Background: Teachers’ knowledge of mathematical reasoning and how to foster it in pupils influence the way they plan and conduct their lessons. In geometry, it implies developing visualisation and spatial structuring. Objectives: This article addresses the knowledge of the preservice and in-service primary teachers about reasoning processes, namely the way they relate several reasoning processes when solving a didactical task involving geometry. Design: The study reported here followed a qualitative-interpretative approach, adopting a design-based research modality. Setting and Participants: The teacher education experiments were developed with 31 preservice primary teachers and 19 in-service teachers of grades 1 to 6. The participants were not selected since they were the unique classes of pre- and in-service primary teachers in the institution. Data collection and analysis: Data were collected by audio and video records of lessons, participant observation and the collection of written records of the preservice teachers. We used content analysis of the data using the framework we elaborated on before concerned with knowledge of reasoning processes. Results: The preservice teachers identified the process of generalising, relating it with comparing and exemplifying processes. Regarding the process of justifying, participants used the association to understand why a relationship works as a selection criterion for that process. On the contrary, the distinction between justifying and generalising appeared to be more difficult for in-service teachers. Conclusions: Collaborative work on didactical tasks that are supported by relevant mathematical tasks and real classroom episodes are promising scenarios to develop teachers’ knowledge about mathematical reasoning.
{"title":"Preservice and In-Service Primary Teachers’ Knowledge of Mathematical Reasoning Processes in the Context of a Geometry Task","authors":"Lina Brunheira, Lurdes Serrazina, Margarida Rodrigues","doi":"10.17648/acta.scientiae.7122","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7122","url":null,"abstract":"Background: Teachers’ knowledge of mathematical reasoning and how to foster it in pupils influence the way they plan and conduct their lessons. In geometry, it implies developing visualisation and spatial structuring. Objectives: This article addresses the knowledge of the preservice and in-service primary teachers about reasoning processes, namely the way they relate several reasoning processes when solving a didactical task involving geometry. Design: The study reported here followed a qualitative-interpretative approach, adopting a design-based research modality. Setting and Participants: The teacher education experiments were developed with 31 preservice primary teachers and 19 in-service teachers of grades 1 to 6. The participants were not selected since they were the unique classes of pre- and in-service primary teachers in the institution. Data collection and analysis: Data were collected by audio and video records of lessons, participant observation and the collection of written records of the preservice teachers. We used content analysis of the data using the framework we elaborated on before concerned with knowledge of reasoning processes. Results: The preservice teachers identified the process of generalising, relating it with comparing and exemplifying processes. Regarding the process of justifying, participants used the association to understand why a relationship works as a selection criterion for that process. On the contrary, the distinction between justifying and generalising appeared to be more difficult for in-service teachers. Conclusions: Collaborative work on didactical tasks that are supported by relevant mathematical tasks and real classroom episodes are promising scenarios to develop teachers’ knowledge about mathematical reasoning.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44395470","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}
Pub Date : 2023-04-12DOI: 10.17648/acta.scientiae.7056
Maria Cristina Araújo de Oliveira, Reginaldo Fernando Carneiro
Background: Geometry seems to cause some strangeness and resistance when present in children's education over time and suggests that this characteristic is not exclusive to primary education or the initial years. Objective: To historically analyse two discourses that integrate proposals for teaching geometry present in current documents and programs, especially the National Common Curricular Base (BNCC) and the National Pact for Literacy at the Right Age (PNAIC): the plane-space relationship and the prominence of observation, manipulation, comparison, and visualization in learning geometry. Design: Based on themes for teaching geometry, proposals for teaching geometry in the early years and the historical relationships that can be established around them are discussed. Settings and Participants: current documents and programs that integrate proposals for teaching geometry in the early years. Data collection and analysis: Considering results obtained within the scope of research projects about the teaching of geometry in a historical perspective, located in the field of History of Mathematics Education and also in studies on the BNCC and the PNAIC, we proceeded with a new analytical elaboration. Results: Proposals for teaching geometry that last for many generations are highlighted, even with different objectives and purposes in each era. Observation, manipulation and comparison are also verified as strategies for teaching this theme that last over time. Conclusions: The dialogue between geometry teaching issues and its history of this teaching makes it possible to build a broader understanding of the difficulties and to elaborate proposals that can take into account the knowledge already produced.
