Mathematics knowledge for teaching and the classroom environment

This study investigated the classroom environment in an underperforming mathematics classroom. The objectives were: (1) to investigate the classroom environment and identify influences upon it, and (2) to further explore those influences (i.e., teacher knowledge). This was completed using a diachronic case study approach in which data were gathered during lesson observations and coaching sessions. These data were analysed to describe and exemplify the classroom environment, then further described against forms of teacher knowledge. Conjectures regarding the importance of teacher knowledge of content were made which formed a base for developing a model of teacher planning and pedagogy.

Use of genetic decompositions to scaffold the development of a structurally sequenced curriculum for mathematics acceleration

The authors have collaboratively used a graphical language to describe their shared knowledge of a small domain of mathematics, which has in turn scaffolded their re-development of a related curriculum for mathematics acceleration. This collaborative use of the graphical language is reported as a simple descriptive case study. This leads to an evaluation of the graphical language’s usefulness as a tool to support the articulation of the structure of mathematics knowledge. In turn, implications are drawn for how the graphical language may be utilised as the detail of the curriculum is further elaborated and communicated to teachers.

Mathematics Game e-Library for Elementary School, study case: Mexico

One of the most relevant subjects for the intellectual formation of elementary school students is Mathematics where its importance goes back to ancient civilizations and which its importance is underestimated nowadays. This phenomenon occurs in Mexico, where 63.1% of the total population of elementary school students between the third and sixth grade have insufficient/elemental level of mathematics knowledge. This has resulted in the need to use a new mechanism to complement student’s classroom learning. With the rapid growth of wireless and mobile technologies, the mobile learning has been gradually considered as a novel and effective form of learning due to it inherits all the advantages of e-learning as well as breaks the limitations of learning time and space occurring in the traditional classroom teaching. This project proposes the use of a Mathematics Game e-Library integrated by a set of games for mobile devices and a distribution/management tool. The games are developed for running on mobile devices and for cover the six competencies related with the mathematics learning approach established in Mexico. The distribution/management tool allows students to reach contents according to their needs; this is achieved through a core engine that infers, from an initial profile, the games that cover the user’s knowledge gaps.

STEM learning through engineering design: fourth-grade students' investigations in aerospace

Background: Internationally, there is a growing concern for developing STEM education to prepare students for a scientifically and technologically advanced society. Despite educational bodies lobbying for an increased focus on STEM, there is limited research on how engineering might be incorporated especially in the elementary school curriculum. A framework of five comprehensive core engineering design processes (problem scoping, idea generation, design and construction, design evaluation, redesign), adapted from the literature on design thinking in young children, served as a basis for the study. We report on a qualitative study of fourth-grade students’ developments in working an aerospace problem, which took place during the first year of a 3-year longitudinal study. Students applied design processes together with their mathematics and science knowledge to the design and redesign of a 3-D model plane. Results: The study shows that through an aerospace engineering problem, students could complete initial designs and redesigns of a model plane at varying levels of sophistication. Three levels of increasing sophistication in students’ sketches were identified in their designs and redesigns. The second level was the most prevalent involving drawings or templates of planes together with an indication of how to fold the materials as well as measurements linked to the plane’s construction. The third level incorporated written instructions and calculations. Students’ engagement with each of the framework’s design processes revealed problem scoping components in their initial designs and redesigns. Furthermore, students’ recommendations for improving their launching techniques revealed an ability to apply their mathematics knowledge in conjunction with their science learning on the forces of flight. Students’ addition of context was evident together with an awareness of constraints and a consideration of what was feasible in their design creation. Interestingly, students’ application of disciplinary knowledge occurred more frequently in the last two phases of the engineering framework (i.e., design evaluation and redesign), highlighting the need for students to reach these final phases to enable the science and mathematics ideas to emerge. Conclusions: The study supports research indicating young learners’ potential for early engineering. Students can engage in design and redesign processes, applying their STEM disciplinary knowledge in doing so. An appropriate balance is needed between teacher input of new concepts and students’ application of this learning in ways they choose. For example, scaffolding by the teacher about how to improve designs for increased detail could be included in subsequent experiences. Such input could enhance students’ application of STEM disciplinary knowledge in the redesign process. We offer our framework of design processes for younger learners as one way to approach early engineering education with respect to both the creation of rich problem experiences and the analysis of their learning.

