Pub Date : 2023-02-11DOI: 10.17648/acta.scientiae.7153
I. Giongo, Sonia Elisa Marchi Gonzati, M. Quartieri, Marcia Jussara Hepp Rehfeldt
Context: Assessment could provide feedback to both students and teachers on teaching and learning processes. However, this perspective coexists with an evaluation dynamic focused on performance and results. Objectives: This research intends to problematize what a group of Engineering students says about the evaluation processes and their purposes in Mathematics and Physics subjects, offered in the context of remote teaching. Design: Ideas from qualitative research in a Foucauldian perspective. Environment and participants: The sample consisted of 85 engineering students, enrolled in Physics and Calculus subjects, in the first semester of 2021. Data collection and analysis: Application of an online questionnaire, with six Physics or Calculus classes, in a community university of Rio Grande do Sul. Results: The discourse analysis according to the Foucauldian perspective produced two analysis units that indicate how the eighty-seven participating students conceive evaluation in their utterances. The first one indicates that they think evaluation enables their own learning to be monitored and assessed, and decisions to be made by professors. The other one points out that students conceive evaluation as classifying and meritocratic, focusing on performance, outcomes, and grade measurement. Conclusions: Contradictory and complementary conceptions coexist, indicative of the different roles attributed to assessment in formal education contexts. In general, the research participants evidence the reproduction of statements that circulate socially about the evaluation and its roles. Such results can be productive for teachers and institutions to understand that they also meet the expectations of an evaluation system with an emphasis on regulation and control.
{"title":"Engineering Students’ Utterances about Evaluation and Its Roles in the Courses of Physics and Calculus","authors":"I. Giongo, Sonia Elisa Marchi Gonzati, M. Quartieri, Marcia Jussara Hepp Rehfeldt","doi":"10.17648/acta.scientiae.7153","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7153","url":null,"abstract":"Context: Assessment could provide feedback to both students and teachers on teaching and learning processes. However, this perspective coexists with an evaluation dynamic focused on performance and results. Objectives: This research intends to problematize what a group of Engineering students says about the evaluation processes and their purposes in Mathematics and Physics subjects, offered in the context of remote teaching. Design: Ideas from qualitative research in a Foucauldian perspective. Environment and participants: The sample consisted of 85 engineering students, enrolled in Physics and Calculus subjects, in the first semester of 2021. Data collection and analysis: Application of an online questionnaire, with six Physics or Calculus classes, in a community university of Rio Grande do Sul. Results: The discourse analysis according to the Foucauldian perspective produced two analysis units that indicate how the eighty-seven participating students conceive evaluation in their utterances. The first one indicates that they think evaluation enables their own learning to be monitored and assessed, and decisions to be made by professors. The other one points out that students conceive evaluation as classifying and meritocratic, focusing on performance, outcomes, and grade measurement. Conclusions: Contradictory and complementary conceptions coexist, indicative of the different roles attributed to assessment in formal education contexts. In general, the research participants evidence the reproduction of statements that circulate socially about the evaluation and its roles. Such results can be productive for teachers and institutions to understand that they also meet the expectations of an evaluation system with an emphasis on regulation and control.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45465268","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 : 2023-01-06DOI: 10.17648/acta.scientiae.7356
Camilo Andrés Rodríguez-Nieto, Yeimer Carlos Escobar-Ramírez, Vicenç Font Moll, Armando Aroca Araújo
Background : Connections are essential for understanding concepts, but difficulties have been evidenced in connecting representations and meanings of concepts and creating contextualised mathematical problems by teachers and students. Objective : Therefore, ethnomathematical and mathematical connections were analysed in a teacher’s mathematical activity when posing and solving mathematical problems. Design : The methodology was qualitative-ethnographic, developed in a workshop done in stages. Setting and participants : An indigenous Mokaná teacher from Sibarco was selected. Data collection and analysis : Semi-structured interviews were conducted in the workshop
{"title":"Ethnomathematical and Mathematical Connections Activated by a Teacher in Mathematical Problems Posing and Solving","authors":"Camilo Andrés Rodríguez-Nieto, Yeimer Carlos Escobar-Ramírez, Vicenç Font Moll, Armando Aroca Araújo","doi":"10.17648/acta.scientiae.7356","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7356","url":null,"abstract":"Background : Connections are essential for understanding concepts, but difficulties have been evidenced in connecting representations and meanings of concepts and creating contextualised mathematical problems by teachers and students. Objective : Therefore, ethnomathematical and mathematical connections were analysed in a teacher’s mathematical activity when posing and solving mathematical problems. Design : The methodology was qualitative-ethnographic, developed in a workshop done in stages. Setting and participants : An indigenous Mokaná teacher from Sibarco was selected. Data collection and analysis : Semi-structured interviews were conducted in the workshop","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48716499","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 : 2023-01-03DOI: 10.17648/acta.scientiae.6974