{"title":"Geometry Teaching in the Early Years: A History that Encourages Reflections on the Present","authors":"Maria Cristina Araújo de Oliveira, Reginaldo Fernando Carneiro","doi":"10.17648/acta.scientiae.7056","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7056","url":null,"abstract":"Background: Geometry seems to cause some strangeness and resistance when present in children's education over time and suggests that this characteristic is not exclusive to primary education or the initial years. Objective: To historically analyse two discourses that integrate proposals for teaching geometry present in current documents and programs, especially the National Common Curricular Base (BNCC) and the National Pact for Literacy at the Right Age (PNAIC): the plane-space relationship and the prominence of observation, manipulation, comparison, and visualization in learning geometry. Design: Based on themes for teaching geometry, proposals for teaching geometry in the early years and the historical relationships that can be established around them are discussed. Settings and Participants: current documents and programs that integrate proposals for teaching geometry in the early years. Data collection and analysis: Considering results obtained within the scope of research projects about the teaching of geometry in a historical perspective, located in the field of History of Mathematics Education and also in studies on the BNCC and the PNAIC, we proceeded with a new analytical elaboration. Results: Proposals for teaching geometry that last for many generations are highlighted, even with different objectives and purposes in each era. Observation, manipulation and comparison are also verified as strategies for teaching this theme that last over time. Conclusions: The dialogue between geometry teaching issues and its history of this teaching makes it possible to build a broader understanding of the difficulties and to elaborate proposals that can take into account the knowledge already produced.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45398782","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}
Pub Date : 2023-04-05DOI: 10.17648/acta.scientiae.7160
Luiza Destefani Alves, Luciane Ferreira Mocrosky, Josiel de Oliveira Batista, José Sávio Bicho
Background: Mathematical literacy has been thematised in our studies by the importance of the initial ideas of mathematics in school paths. In this investigative path, the phenomenon of mathematics-literacy-from-Montessori-perspective stood out. Objectives: To answer the question: What is this, mathematical literacy from Montessori’s perspective? Design: Research of a theoretical nature, with a hermeneutic study of three works by Montessori closest to the phenomenon: The Discovery of the Child, Psychoarithmetic and Psychogeometry. After successive readings, we highlighted in each work excerpts that approached the question, calling them Units of Meaning (UM). Each UM was interpreted in dialogue with the work itself and other relevant authors. In all, 84 UMs were evidenced, which converged to 15 core ideas (CI). Placing all these CI side by side and asking what they said in the light of the guiding question, they enabled new convergence movements, evidencing basic characteristics of the phenomenon and geometry revealed itself as one of the guiding threads of mathematics teaching that aims at students’ learning. Setting and Participants: The theoretical study analysed the three works mentioned above. Data collection and analysis: The works that were closest to the highlighted phenomenon were selected and analysed hermeneutically. Results: The movement of understanding geometry, emerging from a larger study, clarifies Montessori’s understanding of the arithmetic-algebra-geometry triad, with a strong appeal to sensations and perception, emphasising the use of manipulative material, and with sequences that privilege abstractions. Conclusion: Knowing Montessori’s pedagogical proposal favours expanding teaching knowledge about mathematical literacy, woven in the close connection between methodologies, manipulative materials, articulation of mathematics, and teaching posture.
