In this investigation, two schools - a control school and an experimental school – were compared in terms of learner performance in two traditional grade 11 mathematics tests, namely the pre-intervention test and the post-intervention test. Both schools completed the two tests simultaneously. Educators saw both tests before intervention. In the experimental school, four grade 11 mathematics classes were studied. The four classes were given worksheets that complied with an open-ended approach (OEA) to mathematics teaching and learning for learners to work independently on, with the teacher only facilitating. The learner-centredness expressed in the OEA complied with learner-centredness as envisaged by the National Curriculum Statement (NCS), and was predominantly constructivist in character. Throughout the five-month intervention, the author observed proceedings in two of the four classes in the experimental school, ensuring that questions the teacher asked complied with the OEA. The two classes would be referred to as monitored classes. The other two classes at the experimental school worked on the worksheet, with the teacher having been briefed about what was expected of the learners using the worksheet -basically that the learners would have to take own initiatives in solving the mathematics problems with minimal teacher intervention. The two grade 11 mathematics classes were monitored, but not as frequently as the monitored classes. The classes will be referred to as unmonitored classes. At the control school the educators followed their usual (traditional) teaching approach. Both the experimental and control schools followed the same grade 11 mathematics work schedule. The educators in the control school taught without any interference from the author, but the classes at the control school were occasionally observed by the author. In addition to the intervention comparison, the author also gathered qualitative information about participating educators' and learners' experiences and opinions about the OEA at the experimental school by using interviews. The results of the pre-intervention test showed no statistical difference between the experimental and control school performance, meaning that the learners from both schools were of comparable pre-requisite knowledge. In the post-intervention test, learners from the two monitored classes meaningfully outperformed those from the two unmonitored experimental classes and those from the control school. However, there was no significant difference in performance between learners from the two unmonitored classes and those from control school, The study concludes that the appropriate OEA intervention was responsible for the good results of the monitored classes., and then uses the gathered qualitative information to design a model for the successful implementation of' OEA in mathematics classes. / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2010.

In this investigation, two schools - a control school and an experimental school – were compared in terms of learner performance in two traditional grade 11 mathematics tests, namely the pre-intervention test and the post-intervention test. Both schools completed the two tests simultaneously. Educators saw both tests before intervention. In the experimental school, four grade 11 mathematics classes were studied. The four classes were given worksheets that complied with an open-ended approach (OEA) to mathematics teaching and learning for learners to work independently on, with the teacher only facilitating. The learner-centredness expressed in the OEA complied with learner-centredness as envisaged by the National Curriculum Statement (NCS), and was predominantly constructivist in character. Throughout the five-month intervention, the author observed proceedings in two of the four classes in the experimental school, ensuring that questions the teacher asked complied with the OEA. The two classes would be referred to as monitored classes. The other two classes at the experimental school worked on the worksheet, with the teacher having been briefed about what was expected of the learners using the worksheet -basically that the learners would have to take own initiatives in solving the mathematics problems with minimal teacher intervention. The two grade 11 mathematics classes were monitored, but not as frequently as the monitored classes. The classes will be referred to as unmonitored classes. At the control school the educators followed their usual (traditional) teaching approach. Both the experimental and control schools followed the same grade 11 mathematics work schedule. The educators in the control school taught without any interference from the author, but the classes at the control school were occasionally observed by the author. In addition to the intervention comparison, the author also gathered qualitative information about participating educators' and learners' experiences and opinions about the OEA at the experimental school by using interviews. The results of the pre-intervention test showed no statistical difference between the experimental and control school performance, meaning that the learners from both schools were of comparable pre-requisite knowledge. In the post-intervention test, learners from the two monitored classes meaningfully outperformed those from the two unmonitored experimental classes and those from the control school. However, there was no significant difference in performance between learners from the two unmonitored classes and those from control school, The study concludes that the appropriate OEA intervention was responsible for the good results of the monitored classes., and then uses the gathered qualitative information to design a model for the successful implementation of' OEA in mathematics classes. / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2010.

Thesis (Ph. D.)--Universidad Complutense de Madrid, 1980. / Includes bibliographical references (p. 1052-1070).

