Search

This article focuses on initial teacher education, in the development of teaching study tasks, especially related to the end-of-course work. The research question is: Which reasons support the mathematics undergraduates' choices for the theme and development of the end-of-course work? In connection with the problem, this research analyzes the reasons that justify undergraduates' choices in the production of that work. The text is based on historical-cultural theory, with emphasis on the psychological and didactic principles of activity theory, on the development of students' reasons and meanings when faced with the social meanings of initial education. The methodology is developed through a formative pedagogical intervention carried out with two mathematics undergraduate students. The data production has an empirical reference in the transcripts of interviews and moments of collective advice for the development of academic work materialized in article format. The analysis is carried out from the perspective of historical-dialectical materialism, which demonstrates results through the reasons that lead students to create meanings of their experiences in the development of initial training, especially during the training processes throughout graduation. In addition to these cases, the persuasion of peers was also observed, demonstrating relationships on the theoretical-methodological/ideological orientations in their perceptions about the pedagogical activity in the interventions carried out. [ABSTRACT FROM AUTHOR]

In this article we aim to analyze the effective practices of students in the 2nd grade of high school when they perform tasks on the representation of geometric solids in the paper/pencil environment, based on the manipulation of Concrete Object Construction Project (PCOC) models, obtained by rapid prototyping on the 3D printer. For that, we appropriated the Institutional Analysis and Didactic Sequence as a research methodology. We immerse our studies in the theoretical framework constituted by the Anthropology Theory of Didactics, with emphasis on its praxeological approach, to provide us with elements of analysis of the techno-theoretical techniques and speeches in Spatial Geometry, mobilized by the students in their effective practices. The results reveal that students can represent the solids considered in the paper/pencil environment but do not indicate or describe the techniques they use in the referred representations during their effective practices. Therefore, this is a problem of the reference institution, particularly the 2nd grade of high school, which does not provide training to students involving the indications and descriptions, as we proceeded in developing our a priori analysis around the PCOCs that we worked on with these students. [ABSTRACT FROM AUTHOR]

This paper aimed to analyze proposals of teaching 2nd degree Equations developed in research's postgraduate with a focus on problem solving and the conceptions of Algebra. We developed bibliographic research in which we obtained two dissertations that underwent a meta-analysis. The results show that both are interested in teaching approaches to 2nd degree Equations related to Problem Solving. However, misunderstandings between theory and practice are evident regard to limitations and potential of each approach to Problem Solving, in addition to the recurrence of exercises related to the systematization of techniques through repetition, reinforcing a fundamentalist-analytical view of Algebra. It is necessary to consider the importance of expanding studies that present sequential proposals for teaching 2nd degree Equations in the midst of Problem Solving, consistently employing the different approaches (about, for and via), and the conceptions of Algebra that are linked to this teaching. [ABSTRACT FROM AUTHOR]

This paper aims to problematize the Sociology proposed by the French anthropologist Florence Weber to mathematical Education, taking her concept of social scene as the articulation axis, and the theorization on language games developed by the Austrian-British philosopher Ludwig Wittgenstein. The idea is to create possibilities to think about mathematical Education in a different way, develop new thoughts and give new meanings to it. This paper lists some modern elements in the making of Mathematics and shows that it was established as a form of true knowledge in Western society in different times and spaces. Afterwards, it introduces Mathematics as a language game and as a social scene. Finally, some considerations are made about a possible direction for Mathematics Education, suggesting that it should be seen in a different way, not as a hard science, but as something that transcends exact calculations and can be found in the ways of knowing and doing in different cultures. Thus, strategies that differ from those imposed by the school could be taken into account and enable new ways of mathematizing that may be silent. [ABSTRACT FROM AUTHOR]

In this paper, we report the experience of a mathematics teacher educator, who is a mathematician, while teaching the Euclidean Division Algorithm Theorem in a Number Theory course for prospective mathematics teachers. Considering that the knowledge of a Mathematics teacher is specialized, from the perspective of the Mathematics Teachers' Specialised Knowledge model, we intended to identify which knowledge is mobilized when the teacher educator addresses this algebraic result. Some activities were conducted by the professor in an attempt to understand how the prospective teachers performed the division of integers before, during, and after knowing the theorem; our analysis focuses on these different moments. Regarding the prospective teachers' knowledge, it was possible to observe, primarily, knowledge related to procedures involving the algorithm. However, throughout the conducted activities, they were able to establish different connections concerning the Euclidean Division Algorithm Theorem. About the teacher educator, we emphasize that his mathematical and pedagogical knowledge, combined with the goal of effectively prepare future Mathematics teachers, has the potential to promote specialized knowledge in the prospective teachers regarding the subject matter. [ABSTRACT FROM AUTHOR]

