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Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Cadernos de Pesquisa is the property of Fundacao Carlos Chagas and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article is an excerpt from a master's thesis developed in Brazil, in which we approach recurrent and linear sequences, given some intriguing particularities in their definitions and the scarcity of discussion of this topic in the literature of the History of Mathematics, especially with regard to its geometric representation. Thus, we aim to present the identities of Fibonacci, Lucas, Jacobsthal and Padovan in a three-dimensional visualization with the contribution of GeoGebra software. The research methodology chosen was bibliographical, exploratory in nature, where we have theoretical support in works such as Oliveira and Alves (2019), Silva (2017), Souza and Alves (2018), Vieira and Alves (2020). This research brings as results a set of geometric constructions of the identities of the proposed sequences, in three-dimensional perspective, being a support for future works developed around this theme. GeoGebra was essential in the process of constructing and visualizing the sequences, as it provided strategies for understanding the recurrence relations and the properties of the Fibonacci, Lucas, Jacobsthal and Padovan sequences, through the behavior of the visual representations of these identities. [ABSTRACT FROM AUTHOR]

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The present work presents some examples of data originated from a set of investigations developed in Brazil, at the Federal Institute of Education, Science and Technology of the State of Ceará - IFCE, in the context of teacher education, and the consideration of elements of a historical, mathematical, and evolutionary nature. Thus, from a perspective of theoretical complementarity involving the research elements derived from the notion of the didactic engineering for development and some assumptions of the French aspect of the professional didactics, two sets of data are discussed. The first set involved research carried out between 2017 and 2020. The second set considered involved studies still under development in Brazil, considering the period of 2020 - 2023. The historical landscape of investigation rests on considering the recurring number sequences of Fibonacci, Lucas, Pell, Jacobsthal, Coordonier or Padovan, Perrin, Mersenne, Oresme, Naraynna, and Leonardo. Furthermore, in a broad sense, the study aims to provide a learning scenario for the teacher, affected by a perspective of mathematical knowledge evolution, including the repercussions and applications with current technology. [ABSTRACT FROM AUTHOR]

The field of the history of mathematics education, inscribed in the field of research on mathematics education in Brazil, has been developed as a result of the work of many groups of researchers, dedicated to varied themes under the light of various theoretical and methodological approaches. While it is impossible to describe in detail such studies in a single article, the objective of this text is to offer an overview of research results on a specific topic - mathematics in secondary education and training of teachers to teach at this level, over the years. The current situation of the country regarding education in general is related to the past and different Brazilian political periods: Colony, Empire and Republic. We will succinctly examine the beginnings of Brazilian basic school education before the Republic, seeking to highlight characteristics of secondary school studies, especially regarding the teaching of mathematics. Then, we will focus on the same themes during the period after the establishment of the Republican regime. Finally, we will discuss the historical trajectory of the training mathematics teachers who work on secondary education in the country. [ABSTRACT FROM AUTHOR]

In this research we investigate how mathematics teachers, as graduate students, estimate the value of π by exploring the problem of squaring the circle using digital technology. Initially, we mention some aspects of teaching and learning of calculus in the literature, emphasizing studies that use the notion of humans-with-media to highlight the role of technology in mathematical thinking and knowledge production. Insights on the history of mathematics in calculus are also discussed. We developed a qualitative study based on three different solutions created by groups of teachers using the software GeoGebra and Microsoft Excel. All the teachers' solutions improved the approximation (8/9)2 ≈ π/4, by determining p and q for (p/q)2 ≈ π/4. The first two solutions with GeoGebra emphasized experimentation and visualization, improving the approximation from one to three decimal places. The third solution with Excel pointed out the elaboration of a formula and improved it up to six decimal places. We emphasize how media shaped the strategies and solutions of the groups. Based on these solutions, we explore an approach for cubing the sphere, discussing approximations for π, highlighting the role of media in enhancing conceptual complexity in the solution of mathematical problems. The nature of the strategies for solving a problem is discussed, especially regarding different ways of thinking-with-technology developed by collectives of teachers-with-media. Although we acknowledge an alternative design for the proposed task, the exploration of problems using aspects of the history of mathematics contributes to the state of the art concerning the studies in calculus developed by the Research Group on Technology, other Media, and Mathematics Education in Brazil. [ABSTRACT FROM AUTHOR]

