiás (UCG) and the Federal University of Goiás (UFG), by following the historical path of each through written documentation and the memories of their founders. The study touches on their high points, crises and contribution to society in the formation of teachers and Bachelors. It traces the history of the courses from their foundation, with particular emphasis on moments such as the beginning of the 60s. It analyzes the repercussions of the 1964 military coup and the 1968 university reforms on the two courses. It looks at the formation of the university and Third Level teaching of Mathematics at different times and points to the significance of the foundation of the Catholic University of Goiás (1959) and the Federal University of Goiás (1960). It is a qualitative research which uses the resources of oral history. Semi-structured interviews with lecturers, former lecturers and idealizers of the courses in question, written documents such as minutes, yearbooks, bulletins, legal documents and secretarial records were used. Even though the courses were set up within a Faculty of Science and Letters with the aim of forming teachers to respond to the need for qualified personnel in the teaching of Mathematics in the State of Goiás, from the study, it could be concluded that, with the passage of time, both courses presented distinctive characteristics: the UCG course became part of the Department of Mathematics and Physics while maintaining its ideal of forming teachers, while the UFG course of the then Institute for Mathematics and Physics aims at forming Bachelors, even though nowadays it tends more towards the Licentiate. / A presente pesquisa tem como objetivo compreender e analisar o processo de criação e consolidação dos cursos de Matemática da Universidade Católica de Goiás (UCG) e da Universidade Federal de Goiás (UFG), reconstruindo a trajetória histórica de cada um, por meio de documentos escritos e da memória de seus construtores. Aborda seus pontos altos, suas crises e sua contribuição para a sociedade goiana na formação de professores e bacharéis. Resgata a história dos cursos desde a sua criação, destacando vários momentos como o início da década de 1960. Analisa a repercussão do golpe militar de 1964 e da reforma universitária de 1968 nos dois cursos. Busca as raízes da criação da universidade e do ensino superior de Matemática em diversas épocas e enfatiza a criação da Universidade Católica de Goiás (1959) e da Universidade Federal de Goiás (1960). Trata-se de uma pesquisa qualitativa que utiliza os recursos da história oral. Foram usadas entrevistas semi-estruturadas com professores, ex-professores e idealizadores dos cursos em questão, documentos escritos, como atas, anuários, boletins, processos, livros de registros das secretarias. O estudo permite concluir que, embora tenham sido criados em Faculdade de Ciências e Letras, com o objetivo de formar professores para atender à necessidade de professores qualificados para o ensino de Matemática no estado de Goiás, no decorrer dos anos, os dois cursos passaram a apresentar características distintas: o da UCG passou a integrar o Departamento de Matemática e Física, continuando com seu ideal de formar professores, ao passo que o da UFG, do então Instituto de Matemática e Física, tem como objetivo a formação de bacharéis, embora atualmente haja uma vertente mais acentuada para a licenciatura.

本研究主要是針對高中數學課程中「信賴區間」的這個單元，依據99 課綱中的課程規劃，設計出一套專題式的研究教材，並以筆者所任教高中的高二及高三學生作為研究對象，進行專題性的課程授課，且對其學習成果進行評量。主要研究結果如下： 一、高三學生雖已進行過「信賴區間」及其先備知識之授課，但前測的成績並不理想。 二、高二與高三學生經由筆者授課教學後，其後測成績均較前測成績有非常明顯之進步，不過高二與高三學生的後測成績並無顯著差異。 三、高二自然組與高二社會組學生經由筆者授課教學後，其學習成效亦無顯著差異，但社會組學生學習上普遍較為認真，後測成績稍高於自然組。 四、高三自然組與高三社會組學生經由筆者授課教學後，其後測成績具顯著差異，而進步成績的學習成效亦具有顯著差異，自然組優於社會組。 五、依高中數學學習成就分成高分群、中分群與低分群三群，雖然在前測與後測成績表現上顯著不同，但進步的成績則三群並無顯著差異。 此外，筆者於本次研究中也對學生問卷調查一些筆者有興趣的相關議題，並進行問卷分析，得到以下結果： 一、對於本研究所編撰「信賴區間」之課程教材，學生普遍能夠接受且瞭解，並知曉「信賴區間」在生活上的用處，且能解讀其資訊。唯實務面上，他們對「信賴區間」之學習則持可有可無的態度。 二、本次研究的授課方式對於自然組與社會組學生的接受程度是具有差異的，其中自然組學生較能接受本次非傳統型的授課方式。 三、學生普遍認為高中數學中，「非統計類數學課程」是比較有趣的，「統計類數學課程」則在學習上具相對困難性。而在統計的課程中，「信賴區間」倒是比較感興趣的這單元。 整體而言，本次研究對學生進行信賴區間的教學結果，是具有學習成效的。 / Based on the 99 Curriculum Guidelines for the Senior High School Math, a special set of study material for Confidence Interval was composed. Eleventh and twelfth grade students from a girl’s senior high school were recruited voluntarily and lectured, and their learning performance were evaluated before and after the completion of the lecture. The primary findings are as the following: 1. Though twelfth grade students have already studied Confidence Interval before the lecture, their pre-test scores were still low. 2. On the average, both eleventh and twelfth grade students performed better after the lecture, and no significant differences were observed between them. 3. For the eleventh grade students, no significant differences were observed between social science and natural science groups. However, students in social science group appeared to work harder, and their post-test results were slightly better than those in natural science group. 