Acta Scientiae最新文献

{"title":"Straight Lines and Angles that Move, Students’ Ideas that Touch and Add","authors":"Marcos Paulo Henrique, M. Bairral","doi":"10.17648/acta.scientiae.7129","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7129","url":null,"abstract":"Background: Visualisation is a crucial skill for several everyday life activities and conceptual construction and development. Objectives: As it represents a substantial part of Euclidean geometry, this article addresses: the study and analysis of the relationships between angles formed from two parallel lines intersected by a transversal and the role of visualisation in the construction and development of geometric concepts imbricated in the mathematical relationships underlying the theme. Design: The methodological approach adopted was Design Experiments. Settings and participants: A teaching situation is presented, in which students from the 8th grade of elementary school at a state public school in Rio de Janeiro, Brazil, performed manipulations on the smartphone screen while carrying out an activity. Data collection and analysis: To analyse this activity, we selected events from a video obtained from the smartphone used by the students. Results: Through interactions and handlings, students visualised, analysed, and built the concepts of corresponding angles and collateral angles by studying a geometric object on the smartphone screen through the GeoGebra application. Conclusions: The geometric work mediated by mobile devices with touch screens enables the curricular reorganisation of Geometry and the articulation and the breaking of the hierarchy of concepts.","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":"45547746","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":"Experimental Geometry, Pythagorean Theorem and Montessori","authors":"Circe Mary Silva Silva","doi":"10.17648/acta.scientiae.7023","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7023","url":null,"abstract":"Background: Some 19th and 20th-century geometry textbooks show methodological innovations in relation to the traditional books that followed Euclid's logical-deductive proposal. Objective: To analyse in the book Psico Geometria: el estúdio de la geometria basado en la psicologia infantil by Maria Montessori (1934) as the didactic approach of the Pythagorean theorem, proposed by her, fits into an experimental geometry perspective. Design: Using documentary analysis, we analysed the books of the following authors: Hoüel (1867), Méray (1874), Laisant (1898, 1906), Calkins (1861), Bert (1886), Prestes (1895), Lyra da Silva (1923), Wentworth and Hill (1901) and Montessori (1916, 1934) to understand the approach to teaching geometry.Environment and participants:The research sources collected in the National Library of France (BNF) and in the Universidade Federal de Santa Catarina (UFSC) Digital Repository refer to the geographic environment of authors from four countries Data collection and analysis: The selected and analysed documents can be found at BNF – Gallica in a digitized version, as well as at the UFSC Digital Repository. Based on the documentary analysis of these books, we found that the methodological proposals seek to escape from a deductive presentation of elementary geometry and include in their texts experiences for the introduction of concepts and visual demonstrations of elementary geometry. Results: The authors of the analysed works, from different countries, criticized the elementary teaching of geometry, especially the authors of textbooks, for the fact that they approach deductive geometry in the initial classes, favouring a deductive presentation of mathematics. Montessori's book shows an experimental geometry proposal for the Pythagorean theorem. Conclusion: We found that Montessori's proposal, besides presenting characteristics of an experimental geometry, also inserts some deductive reasoning.","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":"42224699","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":"The Fabrication of Scientists through School Geometry","authors":"Melissa Andrade Molina","doi":"10.17648/acta.scientiae.7179","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7179","url":null,"abstract":"Context : Visuospatial abilities that derive from perception, for example, are not usually considered one of the mathematical abilities developed in the national school geometry curricula. Objective : This work aims to explore school practices that seek to guide the ways of being and acting of students in Chile. Design : This is done by mapping the geometry school curriculum to trace the system of reason that makes possible the fabrication of particular kinds of people. The study uses a Foucaultian toolbox to address school geometry as a technology of government that has power effects in shaping students' subjectivities. Data : School textbooks distributed by the Chilean Ministry of Education, MINEDUC, from the final six levels of school education (13 to 18 years) were analyzed. Data analysis : The school textbooks were explored, through discourse analysis, to map the connections between the activities proposed in the geometry units for each level in order to trace the paths that allow for guiding students’ ways of being and acting. Results : Evidence compiled from an analysis of current Chilean mathematics textbooks shows that geometry school practices are constructed to train the eye so