{"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":" ","pages":""},"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}
Ethnomodelling can be considered as the association between ethnomathematics and mathematical modelling that enables members of distinct cultural groups to perceive a different reality in relation to the nature of mathematical knowledge. It also provides insights into many diverse forms of mathematics developed locally. Thus, ethnomodelling is defined as the study of mathematical phenomena that adds cultural components to the modelling process. The development of this connection is conducted through three cultural approaches: local, global, and glocal, which are used in the conduction of ethnomodelling investigations that aim to work against colonialism in order to value and respect sociocultural diversity of members of distinct cultural groups. Because ethnomodelling seeks to promote the development of understanding of differences through dialogue; it is important to argue for its inclusion as a translational process for systems taken from the reality of the members of diverse cultures. In this article we argue that ethnomodelling creates a firm foundation that allows for the integration of these three cultural approaches in exploring mathematical knowledge developed in distinct cultural groups through cultural dynamism.
{"title":"Ethnomodelling as a glocalization process of mathematical practices through cultural dynamism","authors":"D. Orey, M. Rosa","doi":"10.54870/1551-3440.1533","DOIUrl":"https://doi.org/10.54870/1551-3440.1533","url":null,"abstract":"Ethnomodelling can be considered as the association between ethnomathematics and mathematical modelling that enables members of distinct cultural groups to perceive a different reality in relation to the nature of mathematical knowledge. It also provides insights into many diverse forms of mathematics developed locally. Thus, ethnomodelling is defined as the study of mathematical phenomena that adds cultural components to the modelling process. The development of this connection is conducted through three cultural approaches: local, global, and glocal, which are used in the conduction of ethnomodelling investigations that aim to work against colonialism in order to value and respect sociocultural diversity of members of distinct cultural groups. Because ethnomodelling seeks to promote the development of understanding of differences through dialogue; it is important to argue for its inclusion as a translational process for systems taken from the reality of the members of diverse cultures. In this article we argue that ethnomodelling creates a firm foundation that allows for the integration of these three cultural approaches in exploring mathematical knowledge developed in distinct cultural groups through cultural dynamism.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43207717","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}
Maria Laura Magalhães Gomes, Antonio Vicente Marafioti Garnica
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.
{"title":"History of Mathematics Education in Brazil: an overview of secondary education","authors":"Maria Laura Magalhães Gomes, Antonio Vicente Marafioti Garnica","doi":"10.54870/1551-3440.1530","DOIUrl":"https://doi.org/10.54870/1551-3440.1530","url":null,"abstract":"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.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44782545","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":"A Study on the indications to the use of Base Ten Blocks and Green Chips in Mathematics textbooks in Brazil","authors":"Everaldo Silveira","doi":"10.54870/1551-3440.1534","DOIUrl":"https://doi.org/10.54870/1551-3440.1534","url":null,"abstract":"","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43184762","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}
Juliana Azevedo Montenegro, Rute E. de S. Rosa Borba, Marilena Bittar
In order to analyze advances in the resolution of combinatorial situations, due to the identification, conversion and treatment of semiotic registers, two studies were carried out. In the first study, 5th grade students identified, from problems in natural language, registers in trees of possibilities, lists and numerical expressions. The second study, carried out with 5th, 7th and 9th grade students, was configured as an intervention study in which trees or lists were used as an intermediate representation of the departure register (natural language) to the arrival register (numerical expression). The results of the studies confirmed the hypothesis that the conversion to numerical expression is more complex than the conversion to trees or lists. It was also confirmed that trees are more congruent, than lists, with registers in numerical expression. It is concluded that the use of intermediate representations, such as trees or systematic lists, is a good teaching strategy for advances in the combinatorial reasoning of students in the early and middle years of schooling.