The objective of this paper is to look for evidence of the attribution of meaning to mathematical objects through the signs associated with doing mathematical modeling. To do so, we analyzed two mathematical modeling activities developed in the early years of Elementary School, with the theoretical contribution of Mathematical Modeling, with attention to children's cognitive actions and Peircean semiotics, with regard to signs and the epistemological triangle, which considers them in association with two other elements: the context of reference and its concept. The qualitative methodology is the one that supports this study since we focus on the signs produced by the children, for mathematical objects, when they develop mathematical modeling activities. We interpret them from the epistemological triangles we build. From these triangles, we consider that the attribution of meaning to mathematical objects emerging in mathematical modeling activities developed is imbricated with the situation that originated the activity, signaling that such attribution is a compound that considers the situation and mathematics in an articulated way. Furthermore, attributing meaning to mathematical objects gains consistency as the signs change, alter, and complement each other in the face of children's cognitive actions. [ABSTRACT FROM AUTHOR]

This paper analyzes the coherence between objectives and activities proposed in Mathematics lesson plans for the literacy cycle. Planning is recognized as an important moment of pedagogical work and as being able to model the curriculum that will be developed with students. This study is qualitative in origin, using a documentary research design. In order to achieve this aim, lesson plans, of the remote teaching period, of teachers of the literacy cycle were analyzed in a descriptive way in terms of the announced objectives and the proposed activities. It was possible to conclude, in this study, that a large part of the analyzed lesson plans did not present coherence between what they claim to develop in the objectives, such as the skills and how they were operationalized these intentions in the activities. In conclusion, it is possible to say that curricula may lose their strength if planning is only focused on the execution of the activities. [ABSTRACT FROM AUTHOR]

This paper presents the results of a qualitative and interpretive research and has as its theme the mathematical reasoning and the actions of the teacher when supporting their development. The purpose was to analyze the actions developed by a teacher in the elementary school when conducting a collective discussion of an exploratory math task with 1st grade class. There was a theoretical discussion about mathematical reasoning and its processes and about teacher actions that support the development of mathematical reasoning. The data were collected by audio and video recordings, during the collective discussion of the task and they were analyzed for four categories of actions: invite; guide/support; inform/suggest and challenge. The results indicate that the actions performed by the teacher involved the four categories and that these led the students in the processes of conjecturing, identifying patterns, validating, justifying and generalizing. [ABSTRACT FROM AUTHOR]

This paper discusses a first teaching experience in which a Basic Education teacher investigates her own practice, and it aims at investigating learnings that made her reflections evident, which are shared with a research group in which she participates, while performing and analyzing her practice based on exploratory statistics teaching. Data analyzed consider audio recording transcription of this first teaching experience, and video recording of interactions with the research group from episodes and comments intentionally selected by the research-teacher. The episodes analyzed make evident learnings which emerge from the implementation of lessons based on the exploratory statistics teaching, which revels this complex path marked by the importance of individual and collective reflection in sharing and contraposition context, expanding the teacher-researcher perceptions and professional strengthening based on a previously carried out planning. Investigation of the own practice, despite requiring courage and public exposition, when performed in an honest and responsible way, demonstrates its relevance for the teacher’s professional learning. The experience also has allowed noticing out the exploratory teaching perspective as able to promote students’ reasoning in complex situations, such problematization in this practice, revealing itself as possible and promising for teaching in Basic Education. [ABSTRACT FROM AUTHOR]

This article aimed to analyze the profile and the scientific production of researchers awarded with CNPq research productivity grants who worked in mathematics education in 2021. We considered the following investigative problem: What profile and scientific production do CNPq research productivity grantees who work in mathematics education have? For the 37 grantees identified, we considered the following variables: time of doctoral studies; leadership in research groups and research lines; completed supervisions; bibliographic production, and vehicles for the publication. The theoretical and methodological contributions are connected to the specific literature on mathematics education, the norms/resolutions of CNPq and the productivity grant (PQ), and the descriptive survey research with a comparative and qualitative-quantitative approach. For data production, we consulted information from the grantees in CNPq, Currículo Lattes, and Directory of Research Groups in Brazil. The main results revealed that the time it took for the grantees to obtain their doctorates varied between 9 and 48 years, with an average of 19 years; most grantees are leaders in research groups and plural in research lines; the human resources training for doctorates was carried out mostly by grantees 1 (A, B and C) and for masters' degree by grantees 1C and 2; the most outstanding scientific productions were full papers in proceedings (3,514) and articles published in journals (3,267); and the articles were published in 618 different journals with a predominance of national journals (449). Interlacements between our research and academic productiveness evoked future studies. [ABSTRACT FROM AUTHOR]

