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.
{"title":"Didactic Engineering (DE) and Professional Didactics (PD): A Proposal for Historical Eesearch in Brazil on Recurring Number Sequences","authors":"Francisco Régis Vieira Alves","doi":"10.54870/1551-3440.1551","DOIUrl":"https://doi.org/10.54870/1551-3440.1551","url":null,"abstract":"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.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44458010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marcelo Almeida Bairral, Marcos Paulo Henrique, A. Assis
{"title":"Moving Parallel and Transversal Lines with Touches on Smartphones: A Look through Screenrecording","authors":"Marcelo Almeida Bairral, Marcos Paulo Henrique, A. Assis","doi":"10.54870/1551-3440.1546","DOIUrl":"https://doi.org/10.54870/1551-3440.1546","url":null,"abstract":"","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46765975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Elizabeth Gomes Souza, C. Tamayo, Marcia Maria Bento
This article aims to describe discursive regularities of theses and dissertations by researchers from the Group “Research, Education, Language, Cultural Practices” Phala and their effects for / on Mathematics Education. Due to the nature of the proposed study, three axes of description emerged: (1) starting cultural archive and the literatures-traces triggered with respect to Mathematics; (2) therapeutic analog movements operated in research, and (3) aesthetics and writing style. We identified that the archives, taking deconstructionist therapy as a research lens, expand the debates about the understanding of Mathematics as a fixed, linear, compartmentalized, abstract and hierarchical set of knowledge, shaped to meet cognitive, structuralist and neoliberal school learning projects; as well as they broaden the debates about the ways of practicing research in a hermeneutic-analytical way, addressing problems that involve modern schooling, teacher training, indigenous and non-indigenous education, assessment of learning and historiographic and non-historiographical aspects of undertaking research in Mathematics Education
{"title":"Ludwig Wittgenstein, Mathematics, Therapy and Life: research from the group on Education, Language and Cultural Practices in Brazil","authors":"Elizabeth Gomes Souza, C. Tamayo, Marcia Maria Bento","doi":"10.54870/1551-3440.1552","DOIUrl":"https://doi.org/10.54870/1551-3440.1552","url":null,"abstract":"This article aims to describe discursive regularities of theses and dissertations by researchers from the Group “Research, Education, Language, Cultural Practices” Phala and their effects for / on Mathematics Education. Due to the nature of the proposed study, three axes of description emerged: (1) starting cultural archive and the literatures-traces triggered with respect to Mathematics; (2) therapeutic analog movements operated in research, and (3) aesthetics and writing style. We identified that the archives, taking deconstructionist therapy as a research lens, expand the debates about the understanding of Mathematics as a fixed, linear, compartmentalized, abstract and hierarchical set of knowledge, shaped to meet cognitive, structuralist and neoliberal school learning projects; as well as they broaden the debates about the ways of practicing research in a hermeneutic-analytical way, addressing problems that involve modern schooling, teacher training, indigenous and non-indigenous education, assessment of learning and historiographic and non-historiographical aspects of undertaking research in Mathematics Education","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49460716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"About the Teaching and Learning of Differentiability for Piecewise Functions in Science Degrees’ First-Year Calculus Courses","authors":"J. Apraiz","doi":"10.54870/1551-3440.1568","DOIUrl":"https://doi.org/10.54870/1551-3440.1568","url":null,"abstract":"","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70968721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Course-based Undergraduate Research Experiences (CUREs) have been well developed in the hard sciences, but math CUREs are all but absent from the literature. Like biology and chemistry, math programs suffer from a lack of research experiences and many students are not able to participate in programs like REUs (Research Experiences for Undergraduates). CUREs are a great alternative, but the current definition of CURE (see [1]) has potential barriers when applied to mathematics (e.g. time, novelty of project). Our solution to these barriers was to develop a math CURE pathway in which students complete “Math CUREs” in targeted courses. After finishing the pathway (or part of the pathway), students complete a research project in at least one of the following areas: Lie theory, representation theory, or combinatorics. The focus of this paper is the math CURE implemented in a discrete mathematics course for math and computer science majors. We share our experiences with the development and implementation of this CURE over several iterations as well as the impact of the CURE on students experiences through participant survey data obtained from this CURE.