Francisco Rodríguez-Alveal, Maitere Aguerrea, Danilo Díaz-Levicoy
Background: Randomness is a fundamental concept in the formation of citizens because it intervenes in various daily life situations. In addition, it is present in the school curriculum of various countries, such as Chile. Objective : To analyse the teaching of the concept of randomness in primary education mathematics textbooks in Chile. Design: The research uses a qualitative methodology and uses the content-analysis method. Setting and participants : 42 textbooks were analysed, including student texts and activity logs. Data collection and analysis : Through content analysis, the sections and segments of the textbooks in which the concept of randomness intervenes are studied, relating them to definitions, problem situations, cognitive levels that should be developed, and the use of technological tools. Results : The concept of randomness is introduced through random games and concepts associated with random experiment, chance, random, and sample space, without delving into the definition of some cardinal concepts such as chance and randomness. Conclusions : The textbooks partially conform to the Chilean curricular guidelines. In addition, activities related to the concept of randomness generally refer to the use of physical devices and, on a small scale, to the use of technological tools. Finally, the textbooks present a small number of problem situations with an adequate cognitive level that favours the development of skills necessary for primary education students’ acquisition of probabilistic thinking.
{"title":"The Concept of Randomness in Chilean Primary School Textbooks","authors":"Francisco Rodríguez-Alveal, Maitere Aguerrea, Danilo Díaz-Levicoy","doi":"10.17648/acta.scientiae.6974","DOIUrl":"https://doi.org/10.17648/acta.scientiae.6974","url":null,"abstract":"Background: Randomness is a fundamental concept in the formation of citizens because it intervenes in various daily life situations. In addition, it is present in the school curriculum of various countries, such as Chile. Objective : To analyse the teaching of the concept of randomness in primary education mathematics textbooks in Chile. Design: The research uses a qualitative methodology and uses the content-analysis method. Setting and participants : 42 textbooks were analysed, including student texts and activity logs. Data collection and analysis : Through content analysis, the sections and segments of the textbooks in which the concept of randomness intervenes are studied, relating them to definitions, problem situations, cognitive levels that should be developed, and the use of technological tools. Results : The concept of randomness is introduced through random games and concepts associated with random experiment, chance, random, and sample space, without delving into the definition of some cardinal concepts such as chance and randomness. Conclusions : The textbooks partially conform to the Chilean curricular guidelines. In addition, activities related to the concept of randomness generally refer to the use of physical devices and, on a small scale, to the use of technological tools. Finally, the textbooks present a small number of problem situations with an adequate cognitive level that favours the development of skills necessary for primary education students’ acquisition of probabilistic thinking.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45193740","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 : 2023-01-03DOI: 10.17648/acta.scientiae.7289
Danila Brígida Santana Imafuku, Maria Elisa Esteves Lopes Galvão, Angélica Da Fontoura Garcia Silva
Background: The studies emphasise the importance of a kind of teaching that contributes to understanding the concept and the calculus of the area of plane figures, considering the textbooks that are often the main resource teachers use to prepare classes. Objective: To investigate how the topic area of flat figures is introduced and guided in elementary school textbooks and to verify the potential and limitations of the proposals to mobilise the figural apprehensions and acquire knowledge. Design: This is a documentary research with a methodology based on the content analysis proposed by Bardin. Setting and participants: Four collections approved by the PNLD in 2019 and 2020 were selected. Data collection and analysis: In these collections, the volumes and units that addressed the topic in question were identified. The data analysis, carried out in light of Duval’s figural apprehensions and the four stages suggested by Clements and Stephan for constructing the concept of plane figure areas, seeks to identify whether the mathematical skills described by the BNCC can be favoured. Results: the proposals of the collections show the importance of using the grid for introducing the concept and calculation of the area of plane figures at the different levels of education; however, few activities mobilise reconfiguration processes. Conclusions: It is essential to propose activities that allow students to understand the area equivalence between the modified figures and lead them to understand the rectangular configuration and the formulas for area calculation.