The present work presents a proposal for study and investigation, in the context of the teaching of Mathematics, through the history of linear and recurrent 2nd order sequences, indicated by: Fibonacci, Lucas, Pell, Jacobsthal, Leonardo, Oresme, Mersenne, Padovan, Perrin and Narayana. Undoubtedly, starting from the Fibonacci sequence, representing the most popular in the referred scenario of numerical sequences, it was possible to notice the emergence of other sequences. In some cases, being derived from Fibonacci, in others, changing the order of the sequence, we thus have the historical study, with the use of mathematical rigor. Besides, their respective recurrence formulas and characteristic equations are checked, observing their roots and the relationship with the number of gold, silver, bronze and others. The results indicated represent an example of international research cooperation involving researchers from Brazil and Portugal. [ABSTRACT FROM AUTHOR]

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the training of mathematics teachers in Brazil we can not disregard the historical and epistemological component aiming the transmission of mathematics through a real understanding of the nature of classic concepts and foundamental definitions to Mathematics, whether in the school context or in the academic context. In this sense, the present work addresses a discussion about the introduction and formulation of Dedekind's cut. Such terminology became popular from the work and pioneering research developed by Richard Dedekind (1831 - 1916), although in the set of his contemporaries, as in the case of A. L. Cauchy (1789 - 1857), the proposition of the construction of the real numbers through other notions and others mathematical methods became known. Thus, a historical and epistemological way for the definition of cut is observed and considered. However, Dedekind did not formally answered mainly some of the questions about this notion. The understanding of this epistemological and mathematical process, on the part of the teacher, in which the mathematical intuition and heuristics has an essencial place and requires more attention. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to discuss the production of meaning of the Modern Math Movement. The main sources were data available in school archives and interviews with former teachers that we use in order to focus on the diversity of perspectives -that complement it or oppose it-, which comes up when teachers refer to the Movement. Using this process of signification, teachers whether accept it, invalidate it or adapt it to guidelines imposed to them in their teaching activities. We establish a methodology by following the premises of Oral History to gather oral testimonies. The theoretical foundations in which this article is written are the guidelines of Paul Ricoeur's Hermeneutics, John Thompson's Depth Hermeneutics and Bolívar's narrative analysis. [ABSTRACT FROM AUTHOR]

In this paper it is presented a characterization of trends in studies and research in the history of mathematics in Brazil, taking the dissertations and theses in Brazil between 1990 and 2010 as reference. The main objective is to identify and characterize the basis of epistemological and methodological basis of studies related to the history of mathematics and its relationships with mathematics education in several post-graduate programs in Brazil. The results pointed out about eleven trends that shape a historical overview of Brazilian research involving history and mathematics education, of which it is evident an exercise of theoretical migration that contribute to enlarge the framework of sustenance of the historiographic production on Brazilian Mathematics in epistemological, sociological and pedagogical dimensions. [ABSTRACT FROM AUTHOR]

First, I present the distinction between history and historiography according to realist and anti-realist points of view, and its implications for historical analysis and writing -- the concept of historical document and anachronism. Then I study this distinction and these problems in historiography of mathematics, focusing Sabetai Unguru's seminal work on early greek mathematics and Bruno Belhoste's claim on the role of teaching on the historiography. So I deal with two problems, a priori opposition between production and reproduction of mathematics in historiography and the back influence of readers on historians theoretical and methodological choice. All these aspects are considered in respect to recent born historiography of mathematics education and the most important challenge for its historians, the theoretical and methodological dialogue with the professional field of history. [ABSTRACT FROM AUTHOR]

The text aims at characterizing and analyzing the production of the history of mathematics education in Brazil. The study takes the presentations from the last National Seminar of History of Mathematics as a starting point. Such event gathered researchers, in a more significant and comprising way, interested in historical studies of mathematics and its teaching. The characterization points at the existence of four different tendencies: a production that considers the studies about history of mathematics education as part of the research about history of mathematics; a trend of opinions that takes into account the pedagogical use of history in mathematics education and establishes conditions for the research in the history of mathematics education; studies that use oral history for mathematics teachers’ training courses; and, finally, another trend that treats the history of mathematics education as history, that means, a specificity of historical production, having the mathematics education as an object. It will be shown that the characterization of those trends reveals different ways of representing the past of mathematics education, as well as the relationships Brazilian researches keep with international studies about this subject. [ABSTRACT FROM AUTHOR]

The development of mathematics, particularly in Europe during the period prior to the great age of navigation, and the revolutionary influences that this knowledge provided for the expansive initiatives of the Portuguese are presented here, concluding with an analysis of the acquisition of knowledge between dominator and dominated. [ABSTRACT FROM AUTHOR]

The article presents the author's views on the role played by periodical "Rem: Revista Escola de Minas," in the growth of Brazilian mining publications. Various topics discussed include impact of economic instability on the credibility of researches, contribution of 19th century mathematics in scientific works and importance of articles for distributing mineral science knowledge.