4. For the twelfth grade students, significant differences were observed between social science and natural science groups. Natural science group students appeared to outperform their counterparts in social science group. 5. Among the top third, the middle third, and the bottom third of all the participating students, although their pre-test and post-test scores differed significantly, the differences between the two tests were not significant. In addition, some secondary issues were also explored, and the related findings are summarized as follows: 1. Students showed appreciation for the study material, understood the concept of Confidence Interval better after the lecture and even realize how to apply the concept to their daily life. Surprisingly, however, they didn’t think learning Confidence Interval would make any difference in their life. 2. Students in the natural science group appeared to have greater acceptance toward the unconventional teaching method than those in the social science group. 3. For the topics covered in senior high school math, students generally considered those unrelated to statistics more interesting, and thought that statistics-related topics were more difficult to learn. However, among the statistics-related topics, Confidence Interval was the most intriguing one. In conclusion, this study reveals that the experimental teaching approach concerning Confidence Interval are apparently positive and effective.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2015-12-03T09:31:34Z No. of bitstreams: 2 Dissertação - Liviam Santana Fontes - 2015.pdf: 1855378 bytes, checksum: a223bc0cfd9826481481645ddce26389 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-12-04T07:44:17Z (GMT) No. of bitstreams: 2 Dissertação - Liviam Santana Fontes - 2015.pdf: 1855378 bytes, checksum: a223bc0cfd9826481481645ddce26389 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-12-04T07:44:17Z (GMT). No. of bitstreams: 2 Dissertação - Liviam Santana Fontes - 2015.pdf: 1855378 bytes, checksum: a223bc0cfd9826481481645ddce26389 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-09-24 / In this dissertation, we present a qualitative investigation about assessment of learning in Differential and Integral Calculus (DIC) in Science and Mathematics courses. We did a survey about scientific production on assessment of learning in higher education from 2009 to 2013. We observed that the predominant conception of evaluation is the traditional one, which values accumulation of information and reproduction of concepts. The evaluative instruments more often used are individual written examinations. Some research shows others perspectives of evaluation, such as the formative assessment, which aims to improve learning though a process of information gathering for further reflection and action. We also investigated the assessment of learning according to teacher and student comprehension in DIC, in Science - Biology, Physics and Chemistry – and Mathematics degrees of the Unidade Universitária de Ciências Exatas e Tecnológicas of the Universidade Estadual de Goiás. We verified that traditional evaluation is predominant in this institution much like the scientific production showed us, but some teachers have tried different evaluation procedures in favor of student learning. After this investigation, we analyze other evaluation proposal, apart from written examination, which emerged in published articles, theses, dissertations and books. We also considered the suggestions of teachers who participated in this study, and the impressions and proposals from students interviewed about this topic. With all this information, we planned and created pedagogical interventions with a group of Degree in Physics in this university. We utilized evaluative activities that could indicate learning problems to solve them through a teaching learning environment. We evidenced that the activities contributed to the teaching-learning process in a positive way. They caused changes in the teacher/researcher about her way of thinking and acting, and getting her to realize the importance of systematizing evaluation results to show to students and for better planning work. / Nesta dissertação apresentamos uma pesquisa qualitativa sobre avaliação da aprendizagem em Cálculo Diferencial e Integral (CDI) nos cursos de Licenciatura em Ciências e Matemática. Fazemos um levantamento da produção científica sobre o tema avaliação da aprendizagem no ensino superior do período de 2009 a 2013 e destacamos que a