{"title":"Bringing a CURE into a Discrete Mathematics Course and Beyond","authors":"Lipika Deka, Peri Shereen, Jeffrey O. Wand","doi":"10.54870/1551-3440.1576","DOIUrl":"https://doi.org/10.54870/1551-3440.1576","url":null,"abstract":"Course-based Undergraduate Research Experiences (CUREs) have been well developed in the hard sciences, but math CUREs are all but absent from the literature. Like biology and chemistry, math programs suffer from a lack of research experiences and many students are not able to participate in programs like REUs (Research Experiences for Undergraduates). CUREs are a great alternative, but the current definition of CURE (see [1]) has potential barriers when applied to mathematics (e.g. time, novelty of project). Our solution to these barriers was to develop a math CURE pathway in which students complete “Math CUREs” in targeted courses. After finishing the pathway (or part of the pathway), students complete a research project in at least one of the following areas: Lie theory, representation theory, or combinatorics. The focus of this paper is the math CURE implemented in a discrete mathematics course for math and computer science majors. We share our experiences with the development and implementation of this CURE over several iterations as well as the impact of the CURE on students experiences through participant survey data obtained from this CURE.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70968924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper describes the Applied Mathematics Laboratory (AML), a course-based model of undergraduate research engagement in applied mathematics at Towson University. We provide historical background of similar programs at other institutions in the US; describe the implementation and the logic model of the AML; include an example of a recent project; and describe the place of the AML in the context of other course-based student research experiences in STEM.
{"title":"Applied Mathematics Laboratory: A Course-Based Research Internship","authors":"Mathew R. Gluck, Alexei S. Kolesnikov","doi":"10.54870/1551-3440.1577","DOIUrl":"https://doi.org/10.54870/1551-3440.1577","url":null,"abstract":"The paper describes the Applied Mathematics Laboratory (AML), a course-based model of undergraduate research engagement in applied mathematics at Towson University. We provide historical background of similar programs at other institutions in the US; describe the implementation and the logic model of the AML; include an example of a recent project; and describe the place of the AML in the context of other course-based student research experiences in STEM.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70969427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces the model of instrumental meta-orchestration (IMO), as an extension of the model of instrumental orchestration. This IMO model is defined as a systematic and intentional monitoring, by a teacher educator, of artefacts and teachers (or pre-service teachers) for facing a Metasituation, defined as a composition of situations of different natures and difficulty levels. An IMO, in itself, is a composition of instrumental orchestrations (sequenced or interwoven). This paper presents and discusses an instrumental meta-orchestration experienced in a class of undergraduate mathematics teachers. The development of the initial model results in: new concepts, such as ad hoc reaction, didactic meta-configuration, exploitation modes and didactic meta-performance; new features, such as flexibility and interactivity; and new phenomena, such as cascade effects. It also reveals the importance of unexpected events that occur between orchestrations. Moreover, it expanded the forms of destination for evaluating specific online documents, which are named webdocs. Finally, the paper discusses the contribution to mathematics teacher education of such an extended model.
{"title":"Teacher education for integrating resources in mathematics teaching: contributions from instrumental meta-orchestration","authors":"Rosilângela Lucena, Verônica Gitirana, L. Trouche","doi":"10.54870/1551-3440.1549","DOIUrl":"https://doi.org/10.54870/1551-3440.1549","url":null,"abstract":"This paper introduces the model of instrumental meta-orchestration (IMO), as an extension of the model of instrumental orchestration. This IMO model is defined as a systematic and intentional monitoring, by a teacher educator, of artefacts and teachers (or pre-service teachers) for facing a Metasituation, defined as a composition of situations of different natures and difficulty levels. An IMO, in itself, is a composition of instrumental orchestrations (sequenced or interwoven). This paper presents and discusses an instrumental meta-orchestration experienced in a class of undergraduate mathematics teachers. The development of the initial model results in: new concepts, such as ad hoc reaction, didactic meta-configuration, exploitation modes and didactic meta-performance; new features, such as flexibility and interactivity; and new phenomena, such as cascade effects. It also reveals the importance of unexpected events that occur between orchestrations. Moreover, it expanded the forms of destination for evaluating specific online documents, which are named webdocs. Finally, the paper discusses the contribution to mathematics teacher education of such an extended model.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47945051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Acevedo-Rincón, Gabriela Guarneri de Campos Tebet
