From the 1990s, teachers have been provided with a considerable number of materials produced and distributed by different governments to develop a mathematics curriculum to perform as curriculum implementers and promote the mathematical reform of different teaching systems. These resources have been researching tools. However, the types of use that teachers make of them are still little explored. In this article, we present the results of a study that aimed to understand the relationship between teacher-curriculum materials in the area of mathematics education, which takes discussions about teaching competencies of curriculum design as theoretical contributions. The research analysed a research report, and meta-analysis was the methodology adopted. The results indicate that affordances and constraints qualify the materials and potentiate the agency and its displacement, both for teachers and for materials, thus imparting different interactions between these two agents of curriculum development in mathematics.
Background: The curricula of the undergraduate programmes for pre-service mathematics teachers' education have been debated (and disputed) in Brazilian academic communities over the past decades. Objectives: To investigate actions and disputes among mathematicians and mathematics educators which took place during the curricular changes and creation of the night undergraduate programme for pre-service mathematics teachers' education at UFRJ. Design: Fictional dialogues were built to present and analyse data from individual interviews. Setting and Participants: Interviews were conducted with seven lecturers, five retired and two in office, who have played central roles in the institution or in designing curricula for the programme. Data collection and analysis: Data analysis and production were conducted through the re-storying methodology. Results: The dialogues indicate that the modification in the priorities of the group of Mathematics Education teachers at the IM-UFRJ moved the faculty away from the discussions that culminated in the curricular changes of 2001 and 2008, either from the understanding of what the laws and resolutions said, or in internal spaces for debate, such as the Fundão Project. Conclusions: Our analysis indicates that disputes take place in a landscape that transcends teachers' education and reaches more complex political and epistemic terrains, partially related to tensions between mathematics and mathematics education, but that cannot be reduced to this binarism.
In 'The Oxford Handbook of Wittgenstein', Michael Potter's essay 'Wittgenstein on mathematics' offers not only an analysis on why Wittgenstein's philosophy of mathematics is so controversial among philosophers and mathematicians but also justifies such controversy. For that purpose, Potter emphasizes that Wittgenstein's discussions on math are unfinished. This article sheds light on some inconsistencies and contradictions pertaining Wittgenstein's mathematic thoughts which, although reinforcing the decade-long criticism on the author, did not interest scholars as much as Wittgenstein's comments on Kurt Gödel's incompleteness theorems and his dialogues with Alan Turing on the foundations of mathematics.
The mathematics teacher initial training has been the subject of discussion in the governmental spheres and in the Brazilian Societies of Mathematical Education and of Mathematics. As a consequence of this, we notice advances in some critical points, among which stands out - the excess of academic mathematics disarticulated from the school mathematics; and - the approximation of the mathematics education theoretical-methodological trends with the mathematics undergraduate courses curricular organization. However, there are still absent the conversations involving the different and varied dimensions that interfere in the teaching and learning process of school mathematics; and the different curriculum theories. As a result, the neutrality of mathematical knowledge and the excessive concern with the normative dimension of the curriculum continue being protagonists in the mathematics teacher initial training. In this sense, this article aimed to investigate aspects related to the perception and understanding of basic education mathematics teachers about the school subjects, the school, the school education and about being a math teacher. Methodologically, it is included in a quali-quantitative research approach, in which, in order to achieve the project's objectives, a field research, through a questionnaire available in the "Google docs", was carried out with the public network mathematics teachers from São Paulo state. Theoretically, it was based on studies about curriculum theories. It was tangible that the collaborating teachers are still very attached to the normative dimension of the curriculum, always prioritizing what to teach, how to teach and how to evaluate, without worrying about other dimensions (cultural, social, political) that interfere in the curriculum organization.of the school mathematics. ; A formação inicial do professor de matemática tem sido objeto de discussão nas esferas governamentais e nas Sociedades Brasileiras de Educação Matemática e de Matemática. Por consequência disso, percebe-se avanços em alguns pontos críticos, dentre os quais destaca-se – o excesso de matemática acadêmica desarticulada da matemática escolar; e – a aproximação das tendências teórico-metodológicas da educação matemática com a organização curricular dos cursos de licenciatura em matemática. Todavia, ainda estão ausentes as conversas envolvendo as distintas e variadas dimensões que interferem no processo de ensino e aprendizagem da matemática escolar; e as diferentes teorias do currículo. Em virtude disso, a neutralidade do conhecimento matemático e a excessiva preocupação com a dimensão normativa do currículo continuam sendo protagonistas na formação inicial do professor de matemática. Neste sentido, o presente artigo teve como objetivo investigar aspectos relacionados à percepção e entendimento de professores da disciplina de matemática na educação básica, acerca das disciplinas escolares, da escola, da educação escolar e do ser professor de matemática. Metodologicamente, incluiu-se numa abordagem quali-quantitativa de pesquisa, na qual, para alcançar os objetivos do projeto, realizou-se junto aos professores de matemática da rede pública do estado de São Paulo uma pesquisa de campo, por meio de questionário disponibilizado no "google docs". Teoricamente, fundamentou-se em estudos sobre teorias do currículo. Mostrou-se tangível que os professores colaboradores ainda estão muito presos à dimensão normativa do currículo, priorizando sempre o que ensinar, como ensinar e como avaliar, sem se preocuparem com outras dimensões (cultural, social, política) que interferem na organização curricular da matemática escolar.
Background: The study of the history of mathematics teaching can be approached from different perspectives, defining contours from which the researcher performs the analysis focused on a process characterised by continuity, or by adopting periodisation. Objective: In this article, we seek to conduct a study based on the delimitation of periods, according to Le Goff's (2014) argument, and in the light of the depth hermeneutics, based on Thompson (2011). Design: Given the premises above, we conducted a documentary analysis of two historical processes within the scope of mathematics teaching, one focusing on the municipal public schools of Canoas, and the other on a technical course in chemistry of a school in the city of Novo Hamburgo, both in the state of Rio Grande do Sul. Setting and participants: A timeline with conspicuous events used to periodicise both historical processes analysed by the authors. Data collection and analysis: Analysis of documents relevant to the history of the technical school investigated and education in the municipality of Canoas. Results: In both cases, it was possible to characterise the historical processes in periods based on events and official documents that generate changes in mathematics teaching. Conclusions: The historical processes analysed are characterised by ruptures resulting from changes, especially in the legislation, both in the municipal public network and in the technical education institution researched, enabling the realisation of changes and the characterisation of distinct periods, with their nuances.