{"title":"Movement of Understanding of Mathematical Literacy from Montessori’s Perspective: An Approach to the Teaching Processes of Geometry","authors":"Luiza Destefani Alves, Luciane Ferreira Mocrosky, Josiel de Oliveira Batista, José Sávio Bicho","doi":"10.17648/acta.scientiae.7160","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7160","url":null,"abstract":"Background: Mathematical literacy has been thematised in our studies by the importance of the initial ideas of mathematics in school paths. In this investigative path, the phenomenon of mathematics-literacy-from-Montessori-perspective stood out. Objectives: To answer the question: What is this, mathematical literacy from Montessori’s perspective? Design: Research of a theoretical nature, with a hermeneutic study of three works by Montessori closest to the phenomenon: The Discovery of the Child, Psychoarithmetic and Psychogeometry. After successive readings, we highlighted in each work excerpts that approached the question, calling them Units of Meaning (UM). Each UM was interpreted in dialogue with the work itself and other relevant authors. In all, 84 UMs were evidenced, which converged to 15 core ideas (CI). Placing all these CI side by side and asking what they said in the light of the guiding question, they enabled new convergence movements, evidencing basic characteristics of the phenomenon and geometry revealed itself as one of the guiding threads of mathematics teaching that aims at students’ learning. Setting and Participants: The theoretical study analysed the three works mentioned above. Data collection and analysis: The works that were closest to the highlighted phenomenon were selected and analysed hermeneutically. Results: The movement of understanding geometry, emerging from a larger study, clarifies Montessori’s understanding of the arithmetic-algebra-geometry triad, with a strong appeal to sensations and perception, emphasising the use of manipulative material, and with sequences that privilege abstractions. Conclusion: Knowing Montessori’s pedagogical proposal favours expanding teaching knowledge about mathematical literacy, woven in the close connection between methodologies, manipulative materials, articulation of mathematics, and teaching posture.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47361426","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}
Pub Date : 2023-04-05DOI: 10.17648/acta.scientiae.7238
J. Cogolludo-Agustín, Paola Magrone, Elena Gil Clemente, Ana Millán Gasca
Background : Studies on cognition in children with Down Syndrome (Trisomy 21) have described poor performance manipulating numbers. Elisabetta Monari Martinez's (2002) research suggest that considering mathematics as a universe of exploration beyond written arithmetic can offer them an opportunity for “human flourishing” (Su, 2020). Geometry offers a suitable starting point. Objective : Exploring the use of geometrical activities for introducing children with T21 to integer and rational numbers. Design : A series of 7 workshops were designed to convey arithmetic concepts (counting, comparing and measuring) through plane geometry activities. Setting and Participants : Seven children aged 9 to 13, who had already completed a 3-year work on geometry, participated in the workshops held at the venue of the Spanish association Sesdown in Zaragoza, in leisure time. Data collection and analysis : Raw data consisted of 1) written reflections of lived experience (Van Manen, 1990) by all adults participating in the experiment, following a shared protocol observation guide; 2
{"title":"Geometrical Awareness Enhances Numeracy in Children with Trisomy 21","authors":"J. Cogolludo-Agustín, Paola Magrone, Elena Gil Clemente, Ana Millán Gasca","doi":"10.17648/acta.scientiae.7238","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7238","url":null,"abstract":"Background : Studies on cognition in children with Down Syndrome (Trisomy 21) have described poor performance manipulating numbers. Elisabetta Monari Martinez's (2002) research suggest that considering mathematics as a universe of exploration beyond written arithmetic can offer them an opportunity for “human flourishing” (Su, 2020). Geometry offers a suitable starting point. Objective : Exploring the use of geometrical activities for introducing children with T21 to integer and rational numbers. Design : A series of 7 workshops were designed to convey arithmetic concepts (counting, comparing and measuring) through plane geometry activities. Setting and Participants : Seven children aged 9 to 13, who had already completed a 3-year work on geometry, participated in the workshops held at the venue of the Spanish association Sesdown in Zaragoza, in leisure time. Data collection and analysis : Raw data consisted of 1) written reflections of lived experience (Van Manen, 1990) by all adults participating in the experiment, following a shared protocol observation guide; 2","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41906228","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}
Pub Date : 2023-04-04DOI: 10.17648/acta.scientiae.7185
Carlos Rojas Suárez, Tomás Ángel Sierra Delgado
Background: The analysis of the geometric knowledge presented in the secondary education curriculum reveals phenomena such as the separation between 2D and 3D geometry and the weakening of the modelling activity in geometry. Brousseau considers that the construction of figures is a first example of geometrical modelling. Objectives: To build a reference epistemological model that clearly sets out the conditions that allow determining the shape and size of a solid and looking for possible techniques that enable constructing it. Design: theoretical research within the framework of the Anthropological Theory of the Didactic. Setting and participants: The model built is the result of several activities carried out in the last three years: an analysis of school texts, and the design, implementation, and analysis of a study and research path regarding the design of a container in two secondary schools with students aged between 14 and 17. Data collection and analysis: The model is based on the analysis of information collected from scientific texts by Pólya and other authors, from official texts and secondary education textbooks, and from the experiments carried out. Results: The model is based on the structured study of twoand three-dimensional geometry and allows guiding study processes aimed at consistently addressing the problem of determining a solid and its construction. Conclusions: The model developed includes questions regarding spatial-geometric modelling considered to be central in the introduction to geometry in secondary education.