Nesta dissertação desenvolvemos e analisamos uma proposta de ensino-aprendizagem de matemática para alunos de sexta série do ensino fundamental, com base nas pesquisas e inovações realizadas no Laboratório de Estudos Cognitivos da Universidade Federal do Rio Grande do Sul (LEC/UFRGS) – com a coordenação da professora Léa da Cruz Fagundes – e nas experiências desenvolvidas no Projeto Amora do Colégio de Aplicação dessa universidade (Projeto Amora/CAp/UFRGS), todas focadas no desenvolvimento de Projetos de Aprendizagem com uso dos recursos digitais oferecidos pelas novas tecnologias de informação e comunicação e à luz da teoria psicogenética de Jean Piaget. Na proposta, alunos da sexta série do ensino fundamental desenvolvem Projetos de Aprendizagem como estratégia pedagógica das aulas de matemática e, com eles, constroem as suas aprendizagens de matemática. Por consequência, o currículo de matemática desses alunos é constituído pelas construções conceituais de matemática impulsionadas pelo desenvolvimento dos seus Projetos de Aprendizagem. Analisamos as aprendizagens de matemática dos alunos envolvidos nesta investigação e comparamos com as sequências curriculares tradicionalmente propostas para a mesma etapa escolar, concluindo que as construções conceituais de matemática via Projetos de Aprendizagem superam as listas de conteúdos tradicionalmente propostas. Analisamos, também, se a proposta contribui para uma mudança de postura e atitude dos alunos frente à matemática e à aprendizagem escolar. Concluímos que os alunos desenvolvem uma postura investigativa e passam a utilizá-la ao encarar os desafios matemáticos e que as suas atitudes são positivas, demonstrando alegria e realização ao aprender matemática Expomos, por fim algumas repercussões deste estudo, entre elas a reestruturação curricular das séries finais do ensino fundamental da Escola Municipal de Ensino Fundamental Paul Harris de São Leopoldo/RS, a qual passou a desenvolver Projetos de Aprendizagem como estratégia pedagógica vinculada a todas as áreas de conhecimento privilegiadas pela escola. Os resultados decorrentes deste estudo apresentam possibilidades de aplicação em diversas áreas de conhecimento e etapas letivas. Com o objetivo de amplificar essas repercussões, construímos um conjunto de orientações e sugestões para o desenvolvimento de Projetos de aprendizagem, o qual poderá ser utilizado por educadores sem a necessidade de recorrer a qualquer outra parte desta dissertação. / In this dissertation we developed and analyzed a proposal of mathematics teaching-learning to the sixth grade pupils of the Basic Teaching, based on the search and innovations realized in the Laboratory of Cognitive Studies of the Federal University of Rio Grande do Sul (LEC/UFRGS) – under the coordination of Professor Léa da Cruz Fagundes – and on the experiences developed by the Amora Project of the Aplicação School, of this University (Amora Project/CAp/UFRGS), all focused in the development of Learning Projects, using the digital resources offered by the new technologies of information and communication and an overall view of the psychogenetic theory of Jean Piaget. In the proposal, students of the sixth grade of the basic teaching developed Learning Projects as a Pedagogic Strategy for the mathematics classes and, with them, the students will build their own mathematics learning. Consequently, the mathematics curriculum of these students are constituted by the conceptual constructions of mathematics driven by the development of their Learning Projects. We analyzed the students’ mathematics learning involved in this investigation, and compared with the curricular sequences traditionally proposed for the same school stage, concluding that mathematics conceptual constructions by learning Projects surpass the lists of contents traditionally proposed. We also analyze, if the proposal contributes to a change of posture and attitude of the students towards mathematics and the school learning. We came to the conclusion that the pupils develop an investigative posture and start to use it while facing the mathematical challenges and that their attitudes are positive, demonstrating joy and realization while learning mathematics. Finally, we expose some repercussions of this study, like the school curriculum restructuration in the final grades of the basic teaching in the Municipal School of Fundamental Teaching – Paul Harris in São Leopoldo/RS, which started to develop Learning Projects as Pedagogic Strategy linked to all the knowledge areas privileged by the school. The results deriving from this study, presents, means of application in several areas of knowledge and school stages. With the objective to amplify these repercussions, we build a set of orientation and suggestions for the development of Learning Projects, which will be able to be used by educators without the necessity of resorting to any other part of this dissertation. / En esta tesis desarrollamos y analizamos una propuesta para la enseñanzaaprendizaje de las matemáticas para los estudiantes de sexto grado de la escuela