In the fall of 2018, programming was implemented in the swedish curriculum and then became a new element in mathematics education for grades 1-3. Teachers who took their degree before the implementation, lacks education in programming and there is interest in finding out how teaching about programming is conducted since it became part of the curriculum. The purpose of this study was to contribute with knowledge about how teachers have implemented programming in their teaching even though they lack education in it. Four semi-structured interviews have been conducted where the data from the interviews has been analyzed from Mathematical Knowledge for Teaching. The result shows that teachers without education in programming find it difficult to plan instruction in programming by themselves. In the teaching of programming the teachers focus on the central concepts in programming and that the programming should interest the students. It was difficult for teachers to assess the students in programming and the only assessment that teachers make is the formative assessment. / Sammanfattning Hösten 2018 implementerades programmering i den svenska läroplanen och blev då ett nytt moment inom matematikundervisningen för årskurs 1-3. Lärare som innan detta tog sin lärarexamen saknar utbildning inom programmering och det finns intresse att ta reda på hur undervisningen kring programmering bedrivs sedan det blev en del av läroplanen. Syftet med denna studie var att bidra med kunskap om hur lärare har implementerat programmering i sin undervisning trots att de saknar utbildning inom det. Fyra stycken semistrukturerade intervjuer har gjorts där datan från intervjuerna har analyserats utifrån Mathematical Knowledge for Teaching. Resultatet visar på att lärare utan utbildning inom programmering har svårigheter att på egen hand planera undervisning i programmering. Under genomförandet av undervisningen fokuserar lärarna på att befästa centrala begrepp inom programmering och att väcka ett intresse hos eleverna. Det upplevdes svårt för lärarna att bedöma eleverna inom programmering och den enda bedömning som lärarna gör är den formativa bedömningen.

Submitted by Liliane Ferreira (ljuvencia30@gmail.com) on 2018-03-12T11:49:00Z No. of bitstreams: 2 Dissertação - Joana D'Arc dos Santos Gomes - 2017.pdf: 4274557 bytes, checksum: 79355cdc4aa4977721058571e98ed0bf (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-03-12T14:18:50Z (GMT) No. of bitstreams: 2 Dissertação - Joana D'Arc dos Santos Gomes - 2017.pdf: 4274557 bytes, checksum: 79355cdc4aa4977721058571e98ed0bf (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-03-12T14:18:50Z (GMT). No. of bitstreams: 2 Dissertação - Joana D'Arc dos Santos Gomes - 2017.pdf: 4274557 bytes, checksum: 79355cdc4aa4977721058571e98ed0bf (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-08-28 / The present research, entitled "1, 2, beans and rice ...": the mathematical knowledge in Infantile Education, is linked to the research line "Training, Teaching Professionalization and Educational Work", of the Graduate Program in Education, Faculty of Education of the Federal University of Goiás (FE/UFG). It also includes the project "Public Policies and Education of Children in Goiás: history, conceptions, projects and practices", developed by the Center for Studies and Research of Childhood and its Education in Different Contexts (Nepiec) of FE/UFG. It was understood that mathematics is a human and cultural production present in the life of children since its birth and also in the institutions of Infantile Education, which are configured as a privileged locus of human formation, enabling the insertion of children in culture through scientific instruments and knowledge. Based on these premises, the way mathematical knowledge is present in Infantile Education was investigated, in order to understand the conceptions around this knowledge, and the situations in which it is approached in the institutions. Based on historical-dialectical materialism, a theoretical and empirical research was carried out involving teachers, educational agents and children of the municipal education network of Senador Canedo/GO. For the empirical realization of the research, different methodological procedures were used, such as: questionnaires, observations, dialogues, records in photographic field journals and with recorders. It was observed that mathematics is present in the institutions of Infantile Education in various situations, passing through pedagogical practice, through the actions and interactions of children and teachers. However, it was considered that these situations did not involve children in significant moments of mathematical learning, limiting them to everyday experiences and actions with mathematics. It was understood that situations