This paper investigates how STEM education is mobilized in the development of mathematical modeling activities with experimentation. For this, it was based on a theoretical framework that considers elements of experimentation, mathematical modeling, and the integration of STEM education. The activities analyzed were developed by three groups of students from a 9th-grade class of elementary school from a private school in the state of Paraná, in the mathematics subject, in the year 2018. In these activities, gathered in groups, the students chose the theme of experimentation to be carried out, defined a problem, collected empirical data, performed a mathematical approach, and obtained a solution to the problem. For the analyses, audio and video recordings and written records of reports delivered by students were used. Through qualitative analysis, inspired by the research design, it became evident that experimentation was configured as a structure that allowed the integration between STEM areas through studies and research on the studied phenomena, manipulation of software for curve adjustments, use of laboratory equipment and its implications for the experimentation carried out, and on the mathematical content necessary to obtain a solution to the problem. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to reflect on the functioning of language expressed in language games in mathematical modelling activities. The reflection is guided by a theoretical framework related to the considerations of Ludwig Wittgenstein's philosophy and the students' referrals in a modelling activity developed in a Mathematical Modelling discipline by students in the seventh period of a mathematics degree. The data comes from students' reports and teacher's class notes. The analysis of the activity, following a therapeutic attitude, as we read in philosophy according to Wittgenstein, on the one hand, leads us to consider that modelling activities free us from the imposition of language games often practiced in mathematics classes, enabling language games that act as a way of organizing our experiences with the world through mathematics. On the other hand, mathematical modelling in the classroom can be organized by language games that do little to free us from fundamentalist mathematics, imprisoning us in a set of rules in which we follow steps associated with a modelling activity, but we deviate little from the symbolic language admittedly accepted in a way of life, not letting the knowledge and unpredictability of language games flow, as mentioned by Wittgenstein. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the tensions and interferences between philosophy and mathematics in the context of the emergence of pure mathematics in Prussia in the 19th century. In historiography the occurrence of an epistemological turn in mathematics in that century is well known. Such occurrence came to restructure the internal conceptions of its objects, in detriment of a quantitative notion and instead from a relational conception. We argue here that this change was facilitated, precisely, by the Kantian understanding that mathematics, by dealing with synthetic a priori judgments, would conceive itself as the foundation of thinkability. Our approach resides upon investigating how these notions were addressed and conceived of in the works of two authors: Jakob Fries, philosopher of science and mathematics at the beginning of the 19th century, and Hermann Grassmann, mathematician whose work would influence new conceptions by the second half of that century. Our research identifies, in the perspectives and practices of Fries and Grassmann, a conceptual unity, regarding the foundational reflection of mathematics from abstract structures of thinking. This finding reveal, on the other hand, the intervention of philosophical practices and references within the mathematical practice, producing tensions and encompassing a relevant role in the epistemological change in question. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the estrangement caused by the mathematics of the mathematician as a possibility for the education of pre-service early years and primary teachers, from two autobiographical narratives. The narratives were produced from the didactic actions of the authors in two bachelor's degree in education courses, reporting the interactions with the students that took place in classes that had Peano axioms as objects of discussion. The analysis of this material is carried out according to the procedure characteristic of the model of semantic fields (MSF). In the discussions, we present our understanding of the mathematics of the mathematician and the main notions of the MSF mobilized in the analysis. We then highlight the links between the discussions that we carry out here and what is shown in the related literature. We consider that the mathematics of the mathematician enables an expansion of the mathematical lucidity of pre-service early years and primary teachers by providing them with the expansion of their repertoires of legitimate ways of producing meaning. We also present considerations concerning the mobilization of the MSF as a theoretical reference in the scope of the philosophy of mathematics education. By focusing on epistemological aspects of the interaction between teachers and students, this theoretical model contributes to the discussions in this region of inquiry. [ABSTRACT FROM AUTHOR]

This article aims to reflect on how critical mathematics education has been discussed in teaching processes and in the pedagogical practice of teachers in the early years of elementary school. For this purpose, it presents an exploratory study based on the mapping of Brazilian scientific productions that addressed teaching of mathematics in the Critical Perspective. 174 papers were analyzed, including articles, dissertations and theses from the National Bank of theses from the Coordination of the Improvement of Higher Education Personnel (Capes) and from the Scientific Library Electronic Online (SciELO) in the period from 2002 to 2019. These works were categorized according to the subjects/focus of the research based on this organization. We identified the educational levels in which teaching mathematics from a critical perspective is discussed more frequently, which made it possible to foster reflections on the need to conduct research on this theme in levels less frequently. For interpretative analysis, presentation of results and survey of discussions on the theme in the early years of elementary school, we selected 11 papers. The results showed that there is a tendency to relate Critical Mathematics Education to activities that discuss Mathematical Modeling or Financial Mathematics. Critical perspective, dialogue is seen as an indispensable communication pattern for the collective investigation and reflection process, as it promotes the development of autonomy and the formation of critical citizenship. [ABSTRACT FROM AUTHOR]

This study is part of the research project I conducted during the 80s on junior high school students' conceptions of proof in mathematics before the teaching of mathematical proof [in French: démonstration]. The first part of this project resulted in the identification of different types of proofs students may rely on. The second part investigated the principle of design of situations which could support an evolution of students' conceptions of proofs likely to serve as a basis for teaching mathematical proof; this paper reports on two case studies carried out within this project. It details the principles of design, the implementation, and the analysis of a sequence of situations aimed at generating debate on proofs and refutations. It takes up the challenge of rejecting empirical proofs to open the way to intellectual proofs on which teaching could ground the introduction of mathematical proof. This translation of the report includes comments, notes (Note2020) and new references to facilitate the reading and understanding of the contemporary reader. [ABSTRACT FROM AUTHOR]