{"title":"A Reference Epistemological Model Regarding the Determination and Construction of Solids for Compulsory Secondary Education","authors":"Carlos Rojas Suárez, Tomás Ángel Sierra Delgado","doi":"10.17648/acta.scientiae.7185","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7185","url":null,"abstract":"Background: The analysis of the geometric knowledge presented in the secondary education curriculum reveals phenomena such as the separation between 2D and 3D geometry and the weakening of the modelling activity in geometry. Brousseau considers that the construction of figures is a first example of geometrical modelling. Objectives: To build a reference epistemological model that clearly sets out the conditions that allow determining the shape and size of a solid and looking for possible techniques that enable constructing it. Design: theoretical research within the framework of the Anthropological Theory of the Didactic. Setting and participants: The model built is the result of several activities carried out in the last three years: an analysis of school texts, and the design, implementation, and analysis of a study and research path regarding the design of a container in two secondary schools with students aged between 14 and 17. Data collection and analysis: The model is based on the analysis of information collected from scientific texts by Pólya and other authors, from official texts and secondary education textbooks, and from the experiments carried out. Results: The model is based on the structured study of twoand three-dimensional geometry and allows guiding study processes aimed at consistently addressing the problem of determining a solid and its construction. Conclusions: The model developed includes questions regarding spatial-geometric modelling considered to be central in the introduction to geometry in secondary education.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46997118","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}
Pub Date : 2023-03-31DOI: 10.17648/acta.scientiae.7128
Mariana Duarte De Souza, Thiago Pedro Pinto
Background: Math teacher training in Brazil has been the subject of numerous studies under the most diverse approaches. From a historiographical perspective, we can highlight the performance of the Oral History and Mathematics Education Group and the History of Mathematics Education in the Research Group, both acting more directly with the narratives. Disciplines with the content of Geometric Constructions have historically been part of the training of Mathematics teachers. At issue in this text is the contribution of these disciplines to the formation of future teachers. Objective: This paper adds elements to mapping Mat teacher training and performance in the state of Mato Grosso do Sul and in Brazil, expanding discussions about the state and the possible role of geometric disciplines in undergraduate courses. Design: We present the normative documents of such courses and disciplines and the narratives, in the end, comparing the relevant literature for their analysis based on the researchers' questions. Environment and participants: Courses of Math Teacher Training at the Federal University of Mato Grosso do Sul – Brazil. The time frame of the research ranged from 2004 to 2019, the period in which the seven interviewees taught the subjects mentioned earlier. Data collection and analysis: The narratives of the interviewees, the teaching materials presented by them, and the normative documents are analyzed. Results: The narratives and pertinent literature allowed us a dispersive look, which turned outside the narratives themselves, having in them the triggering movement of reflections. Thus, we could produce questions and possible answers to such inquiries. Conclusions: Among the final notes, the following stand out: the importance of these disciplines, identified as “basic” in the course, to recover Geometry contents that students should have studied in Basic Education; the relevance of failure as a stimulus for the study; and the choice of materials that focus on other aspects of geometry. Such subjects are often intended for the substitute teacher, and there is no prior training to work in this discipline with a specific focus on teacher training.