{"title":"The Surface Area of Plane Figures in Textbooks throughout Elementary School","authors":"Danila Brígida Santana Imafuku, Maria Elisa Esteves Lopes Galvão, Angélica Da Fontoura Garcia Silva","doi":"10.17648/acta.scientiae.7289","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7289","url":null,"abstract":"Background: The studies emphasise the importance of a kind of teaching that contributes to understanding the concept and the calculus of the area of plane figures, considering the textbooks that are often the main resource teachers use to prepare classes. Objective: To investigate how the topic area of flat figures is introduced and guided in elementary school textbooks and to verify the potential and limitations of the proposals to mobilise the figural apprehensions and acquire knowledge. Design: This is a documentary research with a methodology based on the content analysis proposed by Bardin. Setting and participants: Four collections approved by the PNLD in 2019 and 2020 were selected. Data collection and analysis: In these collections, the volumes and units that addressed the topic in question were identified. The data analysis, carried out in light of Duval’s figural apprehensions and the four stages suggested by Clements and Stephan for constructing the concept of plane figure areas, seeks to identify whether the mathematical skills described by the BNCC can be favoured. Results: the proposals of the collections show the importance of using the grid for introducing the concept and calculation of the area of plane figures at the different levels of education; however, few activities mobilise reconfiguration processes. Conclusions: It is essential to propose activities that allow students to understand the area equivalence between the modified figures and lead them to understand the rectangular configuration and the formulas for area calculation.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46728326","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 : 2023-01-03DOI: 10.17648/acta.scientiae.6819
Francisco Wagner Soares Oliveira, A. C. Pereira
Background: This work follows in the direction of research dedicated to articulating historical instruments to teach mathematics. Objectives: To analyse the use of the instrument to find the altitude of the Sun as a didactic resource for teaching and learning the concepts of chord and arc of a circle in the education of undergraduate students in mathematics. Design: The research takes place through a university extension course that uses the theoretical and methodological foundations of the teaching guidance activity. Setting and Participants: The research environment is the training of students at the State University of Ceará. The training action was attended by 12 participants. The choice criterion was that they were studying for a degree in mathematics, and the selection took place in the order of enrollment in the activity. Data collection and analysis: From the assumptions of the teaching guidance activity, data collection was carried out with the recording of videos and audio, photographic records and students’ writings, while the analysis was based on connections and interconnections on the action of the subjects, and on the conceptual nexuses. Results: The new instrument to find the altitude of the Sun has didactic potential to work with the concepts of arc and chord of circumference because, from it, these concepts are mobilised as practice, and it is possible to see how they relate. Conclusions: The new instrument to find the altitude of the Sun can be explored in the interface between history and mathematics teaching as a resource to favour teaching and learning, whether in basic education or higher education.
{"title":"A Nautical Instrument Lying of the Plane in Teaching the Concepts of Chord and Arc of Circumference","authors":"Francisco Wagner Soares Oliveira, A. C. Pereira","doi":"10.17648/acta.scientiae.6819","DOIUrl":"https://doi.org/10.17648/acta.scientiae.6819","url":null,"abstract":"Background: This work follows in the direction of research dedicated to articulating historical instruments to teach mathematics. Objectives: To analyse the use of the instrument to find the altitude of the Sun as a didactic resource for teaching and learning the concepts of chord and arc of a circle in the education of undergraduate students in mathematics. Design: The research takes place through a university extension course that uses the theoretical and methodological foundations of the teaching guidance activity. Setting and Participants: The research environment is the training of students at the State University of Ceará. The training action was attended by 12 participants. The choice criterion was that they were studying for a degree in mathematics, and the selection took place in the order of enrollment in the activity. Data collection and analysis: From the assumptions of the teaching guidance activity, data collection was carried out with the recording of videos and audio, photographic records and students’ writings, while the analysis was based on connections and interconnections on the action of the subjects, and on the conceptual nexuses. Results: The new instrument to find the altitude of the Sun has didactic potential to work with the concepts of arc and chord of circumference because, from it, these concepts are mobilised as practice, and it is possible to see how they relate. Conclusions: The new instrument to find the altitude of the Sun can be explored in the interface between history and mathematics teaching as a resource to favour teaching and learning, whether in basic education or higher education.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45073686","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 : 2022-12-21DOI: 10.17648/acta.scientiae.7402
Janice Rachelli, Ana Lúcia Uberti Pinheiro, Leonard Porta
Background: Guy Brousseau’s theory of didactic situations has been considered an apparatus for the methodological structuring of didactic sequences configured in didactic and adidactic situations. Objectives: To investigate the contributions of the theory of didactic situations to the study of round bodies, focused on a praxis that meaningfully consolidates knowledge for the students. Design: We propose solving problem situations concerning the calculus of surface areas and volumes of round bodies using Cavalieri’s principle and Pappus’s theorems. Setting and participants: The research was conducted with two high school third-grade classes of a state institute of education located in the municipality of Júlio de Castilhos, RS, Brazil, with the participation of 25 students. Data collection and analysis: It was carried out through activities developed in the classroom and feedback given through Google Classroom. It was subsidised by the documental transcription of students’ records. Results: The research indicated that the didactic sequence development favoured intellectual autonomy and meaningful learning about the object of knowledge. Conclusions: The theory of didactic situations provided important subsidies for didactic organisation and analysis of the knowledge consolidation process involving the study of round bodies, indicating its application in the study of other mathematical objects in high school and higher education.