We investigate in this paper the complexity of modeling students knowing of mathematics under the constraints of acknowledging both their possible lack of coherency and their local efficiency. For this purpose, we propose a formalization of "conception" as a possible tool to answer the epistemological problem we identify. We apply then this approach to the study of the possible conceptions of "function" from a historical and then an epistemic point of view. We report the result of a case study to illustrate the benefit we expect from this approach. The notions of "conception", "knowing", and "concept" are then related one to the other within the model presented. [ABSTRACT FROM AUTHOR]

This paper aims to investigate and map the scientific production of research carried out in the area of Statistical Education published in the annals of the International Seminar of Research in Mathematical Education - SIPEM in the Working Group - Statistical Education (GT12) of the Brazilian Society of Mathematical Education (SBEM) in the last eighteen years. The choice of this event is due to its importance for the research area of Mathematical Education and Statistical Education. In this sense, a research was developed that allowed to systematically categorize and map the 61 works published in GT12 - Statistical Education - presented in all editions of the event carried out so far, to identify thematic trends, researchers, institutions and content addressed. Its was identified 5 thematic focuses and 20 thematic subfocus. It was evidenced that the greatest number of papers presented at the event come from the Postgraduate Studies Program in Mathematics Education of Pontifícia Universidade Católica de São Paulo followed by Universidade Federal de Pernambuco and by Universidade Cruzeiro do Sul. [ABSTRACT FROM AUTHOR]

This paper presents an interpretation on the Brazilian production of Papy's Minicomputer, a courseware developped by Georges Papy. The following question is discussed: how can the production of this courseware in Brazil be understood given the diversity of school practices during the New Math Movement? A brief on how the Minicomputer works is presented, along with the ideas wich originated the artifact. Documents from Georges and Fréderique Papy are used fot that. On the sequence, the paper argues that a net around the ideias and the methodological suggestions of Papy is formed in Rio de Janeiro; thereafter, new methods on teaching mathematics are institutionalized. The third and last part of the paper brings situations on the use of the Minicomputer and on pedagogical and educacional practices envolving the artifact. A description of the model produced by Didacta Sistemas Educacionais S.A, an affiliate of the publishing house José Olympio, is also presented. [ABSTRACT FROM AUTHOR]

This paper introduces the notion of Online Instrumental Orchestration as an adaptation of the instrumental orchestration model in remote-emergency teaching and for the future of online education. The characteristics already pointed out in Instrumental Orchestration and the differences emanating from this teaching structure, in which the geographic space of the classroom expands, invading the personal space of teachers and students, are taken up. Specific aspects of the online didactic configuration are discussed and indicated from the data collected in a project of six online workshops developed within the scope of the GERE - Study Group on Resources for Education and in the Project GERE on Tuesdays, experienced as an extension project. The analysis brings the evolution of aspects of adaptation of IO online in the workshops. We clarify the flexibility, the change in the classroom geography, the need to understand the articulation between instrumental orchestrations and the protocols of course participants, monitors, and educators. These artefacts help prepare the part of the classroom in the students' place, the asynchronous orchestrations, and the connections that the students must follow at each workshop stage. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the integration of the Theory of Documentational Approach to Didactics (DAD) with a design process, as a methodology for the construction of an artifact directed to teaching geometry online. The ADA provides theoretical support to guide the analysis of resource choices and production of teachers' documents and brings reflexive research as a methodological part to analyze the actions of the teacher in documentational genesis. Thus, following seven steps of a design process: define, research, ideate, prototype, select, implement, and learn, we relate design techniques to scientific research methods. Aiming to solve the difficulties of online teacher planning of geometry, we set up a methodological structure for the construction of a platform. The methodological structure was composed of the application of field research, problem mapping, question method, reflexive investigation, brainstorming and prototype. The methods were chosen according to the objectives of each of the seven stages of the design process. In a first analysis, it is possible to identify the potentialities of the integration of the ADA with design processes, to produce an artifact that assists teaching activities. [ABSTRACT FROM AUTHOR]