{"title":"REGISTERS OF SEMIOTIC REPRESENTATIONS AIDING THE LEARNING OF COMBINATORIAL SITUATIONS","authors":"Juliana Azevedo Montenegro, Rute E. de S. Rosa Borba, Marilena Bittar","doi":"10.54870/1551-3440.1537","DOIUrl":"https://doi.org/10.54870/1551-3440.1537","url":null,"abstract":"In order to analyze advances in the resolution of combinatorial situations, due to the identification, conversion and treatment of semiotic registers, two studies were carried out. In the first study, 5th grade students identified, from problems in natural language, registers in trees of possibilities, lists and numerical expressions. The second study, carried out with 5th, 7th and 9th grade students, was configured as an intervention study in which trees or lists were used as an intermediate representation of the departure register (natural language) to the arrival register (numerical expression). The results of the studies confirmed the hypothesis that the conversion to numerical expression is more complex than the conversion to trees or lists. It was also confirmed that trees are more congruent, than lists, with registers in numerical expression. It is concluded that the use of intermediate representations, such as trees or systematic lists, is a good teaching strategy for advances in the combinatorial reasoning of students in the early and middle years of schooling.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44536604","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}
Rosa Monteiro Paulo, A. Pereira, Elisangela Pavanelo
Digital Technologies are increasingly present in our activities. Many things we do we are not even able to imagine how they would be done, if we did not have the technological resources at hand. However, perhaps in the opposite direction of this, in the school context, or in teaching and learning, the discussion about the potential and the viability of these resources is still subject of a non-consensual discussion. When this context is Higher Education, specifically in undergraduate courses, the situation is even worse, as stated by research that we bring in this text. In disciplines such as Differential and Integral Calculus, Digital Technologies (DT) can contribute to a treatment in which aspects related to research and visualization are explored. Apps such as GeoGebra Augmented Reality, enhance the exploration of function graphs, for example, and, through movement, allow the analysis of invariants, favoring conceptual understanding. As we saw in the context of an activity proposed for students of a Mathematics Degree course, the app allows for interaction between students and enables them to conduct explorations that allow them to assign meaning to the contents of the Calculus discipline. This, therefore, is the theme that we deal with in this article, using a phenomenological stance to expose the meaning of what constitutes knowledge for us with DT.
{"title":"The constitution of mathematical knowledge with augmented reality","authors":"Rosa Monteiro Paulo, A. Pereira, Elisangela Pavanelo","doi":"10.54870/1551-3440.1539","DOIUrl":"https://doi.org/10.54870/1551-3440.1539","url":null,"abstract":"Digital Technologies are increasingly present in our activities. Many things we do we are not even able to imagine how they would be done, if we did not have the technological resources at hand. However, perhaps in the opposite direction of this, in the school context, or in teaching and learning, the discussion about the potential and the viability of these resources is still subject of a non-consensual discussion. When this context is Higher Education, specifically in undergraduate courses, the situation is even worse, as stated by research that we bring in this text. In disciplines such as Differential and Integral Calculus, Digital Technologies (DT) can contribute to a treatment in which aspects related to research and visualization are explored. Apps such as GeoGebra Augmented Reality, enhance the exploration of function graphs, for example, and, through movement, allow the analysis of invariants, favoring conceptual understanding. As we saw in the context of an activity proposed for students of a Mathematics Degree course, the app allows for interaction between students and enables them to conduct explorations that allow them to assign meaning to the contents of the Calculus discipline. This, therefore, is the theme that we deal with in this article, using a phenomenological stance to expose the meaning of what constitutes knowledge for us with DT.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46690177","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}
In this article, I carry out a qualitative metasynthesis of six doctoral theses that were directed by me, identifying the theoretical and methodological frameworks that support these researches, and how the articulations were made between different theories chosen. I also revisit the results achieved by the studies to highlight their relevance to the Mathematics Education area. This study, although not exhaustive, provides a vision of possible dialogs of Mathematics Education (or education) theories related to teaching and learning of mathematics and the Didactics of Mathematics. The diversity of theories and the specificities of each of them confirm the idea that a single theoretical tendency, or a single model, hardly ever explains and makes explicit all the phenomena involved in the teaching and learning processes of mathematical concepts. All the research works analyzed were used to study the epistemological, ecological, and economic dimensions, to identify the different forms of conceptions of a given mathematical object to help them in the didactic analysis of the findings. This study allowed us to identify, among other aspects, the reasons for being of the mathematical objects and the problems of their teaching. For teacher education, all mapped research, except one, has been supported in teacher education trajectories. The objective of these investigations is to familiarise teachers in initial or continuing education with these training trajectories as a didactic device that has the potential for their professional development, preparing them for an effective transition from the monumentalist paradigm to the world’s questioning paradigm. For the teachers’ training, the researchers presented didactic devices not based solely on the monumentalist paradigm, and somehow resorted to devices with PEP-FP-type structure.