primaria (enseñanza fundamental básica), basada en las investigaciones e innovaciones realizadas en el Laboratorio de Estudios Cognitivos de la Universidad Federal de Rio Grande do Sul (LEC/UFRGS) – con la coordinación de la profesora Léa da Cruz Fagundes – y en las experiencias desarrolladas en el proyecto Amora del Colegio de Aplicação de esta universidad. (Proyecto Amora/CAp/UFRGS), todas enfocadas en el desarrollo de Proyectos de aprendizaje con el uso de los recursos digitales que son ofrecidos por las nuevas tecnologías de Información y Comunicación y a la luz de la teoría psicogenética de Jean Piaget. En la propuesta, alumnos del sexto grado de la enseñanza primaria desarrollan Proyectos de Aprendizaje como una estrategia pedagógica de las aulas de matemáticas y, con ellos, construyen sus aprendizajes de matemática. En consecuencia, el curriculum de matemáticas de estos alumnos se constituye por las construcciones conceptuales de matemática impulsadas por el desarrollo de sus Proyectos de Aprendizaje. Analizamos los aprendizajes de matemáticas de los estudiantes implicados en esta investigación, y comparamos con las secuencias curriculares propuestas tradicionalmente para el mismo nivel escolar, concluyendo que las construcciones conceptuales de matemática por la vía de Proyectos de Aprendizaje superan a las listas de contenidos tradicionalmente propuestos. También hemos analizado si la propuesta contribuyó para un cambio de postura y actitud de los alumnos frente a la matemática y al aprendizaje escolar. Se concluyó que los estudiantes desarrollan una actitud de investigación y empezaron a usarla para hacer frente a los desafíos matemáticos, y sus actitudes son positivas demostrando alegría y realización con el aprendizaje de las matemáticas. Por fin, exponemos algunas repercusiones de este estudio, tales como la reestructuración curricular de los últimos grados de La enseñanza primaria de La Escuela Municipal de Educación Fundamental Paul Harris de São Leopoldo/RS, que pasó a desarrollar Proyectos de Aprendizaje como estrategia pedagógica vinculada a todas las áreas de conocimiento privilegiadas por la escuela. Los resultados consecuentes de este estudio presentan posibilidades de aplicación en diversas áreas de conocimiento y etapas lectivas. Con el objetivo de amplificar esas repercusiones, construimos un conjunto de orientaciones y sugestiones para el desarrollo de Proyectos de aprendizaje, que podrá ser utilizado por educadores sin la necesidad de recurrir a cualquier otra parte de esta disertación.

Nesta dissertação desenvolvemos e analisamos uma proposta de ensino-aprendizagem de matemática para alunos de sexta série do ensino fundamental, com base nas pesquisas e inovações realizadas no Laboratório de Estudos Cognitivos da Universidade Federal do Rio Grande do Sul (LEC/UFRGS) – com a coordenação da professora Léa da Cruz Fagundes – e nas experiências desenvolvidas no Projeto Amora do Colégio de Aplicação dessa universidade (Projeto Amora/CAp/UFRGS), todas focadas no desenvolvimento de Projetos de Aprendizagem com uso dos recursos digitais oferecidos pelas novas tecnologias de informação e comunicação e à luz da teoria psicogenética de Jean Piaget. Na proposta, alunos da sexta série do ensino fundamental desenvolvem Projetos de Aprendizagem como estratégia pedagógica das aulas de matemática e, com eles, constroem as suas aprendizagens de matemática. Por consequência, o currículo de matemática desses alunos é constituído pelas construções conceituais de matemática impulsionadas pelo desenvolvimento dos seus Projetos de Aprendizagem. Analisamos as aprendizagens de matemática dos alunos envolvidos nesta investigação e comparamos com as sequências curriculares tradicionalmente propostas para a mesma etapa escolar, concluindo que as construções conceituais de matemática via Projetos de Aprendizagem superam as listas de conteúdos tradicionalmente propostas. Analisamos, também, se a proposta contribui para uma mudança de postura e atitude dos alunos frente à matemática e à aprendizagem escolar. Concluímos que os alunos desenvolvem uma postura investigativa e passam a utilizá-la ao encarar os desafios matemáticos e que as suas atitudes são positivas, demonstrando alegria e realização ao aprender matemática Expomos, por fim algumas repercussões deste estudo, entre elas a reestruturação curricular das séries finais do ensino fundamental da Escola Municipal de Ensino Fundamental Paul Harris de São Leopoldo/RS, a qual passou a desenvolver Projetos de Aprendizagem como estratégia pedagógica vinculada a todas as áreas de conhecimento privilegiadas pela escola. Os resultados decorrentes deste estudo apresentam possibilidades de aplicação em diversas áreas de conhecimento e etapas letivas. Com o objetivo de amplificar essas repercussões, construímos um conjunto de orientações e sugestões para o desenvolvimento de Projetos de aprendizagem, o qual poderá ser utilizado por educadores sem a necessidade de recorrer a qualquer outra parte desta dissertação. / In this dissertation we developed and analyzed a proposal of mathematics