with mathematical knowledge in Infantile need to enable children to understand the relationships, uses and social functions of this knowledge, expanding and systematizing it. In this sense, mathematical knowledge, in the pedagogical practice of the first stage of Basic Education, must go beyond everyday experiences and contacts, considering that, limited to this, it can lead the child to the instrumental and utilitarian knowledge of mathematics. Thus, it is fundamental to involve children in situations that lead them to reflect theoretically on mathematics, so that they can form concepts. / A presente pesquisa, intitulada “1, 2, feijão com arroz...”: o conhecimento matemático na Educação Infantil, se vincula à linha de pesquisa “Formação, Profissionalização Docente e Trabalho Educativo”, do Programa de Pós-Graduação em Educação, da Faculdade de Educação da Universidade Federal de Goiás (FE/UFG). Compõe, ainda, o projeto “Políticas Públicas e Educação da Infância em Goiás: história, concepções, projetos e práticas”, desenvolvido pelo Núcleo de Estudos e Pesquisas da Infância e sua Educação em Diferentes Contextos (Nepiec) da FE/UFG. Compreendeu-se que a matemática é uma produção humana e cultural presente na vida das crianças desde o seu nascimento e, também, nas instituições de Educação Infantil, que se configuram como lócus privilegiado de formação humana, possibilitando a inserção das crianças na cultura por meio dos instrumentos e conhecimentos científicos. Com base nessas premissas, investigou-se como o conhecimento matemático está presente na Educação Infantil, com o propósito de compreender as concepções em torno desse conhecimento, e as situações em que ele é abordado nas instituições. Baseado no materialismo histórico-dialético, realizou-se uma pesquisa teórica e empírica envolvendo professoras, agentes educativas e crianças da rede municipal de educação do município de Senador Canedo/GO. Para a realização da etapa empírica da pesquisa, utilizaram-se diferentes procedimentos metodológicos, tais como: questionários, observações, diálogos, registros em diários de campo fotográficos e com gravadores. Observou-se que a matemática está presente nas instituições de Educação Infantil em diversas situações, perpassando pela prática pedagógica, pelas ações e interações das crianças e professoras. Todavia, considerou-se que essas situações não envolveram as crianças em momentos significativos de aprendizagem matemática, limitando-as a experiências e ações cotidianas com a matemática. Entendeu-se que as situações com o conhecimento matemático na Educação Infantil necessitam possibilitar às crianças compreenderem as relações, os usos e as funções sociais deste conhecimento, ampliando-o e sistematizando-o. Neste sentido, o conhecimento matemático, na prática pedagógica da primeira etapa da Educação Básica, precisa ir além de experiências e contatos cotidianos, tendo em vista que, se limitando a isso, pode levar a criança ao conhecimento instrumental e utilitarista da matemática. Assim, faz-se fundamental envolver as crianças em situações que as levem a refletir teoricamente sobre a matemática, para que assim possam formar conceitos.

Submitted by Jorge Silva (jorgelmsilva@ufrrj.br) on 2018-02-27T17:45:04Z No. of bitstreams: 1 2017 - Jos?lio Rodrigues Ramos.pdf: 3173266 bytes, checksum: 01a74160ed6c5964165f996d2c5b2d03 (MD5) / Made available in DSpace on 2018-02-27T17:45:16Z (GMT). No. of bitstreams: 1 2017 - Jos?lio Rodrigues Ramos.pdf: 3173266 bytes, checksum: 01a74160ed6c5964165f996d2c5b2d03 (MD5) Previous issue date: 2017-06-12 / Agriculture is one of the activities that has impacted the environment more current day; Producing food in ways that reduce the impact of nature is a challenge to be overcome. The agroforestry system is an alternative of agricultural production associated to the cultivation of trees that reduce the devastation of nature. Through this research, possibilities of minimizing environmental impacts in agriculture were studied, based on the use of mathematical knowledge. This research has a qualitative approach, initially consisted of the application of questionnaires with open and closed questions to ten teachers and twenty students of a Technical Course in Agropecu?ria Integrated to High School in Par? Federal Institute of Education, Science and Technology, Marab? Rural Campus. During the development of the research several educational practices were carried out; In these activities, the students participated actively and in the end the action and its importance in the agricultural context was reassessed, always trying to enable those involved to perceive the importance of the knowledge built in the school in the daily activities. The objective was to investigate the view of both regarding the importance of educational