that students conceive and experience space not through their senses but through reason and logic, which inserts students in the modern process of training scientific minds of the future.","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":"46849347","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 quantitative study of French 19th century geometry textbooks","authors":"C. Guillet","doi":"10.17648/acta.scientiae.7191","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7191","url":null,"abstract":"Background: School textbooks constitute a valuable material of investigation in the history of education, which has developed in many disciplines, in connection with their history. In history of mathematics education, some studies are based on a qualitative analysis of a small number of textbooks, whereas others use quantitative arguments in addition. In this framework, my approach is to analyse the use of areas in French geometry textbooks of the 19th century, by articulating qualitative and quantitative methods, from a corpus that I have built. Objectives: In my study paper, I analyse information from statistical data collected on this corpus, and I put these results in perspective with other studies conducted in the history of school publishing and mathematics education. Design: My methodology consists in starting from hypotheses accepted in related studies, confronting them with my quantitative data, and then putting results into a qualitative perspective. Setting and participants: This work was carried out in conjunction with training on quantitative tools in human and social sciences provided by PROGEDO Loire in Nantes. Data collection and analysis: I first built up a database of geometry textbooks using a general source and exploited it statistically. Then, I studied specifically a more restricted corpus, focused on the notion of area, using multivariate analysis tools. Results: My results confirm some of the assumptions assumed in other studies (evolution of school publishing, porosity of primary and secondary education orders), challenge others (opposition between theoretical and practical geometry) and sometimes deepen them with additional information. Conclusion: This work answered questions but raised new ones, notably on links between sustainability, target audience and content on areas of a textbook.","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":"43090225","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":"Geometry in Mathematics Teaching in Undergraduate Courses at Brazilian Federal Universities","authors":"Person Gouveia Moreira, Thiago Pedro Pinto","doi":"10.17648/acta.scientiae.7133","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7133","url":null,"abstract":"Background: Geometry has been an essential point of reflection in Mathematics Education, especially in teaching. Objective: We conducted a numerical calculation to quantify the study load of Euclidean geometry concerning the total course load. From this data, we established different pathways to explore the Geometry subjects of these courses and their approaches. We aimed to outline an understanding of Geometry teaching in Mathematics teaching courses in the selected universities. Design: We consulted the CPPs through the official websites of the universities. We catalogued the total study load, the subjects of Geometry, and a comparison of the Geometry subjects and their occurrence. Finally, we analysed the syllabuses and bibliography of one subject listed. Context and participants: We surveyed 68 Brazilian Federal Universities, all institutions that offer the Mathematics Teaching course. Data collection and analysis: We treated the data through qualitative analysis and presented them in a large table subdivided into smaller tables to present the data. Results: After analysing the tabulated data, its result corroborated the research of Crescenti (2005), Lorenzato (1995), Lovis (2009, 2013), Pavanello (1989, 1993), Perez (1991, 2000), Serralheiro (2007) that Geometry is little taught in educational institutions, be them K-12 or higher education. Conclusions: We have identified a significant variation in each course's study load percentage dedicated to Geometry. Even among those that reached the highest values, it is still possible to question if those numbers are enough to solve the issues pointed out by K12 teachers. We have also identified divergencies in the approach suggested in the syllabuses and bibliographies of the subject Plane Geometry. Such numerical and approach deviations need to be deepened by other works.","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":"48182328","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":"Relationships between Area and Perimeter by Students with the Autism Spectrum Disorder. An Exploratory Study","authors":"Ainhoa Berciano Alcaraz, Juncal Goñi Cervera, I. Polo, Cristina López de la Fuente","doi":"10.17648/acta.scientiae.7015","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7015","url":null,"abstract":"Background: One of the difficulties that appear systematically in learning the geometric quantities area and perimeter is associated with the intuitive idea of the existence of a relationship of dependence between the two. This difficulty is common to students of different ages and has been analysed in contexts of typical development. Objective: To investigate what happens to students with autism spectrum disorder (ASD) when