Introducing the multi-faceted teaching experiment

A mathematics classroom is comprised of many mathematicians with varying understanding of mathematics knowledge, including the teacher, students and sometimes researchers. To align with this conceptualisation of knowledge and understanding, the multi-faceted teaching experiment will be introduced as an approach to study all classroom participants’ interactions with the shared knowledge of mathematics. Drawing on the experiences of a large curriculum project, it is claimed that, unlike a multi-tiered teaching experiment, the multi-faceted teaching experiment provides a research framework that allows for the study of mathematicians’ building of knowledge in a classroom without privileging the experience of any one participant.

Ensaio da Ferramenta DIA Diagnóstico e Informação do aluno

Apresentamos os resultados de nossa pesquisa para concepção, execuçãoo e avaliação de uma ferramenta adaptativa informatizada, denominada DIA, que permita tanto avaliar como fornecer feedback a estudantes sob uma perspectiva de avaliação formativa. Na primeira etapa, usamos os PCN: Ciências da Natureza, Matemática e suas Tecnologias (BRASIL, 1998) e as Matrizes Curriculares de Referência do Instituto Nacional de Estudos e Pesquisas Educacionais - INEP, para o Sistema de Avaliação para a Educação Básica- SAEB (BRASIL, 2005), para construir uma escala, em que os objetivos estão em ordem crescente, de acordo com o desenvolvimento vertical da construção do conhecimento em Matemática. Entrelaçamos os objetivos propostos para criar um Banco de Itens (BI), que foi usado em nossas simulações. Analisamos os resultados obtidos em nosso ensaio para avaliar o diálogo entre o BI e a escala sob a perspectiva de oferecer um diagnóstico de lacunas na construção do conhecimento matemático. Em nosso ensaio, simulamos o funcionamento da ferramenta DIA através de um teste adaptativo informatizado baseado na Teoria de Resposta ao Item (TRI). Também estamos interessados em determinar um perfil de um Banco de Itens, que seja capaz de forma significativa de dialogar com nossa escala através de TRI. A escala e o banco de itens a ela associado devem viabilizar um feedback construtivo que ajude os alunos a desenvolverem competências metacognitivas.

O ensino de matemática nos cursos de ciências biológicas: uma proposta de conteúdos adequados

Pós-graduação em Educação para a Ciência - FC

A resolução de problemas no processo ensino-aprendizagem-avaliação de matemática na e além da sala de aula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Trabalhando conceitos matemáticos com tecnologias informáticas por meio da elaboração de projetos de construção civil