practices developed in the agricultural context and the use of mathematical knowledge to reduce the damage caused to nature, particularly the agroforestry system. The results point to the importance of mathematics contents, articulated with the other areas of the curriculum, in the search for alternatives that reduce the environmental impacts on agricultural activity. / A agricultura ? uma das atividades que mais tem impactado o meio ambiente nos dias atuais. Produzir alimentos de forma que reduza o impacto causado a natureza ? um desafio a ser superado. O sistema agroflorestal, ? uma alternativa de produ??o agr?cola associada ao cultivo de ?rvores que reduzem a devasta??o da natureza. Atrav?s desta pesquisa, foram estudadas possibilidades de minimizar os impactos ambientais na agricultura, a partir do uso do conhecimento matem?tico. Esta pesquisa tem abordagem qualitativa, consistiu inicialmente na aplica??o de question?rios com perguntas abertas e fechadas a dez docentes e vinte discentes de um Curso T?cnico em Agropecu?ria Integrado ao Ensino M?dio do Instituto Federal de Educa??o, Ci?ncia e tecnologia do Par?, Campus Rural de Marab?. Durante o desenvolvimento da pesquisa v?rias pr?ticas educativas foram realizadas; nessas atividades os estudantes participavam ativamente e ao final foi reavaliada a a??o e a sua import?ncia no contexto agr?cola, procurando sempre possibilitar que os envolvidos percebessem a import?ncia dos conhecimentos constru?dos na escola nos afazeres do cotidiano. O objetivo foi investigar a vis?o de ambos em rela??o a import?ncia de pr?ticas educativas, desenvolvidas no contexto agr?cola, e o uso dos conhecimentos matem?ticos para a redu??o dos danos causados ? natureza, em particular ao sistema agroflorestal. Os resultados apontam para a import?ncia dos conte?dos de matem?tica, articulado com as demais ?reas do curr?culo, na busca de alternativas que reduzam os impactos ambientais na atividade agr?cola.

Submitted by Celso Magalhaes (celsomagalhaes@ufrrj.br) on 2018-03-14T16:34:36Z No. of bitstreams: 1 2016 - Dejildo Roque de Brito.pdf: 1304009 bytes, checksum: 003cb775c72bef034b53d252af97ad64 (MD5) / Made available in DSpace on 2018-03-14T16:34:36Z (GMT). No. of bitstreams: 1 2016 - Dejildo Roque de Brito.pdf: 1304009 bytes, checksum: 003cb775c72bef034b53d252af97ad64 (MD5) Previous issue date: 2016-11-16 / This dissertation is a research work in a agricultural community in the municipality of Porto Grande, in the state of Amap? in Brazil. The research aimed to investigate the produced knowledge and practices and practiced by farmers in their working practice and the relationship of these with the educated knowledge. We propose the use of Ethnomathematics as a form of reflection on the activities of this social group. Data collected from visits in loci surveyed treat the mathematical methods used by these groups of workers and the application possibilities of these in the classroom. The methodology used for this research is a qualitative approach. We discuss the work of the farmers in that community. We interviewed farm workers in their working environment and analyzed the existing mathematical knowledge in their work activities. We present two schools of Macap? some of the problems dealt with farmers to analyze the content or not schooled students facing such problems. We realize that students have difficulties to solve problems because they can not relate them to the everyday agricultural activities. / Esta disserta??o ? um trabalho de pesquisa desenvolvido em uma Comunidade Agr?cola localizada no munic?pio de Porto Grande, no Estado do Amap?, no Brasil. A pesquisa teve como objetivo principal investigar os saberes e fazeres produzidos e praticados por agricultores em sua pr?tica laboral e a rela??o desses com os conhecimentos escolarizados. Propomos a utiliza??o da Etnomatem?tica como uma forma de reflex?o sobre as atividades desse grupo social. Os dados coletados nas visitas realizadas nos l?cus pesquisados tratam dos m?todos matem?ticos utilizados por esses grupos de trabalhadores e as possibilidades de aplica??o desses em sala de aula. A metodologia utilizada para a realiza??o desta pesquisa tem uma abordagem qualitativa. Discorremos sobre o trabalho desenvolvido pelos agricultores na referida comunidade. Entrevistamos trabalhadores agr?colas em seu ambiente de trabalho e analisamos os conhecimentos matem?ticos existentes em suas atividades laborais. Apresentamos em duas escolas de Macap? alguns dos problemas tratados com os agricultores para analisarmos os conte?dos escolarizados ou n?o dos alunos diante de tais problemas. Percebemos que os alunos t?m dificuldades para solucionar os problemas por n?o conseguirem relacionar os mesmos com as atividades agr?colas cotidianas