teaching-learning to the sixth grade pupils of the Basic Teaching, based on the search and innovations realized in the Laboratory of Cognitive Studies of the Federal University of Rio Grande do Sul (LEC/UFRGS) – under the coordination of Professor Léa da Cruz Fagundes – and on the experiences developed by the Amora Project of the Aplicação School, of this University (Amora Project/CAp/UFRGS), all focused in the development of Learning Projects, using the digital resources offered by the new technologies of information and communication and an overall view of the psychogenetic theory of Jean Piaget. In the proposal, students of the sixth grade of the basic teaching developed Learning Projects as a Pedagogic Strategy for the mathematics classes and, with them, the students will build their own mathematics learning. Consequently, the mathematics curriculum of these students are constituted by the conceptual constructions of mathematics driven by the development of their Learning Projects. We analyzed the students’ mathematics learning involved in this investigation, and compared with the curricular sequences traditionally proposed for the same school stage, concluding that mathematics conceptual constructions by learning Projects surpass the lists of contents traditionally proposed. We also analyze, if the proposal contributes to a change of posture and attitude of the students towards mathematics and the school learning. We came to the conclusion that the pupils develop an investigative posture and start to use it while facing the mathematical challenges and that their attitudes are positive, demonstrating joy and realization while learning mathematics. Finally, we expose some repercussions of this study, like the school curriculum restructuration in the final grades of the basic teaching in the Municipal School of Fundamental Teaching – Paul Harris in São Leopoldo/RS, which started to develop Learning Projects as Pedagogic Strategy linked to all the knowledge areas privileged by the school. The results deriving from this study, presents, means of application in several areas of knowledge and school stages. With the objective to amplify these repercussions, we build a set of orientation and suggestions for the development of Learning Projects, which will be able to be used by educators without the necessity of resorting to any other part of this dissertation. / En esta tesis desarrollamos y analizamos una propuesta para la enseñanzaaprendizaje de las matemáticas para los estudiantes de sexto grado de la escuela primaria (enseñanza fundamental básica), basada en las investigaciones e innovaciones realizadas en el Laboratorio de Estudios Cognitivos de la Universidad Federal de Rio Grande do Sul (LEC/UFRGS) – con la coordinación de la profesora Léa da Cruz Fagundes – y en las experiencias desarrolladas en el proyecto Amora del Colegio de Aplicação de esta universidad. (Proyecto Amora/CAp/UFRGS), todas enfocadas en el desarrollo de Proyectos de aprendizaje con el uso de los recursos digitales que son ofrecidos por las nuevas tecnologías de Información y Comunicación y a la luz de la teoría psicogenética de Jean Piaget. En la propuesta, alumnos del sexto grado de la enseñanza primaria desarrollan Proyectos de Aprendizaje como una estrategia pedagógica de las aulas de matemáticas y, con ellos, construyen sus aprendizajes de matemática. En consecuencia, el curriculum de matemáticas de estos alumnos se constituye por las construcciones conceptuales de matemática impulsadas por el desarrollo de sus Proyectos de Aprendizaje. Analizamos los aprendizajes de matemáticas de los estudiantes implicados en esta investigación, y comparamos con las secuencias curriculares propuestas tradicionalmente para el mismo nivel escolar, concluyendo que las construcciones conceptuales de matemática por la vía de Proyectos de Aprendizaje superan a las listas de contenidos tradicionalmente propuestos. También hemos analizado si la propuesta contribuyó para un cambio de postura y actitud de los alumnos frente a la matemática y al aprendizaje escolar. Se concluyó que los estudiantes desarrollan una actitud de investigación y empezaron a usarla para hacer frente a los desafíos matemáticos, y sus actitudes son positivas demostrando alegría y realización con el aprendizaje de las matemáticas. Por fin, exponemos algunas repercusiones de este estudio, tales como la reestructuración curricular de los últimos grados de La enseñanza primaria de La Escuela Municipal de Educación Fundamental Paul Harris de São Leopoldo/RS, que pasó a desarrollar Proyectos de Aprendizaje como estrategia pedagógica vinculada a todas las áreas de conocimiento privilegiadas por la escuela. Los resultados consecuentes de este estudio presentan posibilidades de aplicación en diversas áreas de conocimiento y etapas lectivas. Con el objetivo de amplificar esas repercusiones, construimos un conjunto de orientaciones y sugestiones para el desarrollo de Proyectos de aprendizaje, que podrá ser utilizado por educadores sin la necesidad de recurrir a cualquier otra parte de esta disertación.