In this paper we investigate how the planning and implementation of a mathematical modeling activity that includes information processing, based on the Documentational Approach to Didactics is. The activity analyzed was planned by teachers in continuing education within the scope of a discipline of Mathematical Modeling of the Master's in Mathematics Teaching of Universidade Tecnológica Federal do Paraná. The activity was implemented in four classes with a group of the 7th grade of elementary school by a pair of teachers. The data that supported our analysis came from audio and video recordings of the planning and implementation of the activity, the recording of the lesson plan, the reports delivered by the 7th grade students and a questionnaire about the activity. Through qualitative analysis supported by the Documentational Approach to Didactics and Trees of Association of Ideas, we show that the plan initially structured by the pair was re-elaborated considering suggestions from other teachers in continuing education prior to the implementation of classes, necessary changes during classes and subsequent suggestions to classes with the reports of the pair in a conversation round of the discipline. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the integration of the Theory of Documentational Approach to Didactics (DAD) with a design process, as a methodology for the construction of an artifact directed to teaching geometry online. The ADA provides theoretical support to guide the analysis of resource choices and production of teachers' documents and brings reflexive research as a methodological part to analyze the actions of the teacher in documentational genesis. Thus, following seven steps of a design process: define, research, ideate, prototype, select, implement, and learn, we relate design techniques to scientific research methods. Aiming to solve the difficulties of online teacher planning of geometry, we set up a methodological structure for the construction of a platform. The methodological structure was composed of the application of field research, problem mapping, question method, reflexive investigation, brainstorming and prototype. The methods were chosen according to the objectives of each of the seven stages of the design process. In a first analysis, it is possible to identify the potentialities of the integration of the ADA with design processes, to produce an artifact that assists teaching activities. [ABSTRACT FROM AUTHOR]

This paper aims to describe and analyze an instrumental orchestration which aimed to apply the double integral in determining the center of mass of a variable density blade and the electrical charge in a given region. The study, qualitative in nature, involved undergraduate mathematics and engineering students of a public university in Amazonas, and the data were collected by observation of classroom activities and recorded through video recording and an electronic form questionnaire. The theoretical framework is composed of Luc Trouche's Theory of Instrumental Orchestration and Guy Brousseau's Theory of Didactic Situations. The results show, among other things, that the stages of action, formulation, validation, and institutionalization when used in the instrumental orchestration performance mode are important elements of didactic situations and that, through them, the teaching and learning processes contribute to the construction of knowledge. [ABSTRACT FROM AUTHOR]

This paper introduces the notion of Online Instrumental Orchestration as an adaptation of the instrumental orchestration model in remote-emergency teaching and for the future of online education. The characteristics already pointed out in Instrumental Orchestration and the differences emanating from this teaching structure, in which the geographic space of the classroom expands, invading the personal space of teachers and students, are taken up. Specific aspects of the online didactic configuration are discussed and indicated from the data collected in a project of six online workshops developed within the scope of the GERE - Study Group on Resources for Education and in the Project GERE on Tuesdays, experienced as an extension project. The analysis brings the evolution of aspects of adaptation of IO online in the workshops. We clarify the flexibility, the change in the classroom geography, the need to understand the articulation between instrumental orchestrations and the protocols of course participants, monitors, and educators. These artefacts help prepare the part of the classroom in the students' place, the asynchronous orchestrations, and the connections that the students must follow at each workshop stage. [ABSTRACT FROM AUTHOR]

This paper aims to describe and analyze an instrumental orchestration which aimed to apply the double integral in determining the center of mass of a variable density blade and the electrical charge in a given region. The study, qualitative in nature, involved undergraduate mathematics and engineering students of a public university in Amazonas, and the data were collected by observation of classroom activities and recorded through video recording and an electronic form questionnaire. The theoretical framework is composed of Luc Trouche's Theory of Instrumental Orchestration and Guy Brousseau's Theory of Didactic Situations. The results show, among other things, that the stages of action, formulation, validation, and institutionalization when used in the instrumental orchestration performance mode are important elements of didactic situations and that, through them, the teaching and learning processes contribute to the construction of knowledge. [ABSTRACT FROM AUTHOR]

In this paper we investigate how the planning and implementation of a mathematical modeling activity that includes information processing, based on the Documentational Approach to Didactics is. The activity analyzed was planned by teachers in continuing education within the scope of a discipline of Mathematical Modeling of the Master's in Mathematics Teaching of Universidade Tecnológica Federal do Paraná. The activity was implemented in four classes with a group of the 7th grade of elementary school by a pair of teachers. The data that supported our analysis came from audio and video recordings of the planning and implementation of the activity, the recording of the lesson plan, the reports delivered by the 7th grade students and a questionnaire about the activity. Through qualitative analysis supported by the Documentational Approach to Didactics and Trees of Association of Ideas, we show that the plan initially structured by the pair was re-elaborated considering suggestions from other teachers in continuing education prior to the implementation of classes, necessary changes during classes and subsequent suggestions to classes with the reports of the pair in a conversation round of the discipline. [ABSTRACT FROM AUTHOR]

This paper results from a final essay for the pedagogy degree at the Agreste Campus of the Federal University of Pernambuco. The research aimed to understand the place of dialogue in mathematics classes from the point of view of teachers of the early years of elementary school. Based on the concept of dialogue from the Freirean theory and critical mathematics education, we initially conducted a semi-structured interview with five teachers in a state school in the Pernambuco Agreste area, Brazil. Afterward, we requested them to answer two activities. The first consisted of observing two pictures of teachers in a task in the classroom and proposing modifications, whether they considered it necessary, so that the pictures portrayed their mathematics classes. In the second, we asked them to elaborate an activity based on a given image. As the Freirean theory and critical mathematics education proposed, teachers' voices bring dialogue elements, although they did not explicitly use the term. The most emphasised elements are the interactions between teacher and students and between students and community, and establishing the relationships between teaching and students' realities. [ABSTRACT FROM AUTHOR]