背景:盖伊·布鲁梭的教学情境理论被认为是在教学情境和教学情境中配置的教学序列的方法论结构工具。目的:探讨教学情境理论对圆体研究的贡献，着重于为学生有意义地巩固知识的实践。设计:我们提出用卡瓦列里原理和帕普斯定理解决有关圆体表面积和体积计算的问题。环境和参与者:该研究是在巴西RS市Júlio de Castilhos市的一所国立教育学院的两个高中三年级班级进行的，共有25名学生参与。数据收集和分析:通过在课堂上开展的活动和谷歌课堂的反馈来进行。它是由学生记录的文件转录资助的。结果:教学顺序的发展有利于智力自主和对知识对象的有意义学习。结论:教学情境理论为涉及圆体研究的教学组织和知识巩固过程的分析提供了重要的资助，表明其在高中和高等教育中其他数学对象的研究中的应用。
{"title":"Study of Round Bodies: Conceptions and Praxis of a Didactic Sequence in Light of Guy Brousseau’s Theory","authors":"Janice Rachelli, Ana Lúcia Uberti Pinheiro, Leonard Porta","doi":"10.17648/acta.scientiae.7402","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7402","url":null,"abstract":"Background: Guy Brousseau’s theory of didactic situations has been considered an apparatus for the methodological structuring of didactic sequences configured in didactic and adidactic situations. Objectives: To investigate the contributions of the theory of didactic situations to the study of round bodies, focused on a praxis that meaningfully consolidates knowledge for the students. Design: We propose solving problem situations concerning the calculus of surface areas and volumes of round bodies using Cavalieri’s principle and Pappus’s theorems. Setting and participants: The research was conducted with two high school third-grade classes of a state institute of education located in the municipality of Júlio de Castilhos, RS, Brazil, with the participation of 25 students. Data collection and analysis: It was carried out through activities developed in the classroom and feedback given through Google Classroom. It was subsidised by the documental transcription of students’ records. Results: The research indicated that the didactic sequence development favoured intellectual autonomy and meaningful learning about the object of knowledge. Conclusions: The theory of didactic situations provided important subsidies for didactic organisation and analysis of the knowledge consolidation process involving the study of round bodies, indicating its application in the study of other mathematical objects in high school and higher education.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45698600","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 : 2022-12-20DOI: 10.17648/acta.scientiae.6243
Solange Fernandes Maia Pereira, C. Kaiber
Background: The mathematical and didactic knowledge in mathematics teachers’ domain should constitute a permanent focus of investigations and reflections. Objective: To investigate the development of knowledge and procedures concerning geometry teaching among pre-service and in-service mathematics teachers engaged in the final years of elementary school. Design: The investigation is inserted in a qualitative perspective and follows the assumptions of action research. Setting and Participants: Fifty-four pre-service and in-service mathematics teachers from the Brazilian city of Paulo Afonso, Bahia, participated in a teacher education process. Data Collection and Analysis: Participant observation, data collection and analysis following an analysis protocol guided by the constructs of the onto-semiotic approach; analysis of productions. Results: Development and application of 24 sequences of activities focusing on the study of geometry. High epistemic adequacy was observed based on the application of the analysis protocol concerning structuring sequences of activities. Regarding the other dimensions, concerning the analysis of the application of the activities (cognitive-affective, interactional-mediational, ecological), high adequacy was observed. Conclusions: It is relevant to invest in teacher education courses proposing the expansion of didactic-mathematical knowledge to enhance the use of different ways to teach and learn mathematics.
