EISSN : 2178-7727
Current Publisher: Galoa Events Proceedings (10.17648)
Total articles ≅ 191
Latest articles in this journal
Acta Scientiae, Volume 23, pp 1-29; doi:10.17648/acta.scientiae.5905
Background: In recent years, many states and municipalities have adopted official teaching materials to guide teacher practice. However, the relationship between the use of these materials and the continuing education of in-service teachers has been little investigated. Objective: To analyse how the development of the theoretical thinking of teachers about the multiplication of fractions impacts the choice, use, or adequacy of teaching materials. Design: The theoretical and methodological foundation is based on the historical-cultural perspective seeking, in the investigation of human activity, to understand the development of theoretical thinking. Setting and participants: Continuing education with a group of 11 mathematics teachers from the state public network of São Paulo. Learning triggering situations have been proposed to overcome discretisation in the approach to fractions. Data collection and analysis: Data were collected through video recordings, written material produced by teachers and registers in a field diary. Two isolated were organised for analysis “Movement of theoretical thinking about fractions” and “Didactic material as a mediator of the teacher's action.” Results: As they theoretically understand the meaning of multiplication between fractions, teachers overcome the mechanisation of rules and begin to reveal an understanding of the interrelationship of arithmetic, algebraic, and geometric elements in teaching. Conclusion: The development of aspects of theoretical thinking about the multiplication of fractions allowed teachers to organise teaching in order to make explicit the essential and theoretical relationships of the concept. Didactic material is understood as mediation in the teaching process and its use is no longer seen as an end in itself.
Acta Scientiae, Volume 23; doi:10.17648/acta.scientiae.6241
Background: Ethnomodelling methods examine how members of distinct cultural groups have come to develop local mathematical knowledge. However, what may indeed be less evident is how mathematical thinking can be part of the way in which researchers and educators attempt to make sense of the underlying cultural frameworks within which mathematical ideas, procedures, and practices are embedded. Objectives: The main objective of this theoretical article is to present arguments that link mathematics and culture in order to develop an effective understanding of the development of dialogical mathematical knowledge. Design: The theoretical and methodological concepts of this qualitative study are supported by the assumptions of ethnomodelling that adds an important cultural perspective to the modelling process through the development of an extensive literature review on this topic. Results: We present arguments to show that the linking of mathematics and culture is appropriate and necessary for an effective understanding of the development of dialogical mathematical knowledge, which aims at providing a holistic understanding of human knowledge. This means that cognition is a process that is not only embodied and situated, as well as distributed because the members of distinct cultural groups create, process, accumulate, and diffuse mathematical information conjointly. Conclusions: We discuss the role of ethnomodelling in order to develop an understanding the connection between ethnomathematics and modelling. In this context, we present concepts related to the use of both local (emic), global (etic) approaches by applying the glocal (dialogical) approach found in ethnomodelling research.
Acta Scientiae, Volume 23, pp 80-101; doi:10.17648/acta.scientiae.6161
Background: The study of the history of mathematics teaching can be approached from different perspectives, defining contours from which the researcher performs the analysis focused on a process characterised by continuity, or by adopting periodisation. Objective: In this article, we seek to conduct a study based on the delimitation of periods, according to Le Goff’s (2014) argument, and in the light of the depth hermeneutics, based on Thompson (2011). Design: Given the premises above, we conducted a documentary analysis of two historical processes within the scope of mathematics teaching, one focusing on the municipal public schools of Canoas, and the other on a technical course in chemistry of a school in the city of Novo Hamburgo, both in the state of Rio Grande do Sul. Setting and participants: A timeline with conspicuous events used to periodicise both historical processes analysed by the authors. Data collection and analysis: Analysis of documents relevant to the history of the technical school investigated and education in the municipality of Canoas. Results: In both cases, it was possible to characterise the historical processes in periods based on events and official documents that generate changes in mathematics teaching. Conclusions: The historical processes analysed are characterised by ruptures resulting from changes, especially in the legislation, both in the municipal public network and in the technical education institution researched, enabling the realisation of changes and the characterisation of distinct periods, with their nuances.
