A presente investigação se vincula a pesquisa contemplada pelo Projeto Observatório da Educação intitulada: Educação matemática nos anos iniciais do Ensino Fundamental: Princípios e práticas da organização do ensino\". Esta pesquisa é realizada pelo Grupo de Estudo e Pesquisa sobre Atividade Pedagógica GEPAPe/FEUSP e objetiva investigar as relações entre o desempenho escolar dos alunos, representado pelos dados do INEP, e a organização curricular de matemática nos anos iniciais do ensino fundamental. Nossa participação está voltada para a organização do ensino de matemática no contexto da ampliação do ensino fundamental para nove anos no Brasil. A promulgação da Lei de n° 11274/2006, que dispõe a duração do ensino fundamental de nove anos, conduz a relevantes questões para o cenário educacional atual, pois, além de consolidar a política de ampliação do acesso à educação às crianças de 6 anos, é importante assegurar a elas um processo educativo que respeite o tempo da infância e seja consoante à adequação tanto das condições materiais quanto da organização pedagógica, tendo em vista a formação integral da criança. Neste sentido, pretendemos caracterizar a organização do ensino de matemática no primeiro ano do ensino fundamental, a partir de três principais eixos: dos principios, das propostas e do material didático. Apresentamos, inicialmente, os princípios representados pelos documentos legais e de orientação oficial para o ensino de nove anos. As propostas serão indicadas por documentos da Secretaria Municipal de Educação que se constitui o lócus desta pesquisa e por orientações do material didático adotado pela mesma rede. Para observar aspectos da atividade pedagógica, direcionamos nosso olhar para os exercícios de matemática selecionados no material didático voltado ao primeiro ano do ensino fundamental. Esta base material nos dará subsídios para investigar como os princípios e as propostas que orientam a organização curricular no ensino de nove anos se apresentam nos conteúdos propostos no material didático, tornando legítimo, na escola, o que é legalizado pelos documentos, no percurso de efetivação do currículo. Nossos resultados indicam a não existência de um projeto de educação matemática para a infância, bem como a ausência de propostas que contemplem a educação das crianças de 6 anos no ensino fundamental. Portanto, a implantação do ensino de nove anos, vista por muitos como a esperança de um movimento de renovação curricular, se estabeleceu como síntese de um fazer pedagógico direcionado para antecipar as necessidades do mercado e do capital no âmbito de um projeto de sociedade capitalista. / The following research is part of a major research made by the Educational Observatory Project entitled: Math education in elementary school initial years: Teaching practices and principles organization. This research is developed by the Pedagogic Activities Research Group GEPAPe/FEUSP and its goal is to investigate the relations between school performance of the students, presented by INEP data, and math curriculum organization in elementary school initial years. Our participation is on organizing math teaching amplifying elementary school teaching to nine years in Brazil. The promulgation of the Law n° 11274/2006, that disposes about the continuance of nine years teaching, conducts to important questions to the present scenario, because, beyond of consolidating the amplification of access to education to 6 years old children, is import to ensure them an educational process that respects the childhood time according to the adequacy of material conditions as much as pedagogical organization, owing to the child development. In this sense, our intent is to characterize math teaching organization in the first year of elementary teaching, from three main subjects: principles, proposals and didactic materials. We present, initially, legal documents principles and official orientation to nine years education. The proposals will be indicated by the City Educational Secretary that is the data of this research and didactic material used by this same Secretary. To observe pedagogical activities aspects, our focus were in math exercises selected from the didactic materials to elementary school first grades. This base material will give us data to investigate how the principles and proposals that guides curriculum organization in nine years teaching are presented in the content proposed into the didactic material, legitimizing, into school, what is legalized by documents, in the course of realization of the curriculum. Our research results in a lack of math education project in infancy, as well as a lack of proposals that contemplates 6 years old students education in elementary school. Therefore, the implantation of nine years teaching, seen by many as curriculum renovation hope, has established as educational synthesis directed to anticipate the needs of market and capitals in a capitalist scope.