This study investigated how student teachers used their mathematical knowledge for teaching and pedagogical knowledge to design and modify mathematical tasks. It also examined the relationship between teacher knowledge and the cognitive demands of a task. The study relied heavily on the framework in Hill, Ball, and Shilling (2008), which describes the different domains of knowledge in mathematical knowledge for teaching, and the framework on the cognitive demands of mathematical tasks in Stein, Smith, Henningsen, and Silver (2000). Results of the study indicated that the student teachers used their common content knowledge when they lacked sufficient knowledge in other domains, especially specialized content knowledge, to perform a particular job of teaching. There was often a decrease in the cognitive demands of a task when it was modified by the student teachers. These drops were often associated with a lack of specialized content knowledge.

This thesis concerns teaching in mathematics teacher education and is based on the implementation of a learning study at teacher training. The overall purpose was to investigate in what way teacher training could facilitate and improve student teachers’ Mathematical Knowledge for Teaching (MKT). In the learning study design, MKT was conceptualized as an object of learning with a meta-character, which meant that it was applicable to and transferable between different content areas of mathematics. This made it possible to vary the mathematical content between lessons but to keep the object of learning constant. Four critical features of the object of learning were found, giving insight in some of the problems related to teacher education. Student teachers had to be able to formulate proper aims for a lesson and to give detailed descriptions of elements of MKT for coherence in their MKT to occur. A focus on student teachers’ role as mathematics teachers had to be established and finally, sufficient mathematical knowledge was found to be a prerequisite for their MKT to develop. The study shows that enactment of these critical features improved the teaching by the teacher educators, which in its turn improved the student teachers’ learning with regard to MKT. The study also indicates that the prescribed design is worth considering for future collaborative efforts of improving teaching where other objects of learning with a similar meta-character are involved.

Knowledge of curriculum is a significant component of mathematical knowledge for teaching. However, clearly understanding knowledge of curriculum requires further refinement and substantial research. This study consists of three papers that aim to explore prospective and practicing middle school teachers’ Knowledge of Curriculum for Teaching Simple Algebraic Equations (KCTE). The first paper reviews trends in and the evolution of standards and policies and synthesizes significant findings of research on mathematics curriculum and Knowledge of Curriculum for Mathematics Teaching (KCMT). Through this synthesis, the paper examines policy changes and research relevant to mathematics curriculum and KCMT and anticipates future research approaches and topics that show promise. Building on the context provided by the first paper, the following two papers investigate KCTE from the perspectives of prospective and practicing middle school mathematics teachers. For the second paper, data was collected from a convenience sample of 58 prospective middle school mathematics teachers and a subsample of six participants. The findings of this study identify patterns of key mathematical topics in the teaching sequence of simple algebraic equations, compare the participants’ sequences with experts’, reveal participants’ orientations toward KCTE, draw connections between participants’ KCTE and their knowledge of content and teaching, and establish relationships between participants’ KCTE and their knowledge of content and students. Four middle school mathematics teachers participated in the third study. The results indicate that state-level intended curriculum is the most prevailing component of participants’ KCTE. Furthermore, from a vertical view of curriculum, participants’ awareness of their students’ lack of basic mathematical knowledge impacted their KCTE. The paper also identifies the role of the state-level intended curriculum in participants’ KCTE, alternative approaches to curriculum implementation that participants used to respond to the multiple intelligences of their students, and the participants’ lack of lateral curriculum knowledge in KCTE. Together, these three papers offer a closer look at KCMT with a focus on simple algebraic equations. This research broadens our understanding of prospective and practicing middle school teachers’ KCMT and discusses implications for professional development.