{"title":"Geometric Constructions in the Current Math Teacher Training Courses at the Federal University of Mato Grosso do Sul","authors":"Mariana Duarte De Souza, Thiago Pedro Pinto","doi":"10.17648/acta.scientiae.7128","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7128","url":null,"abstract":"Background: Math teacher training in Brazil has been the subject of numerous studies under the most diverse approaches. From a historiographical perspective, we can highlight the performance of the Oral History and Mathematics Education Group and the History of Mathematics Education in the Research Group, both acting more directly with the narratives. Disciplines with the content of Geometric Constructions have historically been part of the training of Mathematics teachers. At issue in this text is the contribution of these disciplines to the formation of future teachers. Objective: This paper adds elements to mapping Mat teacher training and performance in the state of Mato Grosso do Sul and in Brazil, expanding discussions about the state and the possible role of geometric disciplines in undergraduate courses. Design: We present the normative documents of such courses and disciplines and the narratives, in the end, comparing the relevant literature for their analysis based on the researchers' questions. Environment and participants: Courses of Math Teacher Training at the Federal University of Mato Grosso do Sul – Brazil. The time frame of the research ranged from 2004 to 2019, the period in which the seven interviewees taught the subjects mentioned earlier. Data collection and analysis: The narratives of the interviewees, the teaching materials presented by them, and the normative documents are analyzed. Results: The narratives and pertinent literature allowed us a dispersive look, which turned outside the narratives themselves, having in them the triggering movement of reflections. Thus, we could produce questions and possible answers to such inquiries. Conclusions: Among the final notes, the following stand out: the importance of these disciplines, identified as “basic” in the course, to recover Geometry contents that students should have studied in Basic Education; the relevance of failure as a stimulus for the study; and the choice of materials that focus on other aspects of geometry. Such subjects are often intended for the substitute teacher, and there is no prior training to work in this discipline with a specific focus on teacher training.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43188471","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}
Pub Date : 2023-03-27DOI: 10.17648/acta.scientiae.7131
Beatriz Fernanda Litoldo, Rúbia Barcelos Amaral, Lucas Carato Mazzi
Background: Geometry is often seen as an area of mathematics that is present in everyone’s daily life. Looking around, we see it in the shapes of objects, in nature, etc. Therefore, it would be natural to expect that its approach in textbooks, for example, would bring different contexts in which it would be present. Objective: To discuss how contexts are introduced in geometry tasks in a collection of mathematics textbooks. Design: We use a qualitative approach of the documentary type as a methodology. Environment and participants: A collection of high school mathematics textbooks approved by the National Textbook and Didactic Material Program – 2018 was selected. Data collection and analysis: Data were produced, organised, and analysed using horizontal and vertical analysis methods in each collection volume, according to the different references of contexts. Results: They concern the different references of contexts involved in the tasks. From the 1,335 tasks analysed, 1,108 were contextualised in purely mathematical situations, while the rest, 227, were in contexts of reality. In this, there are 215 referring to reasonable semi-realities, and, on the other hand, the real context contemplates only three. Finally, nine concern tasks in unreasonable semi-real contexts. Conclusions: The restriction of the different context references that students can experience from this collection is discussed. The contexts presented do not include a broad spectrum based on a diversity of experiences among the different references of contexts.
{"title":"Contextualisation of Geometry Tasks in High School Mathematics Textbooks","authors":"Beatriz Fernanda Litoldo, Rúbia Barcelos Amaral, Lucas Carato Mazzi","doi":"10.17648/acta.scientiae.7131","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7131","url":null,"abstract":"Background: Geometry is often seen as an area of mathematics that is present in everyone’s daily life. Looking around, we see it in the shapes of objects, in nature, etc. Therefore, it would be natural to expect that its approach in textbooks, for example, would bring different contexts in which it would be present. Objective: To discuss how contexts are introduced in geometry tasks in a collection of mathematics textbooks. Design: We use a qualitative approach of the documentary type as a methodology. Environment and participants: A collection of high school mathematics textbooks approved by the National Textbook and Didactic Material Program – 2018 was selected. Data collection and analysis: Data were produced, organised, and analysed using horizontal and vertical analysis methods in each collection volume, according to the different references of contexts. Results: They concern the different references of contexts involved in the tasks. From the 1,335 tasks analysed, 1,108 were contextualised in purely mathematical situations, while the rest, 227, were in contexts of reality. In this, there are 215 referring to reasonable semi-realities, and, on the other hand, the real context contemplates only three. Finally, nine concern tasks in unreasonable semi-real contexts. Conclusions: The restriction of the different context references that students can experience from this collection is discussed. The contexts presented do not include a broad spectrum based on a diversity of experiences among the different references of contexts.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44816859","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}
Pub Date : 2023-03-27DOI: 10.17648/acta.scientiae.7164
Anna Flávia Magnoni Vieira, M. Cyrino
Background: The study of geometric thinking in the preservice education of mathematics teachers is an emerging theme that can reverberate in the teaching of geometry in basic education. Objectives: To analyse reflections manifested by prospective mathematics teachers (PMTs), working with tasks supported by van Hiele theoretical model to develop geometric thinking. Design: The nature of this study is qualitative and interpretative. Setting and participants: Twenty-four PMTs members of a geometry teaching subject were investigated in a mathematics degree course at a public university in Paraná - Brazil. Data collection and analysis: The data was collected from the video-recorded training sessions, the written production of the PMTs promoted by the tasks and the registers kept on the field diary. The analysis focused on the reflections expressed by PMTs regarding the work with tasks involving geometric thinking, considering the levels of reflection proposed by Muir and Beswick (2007). Results: The results show descriptive, deliberate, and critical reflections, with different levels of incidence, associated with (I) the levels of thought proposed in the van Hiele model; (II) the teacher’s role in classroom practice; and (III) the geometric concepts and properties of flat figures. Conclusions: The promotion of formative actions that privilege discussions and reflections on geometric thinking can allow PMTs to seek connections between knowledge of geometry, geometric thinking, and their future teaching practice.