Nesta dissertação desenvolvemos e analisamos uma proposta de ensino-aprendizagem de matemática para alunos de sexta série do ensino fundamental, com base nas pesquisas e inovações realizadas no Laboratório de Estudos Cognitivos da Universidade Federal do Rio Grande do Sul (LEC/UFRGS) – com a coordenação da professora Léa da Cruz Fagundes – e nas experiências desenvolvidas no Projeto Amora do Colégio de Aplicação dessa universidade (Projeto Amora/CAp/UFRGS), todas focadas no desenvolvimento de Projetos de Aprendizagem com uso dos recursos digitais oferecidos pelas novas tecnologias de informação e comunicação e à luz da teoria psicogenética de Jean Piaget. Na proposta, alunos da sexta série do ensino fundamental desenvolvem Projetos de Aprendizagem como estratégia pedagógica das aulas de matemática e, com eles, constroem as suas aprendizagens de matemática. Por consequência, o currículo de matemática desses alunos é constituído pelas construções conceituais de matemática impulsionadas pelo desenvolvimento dos seus Projetos de Aprendizagem. Analisamos as aprendizagens de matemática dos alunos envolvidos nesta investigação e comparamos com as sequências curriculares tradicionalmente propostas para a mesma etapa escolar, concluindo que as construções conceituais de matemática via Projetos de Aprendizagem superam as listas de conteúdos tradicionalmente propostas. Analisamos, também, se a proposta contribui para uma mudança de postura e atitude dos alunos frente à matemática e à aprendizagem escolar. Concluímos que os alunos desenvolvem uma postura investigativa e passam a utilizá-la ao encarar os desafios matemáticos e que as suas atitudes são positivas, demonstrando alegria e realização ao aprender matemática Expomos, por fim algumas repercussões deste estudo, entre elas a reestruturação curricular das séries finais do ensino fundamental da Escola Municipal de Ensino Fundamental Paul Harris de São Leopoldo/RS, a qual passou a desenvolver Projetos de Aprendizagem como estratégia pedagógica vinculada a todas as áreas de conhecimento privilegiadas pela escola. Os resultados decorrentes deste estudo apresentam possibilidades de aplicação em diversas áreas de conhecimento e etapas letivas. Com o objetivo de amplificar essas repercussões, construímos um conjunto de orientações e sugestões para o desenvolvimento de Projetos de aprendizagem, o qual poderá ser utilizado por educadores sem a necessidade de recorrer a qualquer outra parte desta dissertação. / In this dissertation we developed and analyzed a proposal of mathematics teaching-learning to the sixth grade pupils of the Basic Teaching, based on the search and innovations realized in the Laboratory of Cognitive Studies of the Federal University of Rio Grande do Sul (LEC/UFRGS) – under the coordination of Professor Léa da Cruz Fagundes – and on the experiences developed by the Amora Project of the Aplicação School, of this University (Amora Project/CAp/UFRGS), all focused in the development of Learning Projects, using the digital resources offered by the new technologies of information and communication and an overall view of the psychogenetic theory of Jean Piaget. In the proposal, students of the sixth grade of the basic teaching developed Learning Projects as a Pedagogic Strategy for the mathematics classes and, with them, the students will build their own mathematics learning. Consequently, the mathematics curriculum of these students are constituted by the conceptual constructions of mathematics driven by the development of their Learning Projects. We analyzed the students’ mathematics learning involved in this investigation, and compared with the curricular sequences traditionally proposed for the same school stage, concluding that mathematics conceptual constructions by learning Projects surpass the lists of contents traditionally proposed. We also analyze, if the proposal contributes to a change of posture and attitude of the students towards mathematics and the school learning. We came to the conclusion that the pupils develop an investigative posture and start to use it while facing the mathematical challenges and that their attitudes are positive, demonstrating joy and realization while learning mathematics. Finally, we expose some repercussions of this study, like the school curriculum restructuration in the final grades of the basic teaching in the Municipal School of Fundamental Teaching – Paul Harris in São Leopoldo/RS, which started to develop Learning Projects as Pedagogic Strategy linked to all the knowledge areas privileged by the school. The results deriving from this study, presents, means of application in several areas of knowledge and school stages. With the objective to amplify these repercussions, we build a set of orientation and suggestions for the development of Learning Projects, which will be able to be used by educators without the necessity of resorting to any other part of this dissertation. / En esta tesis desarrollamos y analizamos una propuesta para la enseñanzaaprendizaje de las matemáticas para los estudiantes de sexto