Made available in DSpace on 2016-07-27T13:54:01Z (GMT). No. of bitstreams: 1 Adelino Candido Pimenta.pdf: 652136 bytes, checksum: c0e6315dc38b466836b23f3ed67900be (MD5) Previous issue date: 2001-12-07 / This paper presents a new approach in the study of linear functions. In addition, a brief analysis is made of the most relevant aspects of the history of the theme and its articulation with informatics. Initially, a survey was carried out in Goiânia's principal secondary schools in order to identify the textbooks they use. At this stage, a detailed examination of the predominant concepts in these books was undertaken. An attempt was made to give the proposal a theoretical foundation, maintaining, from start to finhish, a dialogue with the ideas of the principal researchers involved with the chosen theme. With regard to the historical and epistemological aspects, these were based on works orientated by Almounloud of the Pontifícia Universidade Católica de São Paulo, while in the context of informatics there was a constant attentive dialogue with the works of Borba and his disciples and other investigators in the field. with regard to the text, the principal objective of the research, this was based on the publications of the orientator Oliveira Filho. Finally, by using the Linear Web Aplett software, a proposal, which dynamically directs the study of linear functions, was drawn up, while at the same time new concepts were added to those already consolidated. / Esta trabalho apresenta uma nova abordagem noestudo de funções lineares. Analisa, também, os aspectos mais relevantes da história do tema e suas articulações com a informática. Inicialmente, procedeu-se a um levantamento nas principais escolas de ensino médio de Goiânia para identificar os livros didáticos. Nessa etapa, foi realizada uma identificação dos conceitos predominantes no livros. Procurou-se fundamentar teoricamente essa proposta mantendo diálogo, do início ao fim, com as idéias dos principais pesquisadores que se preocupam com a temática eleita. No que diz respeito ao aspecto histórico e epistemólogico, este trabalho apoiou-se especialmente nas análises de Almouloud, da Pontifícia Universidade Católica de São Paulo, ao passo que na área de informática a interlocução deu-se, permanente e atentamente, com a produção de Borba e seus discípulos e outros investigadores. O texto, objeto principal desta pesquisa, baseia-se nas publicações de Oliveira Filho. Finalmente, meidante a utilização do software Linear Web Apllet, elaborou-se uma proposta que norteia o estudo de funções lineares de forma dinâmica e iterativa, ao mesmo tempo que agrega novos conceitos

One purpose of this study was to determine whether any differences in immediate achievement or retention existed between students using manipulatives and students not using manipulatives. Also addressed in this study is whether or not the use of manipulatives is more beneficial for girls than boys and whether the use of manipulatives is more beneficial for low-ability students than for high-ability students. Students selected for this study were from a large suburban school district in Texas. The students were from eight intact classes, four of which were designated as the experimental group and the other four as the control group. The sample consisted of one hundred eighty-seven students. All students were tested with a test developed by the researcher. This same test was administered as a pretest, posttest, and retention test. The following supplemental data were also gathered on the students: mathematics scores from the California Test of Basic Skills and scores from the mathematics section of the Texas Educational Assessment of Minimum Skills test. Analysis of the data revealed no statistical difference in the mean scores of students instructed with or without manipulatives when the test was administered immediately after instruction. Nor was there any statistical difference in the mean scores when the test was administered two months after instruction. There was no statistical difference in the mean gain scores from the pretest to the posttest between boys and girls or between high- and low-achieving students. Nor was there any statistical difference between the mean gain scores from the pretest to the retention test between boys and girls or between high- and low-achieving students. It is recommended that further studies be conducted to investigate achievement and retention of students using manipulatives at the secondary level. It is also recommended that variables other than achievement be studied to determine the effects of manipulatives on secondary students.

Made available in DSpace on 2014-06-11T19:24:54Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-12-14Bitstream added on 2014-06-13T20:27:25Z : No. of bitstreams: 1 salandim_mem_me_rcla.pdf: 2002489 bytes, checksum: 86696317671a475aa79fb5846d7bd95b (MD5) / See-Sp / Neste trabalho, procuramos trazer para o âmbito acadêmico discussões referentes a uma modalidade de ensino que nele tem ocupado pouco espaço: o técnico agrícola. Utilizamos a História Oral como principal metodologia de pesquisa, além de visitas às escolas agrícolas focadas e consultas a documentos em seus arquivos, como antigos livros ponto e livros de ata. A partir de entrevistas com professores de Matemática que atuaram nesses núcleos de ensino nas décadas de 1950 a 1970, tentamos constituir uma história de sua formação em Matemática, suas formas de atuação, especificidades dessas escolas e inserção do discurso desses professores na história da Educação Matemática Brasileira, assumindo o conceito de marginalização como principal eixo para as análises. / This work intends to bring to academic universe a theme that has been usually neglected by researchers: the Agricultural Technical School system. Although Oral History was the main methodological approach chosen, visits to some of these schools were done and also written documentation was used as guides. Our starting point to this study was interviews with Math teachers who had lead classrooms in these schools from 50´s to 70´s. In these interviews they told us about their initial and in-service formation and about the agricultural technical schooling in general. From this we tried to inscribe Agricultural Technical School and its teachers in the discourse of History of Education in Brazil and, particularly, in the History of Brazilian Mathematics Education, assuming the concept of marginalization as the main axis in our analysis.