{"title":"Geometric Thinking: Reflections Manifested by Preservice Mathematics Teachers in van Hiele Model Studies","authors":"Anna Flávia Magnoni Vieira, M. Cyrino","doi":"10.17648/acta.scientiae.7164","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7164","url":null,"abstract":"Background: The study of geometric thinking in the preservice education of mathematics teachers is an emerging theme that can reverberate in the teaching of geometry in basic education. Objectives: To analyse reflections manifested by prospective mathematics teachers (PMTs), working with tasks supported by van Hiele theoretical model to develop geometric thinking. Design: The nature of this study is qualitative and interpretative. Setting and participants: Twenty-four PMTs members of a geometry teaching subject were investigated in a mathematics degree course at a public university in Paraná - Brazil. Data collection and analysis: The data was collected from the video-recorded training sessions, the written production of the PMTs promoted by the tasks and the registers kept on the field diary. The analysis focused on the reflections expressed by PMTs regarding the work with tasks involving geometric thinking, considering the levels of reflection proposed by Muir and Beswick (2007). Results: The results show descriptive, deliberate, and critical reflections, with different levels of incidence, associated with (I) the levels of thought proposed in the van Hiele model; (II) the teacher’s role in classroom practice; and (III) the geometric concepts and properties of flat figures. Conclusions: The promotion of formative actions that privilege discussions and reflections on geometric thinking can allow PMTs to seek connections between knowledge of geometry, geometric thinking, and their future teaching practice.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46884022","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}
Pub Date : 2023-03-27DOI: 10.17648/acta.scientiae.7126
Alexsandra Camara, Maria Célia Leme da Silva, Claudia Regina Boen Frizzarini
Background: Research in the history of mathematics education makes it possible to identify the links between manual practices and the teaching of geometry in the early years since the insertion of the subject Handwork, at the end of the 19th century, to the present time. Objectives: Analyse the interconnections between manual practices and the teaching of geometry developed by the school culture of primary education in São Paulo, since the early Republic. Design: The curricular regulations of the state of São Paulo and the national guidelines – PCN and BNCC – and school manuals that circulated in each historical moment are mobilised together with the results of research already developed in the area. The documents were collated and analysed to produce an understandable and sustainable historical narrative, based on evidence and controls. Data collection and analysis: The study inventoried research results and analysed teaching programs in the State of São Paulo, national guidelines at the end of the 20th century, and school manuals from different periods. Setting and participants: The research sources are documentary, most of them available in the UFSC Digital Repository. Results: The documental examination indicated that manual practices actively participate in the school culture and cause changes, from time to time. Handwork change its status from a school subject to a geometry teaching methodology, intended for the early school years, which we observe to this day. Conclusions: This research concluded that the understanding of the historical perspective contributes to reflection on the current educational problems, on the debate about how to mobilise tools for geometry teaching, questioning the feasibility or not of handwork acting as an appropriate methodology for the first explorations of geometric properties.