grado de la escuela primaria (enseñanza fundamental básica), basada en las investigaciones e innovaciones realizadas en el Laboratorio de Estudios Cognitivos de la Universidad Federal de Rio Grande do Sul (LEC/UFRGS) – con la coordinación de la profesora Léa da Cruz Fagundes – y en las experiencias desarrolladas en el proyecto Amora del Colegio de Aplicação de esta universidad. (Proyecto Amora/CAp/UFRGS), todas enfocadas en el desarrollo de Proyectos de aprendizaje con el uso de los recursos digitales que son ofrecidos por las nuevas tecnologías de Información y Comunicación y a la luz de la teoría psicogenética de Jean Piaget. En la propuesta, alumnos del sexto grado de la enseñanza primaria desarrollan Proyectos de Aprendizaje como una estrategia pedagógica de las aulas de matemáticas y, con ellos, construyen sus aprendizajes de matemática. En consecuencia, el curriculum de matemáticas de estos alumnos se constituye por las construcciones conceptuales de matemática impulsadas por el desarrollo de sus Proyectos de Aprendizaje. Analizamos los aprendizajes de matemáticas de los estudiantes implicados en esta investigación, y comparamos con las secuencias curriculares propuestas tradicionalmente para el mismo nivel escolar, concluyendo que las construcciones conceptuales de matemática por la vía de Proyectos de Aprendizaje superan a las listas de contenidos tradicionalmente propuestos. También hemos analizado si la propuesta contribuyó para un cambio de postura y actitud de los alumnos frente a la matemática y al aprendizaje escolar. Se concluyó que los estudiantes desarrollan una actitud de investigación y empezaron a usarla para hacer frente a los desafíos matemáticos, y sus actitudes son positivas demostrando alegría y realización con el aprendizaje de las matemáticas. Por fin, exponemos algunas repercusiones de este estudio, tales como la reestructuración curricular de los últimos grados de La enseñanza primaria de La Escuela Municipal de Educación Fundamental Paul Harris de São Leopoldo/RS, que pasó a desarrollar Proyectos de Aprendizaje como estrategia pedagógica vinculada a todas las áreas de conocimiento privilegiadas por la escuela. Los resultados consecuentes de este estudio presentan posibilidades de aplicación en diversas áreas de conocimiento y etapas lectivas. Con el objetivo de amplificar esas repercusiones, construimos un conjunto de orientaciones y sugestiones para el desarrollo de Proyectos de aprendizaje, que podrá ser utilizado por educadores sin la necesidad de recurrir a cualquier otra parte de esta disertación.

Orientador: Lourdes de la Rosa Onuchic / Resumo: O principal objetivo deste trabalho foi entender como a Avaliação para a Aprendizagem acontece, ou poderia acontecer, na Metodologia de Ensino-Aprendizagem-Avaliação de Matemática através da Resolução de Problemas. Nossa pesquisa foi amparada pelo Modelo Metodológico de Romberg-Onuchic e possui um viés qualitativo. Para alcançar o nosso objetivo, criamos um Projeto de aplicação dessa Metodologia, que fora desenvolvido no sétimo ano da Educação Básica de um colégio privado da cidade de Lisboa, em Portugal, com 24 alunos com idades entre 12 e 14 anos. O Projeto, com cinco problemas geradores, foi implementado durante o terceiro trimestre do ano letivo de 2017/2018, entre os meses de março e junho. Esses problemas foram trabalhados segundo a Metodologia de Ensino-Aprendizagem-Avaliação de Matemática através da Resolução de Problemas. O registro das aulas foi realizado através da gravação de áudios (distribuídos entre os grupos de alunos), de anotações do pesquisador em diário de campo, pelo recolhimento da produção dos alunos e pelo registro de aula produzido pela lousa eletrônica. Além disso, a pesquisa contou com o registro de algumas aulas, também por áudio, anotações e registros da lousa, e com os depoimentos espontâneos da professora titular da turma e de alguns alunos. Nossa pesquisa revelou que a Metodologia de Ensino-Aprendizagem-Avaliação de Matemática através da Resolução de Problemas pode ser utilizada como um instrumento de Avaliação para a Aprendizagem, segundo os p... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The main objective of this study was to understand how the Assessment for Learning happens, or could happen, in Methodology of Teaching-Learning- Assessment of Mathematics through Problem Solving. Our research was supported by the Romberg-Onuchic Methodological Model and has a qualitative bias. To achieve our goal, we created a Project to apply this Methodology, which was developed in the seventh year of Basic Education of a private school in the city of Lisbon, in Portugal, with 24 students aged 12 to 14 years. The project, with five generating problems, was implemented during the third quarter of the 2017/2018 school year, between March and June. These problems were worked according to the Methodology of Teaching-Learning-Assessment of Mathematics through Problem Solving. Classes were recorded by recording audios (distributed among student groups), notes by the researcher in a field diary, collecting student production and by the class record, produced by the electronic whiteboard. In addition, the research included the recording of some lessons, also by audio, notes and whiteboard records and with the spontaneous testimonials of the head teacher and some students. Our research revealed that the Methodology of Teaching-Learning-Assessment of Mathematics through Problem Solving can be used as an Assessment for Learning tool, according to the principles of the Assessment Reform Group - ARG. This assessment happens naturally during the class that uses this methodology, through... (Complete abstract click electronic access below) / Doutor