Acta Scientiae, Volume 23, pp 170-198; doi:10.17648/acta.scientiae.6152
Background: Educational reforms in mathematics imply a series of changes in teacher training. Some of these modifications accentuate the inclusion of new content, the development of mathematical abilities, skills, or competencies, and the implementation of different teaching and assessment strategies, and the use of technology. Primary and secondary education teachers must be able to respond adequately to these curricular standards. In Costa Rica, mathematics education has undergone changes to promote various cognitive processes in students, such as those of number representation. Objectives: The article highlights the diversity of representation systems assigned to the concept of number, proposed by a group of Costa Rican preservice Primary Education teachers, as a promoting agent for the development of processes of representation in students. Design: Theoretically, the research is structured around proposals for the analysis of the meanings of mathematical concepts as associated to teacher training. It is a descriptive study based on an intrinsic case study. Data collection and analysis: The information was collected through a questionnaire. Information analysis highlights the existence of different forms of representation and the justification arguments that the participants apply for their selection; content analysis was used as the analytical technique. Setting and participants: The study was carried out with 23 preservice Primary Education teachers. Results: The results reveal a trend in the use of representation systems of the same form to present the concept of number, particularly iconic and symbolic-numeric representations. Conclusions: A connection is observed between the proposed representations and situations and contexts that seem to be familiar to Primary Education students; this relation deserves further exploration.
Acta Scientiae, Volume 23, pp 136-169; doi:10.17648/acta.scientiae.6066
Background: Giving up prescriptive views on the teacher’s action in the classroom is necessary for a better understanding of the teaching work. We are also faced with the absence of works that address teaching action under an investigative bias in initial teacher education. Objectives: identify and categorise the actions intended and performed by preservice teachers in a chemistry class, looking for implications for teacher education. Design: the study fits into a qualitative-interpretative research perspective. Setting and Participants: The data analysed comes from the monitoring of chemistry teaching degree students in the Supervised Teaching Practice discipline and their teaching in a 9th-grade class in a public school. Data collection and analysis: data collection took place through different instruments: lesson plans and audio and video recordings of the classes, that enabled interpretations based on the assumptions of the textual discursive analysis. Results: for the actions intended, a small set of five actions was identified (question, write, explain, organise, identify). The actions carried out, on the other hand, include a larger set of 13 actions and, mainly, microactions, made possible by the actions intended. There is a convergence between the actions initially planned and development in the departments, and the emergence of specific actions in the context of the Supervised Practice. Conclusions: Such results indicate the importance of categorising the actions of the undergraduate students in a chemistry class, resulting in a set of actions not yet identified in other studies, and discussing the importance of the Teaching Practice in the constitution of elements of the teaching work.
Acta Scientiae, Volume 23, pp 30-52; doi:10.17648/acta.scientiae.5845
Background: mathematics teachers interested in improving student performance in the face of the low academic results presented, we seek, Objective: articulate the skills of mathematical thinking with the formulation and resolution of verbal statement arithmetic problems (PAVE). Design: the methodology was focused on action research from the design and application of a didactic sequence developed from three categories of analysis: thinking skills, formulation, and solving of arithmetic problems. Setting and participants: basic education students starting high school. Data collection and analysis: we created and implemented a didactic sequence that includes two directions: one for the formulation and the other the resolution of PAVE. Each one was monitored from three activities: opening, development and closing. Results: difficulties in formulating and solving verbal statement arithmetic problems were evidenced in those students. Conclusions: after applying the intervention, changes were evidenced in the formulation and resolution of verbal statement arithmetic problems in the group of students. Some difficulties detected in the students are related to the length of the statement, the order of presentation of data, the situation of the question, the size of the numbers used, elements that affect the syntactic and mathematical structures of the PAVE
Acta Scientiae, Volume 23, pp 102-135; doi:10.17648/acta.scientiae.5892
Background: One of the problems in mathematics education is students’ little understanding of mathematics both at the basic and higher educational levels, which is why we consider essential the design of adequate instruments and methods that can measure understanding about specific concepts. Objective: To assess the understanding of university students of the concept of a real function. Design: The research is qualitative as the attributes of a cognitive construct were analysed and interpreted. Setting and participants: There were 36 students of a degree in mathematics (18-20 years old) whose productions were analysed. All the students had taken the Calculus I course. Data collection and analysis: A test of six items related to tasks that involved the concept of function was applied, the data analysis was carried out from the evaluation categories proposed by Albert and Kim, who consider three categories to assess understanding, those being: the ability to justify, to understand why a particular mathematical statement is true, and to understand where a mathematical rule comes from. Results: The evaluation of the understanding of the concept of function has shown that, in order to achieve a high understanding, not only skills must be developed for the recognition of aspects of the function such as its definition, its discrimination or its application, but the ability to be able to justify such aspects must be considered too. Conclusion: The categories of understanding considered help to strengthen conceptual and procedural understanding, indicating comprehensive understanding.