Pós-graduação em Educação Matemática - IGCE

Resolução de equações algébricas por radicais

Pós-graduação em Educação Matemática - IGCE

Constituir-se professor nas ilhas de Belém: ensinando e aprendendo matemática

O objetivo desta pesquisa é compreender como os professores das Ilhas de Belém constituem-se professores ao longo de uma trajetória de formação profissional nas condições sócio-culturais desta região com destaque para seus saberes matemáticos. Trata-se de professores lotados nas escolas de cinco Ilhas administradas pela Prefeitura Municipal de Belém e pelo Governo do Estado do Pará. Por se tratar de diversificadas formas de saberes buscamos referências nos autores: Tardif, Lorenzato, Fiorentini e Lorenzato, Imbernón, Smole e Diniz, Charlot, Zabala e Perrenoud .para esclarecer e fundamentar teoricamente esta pesquisa. A metodologia é fundamentada na observação participante do pesquisador, também chamada de Etnográfica e na análise do tipo qualitativa das informações obtidas. A pesquisa é baseada na investigação que buscou compreender como constituíram-se os professores nas Ilhas de Belém, com dados registrados: na identificação histórico-cultural das ilhas, das respectivas escolas, por entrevistas aos respectivos professores, por dados obtidos em sala de aula através do Curso de Matemática para os Professores de Séries Iniciais das Ilhas, fotos, vídeos e gravação sonora. A pesquisa mostra que os professores de séries iniciais lidam com conceitos matemáticos em sala de aula, por isso ensinam matemática. Evidencia os desafios e a necessidade de um aprofundamento do domínio desses conceitos, bem como a perseverança diante das dificuldades encontradas frente à busca de formação continuada e também no desenvolvimento da prática docente. A análise mostra que estes professores elaboram/reelaboram seus saberes através do desenvolvimento da prática docente, e também identifica a busca de conhecimentos por estes professores.

Geometria analítica plana: praxeologias matemáticas no ensino médio

O objetivo desta pesquisa é a construção e a aplicação de uma organização didática para a Geometria Analítica Plana, a partir do estudo dos Vetores, no 3º ano do ensino médio, à luz da Teoria Antropológica do Didático de Yves Chevallard e da teoria da Aprendizagem Significativa de David Ausubel. A pesquisa é de natureza qualitativa do tipo etnográfica na educação, de acordo com Marli André, e foi desenvolvido com um grupo de alunos em um contexto específico que é a preparação para o vestibular. A manipulação de objetos ostensivos para compreensão dos objetos não-ostensivos da Matemática serviu de categorias para análise das praxeologias vivenciadas em sala de aula. Concluímos que os alunos ao manipular as representações de objetos ostensivos resgatam conhecimentos matemáticos de forma articulada e integrada para a ancoragem de novos conhecimentos matemáticos. Observou-se também que a organização didática permite “economia de tempo”, no que diz respeito ao estudo destes conteúdos nesta etapa da vida escolar.

El crescimiento poblacional: una propuesta pedagógica para abordar biologia, matemáticas y TICs

In this paper we propose the achievement of an interdisciplinary activity evolving biology and mathematics knowledge with students of the third grade of high school about the population growth theme. The goal of this activity is to offer to the students a wider perception about the ways of population growth of different organisms from their home region, helping them to represent it through mathematics models. The formulation of the research problem is done from the theoretical and empirical data and the student is encouraged to behave in a participative and dialogic way in all stages of the activity. The mathematical modeling and the graphic representation of the population growth are made through the mathematical software Geogebra and we emphasize the qualitative analysis of the data from the biological and environmental education point of view.

Reflexões sobre o desenvolvimento da prática social e a produção e sistematização do conhecimento matemático

The aim of this study is to reflect about the cultural aspects concerning Mathematics Education, from the relationship betwen the development of the social practice and the production and systematization of knowledge about Mathematics. Thus, in first instance, there is a reflection about the producton level of mathematics knowledge in diverse social contexts, facing the level of complexity of the investigated reality. In a second instance, considerations are made about the necessity of understanding the culture phenomenum, in a totalizing perspective and the implications facing the atomization of culture in researches of ethnographic aspects about the production of mathematics in specific social contexts.

Futuros Matemáticos e suas concepções sobre o conhecimento matemático e seu ensino

Taking referential theoretical conceptions of mathematical knowledge present in some of the main mathematics philosophical currents and considering that the teacher´s practice is influenced by his conception of mathematical knowledge, this research aims to understand the conceptions of mathematical knowledge and its teaching and learning teaching of future mathematicians. It follows a qualitative approach (case study) in which the data were collected by semi-structured interviews and document analysis. This investigation has pointed out that Mathematics together with Mathematics Teaching (or part of this: on the didactic and pedagogical knowledge of how to teach) could be important to formation of the future mathematician, who will probably teach in a college or university.