The present paper consists of presenting a mapping of the researches involving the Problem Solving theme that were presented at the International Congress of Teaching Mathematics - CIEM, in the editions of 2013 and 2017. The research locus of this work had as source of data collection the annals of said Congress, available at the event sites. We tried to show how CIEM was evolving and becoming a space of important discussion for Mathematics Education. In a special way, we try to highlight important features of the work that involved Problem Solving as a central theme, considering the variety of the themes belonging to CIEM. The results of the research show, in general, that the papers present convergences with Problem Solving as teaching methodology in favor of the learning process of mathematical contents. [ABSTRACT FROM AUTHOR]

This paper presents an experimentation based on the study by investigation with emphasis in the Theory of the Graphs. The proposal presented in this paper focuses on the elaboration of an essay on the insertion of the Dijkstra Algorithm in Mathematics Education. In order to elaborate this, it is proposed the development of an activity based on study by investigation, where the students were instigated to solve certain problems totally constructed with real data and with information of the scope of the school. During the development of this experiment, peculiarities appeared that allowed us to validate the insertion of an approach based on study by investigation and finally observing the importance of the study of Graph Theory in Basic Education. [ABSTRACT FROM AUTHOR]

The so called Ginásios Vocacionais (Vocational Gymnasiums) were an institution created in São Paulo State (Brazil) in 1962 and extinguished by the Brazilian Dictatorial Government in 1968. The main intention of this paper is to discuss some features of the teaching and learning of Mathematics in such schools. Some data on the general educational context are presented in order to support the discussion about the two central issues of this article: the role of Mathematics in a curricular framework in which integration among disciplines was one of the main principles; and the influence of New Math in these Gymnasiums. This paper is based in a research developed using Oral History as its main methodological guide. [ABSTRACT FROM AUTHOR]

The present investigation discusses an excerpt from a project that aims to discuss the research on Statistical Education in Brazil published in journals in the area of Mathematics Education between the years 2010 to 2019. We set the objective to discuss Brazilian research that addresses the knowledge of young children in kindergarten and students in the early years of elementary school about Combinatorics in this period. Eight papers were identified that deal directly or indirectly with combinatorics knowledge of students' in these schooling stages. We focused on the combinatorial problems used in the research, highlighting aspects such as the different types of problems, the order of magnitude adopted (total number of possibilities), the contexts evidenced by the problems, in addition to the resources used to present the activities to the research participants. We verified that Brazilian research is in line with the investigations from different countries and presents an advance in the sense of allowing the discussion of different types of combinatorial problems in the same study. We consider that further research should be conducted addressing the development of personal arguments in solving combinatorial problems. [ABSTRACT FROM AUTHOR]

This paper describes a comparative analysis of the responses given by undergraduate mathematics students in Brazil on a final assessment. The aim was to identify cognitive aspects related to the construction of tables. The activities addressed knowledge required for collecting, representing, reading, and interpreting data in double-entry tables, as well as for formulating questions whose resolution required mobilising probabilistic knowledge and cross-reading of table data. Previous studies on the subject rarely analysed the construction of tables. A qualitative approach was adopted for this case study. Design of the activity and analysis of subjects' output (16 students) drew on the theory of registers of semiotic representation and on the work of investigators who address table-reading proficiency levels. Compared to performance in a diagnostic evaluation conducted months earlier, most of the future teachers who participated in the final activity proved capable of organising data in table format and crossing the categories depicted in rows and columns to successfully interpret the intersections of events. For conditional events, however, difficulties were detected both in the ability to formalise questions and solve them. [ABSTRACT FROM AUTHOR]

This paper analyses and reflects on the results of the implementation of a teaching sequence in statistics involving quantitative variables and the role of representation records in the transnumeration of raw data in the box-plot. It is a descriptive qualitative field research, covering, as a methodology, the stages of the investigative cycle, in which 31 high school students participated. These students analysed their data on the relationship between study habits and performance in the course of mathematics. As a result, it was possible to verify the complexity of working with quantitative variables, and the complexity of constructing the boxplot with real data in the classroom. The strategies adopted contributed to the understanding of data and statistical concepts in context. Furthermore, the study revealed that the methodology adopted led students to engage in the activity, raised awareness on the factors that interfere with school performance, the importance of proper habits, and the frequency of study for learning. [ABSTRACT FROM AUTHOR]

This research aimed to carry out a bibliographic survey to identify master’s degree theses that used some theory of the didactics of mathematics as a theoretical and/or methodological support for teaching and learning the linear function. To achieve the objective, a survey of papers already produced in the Catálogo de Teses e Dissertações da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior/Catalogue of Dissertations and Theses of the Coordination for the Improvement of Higher Level Personnel (CAPES) was carried out. Through the analyses, it was possible to identify the number of works that approached the didactics of mathematics theories and how the teaching and learning of the linear function were approached. The analyses also indicated that the theory of registers of semiotic representation was the most used in the theses. [ABSTRACT FROM AUTHOR]