Orientador: Antonio Vicente Marafioti Garnica / Banca: Arlete de Jesus Brito / Banca: Maria Ângela Miorim / Resumo: Neste trabalho, procuramos trazer para o âmbito acadêmico discussões referentes a uma modalidade de ensino que nele tem ocupado pouco espaço: o técnico agrícola. Utilizamos a História Oral como principal metodologia de pesquisa, além de visitas às escolas agrícolas focadas e consultas a documentos em seus arquivos, como antigos livros ponto e livros de ata. A partir de entrevistas com professores de Matemática que atuaram nesses núcleos de ensino nas décadas de 1950 a 1970, tentamos constituir uma história de sua formação em Matemática, suas formas de atuação, especificidades dessas escolas e inserção do discurso desses professores na história da Educação Matemática Brasileira, assumindo o conceito de marginalização como principal eixo para as análises. / Abstract: This work intends to bring to academic universe a theme that has been usually neglected by researchers: the Agricultural Technical School system. Although Oral History was the main methodological approach chosen, visits to some of these schools were done and also written documentation was used as guides. Our starting point to this study was interviews with Math teachers who had lead classrooms in these schools from 50's to 70's. In these interviews they told us about their initial and in-service formation and about the agricultural technical schooling in general. From this we tried to inscribe Agricultural Technical School and its teachers in the discourse of History of Education in Brazil and, particularly, in the History of Brazilian Mathematics Education, assuming the concept of marginalization as the main axis in our analysis. / Mestre

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-05-04T15:08:21Z No. of bitstreams: 1 lucianacordeirodias.pdf: 4838035 bytes, checksum: 61e53438a2d0b2e48b9de180e4900ee5 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-06-07T15:34:11Z (GMT) No. of bitstreams: 1 lucianacordeirodias.pdf: 4838035 bytes, checksum: 61e53438a2d0b2e48b9de180e4900ee5 (MD5) / Made available in DSpace on 2016-06-07T15:34:11Z (GMT). No. of bitstreams: 1 lucianacordeirodias.pdf: 4838035 bytes, checksum: 61e53438a2d0b2e48b9de180e4900ee5 (MD5) Previous issue date: 2015-12-04 / Esta pesquisa é de caráter qualitativo, desenvolvida dentro do âmbito da Educação Financeira Escolar (GRIFE/UFJF). O objetivo do trabalho é analisar as ações e tomadas de decisão dos alunos, do 8º ano do ensino fundamental de uma escola da periferia da rede municipal de Juiz de Fora. Os referenciais teóricos são Ole Skovsmose, no que tange cenários de investigação e a importância de se desenvolver um ambiente crítico, e Romulo Campos Lins, no que se refere ao Modelo dos Campos Semânticos. Como resultado de nossa investigação, apresentaremos um produto educacional para utilização nas salas de aula de matemática com situações-problemas de cunho investigativo e com a temática financeiro-econômica. / This research is qualitative and it has been developed within the Financial Education Theme (GRIFE/UFJF). The objective of this work is to analyze the actions and decision-making of the eighth grade students in a outskirts municipal elementary school in Juiz de Fora, Minas Gerais. The theoretical references are Ole Skovsmose, regarding research scenarios and the importance of developing a critical environment, and Romulo Campos Lins, with regard to the model of Semantic Fields. As a result of our investigation, we will present an educational product for use in classrooms of mathematics with situations-problems of investigative and financial-economic-themed.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This study is part of the line of research ―Formation, Knowledge, and Professional Development‖ of the Graduate Program in Education at Federal University at Santa Maria (UFSM) and presents as main objective to investigate the ways students from the Math Teaching Major at UFSM, who are carrying out their supervised practice, understand the Math subject studied in early years of Elementary School. Data collection in the study was organized in three different moments. The first one concerns the bibliographical research developed along four national events. The second moment was the organization of a questionnaire composed of 16 questions, with the purpose of generally identifying the way Math teachers-to-be understand their initial formation. Finally, the third moment was the organization of a formative space where we tried to discuss the construction of the concept of number and its operations by means of Teaching Guiding Activities. The organization of actions and data analysis were performed under the light of Historical-Cultural Theory, Activity