{"title":"Didactic-Mathematical Knowledge and Teacher Education: An Investigation with Pre-Service and In-Service Mathematics Teachers","authors":"Solange Fernandes Maia Pereira, C. Kaiber","doi":"10.17648/acta.scientiae.6243","DOIUrl":"https://doi.org/10.17648/acta.scientiae.6243","url":null,"abstract":"Background: The mathematical and didactic knowledge in mathematics teachers’ domain should constitute a permanent focus of investigations and reflections. Objective: To investigate the development of knowledge and procedures concerning geometry teaching among pre-service and in-service mathematics teachers engaged in the final years of elementary school. Design: The investigation is inserted in a qualitative perspective and follows the assumptions of action research. Setting and Participants: Fifty-four pre-service and in-service mathematics teachers from the Brazilian city of Paulo Afonso, Bahia, participated in a teacher education process. Data Collection and Analysis: Participant observation, data collection and analysis following an analysis protocol guided by the constructs of the onto-semiotic approach; analysis of productions. Results: Development and application of 24 sequences of activities focusing on the study of geometry. High epistemic adequacy was observed based on the application of the analysis protocol concerning structuring sequences of activities. Regarding the other dimensions, concerning the analysis of the application of the activities (cognitive-affective, interactional-mediational, ecological), high adequacy was observed. Conclusions: It is relevant to invest in teacher education courses proposing the expansion of didactic-mathematical knowledge to enhance the use of different ways to teach and learn mathematics.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42242398","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 : 2022-12-19DOI: 10.17648/acta.scientiae.7372
Gleison De Jesus Marinho Sodré, Raquel Soares do Rêgo Ferreira, Renato Borges Guerra
Background: Research in mathematics education shows that mathematical modelling is a practice that seeks to “translate” problem situations into possible mathematical models without, however, explaining the complexity involved in the reverse formulation, starting from the mathematical model to delimit the type of situation. Objective: To highlight the problem of reverse mathematical modelling, in the sense of a reverse formulation that goes from the mathematical model to the situation. Design: For this, a course of study and research was carried out guided by the investigative cycle of mathematical modelling that is based on theoretical-methodological resources of the anthropological theory of the didactic. Setting and Participants: Pre-service teachers of a teaching degree at a public institution were faced with a problem in an unusual context about the decimal number system and, more broadly, the positional number system. Data collection and analysis: We present an empirical approach based on research carried out by Ferreira (2020) with teachers in initial training. Results: The empirical results observed confirm the hypothesis of the existence of the problem of reverse mathematical modelling, even in the face of normative models, in the sense that they can faithfully describe a real situation. Conclusions: Ultimately, the study of a type of problem in an unusual context, in addition to highlighting the encounter of teachers with different objects of knowledge, revealed the remarkable difficulty in delimiting the type of quantification situation that can be associated with the mathematical model of the number and as stimulate future research on the teaching of reverse mathematical modelling.