In this paper we discuss the possibility of, through hermeneutics, constructing a way of interpreting the data of qualitative research that takes on a phenomenological stance. Therefore, we explain the meaning of phenomenological research considering authors like Bicudo (2010, 2011, 2012) and Merleau-Ponty (1990, 1994). About philosophical hermeneutics, authors like Gadamer (2004), Heidegger (1998) and Paul Ricoeur (2000), allow us to elucidate some aspects that make this possibility relevant for the interpretation of data in qualitative research. To exemplify ways in which the interpretation can be conducted, according to this perspective, we bring some dissertations and theses and go deeper with the path constructed in the interpretation of doctoral research data of the first author of this text. In the thesis the focus was on abductive reasoning in the production of mathematical knowledge. In this text, so data research data of meaning, we speak of abduction, knowledge production has for us and we end by presenting the analysis process carried out and the relevance of the hermeneutic interpretative movement for research in Mathematics Education. [ABSTRACT FROM AUTHOR]

In this paper, we discuss some aspects presented by visually impaired students about their inclusive schooling focusing on mathematics. Four subjects, current higher education students, answered semi-structured interviews we prepared guided by a script of questions constructed with subsidies from a previous bibliographic review. In the analysis, we used the assumptions of content analysis, and to expose our results, we used categories listed through the convergences existing in the statements of the respondents. The categories identified were: the teaching differentiation of school content and activities between visually impaired and sighted students; the teachers' lack of knowledge of the educational needs of the visually impaired student; negligence/omissions in teaching visually impaired students, including their learning; isolated attempts at teaching support as a reflection of the lack of broader collective school work. [ABSTRACT FROM AUTHOR]

This paper presents the results of a qualitative investigation, in which future mathematics teachers could (re)formulate and solve a guiding problem with the use of digital technologies, designed by their supervisors, to discuss and reflect on such an experience and produce knowledge. Throughout the process, they worked together collaboratively, used digital technologies, and discussed and reflected as they made decisions. This experience contributed to (re)build the conceptions about problem (re) formulation and solving with the use of digital technologies, the design of open problems, and the approach of themes of social relevance, which foster the teaching and learning of mathematical knowledge. [ABSTRACT FROM AUTHOR]

In this paper, we present some results of two study and research path (SRP) implementations which begin with a question related to mathematics and economy. We consider primarily the characteristic didactic gestures of an SRP, called dialectics. They are described qualitatively and then bivariate statistical technics are used to establish possible associations between them. The so-called didactic gestures of reading and writing are the ones most associated with those of the study and research and to go intoout the mathematics and the economy, and also to establish which knowledge to study and how, in order to answer the derived questions in the SRP. [ABSTRACT FROM AUTHOR]

This paper aims to make discussions about the Potential Didactic Contract (CDP), which refers specifically to the Didactic Contract present in the textbook approach. This contract is not originally defined in the literature, and its definition is a contribution of this study. We consider that the Textbook is written as a function of teacher and hypothetical students, having intentions on how knowledge should be negotiated in the classroom. Based on this assumption, we propose the definition of contractual elements, already discussed in the literature, from the perspective of the Book. Didactic, that is, expectations, potential contract rules, evidence of breaches and evidence of contract effects. The Potential Didactic Contract presents a fruitful field for the investigation of the Textbook from the perspective of the Didactic Contract. [ABSTRACT FROM AUTHOR]

In this article we reflect on the representation records that intervene in the study of curves and surfaces, as reference mathematical objects, exploring the Sieve-Geometric technique. For this, we analyse the GeoGebra software and the practices of the students of a Master course in Mathematics Education to solve a problem using the paper/pencil environment. The results show that students have mastery of their geometric thoughts in the treatment of objects in the two-dimensional plane, but present difficulties in the representation of geometric objects in three dimensions, which are manifested in the inadequate mobilization of geometric thoughts on the curved and surface sieve, delimiting the geometric object involved in the problem, both in Spatial and Analytical Geometry. [ABSTRACT FROM AUTHOR]

This paper aims to present a State of Knowledge of scientific production on teacher education in special editions and a Statistical Education journal. In the content analysis of the 17 selected articles, two categories were considered. In the first, which focused on the initial formation of the Mathematics teacher, researches emerged about the undergraduate curriculum, pedagogical strategies, and technological resources. While in the second, in which the continuous formation of the teacher that teaches Statistics was observed, investigations about formation courses, collaborative contexts, pedagogical activities, teaching perceptions and characterization of these profiles, have also emerged. We identified a leading role in studies about continuing education, especially through courses and collaborative practices. [ABSTRACT FROM AUTHOR]

