A Didactic Engineering in the Research Process of the Generalization of the Padovan Sequence: An Experience in a Pre-Service Teacher Training Course

2020 ◽  
Vol 22 (6) ◽  
Author(s):  
Renata Passos Machado Vieira ◽  
Francisco Regis Vieira Alves ◽  
Paula Maria Machado Cruz Catarino
Keyword(s):  
Teacher Training ◽  
History Of Mathematics ◽  
Research Process ◽  
Teaching Methodology ◽  
Engineering Research ◽  
Training Course ◽  
Theory Of Didactic Situations ◽  
Short Period ◽  
Didactic Engineering ◽  
History Of

Background: Obstacles are found during the epistemological construction of mathematical concepts research, aiming to contribute to the Didactics of Mathematics through a study of Padovan sequence.  Objectives: describe elements of a systematic study, based on Didactic Engineering in conjunction with the Theory of Didactic Situations. I addition, referring to the generalization model of Padovan sequence and promoting a historical-evolutionary understanding and its mathematical properties. Design: it presents the most representative data of an investigation supported by the foundations of Didactic Engineering research design, in association with the Theory of Didactic Situations teaching methodology. Setting and Participants: the research was developed in 2019 and applied in a Pre-Service Mathematics Teacher Training Course in the History of Mathematics discipline, with the eight students enrolled. Data collection and analysis: data validation occurred internally due to the short period of the research. Results: it describes an investigation around the object of study, the Padovan sequence, focusing on the generalization process of this sequence and its properties. Thus, three problem situations are elaborated and analyzed based on the assumed research and teaching methodologies, seeking to examine their properties and the student's intuitive thinking, before the insertion of a historical-epistemological conception of this investigation. Conclusions: the research makes it possible to extract repercussions, suggest and promote research scripts aiming at the formation of teachers (initial) in the context of the teaching of History of Mathematics.

An investigation of the Bivariate Complex Fibonacci Polynomials supported in Didactic Engineering: an application of Theory of Didactics Situations (TSD)

2019 ◽  
Vol 21 (3) ◽  
pp. 170-195 ◽  
Author(s):  
Rannyelly Rodrigues de Oliveira ◽  
Francisco Régis Vieira Alves
Keyword(s):  
History Of Mathematics ◽  
Inferential Reasoning ◽  
Fibonacci Polynomials ◽  
Intuitive Thinking ◽  
Theory Of Didactic Situations ◽  
Epistemological Conception ◽  
Didactic Engineering ◽  
History Of

A research cut will be presented in the Academic Master of the Programa de Pós-Graduação em Ensino de Ciências e Matemática (PGECM) of the Instituto Federal de Educação, Ciência e Tecnologia do Ceará (IFCE). This research used Didactic Engineering with a focus on the Theory of Didactic Situations, evidencing epistemological, cognitive and didactic elements articulated among themselves. This made it possible to mobilize the student's intuitive thinking towards inferential reasoning during the study of the Bivariate Complex Fibonacci Polynomials. Moreover, it had the purpose of inserting an epistemological conception in the teaching of History of Mathematics, considering that the research was applied in the course of Degree in Mathematics in the discipline of History of Mathematics.

scholarly journals O estudo de definições matemáticas no contexto de investigação histórica: um experimento didático envolvendo Engenharia Didática e Sequências Polinomiais de Fibonacci

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
Rannyelly Rodrigues de Oliveira ◽  
Francisco Régis Vieira Alves ◽  
Rodrigo Sychocki da Silva
Keyword(s):  
History Of Mathematics ◽  
Fibonacci Sequence ◽  
Research Approach ◽  
Polynomial Sequence ◽  
Internal Validation ◽  
Generalized Fibonacci Sequence ◽  
Research Activities ◽  
Didactic Engineering ◽  
History Of ◽  
Fibonacci Polynomial