Utgångspunkten för den här litteraturstudien är det sociokulturella perspektivet där lärandet sker i samspelet med varandra. Kamratbedömning delar samma utgångspunkt. Syftet med den här litteraturstudien är att sammanställa och analysera vad forskningen säger om kamrat-bedömningens effekter på matematiklärande. Metoden som används för att få fram ett resultat är en systematisk litteraturstudie. Tjugotre forskningsstudier har kartlagts och analyserats. Resultatet visar att kamratbedömning ger positiva effekter för elevers lärande när det används i ämnet matematik. I det här arbetet delas kamratbedömningens effekter in i två teman (sociala effekter och kognitiva effekter) och fem underteman (samspel, beteende, feedback, reflektion och förståelseutveckling). Resultatet diskuteras utifrån synen på kunskap och lärande utifrån det sociokulturella perspektivet. Avslutningsvis diskuteras vidare forskning och konsekvenser för undervisningen. / The starting point of this literature study is the socio-cultural perspective where learning takes place through interaction with each other. Peer-assessment shares the same point of view. The purpose of this literature study is to compile and analyze what the research says what peer assessment has for effect on mathematics learning. The method that was used for this research is a systematic literature study. Twenty-three research studies have been mapped and analyzed. The result shows that peer tutoring gives positive effects when methods is used it in mathematics. In this study has divided effecter of peer tutoring into two themes (social effects and cognitive effects) and five subthemes (interaction, behavior, feedback, reflection and understanding development). The result is discussed from the viewpoint of knowledge and learning from the socio-cultural perspective. Finally, further research and implications for teaching are discussed.

Detta examensarbete handlar om elevers matematikinlärning och hur elevers förutsättningar till att lyckas med matematikstudierna kan stödjas utanför skolan. Alla elever har inte samma förutsättningar för att studera utanför skolan, vissa kan t.ex. få hjälp av sina föräldrar medan andra elever inte har den möjligheten. Matteboken.se är ett verktyg som erbjuder elever som studerar på högstadie- eller gymnasienivå alternativ hjälp för deras studier i matematik. Ett ytterligare syfte har således varit att undersöka hur matteboken.se fungerar som stöd för elevers matematikstudier och vilka som använder sig av detta redskap. Litteraturstudier och en enkätundersökning användes som metoder för denna studie. Utifrån ett studerandeperskektiv analyseras resultaten med hjälp av Stadlers begrepp, matematikens lärobjekt, matematiska resurser och studenten som lärande aktör. Analysen görs även utifrån teorier från tidigare forskning om nätbaserad undervisning, studier utanför skoltid, motivation att studera samt elevers självbild. Slutsatser som kan dras från undersökningen är att läraren och läroboken är för eleverna de viktigaste resurserna för deras matematikinlärning. Elever med tillgång till hjälp hemma erhåller ett högre medelbetyg än vad elever som inte får någon hjälp gör. De elever som använder matteboken.se är främst elever som läser högskoleförberedande program, elever som får hjälp hemifrån samt elever vars föräldrar har högre utbildningsnivå. Elever får hjälp och stöd genom att utnyttja de olika funktionerna på matteboken.se. Elever lär sig matematik på olika sätt och det gäller för dem själva att veta hur de bör agera för att ta till sig kunskaperna på bästa sätt. Eleverna måste alltså både lära matematik och lära hur man lär matematik. / This thesis is about students' mathematics learning and how students' opportunities to succeed with math studies can be supported outside of school. All students do not have the same opportunities to study outside of school; some may get help from their parents while other students don't have that option. Matteboken.se is a tool that offers students who are studying at lower or upper secondary level alternative means for their studies in mathematics. A further aim of this degree project has thus been to examine how matteboken.se works to support students' mathematics study and which students make use of this tool. Literature studies and a survey are used as methods of this study. From a student perspective the results are analysed by using the concepts developed by