concepção de avaliação predominante é a tradicional, que valoriza a acumulação de informações e a reprodução de conceitos, e os instrumentos avaliativos mais utilizados são as provas escritas individuais. Algumas pesquisas apresentam indicativos de mudanças, com outras perspectivas de avaliação; a formativa é a mais frequente e visa melhorar as aprendizagens por meio de um levantamento de informações para reflexão e ação posteriores. Após esse levantamento, investigamos a avaliação da aprendizagem segundo a compreensão dos professores e dos estudantes da disciplina CDI nos cursos de Licenciatura em Ciências - Ciências Biológicas, Física, Química - e Matemática da Unidade Universitária de Ciências Exatas e Tecnológicas da Universidade Estadual de Goiás. Constatamos que, de modo semelhante ao que se apresentou nas produções científicas, nessa instituição a avaliação tradicional é predominante, mas alguns professores têm buscado procedimentos avaliativos diferenciados em favor da aprendizagem de seus alunos. Após o levantamento dessas informações, analisamos as propostas de avaliação, para além da prova escrita, que emergiram nos artigos científicos, teses, dissertações e livros publicados no período de interesse. Consideramos também as sugestões apontadas pelos professores participantes deste estudo e as impressões e propostas dos alunos entrevistados com relação a estas. Com essas informações, planejamos e realizamos intervenções pedagógicas com uma turma de Licenciatura em Física dessa universidade. Utilizamos atividades avaliativas que pudessem indicar problemas de aprendizagem para que, por meio de estratégias de ensinagem, pudéssemos solucioná-los. Constatamos que as atividades contribuíram com o processo de ensino-aprendizagem e, além disso, provocaram mudanças no modo de pensar e agir da professora/pesquisadora, ao levá-la a perceber a importância de sistematizar os resultados das avaliações, tanto para apresentá-los aos alunos quanto para um melhor planejamento do trabalho.

Submitted by ROSEMEIRE DE FATIMA BATISTELA null (rosebatistela@hotmail.com) on 2017-02-11T02:22:43Z No. of bitstreams: 1 tese finalizada 10 fevereiro 2017 com a capa.pdf: 2263896 bytes, checksum: 413948c6a47fb47a21e1587275d29c03 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2017-02-15T16:56:58Z (GMT) No. of bitstreams: 1 batistela_rf_dr_rcla.pdf: 2263896 bytes, checksum: 413948c6a47fb47a21e1587275d29c03 (MD5) / Made available in DSpace on 2017-02-15T16:56:58Z (GMT). No. of bitstreams: 1 batistela_rf_dr_rcla.pdf: 2263896 bytes, checksum: 413948c6a47fb47a21e1587275d29c03 (MD5) Previous issue date: 2017-02-02 / Apresentamos nesta tese uma proposta de inserção do tema teorema da incompletude de Gödel em cursos de Licenciatura em Matemática. A interrogação norteadora foi: como sentidos e significados do teorema da incompletude de Gödel podem ser atualizados em cursos de Licenciatura em Matemática? Na busca de elaborarmos uma resposta para essa questão, apresentamos o cenário matemático presente à época do surgimento deste teorema, expondo-o como a resposta negativa para o projeto do Formalismo que objetivava formalizar toda a Matemática a partir da aritmética de Peano. Além disso, trazemos no contexto, as outras duas correntes filosóficas, Logicismo e Intuicionismo, e os motivos que impossibilitaram o completamento de seus projetos, que semelhantemente ao Formalismo buscaram fundamentar a Matemática sob outras bases, a saber, a Lógica e os constructos finitistas, respectivamente. Assim, explicitamos que teorema da incompletude de Gödel aparece oferecendo resposta negativa à questão da consistência da aritmética, que era um problema para a Matemática na época, estabelecendo uma barreira intransponível para a demonstração dessa consistência, da qual dependia o sucesso do Formalismo e, consequentemente, a fundamentação completa da Matemática no ideal dos formalistas. Num segundo momento, focamos na demonstração deste teorema expondo-a em duas versões distintas, que para nós se nos mostraram apropriadas para serem trabalhadas em cursos de Licenciatura em Matemática. Uma, como possibilidade de conduzir o leitor pelos meandros da prova desenvolvida por Gödel em 1931, ilustrando-a, bem como, as ideias utilizadas nela, aclarando a sua compreensão. Outra, como opção que valida o teorema da incompletude apresentando-o de maneira formal, portanto, com endereçamentos e objetivos distintos, por um lado, a experiência com a numeração de Gödel e a construção da sentença indecidível, por outro, com a construção formal do conceito de método de decisão de uma teoria. Na sequência, apresentamos uma discussão focada na proposta de Bourbaki para a Matemática, por compreendermos que a atitude desse grupo revela a forma como o teorema da incompletude de Gödel foi acolhido