Resumo: O presente artigo apresenta uma abordagem de investigação no contexto da História da Matemática, envolvendo situações que visam oportunizar o entendimento da extensão, evolução e generalização de propriedades da Sequência de Fibonacci. Dessa forma, abordam-se duas situações. A primeira, envolvendo a descrição da fórmula de Binnet no campo dos inteiros. Logo em seguida, apresenta-se uma descrição e análise dos termos explícitos presentes na Sequência Polinomial de Fibonacci. O escopo da presente proposta de atividade busca a divulgação científica de noções envolvendo a generalização, ainda atual, fato que acentua o caráter ubíquo da Sequência de Fibonacci. À vista disso, a proposta de experimento didático está fundamentada na organização das características da Engenharia Didática. Almeja-se, além da validação interna das hipóteses levantadas durante a investigação, contribuir com a formação inicial de estudantes dos cursos de Licenciatura em Matemática que virem a estudar o tema.Palavras-chave: Atividades de investigação. Engenharia Didática. História da Matemática. Sequência Generalizada de Fibonacci.  THE STUDY OF MATHEMATICAL DEFINITIONS IN THE CONTEXT OF HISTORICAL RESEARCH: A DIDACTIC EXPERIMENT INVOLVING DIDACTIC ENGINEERING AND FIBONACCI POLYNOMIAL SEQUENCESAbstract: This article presents a research approach within the context of History of Mathematics, involving situations that aim to provide an understanding of the extension, evolution and generalization of properties of the Fibonacci Sequence. In this way, two situations are addressed. The first, involving the description of Binet's formula in the integer field. Then, a description and analysis of the explicit terms present in the Fibonacci Polynomial Sequence is presented. The scope of this activity proposal seeks the scientific dissemination of notions involving generalization, still current, a fact that accentuates the ubiquitous character of the Fibonacci Sequence. Thus the proposal of didactic experiment is based on the organized in the characteristics of Didactic Engineering, beyond the internal validation of the hypotheses raised during the investigation this paper aims at contributing to initial education of undergrad   Mathematicsof students that may come to study the subject.Keywords: Research activities. Didactic Engineering. History of Mathematics. Generalized Fibonacci Sequence.

scholarly journals HISTORY OF MATHEMATICS EDUCATION IN PRIMARY SCHOOL AND IN TEACHER TRAINING IN BRAZIL

2020 ◽  
Vol 24 ◽  
Author(s):  
Wagner Rodrigues Valente ◽  
Maria Célia Leme da Silva
Keyword(s):  
Mathematics Education ◽  
Teacher Training ◽  
Primary School ◽  
Mathematics Teaching ◽  
History Of Mathematics ◽  
Theoretical Hypothesis ◽  
Disciplinary Field ◽  
History Of ◽  
The 19Th Century ◽  
The Relationship

Abstract This article discusses results from research developed on the transformations in mathematics teaching in primary school and the mathematics in teacher training from the 19th century to the mid-20th century in Brazil. We have analyzed the understanding of the relationship between the mathematical disciplinary field and pedagogy in order to confirm the theoretical hypothesis that the interactions between the two fields produce mathematics of different natures, which are interconnected.

scholarly journals Reflexões Acerca da História Oral e suas Potencialidades em Pesquisas do Campo da História da Educação Matemática

2019 ◽  
Vol 12 (2) ◽  
pp. 164
Author(s):  
Kátia Guerchi Gonzales ◽  
Ana Carolina De Siqueira Ribas dos Reis
Keyword(s):  
Mathematics Education ◽  
Teacher Training ◽  
Oral History ◽  
History Of Mathematics ◽  
History Of Mathematics Education ◽  
History Of

Este estudo apresenta algumas discussões sobre a metodologia História Oral mobilizada em estudos do campo da Educação Matemática e que tem por objetivo a constituição de fontes de pesquisa a partir da oralidade. Para essa discussão trazemos pressupostos teóricos e procedimentais que fundamentam o trabalho com essa metodologia, os quais abordam desde a concepção de pesquisa historiográfica e fontes até os procedimentos específicos utilizados para a construção das fontes. Apresentamos, também, uma discussão sobre potencialidades do uso da História Oral em pesquisas do campo da História da Educação Matemática, evidenciando como as narrativas criadas têm possibilitado reflexões sobre experiências na formação de professores que ensinam Matemática.Palavras-chave: Formação de Professores. História Oral. Constituição de Fontes.AbstractThis study presents some discussions about Oral History methodology mobilized in studies in the field of Mathematics Education and whose objective is the constitution of research sources from orality. For this discussion we bring theoretical and procedural assumptions that are the foundation for this methodology, which approach from the conception of historiographic research and sources to the specific procedures used for the construction of the sources. We also present a discussion about potentialities of the use of Oral History in researches in the field of History of Mathematics Education, showing how the created narratives have made possible reflections on experiences in the formation of teachers who teach Mathematics.Keywords: Teacher Training. Oral History. Constitution of Sources.