Acta Scientiae, Volume 23; doi:10.17648/acta.scientiae.6183
Background: In science, posing problems is considered as important as solving them, however, school has explored little this type of activity. Objective: To examine the features of mathematical problems posed by elementary school teachers, analysing aspects related to the statement of the problems and the types of problems formulated. Design: Descriptive, qualitative research. Setting and participants: Eighty-seven teachers (45 teaching 1st and 2nd grades, and 42 teaching 3rd, 4th, and 5th grades of elementary school) attending a teacher education course promoted by the Municipal Secretary of Education of Curitiba. Data collection and analysis: The teachers were asked to formulate four problems involving addition, subtraction, multiplication, and division. The types of the quantities involved, the necessary information, the number of steps required for solving the problems, and the types of problems from the theory of conceptual fields were analysed. Results: The problems presented a clear language, sufficient information, required a single operation for their solution, involved discrete quantities, and presented few challenges. The problems of addition and subtraction involved situations of composition and transformation, those of multiplication were of simple proportion, and those of division were of partitive problems. Conclusions: The results suggest that the teachers have a limited conception about the formulation of problems, emphasising the need to promote teacher training courses that develop a greater understanding of the properties of the mathematical concept involved in the problems to be formulated and about resolution procedures to be adopted
Acta Scientiae, Volume 23, pp 53-79; doi:10.17648/acta.scientiae.6204
Background: One of the challenges in pedagogical practice in science in the initial years of elementary school (EF) is focused on developing objects of knowledge with an emphasis on scientific literacy. Objective: To investigate how the pedagogical practices of teachers of the 1st and 2nd grades of the elementary school contribute to promoting access and the development of scientific knowledge to educate a scientifically literate individual. Design: Ethnographic case study, through triangulation of data in a qualitative research perspective. Setting and Participants: Seven basic education women teachers who work in three different schools in the municipality of Vera Cruz/RS participated. Data collection: Observation and description in a logbook, questionnaires and interviews with teachers, as well as one student’s notebook and the official school document (Pedagogical Political Project). Results: The promotion of subsidies for access and mediation of scientific knowledge in teaching actions, although a significant portion of teachers has little corroborated the education of a scientifically literate individual. Conclusions: There must be actions aimed at continuing teacher education to favour significant school environment changes.
Acta Scientiae, Volume 22, pp 25-44; doi:10.17648/acta.scientiae.5816
Background: The inclusion of financial education in the mathematics curriculum of the basic Brazilian education, both in elementary and high school, has been the subject of discussion in recent academic research, as well as in propositional and normative documents, such as the National Common Curricular Base (BNCC). Objective: This article aims to present the theoretical and methodological perspective used to build a history of financial education, which is part of the mathematics curriculum taught in Brazilian public schools. Design: For this, we use conceptual tools proposed by Michel Foucault, inspired by Nietzsche's writings, such as the concepts of Herkunft (provenance) and Entestehung (emergence). Scenario and Participants: We rely on the writings of Michel Foucault, studying the teaching of mathematics, in the specificity of this theme, with contributions from philosophical and historical writing, also inspiring us in the concepts of genealogy, union between philosophy and history, according to Nietzsche. Data collection and analysis: The textbooks were collected from the Museu da Escola Catarinense, while the academic works were retrieved from CAPES data bank for the qualitative analysis. Results: Hence, five methodological precautions for the analysis of power and the constitution of an object called financial education are described, namely: the financial education theme comes from a dispersion of practices, and not from an origin; we are interested in the power relations that are engendered, and that forge a financial education; the subjects are agents and effects of utterances forming a discursive network on economics; the analysis focuses on the mechanisms, techniques, and tactics, not on the centre of the power; financial education is the topic that results from the confrontation of power relations. Conclusions: With this research, we intended to make an extemporaneous intervention so that it is possible for teachers to reflect and problematise their practice in the face of this new role they are attributed.