abstract: Teachers must recognize the knowledge they possess as appropriate to employ in the process of achieving their goals and objectives in the context of practice. Such recognition is subject to a host of cognitive and affective processes that have thus far not been a central focus of research on teacher knowledge in mathematics education. To address this need, this dissertation study examined the role of a secondary mathematics teacher’s image of instructional constraints on his enacted subject matter knowledge. I collected data in three phases. First, I conducted a series of task-based clinical interviews that allowed me to construct a model of David’s mathematical knowledge of sine and cosine functions. Second, I conducted pre-lesson interviews, collected journal entries, and examined David’s instruction to characterize the mathematical knowledge he utilized in the context of designing and implementing lessons. Third, I conducted a series of semi-structured clinical interviews to identify the circumstances David appraised as constraints on his practice and to ascertain the role of these constraints on the quality of David’s enacted subject matter knowledge. My analysis revealed that although David possessed many productive ways of understanding that allowed him to engage students in meaningful learning experiences, I observed discrepancies between and within David’s mathematical knowledge and his enacted mathematical knowledge. These discrepancies were not occasioned by David’s active compensation for the circumstances and events he appraised as instructional constraints, but instead resulted from David possessing multiple schemes for particular ideas related to trigonometric functions, as well as from his unawareness of the mental actions and operations that comprised these often powerful but uncoordinated cognitive schemes. This lack of conscious awareness made David ill-equipped to define his instructional goals in terms of the mental activity in which he intended his students to engage, which further conditioned the circumstances and events he appraised as constraints on his practice. David’s image of instructional constraints therefore did not affect his enacted subject matter knowledge. Rather, characteristics of David’s subject matter knowledge, namely his uncoordinated cognitive schemes and his unawareness of the mental actions and operations that comprise them, affected his image of instructional constraints. / Dissertation/Thesis / Doctoral Dissertation Mathematics Education 2015

abstract: In this mixed-methods study, I examined the relationship between professional development based on the Common Core State Standards for Mathematics and teacher knowledge, classroom practice, and student learning. Participants were randomly assigned to experimental and control groups. The 50-hour professional development treatment was administered to the treatment group during one semester, and then a follow-up replication treatment was administered to the control group during the subsequent semester. Results revealed significant differences in teacher knowledge as a result of the treatment using two instruments. The Learning Mathematics for Teaching scales were used to detect changes in mathematical knowledge for teaching, and an online sorting task was used to detect changes in teachers' knowledge of their standards. Results also indicated differences in classroom practice between pairs of matched teachers selected to participate in classroom observations and interviews. No statistical difference was detected between the groups' student assessment scores using the district's benchmark assessment system. This efficacy study contributes to the literature in two ways. First, it provides an evidence base for a professional development model designed to promote effective implementation of the Common Core State Standards for Mathematics. Second, it addresses ways to impact and measure teachers' knowledge of curriculum in addition to their mathematical content knowledge. The treatment was designed to focus on knowledge of curriculum, but it also successfully impacted teachers' specialized content knowledge, knowledge of content and students, and knowledge of content and teaching. / Dissertation/Thesis / Ph.D. Curriculum and Instruction 2013