they are presented with activities involving the concept of perimeter and area. Design: A qualitative and exploratory methodology was used, specifically, a case study. A specific geometry test consisting of a semi-structured interview and an ad hoc test was designed and validated. Setting and Participants: The sample consisted of three students, two in fourth grade and one in sixth grade, all of them diagnosed with ASD and with an IQ above 80 points on the WISC-V scale. Data collection and analysis: The written productions and the semi-structured interviews were analysed and triangulated according to the categories of Avila and Garcia (2020). Results: All the children affirm that there is no dependency relationship between area and perimeter when area remains unchanged, but two describe a dependency relationship when perimeter remains constant. The requirement to exemplify their answers has helped them to realise their error. Conclusions: A guided intervention focused on the teacher's request to specify the answers through examples has helped to improve the understanding of these concepts and presents lines of future research associated with the creation of teaching practices for this type of students.","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":"42335995","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":"Geometry in Art? Scenes of a Colonisation of the Look and the Thinking in Mathematics Education","authors":"Mônica Maria Kerscher Franco, Cláudia Regina Flores","doi":"10.17648/acta.scientiae.7144","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7144","url":null,"abstract":"Background: Wouldn’t the transformations of artworks over time be the most convincing record of how geometry was historically practised and transformed? Now, it seems that research on geometry, whether as a theory or a school subject, leads us to a no less important problem linked to its effects and modulations on subjectivity. In mathematics education, one sees the agency of art for a very specific purpose: learning geometry through art. However, geometry is not just a set of theorems, concepts, and forms to be apprehended; it is also a device that, imprinted on our thinking, makes us talk about the world and its things. That is, it participates in the game of relations of power, knowledge, being, life, and nature, producing truths reiterated and subordinated by the ways of looking, thinking, and representing. Objectives: This article aims to analyse aspects of the relationship between geometry and art that put into practice a colonial matrix of power in mathematics education. Design: To do so, some scenes are presented, such as body-scene, space-scene, and nature-scene, considering geometry and art in its historical and educational forms. Setting and Participants: It is supported by art, art history, and research that articulates art and geometry. Data collection and analysis: Examples of the use of geometry in art are raised, analysing, through visuality, the functioning of a practice that produces and reproduces the presence and effects of the coloniality of power, knowledge, and being. Results: A geometrised fictional reality is revealed and conditioned by the ways of looking, thinking, and representing, in which geometry, operated with art, conforms and puts into practice a colonial thought, fostering the destabilisation of power and knowledge relations. Conclusions: Finally, the question is: Are we creating in our educational practices possibilities of deterritorialisations, lines of flight, decoloniality, to venture with other attitudes within the disciplinary devices in mathematics education? Therefore, it is necessary to think more about the truths put forward than to affirm them: for a new ethical, aesthetic, and political ethos in mathematics education.","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":"44882963","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":"[Between] the Paintings of the Ndebele Houses: [Geo]metries and Ragged Curricula","authors":"Eric Machado Paulucci, Carolina Tamayo Osorio, Marcelo De Godoy Domingues","doi":"10.17648/acta.scientiae.7159","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7159","url":null,"abstract":"The implementation of Law 10.639/2003 on the Teaching of Afro-Brazilian History and Culture in Schools has demanded from Mathematics Education several studies and problematizations about the nature of the [M]mathematical knowledge present in school curricula. This Law prompts dialogues between different epistemologies, whether of Western origin, Afro-Brazilian origin, or in between these epistemologies, in order to produce new debates that fray the disciplinary logic, neutrality, universality, and uniqueness of Mathematics. Thus, based on the practice of painting houses, which is carried out by women from the Ndebele people of Africa, we can consider the curriculum a place of invention. Objectives: Learning from the Ndebele women, what paintings can emerge? Are curricula invented when Stories and practices of African cultures become the focus of study in Mathematics classes? Design: We are guided by an intervention-research, performing a review of ethnographic investigations on the sociocultural practice of painting Ndebele houses. Environment and participants: The research begins with the subjectivity processes that cross three researchers: two mathematical educators in different stages of life and a philosopher. They are