{"title":"Metasynthesis of Research in Mathematics Education: Foci and Theoretical-Methodological Foundations","authors":"Saddo Ag Almouloud","doi":"10.54870/1551-3440.1531","DOIUrl":"https://doi.org/10.54870/1551-3440.1531","url":null,"abstract":"In this article, I carry out a qualitative metasynthesis of six doctoral theses that were directed by me, identifying the theoretical and methodological frameworks that support these researches, and how the articulations were made between different theories chosen. I also revisit the results achieved by the studies to highlight their relevance to the Mathematics Education area. This study, although not exhaustive, provides a vision of possible dialogs of Mathematics Education (or education) theories related to teaching and learning of mathematics and the Didactics of Mathematics. The diversity of theories and the specificities of each of them confirm the idea that a single theoretical tendency, or a single model, hardly ever explains and makes explicit all the phenomena involved in the teaching and learning processes of mathematical concepts. All the research works analyzed were used to study the epistemological, ecological, and economic dimensions, to identify the different forms of conceptions of a given mathematical object to help them in the didactic analysis of the findings. This study allowed us to identify, among other aspects, the reasons for being of the mathematical objects and the problems of their teaching. For teacher education, all mapped research, except one, has been supported in teacher education trajectories. The objective of these investigations is to familiarise teachers in initial or continuing education with these training trajectories as a didactic device that has the potential for their professional development, preparing them for an effective transition from the monumentalist paradigm to the world’s questioning paradigm. For the teachers’ training, the researchers presented didactic devices not based solely on the monumentalist paradigm, and somehow resorted to devices with PEP-FP-type structure.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42162751","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}
Carlos Eduardo Ferreira Monteiro, Liliane Maria Teixeira Lima de Carvalho
{"title":"Statistics education from the perspective of statistical literacy: Reflections taken from studies with teachers","authors":"Carlos Eduardo Ferreira Monteiro, Liliane Maria Teixeira Lima de Carvalho","doi":"10.54870/1551-3440.1538","DOIUrl":"https://doi.org/10.54870/1551-3440.1538","url":null,"abstract":"","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41863753","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 presents a study using a discursive perspective to develop a theoretical model of Mathematics for Teaching of the function concept, employing the following sources: a systematic review of the research literature, two series of textbooks and a discussion study with a group of teachers. The model presents a descriptive language with a theoretical structure that relies fundamentally on the realization and recognition rules inspired in Basil Bernstein's theory. Also, the model is based on categories of realizations (landscapes) of the concept of function. The landscapes that make up the model are the tabular, diagram, algebraic, transformation machine, graphic, pattern generalization and formal landscapes. The model provides a discursive transparency for the communication about function, which may inform curriculum development and curriculum material design for students and teachers as well as planning strategies to address this topic in educational contexts.
{"title":"A Theoretical Model of Mathematics for Teaching the Concept of Function","authors":"Graça Luzia Dominguez Santos, Jonei Cerqueira Barbosa","doi":"10.54870/1551-3440.1536","DOIUrl":"https://doi.org/10.54870/1551-3440.1536","url":null,"abstract":"This paper presents a study using a discursive perspective to develop a theoretical model of Mathematics for Teaching of the function concept, employing the following sources: a systematic review of the research literature, two series of textbooks and a discussion study with a group of teachers. The model presents a descriptive language with a theoretical structure that relies fundamentally on the realization and recognition rules inspired in Basil Bernstein's theory. Also, the model is based on categories of realizations (landscapes) of the concept of function. The landscapes that make up the model are the tabular, diagram, algebraic, transformation machine, graphic, pattern generalization and formal landscapes. The model provides a discursive transparency for the communication about function, which may inform curriculum development and curriculum material design for students and teachers as well as planning strategies to address this topic in educational contexts.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70968275","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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