In the first months of life, babies develop visual perception. The notions of space evolve in the everyday of experiences, the recognition of the self through your body, and relationships with others. The topological notions developed by babies correspond to closeness, proximity, continuity and separation. As babies grow, their skills are developed both in the projective space and in the geometric space. These even influence the baby's development in an integral way. This article intends to present results of the topological notions of closure, proximity separation and projections in the baby’s space. This qualitative research is developed under a descriptive perspective with interdisciplinary contributions. Data collection was made from cartography, photographic and filmic records of babies in different cities in Brazil and Colombia. The reflections developed point to the development of perception from the offer of multiple experiences since the first months. In addition, it is evident that the understanding of important mathematical concepts happens since the beginning of life, from everyday experiences of exploration and relationship with spaces and regardless of the formal school learning of geometry and its concepts
{"title":"Spaces, movements and topological notions, what do the babies' cartographies show?","authors":"J. Acevedo-Rincón, Gabriela Guarneri de Campos Tebet","doi":"10.54870/1551-3440.1561","DOIUrl":"https://doi.org/10.54870/1551-3440.1561","url":null,"abstract":"In the first months of life, babies develop visual perception. The notions of space evolve in the everyday of experiences, the recognition of the self through your body, and relationships with others. The topological notions developed by babies correspond to closeness, proximity, continuity and separation. As babies grow, their skills are developed both in the projective space and in the geometric space. These even influence the baby's development in an integral way. This article intends to present results of the topological notions of closure, proximity separation and projections in the baby’s space. This qualitative research is developed under a descriptive perspective with interdisciplinary contributions. Data collection was made from cartography, photographic and filmic records of babies in different cities in Brazil and Colombia. The reflections developed point to the development of perception from the offer of multiple experiences since the first months. In addition, it is evident that the understanding of important mathematical concepts happens since the beginning of life, from everyday experiences of exploration and relationship with spaces and regardless of the formal school learning of geometry and its concepts","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70968852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mathematics is a dynamic field of knowledge of human creation and invention that is in continuous expansion. However, the mathematics is presented as a ready and finished field of knowledge in school systems, and there is no concern with the development of cognitive processes other than memorization and symbolic manipulation, therefore, there is no concern with stimulating the development of cognitive processes such as creativity, present in the development of mathematics. On the other hand, the concepts of scientifical mathematics as infinite and infinitely small that are related to the understanding of the dynamics present in phenomena, do not have didactic treatment to be presented to students of basic education. In this work, I will propose an approach of mathematics by mean of the fundamental concepts from the first school levels, approaching mathematics as a semiotic activity based on the possibilities of interpretations of Zeno's aporias, as metaphors of the infinite, to develop creativity in the didactics of mathematics. This work will present description of didactic phenomena during teacher education.
{"title":"Semiosis to Communicate Mathematics: Complementarity in the Circularity of Interpretations in Mathematics for the Development of Creativity","authors":"Lúcia Cristina Silveira Monteiro","doi":"10.54870/1551-3440.1564","DOIUrl":"https://doi.org/10.54870/1551-3440.1564","url":null,"abstract":"Mathematics is a dynamic field of knowledge of human creation and invention that is in continuous expansion. However, the mathematics is presented as a ready and finished field of knowledge in school systems, and there is no concern with the development of cognitive processes other than memorization and symbolic manipulation, therefore, there is no concern with stimulating the development of cognitive processes such as creativity, present in the development of mathematics. On the other hand, the concepts of scientifical mathematics as infinite and infinitely small that are related to the understanding of the dynamics present in phenomena, do not have didactic treatment to be presented to students of basic education. In this work, I will propose an approach of mathematics by mean of the fundamental concepts from the first school levels, approaching mathematics as a semiotic activity based on the possibilities of interpretations of Zeno's aporias, as metaphors of the infinite, to develop creativity in the didactics of mathematics. This work will present description of didactic phenomena during teacher education.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70968943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"How to engender learning in the learning process? Mathematics, events and the invention of a mathematical education","authors":"Sônia Maria Clareto, Giovani Cammarota","doi":"10.54870/1551-3440.1532","DOIUrl":"https://doi.org/10.54870/1551-3440.1532","url":null,"abstract":"","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44822108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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