Theory and Teaching Guiding Activity; by using the idea of episodes proposed by Moura (2004). The results indicate that the teachers-to-be acknowledge the importance of Mathematics taught in early years of education, although they are not very clear on how the organization of the discipline occurs in this stage. They also acknowledge that the pedagogue s work is not an easy task and demonstrate to be concerned and aware that, in early years, education demands well-prepared professionals to develop the teacher s work. As considerations on the study, we point out the importance for Math teachers-to-be who will act in the final years of Elementary School and in High School to become closely connected to Mathematics of early years, in terms of teaching organization as well as contents. Besides that, we point out the limited relations among disciplines in the initial formation course and the lack of space so that the teachers-to-be can discuss their own formation. The lack of relations between disciplines called specific and the ones called pedagogic results in the teacher-to-be experiencing two distinct courses, missing necessary connections in the moment of planning actions to be developed in early years. Another issue we highlight is the fact that the initial formation course does not provide the teacher-to-be with the tools needed to the development of teaching in Basic Education. In other words, after graduating the teacher may not have subsidy to think a differentiated teaching that allows students to articulate Math concepts. We also point out that the constitution of a formative space allows the teachers-to-be to reflect on different ways of organizing teaching so that they attribute a new quality to early years. / O presente estudo insere-se na linha de pesquisa Formação, Saberes e Desenvolvimento Profissional do Programa de Pós-Graduação em Educação da Universidade Federal de Santa Maria e tem como objetivo principal investigar o modo como os acadêmicos do curso de licenciatura em Matemática da Universidade Federal de Santa Maria - UFSM, que estão realizando o Estágio Supervisionado, compreendem a Matemática que é estudada nos anos iniciais do Ensino Fundamental. A coleta de informações deste estudo organizou-se em três momentos distintos. O primeiro diz respeito ao levantamento bibliográfico, realizado em quatro eventos em nível nacional; o segundo momento foi a organização de um questionário composto por 16 questões que buscava identificar, de modo geral, como o futuro professor de Matemática compreende a sua formação inicial. O terceiro e último momento foi a organização de um espaço formativo, em que buscamos discutir a construção do conceito de número e as suas operações a partir de Atividades Orientadoras de Ensino. A organização das ações e a análise dos dados foram realizadas à luz da Teoria Histórico-Cultural, da Teoria da Atividade e da Atividade Orientadora de Ensino; utilizando a ideia de episódios proposto por Moura (2004). A partir dos dados, foi possível identificar que os futuros professores reconhecem a importância da Matemática ensinada nos primeiros anos de escolarização, embora não demonstrem ter muita clareza do modo como se dá a organização dessa disciplina naquela etapa. Também reconhecem que o trabalho do pedagogo não é uma tarefa fácil e demonstram a preocupação e o reconhecimento de que, para os anos iniciais, o ensino necessita de profissionais bem formados para desenvolverem o trabalho docente. Como considerações sobre o estudo, destacamos a importância do futuro professor de Matemática que atuará nos anos finais e no Ensino Médio aproximar-se da Matemática dos anos iniciais, tanto em termos de organização do ensino quanto em termos de conteúdos. Além disso, apontamos para a pouca relação entre as disciplinas no curso de formação inicial e a falta de espaços em que o futuro professor possa discutir a sua própria formação. A falta de relação entre as disciplinas ditas de cunho específico e as pedagógicas faz com que o futuro professor vivencie dois cursos distintos, não fazendo, desse modo, as conexões necessárias no momento de planejar ações para serem desenvolvidas nos anos iniciais. Outro ponto, que destacamos, está no fato do curso de formação inicial não dotar o futuro professor com ferramentas suficientes para o desenvolvimento da docência na Educação Básica, ou seja, ao sair do curso de formação inicial, por vezes, o professor não tem subsídios para pensar em um ensino diferenciado que possibilite aos alunos apropriarem-se dos conceitos Matemáticos. Destacamos, ainda, que a constituição de um espaço formativo permite ao futuro professor refletir sobre um modo diferente de organizar o ensino possibilitando que ele atribua uma qualidade nova a sua formação inicial.