Dissertação(mestrado) - Universidade Federal do Rio Grande, Programa de Pós- Graduação em Educação em Ciências: Química da Vida e Saúde, Instituto de Educação, 2012. / Submitted by EDUARDO PENA (edupenaa@hotmail.com) on 2012-11-23T15:50:07Z No. of bitstreams: 1 PROFESSORES DOS ANOS INICIAIS EXPERIÊNCIAS COM O MATERIAL CONCRETO PARA O ENSINO DE MATEMÁTICA.pdf: 1950437 bytes, checksum: 244684d23fb58923aaf678627305930d (MD5) / Approved for entry into archive by Bruna Vieira(bruninha_vieira@ibest.com.br) on 2012-11-28T21:03:27Z (GMT) No. of bitstreams: 1 PROFESSORES DOS ANOS INICIAIS EXPERIÊNCIAS COM O MATERIAL CONCRETO PARA O ENSINO DE MATEMÁTICA.pdf: 1950437 bytes, checksum: 244684d23fb58923aaf678627305930d (MD5) / Made available in DSpace on 2012-11-28T21:03:27Z (GMT). No. of bitstreams: 1 PROFESSORES DOS ANOS INICIAIS EXPERIÊNCIAS COM O MATERIAL CONCRETO PARA O ENSINO DE MATEMÁTICA.pdf: 1950437 bytes, checksum: 244684d23fb58923aaf678627305930d (MD5) Previous issue date: 2012 / O presente trabalho investiga o uso de Materiais Concretos no que tange ao ensino da Matemática, por professores dos Anos Iniciais do Ensino Fundamental, em três municípios pólos da Universidade Federal do Rio Grande – FURG. O objetivo da pesquisa é compreender as formas como os professores se apropriam dos Materiais Concretos para ensinar Matemática nas primeiras etapas da escolarização. Os registros foram feitos por meio dos seguintes instrumentos: filmagem dos encontros, anotações no diário de campo, diálogo nos fóruns e postagem de tarefas no Ambiente Virtual. Como método para análise das experiências registradas foi utilizada a metodologia da Análise Textual Discursiva (ATD) e, a partir desse processo, foram identificadas duas categorias denominadas: Significação do Material Concreto a partir do experienciar e (Re)significação da prática educativa com a experimentação do Material Concreto. Dessa maneira, o fenômeno investigado é compreendido com base na elaboração de dois metatextos que provem das categorias e que intitulamos como: Significação do Material Concreto no processo de ação reflexão e Prática docente e os saberes matemáticos: uma experiência com o Material Concreto. O primeiro versa sobre as possibilidades apontadas pelos professores na utilização de Materiais Concretos para ensinar Matemática. Os docentes explicitam que estes recursos pedagógicos, ao envolverem a ludicidade, possibilitam a curiosidade, a inventividade e a descoberta de estratégias de soluções pelos estudantes. O segundo metatexto aborda a (re)significação da prática do professor ao experienciar os Materiais Concretos em suas ações pedagógicas. Estes profissionais apontam que a experiência com estes Materiais aprimorou sua prática de ensino, o que os auxilia nas sistematizações conceituais voltadas ao contexto da Matemática. Assim, foi possível concluir que a mudança no ensino desta Ciência nos Anos Iniciais não depende exclusivamente do Material utilizado, mas se vincula às teorias subjacentes à prática de ensino, bem como relaciona-se ao modo como os Materiais subsidiam essas teorias nos contextos reais de ensino e de aprendizagem. / The present study investigates the use of Concrete Materials related to Mathematics teaching, by teachers of the Initial Years of Elementary Education in three cities pole of the Federal University of Rio Grande - FURG. The objective of this research is to understand the ways in which teachers appropriate the Concrete Materials in order to teach Mathematics in the early stages of schooling. The recordings were made through the following instruments: filming of meetings, notes in field diary, dialogue in the forums and tasks posting in Virtual Environment. As analysis method of the experiments recorded was used the methodology of Discourse Textual Analysis (DTA) and, from this process, were identified two categories named: Significance of Concrete Material from the experiencing and (Re)signification of educational practice with the experimentation of Material Concrete. Thus, the investigated phenomenon is comprehended based on the elaboration of two metatexts which prove of the categories and that we entitled as: Significance of Concrete Material in the action reflection process and Teaching practice and mathematical knowledge: an experience with Concrete Materials. The first deals with the possibilities pointed out by teachers in the use of Concrete Materials for teaching Mathematics. The teachers explain that these pedagogical resources, by involving playfulness, allow the curiosity, inventiveness and discovery of solution strategies by students. The second metatext addresses the (re)signification of teacher practice by the experience of Concrete Materials in pedagogical actions. These professionals point out that the experience with these Materials has improved their teaching practice, which assists in the conceptual systematizations focused on the context of Mathematics. Therefore, it was concluded that the change in this Science teaching in Initial Years does not depend exclusively on the Material used, but is linked to the theories underlying the educational practice as well as relates to how the Materials subsidize these theories in real contexts of teaching and learning.