all interested in following different paths with Mathematics Education, Ethnomathematics, Philosophy, and..., which make us professors, determining our conceptions of territory and research. Data collection and analysis: The records and data of this research were produced based on the works of Paulus Gerdes on the paintings of Ndebele houses, as well as other authors of African origin, allowing us to be affected by these productions and question the homogeneous curricular models. Results: With this research, we travel to Africa to find strange the mathematicS practiced by the Ndebele community and to make the mathematics curriculum strange; in this sense, contemplating knowledge at the crossroads of the school curriculum, Law 10.639/2003 and Mathematics, entails producing a notion that is closer to the affective field than the field of meanings. Conclusions: The experience of shifting sociocultural practices to the classroom, such as the sociocultural practice of painting Ndebele houses reveals a curriculum as a place of invention in which mathematicS takes place and composes other curricula capable of painting a different use for Law 10.639/2003 fraying Mathematics' neutrality, universality, and uniqueness, and developing a school curriculum that escapes, leaks, and spreads minor, distinct, and unusual knowledge.","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":"44491996","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":"The City Has Abandoned Geometry: The Countryside Has Not! Reflections on Geometry and Its Teaching from the Perspective of Countryside Education","authors":"F. Fernandes, Flávia Cristina Duarte Pôssas Grossi, Maria de Fátima Almeida Martins","doi":"10.17648/acta.scientiae.7156","DOIUrl":"https://doi.org/10.17648/acta.scientiae.7156","url":null,"abstract":"Background: On the one hand, the history of mathematics teaching in Brazil is marked by the gradual abandonment of Geometry teaching; on the other hand, the countryside has always assumed it as an essential ally in the political and identity affirmation of its populations. Objectives: This paper discusses how Geometry and its teaching can emerge, in the paradigm of Countryside Education, as a possibility of political-epistemic disobedience to a Mathematics Education referenced in the knowledge, procedures, attitudes, and values of urban, industrial, and market forms of life. Design: The research uses qualitative methodology with a focus on Countryside Education. Setting and participants: The investigation was developed in the context of an Undergraduate Teaching Degree in Countryside Education, based on records of students' activities. Data collection and analysis: The text mobilizes formative experiences of a degree in Countryside Education with emphasis on Mathematics to reflect on how Geometry can be articulated to rural peoples' territories and territorialities, aiming to contribute to pedagogical guidelines for teaching K-12 Mathematics. Results: The paper contributes to evaluating epistemological and educational positions regarding Geometry and geometric knowledge commonly established by school cultures, not necessarily limited to schooling in rural regions. Conclusions: Geometry in school cultures can be used to understand the social reality in which subjects, communities and collectives are inserted, mapping inequality relations, and proposing ways to overcome them.","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":"44697946","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":"(Auto)Biographical Narratives and the Professional Development of Mathematics Teachers who Teach Probability and Statistics","authors":"Sidney Silva Santos, Geovane Carlos Barbosa, Douglas da Silva Tinti, Celi Espasandin Lopes","doi":"10.17648/acta.scientiae.6722","DOIUrl":"https://doi.org/10.17648/acta.scientiae.6722","url":null,"abstract":"Background: Investigating narratives from the (auto)biographical perspective has expanded the possibilities of research in mathematics education, in the personal and professional aspects of the individuals and their choices during professional development. Objectives: This article aims to analyse (auto)biographical narratives of mathematics teachers who teach stochastics in basic education and their teacher professional development processes. Design: It is qualitative research, from the (auto)biographical perspective. Setting and Participants: The lexical corpus is composed of ten narratives by teachers from the states of São Paulo and Espírito Santo, Brazil, participants of a continuing education course offered in a virtual learning environment. Data collection and analysis: For the textual and lexical analysis of the content, the IRaMuTeQ software and its respective analysis resources were used: word cloud technique, similarity analysis and the descending hierarchical classification (DHC). Results: From this analysis, four thematic categories emerged: initial education, professional challenges, school practice, and continuing education. Conclusions: We concluded that school practice is directly related to initial education and the challenges the mathematics teacher faces. Second, only by reflecting on their practices can the teacher be convinced of their need for updating in continuing education.","PeriodicalId":36967,"journal":{"name":"Acta Scientiae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43739876","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}