nessa ciência e como ela continuou após este resultado. Nessa exposição aparece que o grupo Bourbaki assume que o teorema da incompletude não impossibilita que a Matemática prossiga em sua atividade, ele apenas sinaliza que o aparecimento de proposições indecidíveis, até mesmo na teoria dos números naturais, é inevitável. Finalmente, trazemos a proposta de como atualizar sentidos e significados do teorema da incompletude de Gödel em cursos de Licenciatura em Matemática, aproximando o tema de conteúdos agendados nas ementas, propondo discussão de aspectos desse teorema em diversos momentos, em disciplinas que julgamos apropriadas, culminando no trabalho com as duas demonstrações em disciplinas do último semestre do curso. A apresentação é feita tomando como exemplar um curso de Licenciatura em Matemática. Consideramos por fim, a importância do trabalho com um resultado tão significativo da Lógica Matemática que requer atenção da comunidade da Educação Matemática, dado que as consequências deste teorema se relacionam com a concepção de Matemática ensinada em todos os níveis escolares, que, muito embora não tenham relação com conteúdos específicos, expõem o alcance do método de produção da Matemática. / In this thesis we present a proposal to insert Gödel's incompleteness theorem in Mathematics Education undergraduate courses. The main research question guiding this investigation is: How can the senses and meanings of Gödel's incompleteness theorem be updated in Mathematics Education undergraduate courses? In answering the research question, we start by presenting the mathematical scenario from the time when the theorem emerged; this scenario proposed a negative response to the project of Formalism, which aimed to formalize all Mathematics based upon Peano’s arithmetic. We also describe Logicism and Intuitionism, focusing on reasons that prevented the completion of these two projects which, in similarly to Formalism, were sought to support mathematics under other bases of Logic and finitists constructs. Gödel's incompleteness theorem, which offers a negative answer to the issue of arithmetic consistency, was a problem for Mathematics at that time, as the Mathematical field was passing though the challenge of demonstrating its consistency by depending upon the success of Formalism and upon the Mathematics’ rationale grounded in formalists’ ideal. We present the proof of Gödel's theorem by focusing on its two different versions, both being accessible and appropriate to be explored in Mathematics Education undergraduate courses. In the first one, the reader will have a chance to follow the details of the proof as developed by Gödel in 1931. The intention here is to expose Gödel’ ideas used at the time, as well as to clarify understanding of the proof. In the second one, the reader will be familiarized with another proof that validates the incompleteness theorem, presenting it in its formal version. The intention here is to highlight Gödel’s numbering experience and the construction of undecidable sentence, and to present the formal construction of the decision method concept from a theory. We also present a brief discussion of Bourbaki’s proposal for Mathematics, highlighting Bourbaki’s group perspective which reveals how Gödel’s incompleteness theorem was important and welcome in science, and how the field has developed since its result. It seems to us that Bourbaki’s group assumes that the incompleteness theorem does not preclude Mathematics from continuing its activity. Thus, from Bourbaki’s perspective, Gödel’s incompleteness theorem only indicates the arising of undecidable propositions, which are inevitable, occurring even in the theory of natural numbers. We suggest updating the senses and the meanings of Gödel's incompleteness theorem in Mathematics Education undergraduate courses by aligning Gödel's theorem with secondary mathematics school curriculum. We also suggest including discussion of this theorem in different moments of the secondary mathematics school curriculum, in which students will have elements to build understanding of the two proofs as a final comprehensive project. This study contributes to the literature by setting light on the importance of working with results of Mathematical Logic such as Gödel's incompleteness theorem in secondary mathematics courses and teaching preparation. It calls the attention of the Mathematical Education community, since its consequences are directly related to the design of mathematics and how it is being taught at all grade levels. Although some of these mathematics contents may not be related specifically to the theorem, the understanding of the theorem shows the broad relevance of the method in making sense of Mathematics.

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