scholarly journals Problems and the history of mathematics education: A proposal for the continued teacher training

2019 ◽  
Vol 21 ◽  
pp. 137-148
Author(s):  
Andreia Fernandes De Souza ◽  
Luciane De Fatima Bertini ◽  
Alan Marcos Silva de Rezende
Keyword(s):  
Mathematics Education ◽  
Teacher Training ◽  
History Of Mathematics ◽  
History Of Mathematics Education ◽  
History Of

Reflections on the Notion of Culture in the History of Mathematics: The Example of “Geometrical Equations”

2016 ◽  
Vol 29 (3) ◽  
pp. 273-304 ◽  
Author(s):  
François Lê
Keyword(s):  
Nineteenth Century ◽  
Social Organization ◽  
Mathematical Knowledge ◽  
History Of Mathematics ◽  
Technical Aspects ◽  
Cultural System ◽  
The Social ◽  
Short Period ◽  
History Of ◽  
Definition Of

ArgumentThis paper challenges the use of the notion of “culture” to describe a particular organization of mathematical knowledge, shared by a few mathematicians over a short period of time in the second half of the nineteenth century. This knowledge relates to “geometrical equations,” objects that proved crucial for the mechanisms of encounters between equation theory, substitution theory, and geometry at that time, although they were not well-defined mathematical objects. The description of the mathematical collective activities linked to “geometrical equations,” and especially the technical aspects of these activities, is made on the basis of a sociological definition of “culture.” More precisely, after an examination of the social organization of the group of mathematicians, I argue that these activities form an intricate system of patterns, symbols, and values, for which I suggest a characterization as a “cultural system.”

scholarly journals A história da matemática contribuindo para a formação de professores indígenas: um olhar sobre a perspectiva sociocultural The history of mathematics contributing to the formation of indigenous teachers: a glimpse at the sociocultural perspective

2017 ◽  
Vol 19 (2) ◽  
Author(s):  
Jonisario Littig ◽  
Leonardo Correia Alves ◽  
Lidiane Lahass
Keyword(s):  
Qualitative Methodology ◽  
Teaching Practice ◽  
History Of Mathematics ◽  
Cultural Representations ◽  
Sociocultural Perspective ◽  
Mathematical Concepts ◽  
Training Course ◽  
History Of ◽  
The City ◽  
Indigenous Teachers

ResumoEsse artigo analisa relatos de formadores de professores indígenas realizado em dezembro de 2014 no município de Aracruz – ES. O curso foi oferecido por meio do projeto “Saberes indígenas”. O artigo objetiva explicitar as contribuições da história da matemática e as representações desse grupo cultural para a formação de seus professores. A metodologia, qualitativa, foi desenvolvida a partir de intervenções por meio do curso de formação. Os instrumentos de coleta de dados foram diários de bordo e entrevista com os formadores. Os resultados apontam as dificuldades de relacionar as representações culturais à matemática apresentada no curso. Concluímos que contemplar a história da matemática desse grupo no curso de formação pode contribuir na construção de conceitos matemáticos e na prática docente.AbstractThis article analyzes reports of trainers of indigenous teachers achieved in December 2014 in the city of Aracruz - ES. The course was offered through the project "Indigenous Knowledge". The article aims to make explicit the contributions of the history of mathematics and the representations of this cultural group to the formation of its teachers. The qualitative methodology was developed from interventions through the training course. The instruments of data collection were logbook and interview with the trainers. The results point out the difficulties of relating the cultural representations to the mathematics presented in the course. We conclude that contemplating the history of mathematics in this group in the training course can contribute to the construction of mathematical concepts and teaching practice.

Historically Speaking, - -

1953 ◽  
Vol 46 (6) ◽  
pp. 419-426
Keyword(s):  
Teacher Training ◽  
Training Programs ◽  
History Of Mathematics ◽  
Secondary Level ◽  
Angular Measure ◽  
Teacher Training Programs ◽  
History Of ◽  
Teaching Of Mathematics

This note is directed toward two complaints heard recently: (1) that the study of the history of mathematics has not significantly improved the teaching of mathematics in spite of having been recommended or required in teacher training programs for years, and (2) that angular measure, radians and mils in particular, is hard to teach, not meaningful, and should be omitted on the secondary level at least.

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