{"title":"Reverse Mathematical Modelling","authors":"Gleison De Jesus Marinho Sodré, Raquel Soares do Rêgo Ferreira, Renato Borges Guerra","doi":"10.17648/acta.scientiae.7372","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7372","url":null,"abstract":"Background: Research in mathematics education shows that mathematical modelling is a practice that seeks to “translate” problem situations into possible mathematical models without, however, explaining the complexity involved in the reverse formulation, starting from the mathematical model to delimit the type of situation. Objective: To highlight the problem of reverse mathematical modelling, in the sense of a reverse formulation that goes from the mathematical model to the situation. Design: For this, a course of study and research was carried out guided by the investigative cycle of mathematical modelling that is based on theoretical-methodological resources of the anthropological theory of the didactic. Setting and Participants: Pre-service teachers of a teaching degree at a public institution were faced with a problem in an unusual context about the decimal number system and, more broadly, the positional number system. Data collection and analysis: We present an empirical approach based on research carried out by Ferreira (2020) with teachers in initial training. Results: The empirical results observed confirm the hypothesis of the existence of the problem of reverse mathematical modelling, even in the face of normative models, in the sense that they can faithfully describe a real situation. Conclusions: Ultimately, the study of a type of problem in an unusual context, in addition to highlighting the encounter of teachers with different objects of knowledge, revealed the remarkable difficulty in delimiting the type of quantification situation that can be associated with the mathematical model of the number and as stimulate future research on the teaching of reverse mathematical modelling.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43256374","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 : 2022-12-19DOI: 10.17648/acta.scientiae.7354
Wagner Rodrigues Valente, Gisele De Gouvêa
Background: The historical analysis of a given curricular production makes it possible to understand how, at a given time, the production of new knowledge occurs, made official in some documents, thus providing references for teaching and teacher education. Objectives: The study intends to answer the following question: How to understand the negative criticisms disseminated by the press to this curricular production, in terms of the elaboration of a new teaching expertise? Design: This study is a research from a historical perspective. This is a documentary research that has as its source material from newspapers from the 1980s. Setting and Participants: The research presents aspects of a curriculum production from the 1980s. Sows the impacts emitted by the newspapers of the time on a curricular production. Data collection and analysis: As an empiric of the research, the articles published in São Paulo newspapers are considered at the time of the elaboration of the proposals. Such a question is justified, therefore, because it makes it possible to explain the process of producing new knowledge for teaching based on the actions of experts. Results: Going through the actions of the experts shows us that it is fundamental to understand the tensions between the fields present behind the scenes of elaboration. From the tensions, knowledge will be theoretically constructed. Conclusions The answer obtained shows the decisive role of the press and the struggles waged for the consolidation of this official curricular document. The curricular documents of a given time govern and provide references for the teaching and training of teachers of that time.
{"title":"The Curriculum Proposals of the State of São Paulo in the 1980s: Impacts of a New Expertise for Teaching","authors":"Wagner Rodrigues Valente, Gisele De Gouvêa","doi":"10.17648/acta.scientiae.7354","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7354","url":null,"abstract":"Background: The historical analysis of a given curricular production makes it possible to understand how, at a given time, the production of new knowledge occurs, made official in some documents, thus providing references for teaching and teacher education. Objectives: The study intends to answer the following question: How to understand the negative criticisms disseminated by the press to this curricular production, in terms of the elaboration of a new teaching expertise? Design: This study is a research from a historical perspective. This is a documentary research that has as its source material from newspapers from the 1980s. Setting and Participants: The research presents aspects of a curriculum production from the 1980s. Sows the impacts emitted by the newspapers of the time on a curricular production. Data collection and analysis: As an empiric of the research, the articles published in São Paulo newspapers are considered at the time of the elaboration of the proposals. Such a question is justified, therefore, because it makes it possible to explain the process of producing new knowledge for teaching based on the actions of experts. Results: Going through the actions of the experts shows us that it is fundamental to understand the tensions between the fields present behind the scenes of elaboration. From the tensions, knowledge will be theoretically constructed. Conclusions The answer obtained shows the decisive role of the press and the struggles waged for the consolidation of this official curricular document. The curricular documents of a given time govern and provide references for the teaching and training of teachers of that time.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43031294","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 : 2022-12-16DOI: 10.17648/acta.scientiae.7019
Mauri Luís Tomkelski, M. Baptista, Adriana Richit
Background: Research concerning teachers’ professional learning in lesson study has been highlighted in Physics teaching; however, studies that examine this process from the elaboration of inquiry tasks are still scarce. This kind of task makes it possible to explore physical concepts and relationships due to their open nature, which contemplates the students’ interest, involves a practical dimension, and promotes successful learning situations. Objectives: To understand Physics teachers’ professional learning in planning inquiry tasks to study Ohm’s Law. Design: The investigation, of a qualitative and interpretive nature, involved 18 meetings of 2.5 hours. Setting and Participants: The lesson study engaged four secondary public school Physics teachers from the state education network. Data collection and analysis: The empirical research material consists of data produced in the development of the inquiry tasks, the transcripts of the audio recordings of the lesson study sessions, the investigative lesson, the material produced by the students, and the transcripts of the interviews carried out at the end of the lesson study. Results: The analysis showed professional learning about the development of inquiry tasks, analysis, argument, and inference of scientific knowledge, passing through engaging, exploring, explaining, elaborating, and evaluating activities on physical concepts. Conclusions: The research contributes to the knowledge development about teachers’ professional learning, especially about the research lesson.
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