{"title":"Handwork and Geometry in the Early Years: Curricular Movements (1890-2020)","authors":"Alexsandra Camara, Maria Célia Leme da Silva, Claudia Regina Boen Frizzarini","doi":"10.17648/acta.scientiae.7126","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7126","url":null,"abstract":"Background: Research in the history of mathematics education makes it possible to identify the links between manual practices and the teaching of geometry in the early years since the insertion of the subject Handwork, at the end of the 19th century, to the present time. Objectives: Analyse the interconnections between manual practices and the teaching of geometry developed by the school culture of primary education in São Paulo, since the early Republic. Design: The curricular regulations of the state of São Paulo and the national guidelines – PCN and BNCC – and school manuals that circulated in each historical moment are mobilised together with the results of research already developed in the area. The documents were collated and analysed to produce an understandable and sustainable historical narrative, based on evidence and controls. Data collection and analysis: The study inventoried research results and analysed teaching programs in the State of São Paulo, national guidelines at the end of the 20th century, and school manuals from different periods. Setting and participants: The research sources are documentary, most of them available in the UFSC Digital Repository. Results: The documental examination indicated that manual practices actively participate in the school culture and cause changes, from time to time. Handwork change its status from a school subject to a geometry teaching methodology, intended for the early school years, which we observe to this day. Conclusions: This research concluded that the understanding of the historical perspective contributes to reflection on the current educational problems, on the debate about how to mobilise tools for geometry teaching, questioning the feasibility or not of handwork acting as an appropriate methodology for the first explorations of geometric properties.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43408466","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}
Pub Date : 2023-03-27DOI: 10.17648/acta.scientiae.7134
Gabriela Daiani de Freitas, Kelly Roberta Mazzutti Lübeck, Marcos Lübeck
Background: Geometry is an important branch of mathematics and there are many arguments in favour of teaching it at all educational levels. Objectives: To analyse the pedagogical projects of the degree in mathematics courses (PPC) of Paraná state universities, to identify how geometry contents are organised for the degree students' education from the perspective of the current regulations. Design: Exploratory research developed from bibliographical and documentary studies, focused on the National Common Core Curriculum (BNCC), the Paraná Curriculum Reference (RCP) and the PPCs of several mathematics degree courses. Setting and participants: We examined the fifteen PPCs of the state universities of Paraná, obtained from the institutional websites or by email via course coordination. Data collection and analysis: We explored the resources and subsequently developed the categories based on the learning objectives of the BNCC, the RCP, and the regulations for initial teacher education courses, supporting the procedures mobilised on the content analysis. Results: We found that the geometry learning objectives in the regulations align with the profiles identified in the PPCs and the contents presented in their syllabuses. Conclusions: We admit the relevance of a complete and broad curriculum for the initial education of mathematics teachers. However, we believe it should not be imposed or inappropriate but the basis for qualifying good professionals who, in the future, will favour the development of students' capacities such as reflection, autonomy, and collaboration.
{"title":"Geometry in the Curriculum Pedagogical Projects of Mathematics Degree Courses at Parana State Universities","authors":"Gabriela Daiani de Freitas, Kelly Roberta Mazzutti Lübeck, Marcos Lübeck","doi":"10.17648/acta.scientiae.7134","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7134","url":null,"abstract":"Background: Geometry is an important branch of mathematics and there are many arguments in favour of teaching it at all educational levels. Objectives: To analyse the pedagogical projects of the degree in mathematics courses (PPC) of Paraná state universities, to identify how geometry contents are organised for the degree students' education from the perspective of the current regulations. Design: Exploratory research developed from bibliographical and documentary studies, focused on the National Common Core Curriculum (BNCC), the Paraná Curriculum Reference (RCP) and the PPCs of several mathematics degree courses. Setting and participants: We examined the fifteen PPCs of the state universities of Paraná, obtained from the institutional websites or by email via course coordination. Data collection and analysis: We explored the resources and subsequently developed the categories based on the learning objectives of the BNCC, the RCP, and the regulations for initial teacher education courses, supporting the procedures mobilised on the content analysis. Results: We found that the geometry learning objectives in the regulations align with the profiles identified in the PPCs and the contents presented in their syllabuses. Conclusions: We admit the relevance of a complete and broad curriculum for the initial education of mathematics teachers. However, we believe it should not be imposed or inappropriate but the basis for qualifying good professionals who, in the future, will favour the development of students' capacities such as reflection, autonomy, and collaboration.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48276648","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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