In introductory biology, college students are taught to predict how populations will grow and change over time by using population growth models. These models are commonly represented as mathematical equations. However, students consistently struggle when math and biology concepts intersect in the classroom, and these struggles lead to suboptimal understanding of how mathematical population models are designed and used. Education literature suggests that students may struggle with population modeling because of math anxiety, the high cognitive load of the task, and the lack of scaffolding for abstract concepts. In our study, we sought to improve student mastery modeling exponential growth, logistic growth, and Lotka-Volterra predator-prey interactions through using pictorial diagrams in modeling pedagogy. We predicted that these diagrams would reduce the amount of triggered math anxiety, lower the cognitive load of the task through reducing element interactivity, and allow for a more scaffolding for abstract symbols through a pictorial representation bridge. To test the effectiveness of population diagrams, we created two versions of a population modeling lesson plan: one version taught using diagrams then equations, while the other taught using purely equations. We also designed practice and assessment questions that tested calculation and model-building ability. We assessed math anxiety, scientific reasoning ability, and math ability at the beginning of the semester and state anxiety, effort of tasks, and difficulty of tasks during each lesson. Over 200 students from a non-major biology course were randomly assigned to each group, and all were given a pre-assessment, four lessons, a practice test, and a unit test on population modeling. Our findings show that while the addition of pictorial models to the traditional pedagogy did not have a significant effect on exponential and logistic growth model mastery, students that were exposed to predator-prey diagrams were more able to create a new model for a three-level predator-prey interaction than students that were only given traditional pedagogy. In addition, students who were exposed to predator-prey interaction diagrams before they derived equations reported a lower cognitive load than students who were only exposed to equations. Although diagrams were not a more helpful calculation tool for students than traditional equations, using population diagrams before to equation derivation may help improve student mastery of growth model creation.

Denna kvalitativa studie genomfördes med syftet att bidra till lärares didaktiska resonemang och planering kring återkoppling inom matematik. Återkoppling inom matematik kan exempelvis vara när en lärare rekommenderar strategier eller förtydligar för eleven vad hen kan och vad nästa mål är (Hattie & Timperley, 2007). I studien undersöks återkoppling utifrån ett socialkonstruktivistiskt perspektiv, vilket innebär en kunskapssyn som antar att individer lär sig och uppfattar olika saker baserat på tidigare erfarenheter (Patel & Davidson, 2019; Säljö, 2015). Detta teoretiska ramverk möjliggjorde synliggörandet av hur återkopplingsinnehåll kan uppfattas utifrån olika perspektiv: lärarens didaktiska resonemang, det praktiska utförandet och elevernas upplevelse. I studien synliggörs också vilket återkopplingsinnehåll som kan identifieras i ett matematikklassrum för årskurs två. Observationer och intervjuer av lärare och elever på en grundskola i Norrbotten antyder på att lärarens resonemang inte alltid stämmer överens med vad som praktiskt sker i klassrummet och hur eleverna uppfattar återkopplingen. Däremot finns det många fall då uppfattningen ur de olika perspektiven stämmer överens. Visst återkopplingsinnehåll verkar förekomma oftare än annat, och frekvensen i vilket innehåll som förekommer stämmer inte helt överens med tidigare forskning som delvis visar på att återkopplingsinnehåll relaterat till vart elever befinner sig just nu verkar vara vanligast förekommande (Brooks et al., 2019a). / This qualitative study was carried out with the aim of contributing to teachers’ didactic reasoning and planning regarding feedback in mathematics. Examples of feedback in mathematics can be when the teacher recommends strategies or clarifies where the pupil is compared to a learning goal (Hattie & Timperley, 2007). The study examines feedback with a social constructivist theoretical view of knowledge, which assumes that individuals learn and perceive the world in different ways based on previous experiences (Patel & Davidson, 2019; Säljö, 2015). This theoretical perspective allowed the study to research how feedback can be perceived from different perspectives: the teacher’s didactic reasoning, the practical execution, and the students’ experience. The study also highlights which content of feedback can be identified in a year two classroom. Observations and interviews of teachers and students at a primary school in northern Sweden suggests that the teacher’s reasoning does not always agree with what happens in the classroom and how the students perceive the feedback. However, there are also cases where the different perspectives do perceive the feedback in the same way. Some feedback content seems to occur more often than others, and the frequency that the different contents of feedback are used does not fully agree with previous research. Brooks et al. (2019a) suggests that feedback regarding where the students are right now in their process is the most common in their study, that was not the case in the current study.

In this confirmatory factor analysis, factors previously identified to explain the variability in Middle School Mathematics Teachers’ perception of the Common Core State Standards of Mathematics were considered as factors hypothesized to effect high school math teachers’ perceptions of challenging math tasks (CMTs). The factor of student characterization (i.e., disposition, academic preparation, and student behavior) was additionally considered as a factor hypothesized to explain teachers’ perceptions of CMTs, as well as site-based variables (i.e., curriculum, assessment and evaluation, professional development, and collaboration). In addition, teachers’ understanding of the importance of the mathematical practice standards and teacher familiarity with enacting CMTs were factors considered in the model. The original septenary factor structure was modified and good model fit was achieved. In addition to the confirmatory factor analysis model which provides a structure for considering teachers perceptions of CMTs, descriptive statistics are presented from the survey developed that captured teachers’ perceptions of CMTs relative to their sites.