In this paper, the contributions of the Anísio Teixeira Institute for the development of mathematical education in Bahia are discussed. It uses bibliographic and documentary analysis as a methodological procedure. The first part deals with the process of creating and installing the IAT; then the activities of the period from 1983 to 1987, in which they were implemented and consolidated, are discussed; and, finally, the activities of the quadrennium from 1987 to 1991 are discussed, during which time their dynamization occurred. The article shows that, in its early years, the activities of the IAT were directed mainly at the demands of the initial series of education, linked to the process of reduction of illiteracy, evasion, action of lay teachers, mapping and organization of structures and demands educational institutions of the State of Bahia. [ABSTRACT FROM AUTHOR]

The new generation of students, called "digital natives", is involved in the most varied types of technology, so promoting the use of technological resources during classes is an essential activity to generate good interaction and promote knowledge in a contextualized way. Thus, it is important to investigate the use of mobile applications, which are so accessible resources today, in the pedagogical practices of the mathematics education professional and to ascertain the teaching knowledge that are present in this process. In this sense, this paper aims to analyze the perception of academics of the degree course in mathematics regarding the use of mobile technologies for teaching functions in mathematics. After some activities involving families of functions, academics produced texts of opinion, the analysis of this material, in the light of Discursive Textual Analysis, revealed that the association of these technology resources promotes improvement in professional training, since the presence of essential knowledge related to teacher's profession is verified. [ABSTRACT FROM AUTHOR]

This paper presents a part of a research whose objective was to present and discuss aspects of the use of proof-writing-in-phases with cheating as a teacher strategy in initial teacher training. For that, Realistic Mathematics Education was taken as an approach to teaching. The interventions inherent to the stages reduce the utility of cheating because they individualize the exam. Within the context of that teacher strategy, cheating misses its purpose, since the exam carried out in stages eliminates the rule of noncommunication. [ABSTRACT FROM AUTHOR]

This paper presents a qualitative study, exploratory study type, which aimed to understand which treatment is being given by researchers in the area of Mathematical Education to the research object defined as curriculum of Mathematics Degree courses. From this study it is possible to state that: (i) the understanding of the curriculum is from the perspective of the implementation of curriculum recommendations, not questioning what is the relevant knowledge in the initial teacher education; (ii) the use of prescribed official documents is common to all analyzed works, with the role of defining "what" and "how", knowledge should be treated; (iii) there is a quantitative increase in studies with the thematic curriculum of Mathematics Degree courses, especially after the publication of the DCNs for Teacher Training in 2002. [ABSTRACT FROM AUTHOR]

The paper presents a study in the area of Statistical Education. The purpose was to map the Brazilian production of dissertations in Statistical Education defended until the middle of 2018. The contributions emerged from a state-of-the-knowledge research. We identified 74 dissertations defended in Brazilian programs in the last 25 years, mainly involving the Education and Mathematics Education programs. Guidance, programs, geographic and temporal distribution were identified, as well as the identification of subjects, subjects and research objects. Statistical Education is developing in the country, but slowly and irregularly. The production of theses has increased due to the growth of postgraduate courses, especially doctorates, in the area of education / education in science and mathematics or in mathematics education/education. Production in these programs is expected to grow significantly in the coming years because many are recent. [ABSTRACT FROM AUTHOR]

This paper has a research that objective to use GeoGebra software in a problem solving approach, for an understanding of the sine and cosine functions. To this end, the use of technological resources in Mathematics classes are discussed, with a view to enabling research. The following is an analysis of an activity, carried out with a second year class in High School, in the area of skills and competences evaluation. The results of the methodology research thus allow the development of autonomy and a collaborative work culture in the construction of concepts, as well as the investigative process would not be possible without the use of technological resources. [ABSTRACT FROM AUTHOR]

This paper aims to analyze how teacher trainer's actively supported the professional agency development of teachers, members of a Community of Practice. Therefore, a qualitative research of their participation in the enterprise Numerical Sets Study, with an interpretative slant, was undertaken. The results show that the teacher trainer fostered the study of ideas and mathematical concepts about irrational numbers; encouraged the teachers to work with challenging mathematic tasks; supported them while planning and with the development of a class planed on inquiry based-teaching about irrational numbers. The closeness among the participants, the former and the teachers of the community, affected their professional identities, by valuing their mathematical practice, in order to foster and reinforce their own professional agency. [ABSTRACT FROM AUTHOR]

The paper approaches the digital technologies use perspectives in the mathematics teacher initial education with emphasis on professional practice in basic education. The analysis was guided by theoretical perspective of technological, pedagogical and contend knowledge of Mishra e Koehler. Thus, we realize the investigation in the course of Mathematics Licentiate of a federal public university of the State of Santa Catarina, Brazil, on which examined institutional curriculum documents and teaching plans of all disciplines. Furthermore, we examined empirical material constituted from questionnaires and interviews realized with teachers and students. The results pointed four perspectives of articulation of the technologies to de pedagogical and content knowledge. The analyses and discussion about these perspectives indicate that the articulation between pedagogical, technological and content knowledge in the formative activities contributes to the teacher initial education in direction to professional practices changes. [ABSTRACT FROM AUTHOR]