Stadler regarding mathematical learning; mathematical learning objects, mathematical resources and student acting as a learner. The analysis is also being made in regards to theories from earlier research on netbased teaching, studysituations outside of school, motivation to study and students' selfimage. Conclusions that can be drawn from the study are that students see the teacher and the textbook as the most important mathematical resources for learning. Students with access to help at home receive a higher average grade than students who do not receive any help. The students who use matteboken.se are primarily students who study college preparatory programs, students who receive assistance from home and students whose parents have a higher level of education. Students receive help and support by exploiting the various features on matteboken.se. Students learn mathematics in different ways, and it is up to them to know how they should act to absorb knowledge in the best way. Students must therefore learn mathematics as well as learn how to learn mathematics.

The contextual factors that affect effective Mathematics learner engagement patterns are due to lack of self-regulated learning and enthusiastic volitional use. An active role for Mathematics learners incorporates use of volitional strategies towards knowledge construction. Self-regulated learning is an important factor for effective learning. However the PISA (2004) survey noted the problem of deficits in cross-curricular academic competencies, which included general self-regulatory strategies. The continued poor performance of learners in mathematics in South Africa at different school levels, especially grade 9 calls for different approach to learning. This research argues that enhanced application of volitional strategies is possible and, in fact desirable if learning situations have to promote mathematics achievement in areas with a presence of traditional teaching style. The purpose of this study is to construct volition enhancing self-regulation model to improve grade 9 mathematics learner performance in rural community schools. The model suggests combining precepts from activity theory and constructivist views as basis. The cyclic learning states of pre-action, action or volition control, and pro-action phases emanating from self-regulation sequence of self-monitoring, self-evaluation and self-reflections form the key concept of the volition model. However the sustained view maintains the education system model as proposed by Howe (2004:153) that includes input, processes and output contributing towards mathematics achievement. Hence the volition model considers the characteristics of teacher, implemented curriculum, teaching and instruction among its components to advance an understanding of their influence in mathematics performance. A mixed method research design, in which quantitative and qualitative are combined to achieve the outcomes of the research problem, is chosen for this research study project to provide a purposeful research framework. The finding revealed that the overall Volition Component Inventory (VCI) in pre - / post - and retention tests displayed good reliability, acceptable communality and acceptable construct validity for the VCI questionnaire. The post-test findings using the Univariate Tests of Significance, Effect Sizes, and Powers with partial eta2 values comparing experimental and control groups indicate the intervention effect of high statistical significance suggesting that the educational intervention enhanced mathematics performance. Another findings on how the experimental and control groups compared on learner VCI fields for in pre - / post - and retention tests using Least Square means crossover design model indicate that the enhanced intervention for volition self-efficacy, emotion control, failure control and self-control pressure, energy usage, planning and initiating ability and attention control was of significant main effect. Also the findings between control and experimental group using a three way and nested ANOVA on both learner use of volition strategy use in pre - / post – and retention test indicate pre-test to post-test, a sharp increasing effect of intervention. Hence the results revealed that it is possible to support volition mode of self-regulation competencies and mathematical achievement by self-regulation intervention within regular mathematics lessons of grade 9 learners. Furthermore the findings from the quantitative and qualitative data-analysis and interpretations, and literature review, guided the researcher in proposing a construct for volition enhancement self-regulation model to improve mathematics learner performance in grade 9 rural community schools. In this context, our study adds to research as it realizes that mathematics learning can be directly influenced by combining mathematics related strategies with cross-curricular self-regulation strategies in order to improve learner performance. / PhD (Mathematics Education), North-West University, Potchefstroom Campus, 2014