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In this article, a systematic literature review is presented and the Active Methodologies (MAs) used by researchers in findings linked to studies in graduate programs are analyzed, with the aim of investigating the thematic characteristics of academic papers on MAs in mathematics teaching, in the period from 2016 to 2021. This is a study with a qualitative approach. The theoretical support to carry out the review was based on Ramos, Faria and Faria (2014). To facilitate understanding, the studies were delimited into three questions: Which active methodologies are subsidizing the research? In which graduate programs were the research developed? What are the conclusions of these studies? With the systematic literature review, 15 papers were identified, including theses and dissertations from the Brazilian Digital Library of Theses and Dissertations (BDTD), which discussed MAs in Mathematics Teaching. It was observed in most of these papers that Project-Based Learning (PBA) is one of the most used MAs in research and that one graduate program, in particular, stands out, for its important contributions to the quantity and quality of research for mathematics teaching. The results showed that MAs are effective in the teaching and learning process, by developing autonomy and encouraging greater student participation in mathematics classes. [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 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 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]

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]

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]

This paper aims to present a possible discussion about influences of the Base Nacional Comum Curricular -- BNCC (Common Curriculum National Base) and the Documento Curricular de Roraima -- DCRR (Curriculum Document of Roraima), on the mathematics curriculum at the elementary education level. The study has a sociocultural perspective and the principles guiding those documents were analyzed. The methodology employed is qualitative and the data was collected using document analysis focusing on the BNCC and the DCRR. Our results pointed out that the documents analyzed put forward relevant guidance following the proposal of curriculum development in a sociocultural perspective, mainly taking into consideration their guiding principles. The documents support new views of mathematics teaching and learning, based on the students' development in their different dimensions. They seek to guarantee their holistic education, respecting diversity, singularity and plurality towards social inclusion, exercising citizenship, work and autonomy in the pursuit of a society based on knowledge and social justice. [ABSTRACT FROM AUTHOR]

This paper aim is to present an integer linear programming model to the problem of the designation of didactical assignments in a university that maximizes professor's abilities and preferences. To validate and evaluate the effectiveness of the model, a preliminary case study was carried out at the Department of Mathematics of the Federal Technological University of Paraná - Cornélio Procópio Campus. In this context, the results obtained are promising, with improvements in indexes related to satisfaction, skill and teacher workload compared to the manual designation adopted by the department and also with another formulation for the problem presented in the literature. [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 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 present the Scratch programming software as a method to the teaching of Mathematics. The aim of this study was to carry out angles and polygons construction, area and perimeter calculations through practical activities that will be guided by the teacher. The methodology consisted of theoretical study, bibliographic research as well as the use of technology in education. In addition, the study's applications were made using the technological hardware. Demand to present the basics of programming and carry out some efficient activities, in such a way, that the students can fully interact with the class of the teacher who will apply such teaching method. With this, expected that students acquire the necessary knowledge that the software has to offer, in addition to stimulating the fixing of the content and the teacher can teach a more dynamic, fun and more productive class using the technological resource that is available to be used in education. [ABSTRACT FROM AUTHOR]

This paper presents the results obtained in the development of an extension program registered at the Federal University of Triângulo Mineiro, titled as Math and Chemistry Show, which used the theater methodology as a form of teaching-learning for Mathematics and Chemistry. This program lasted nine months, and it had several stages, such as study, dissemination and application. The program was applied in some state schools of several regions of the city of Uberaba, State of Minas Gerais, Brazil. The program's preference was to attend students who were studying between the 9th year of elementary school and the 2nd year of high school, but students' enrollments were not forbidden for students in other school years. At the end there was an event with presentations of the students participating, in order to demonstrate how much they learned during the program. [ABSTRACT FROM AUTHOR]

This paper discusses the function of Financial Education and the importance of such a subject to be presented and developed elementary education. It aims to attain a study about the approach of Financial Mathematics and Financial Education, moreover explaining the relevance of contents, which ones prepare the students to be organized people, and thus, dealing with concrete situations, in the context of the new practices rise. In which the mastery of financial matters goes crucial. Methodologically, beyond the bibliographic and documentary research, experience reports are used to contextualize the reflection on Financial Education. The results indicate that Financial Mathematics such as a discipline or a subject school can be a step for the citizen's financial literacy. Financial Education is linked to the awareness development about the money rational using, in order to avoid people of being exploited by the financial system. [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 presents an approach about the interdisciplinarity in Environmental Education as a way to present the student some practical applications on the learning process of concepts and basic fundamentals of disciplines such Mathematics offered along their academic career. This paper presents a contextualization of the Environmental Education and Mathematics teaching, involving the fundamental concepts of mathematics with a practical and current problem in the region of Greater Vitória, the air pollution. An analysis of the air quality in Greater Vitória is covered by some interpretations of data and graphics presented in the Air Quality Report of the Greater Vitória, published for 2013. It is demonstrated that the analysis of air quality in a region is directly related to the learning process of the mathematical fundamentals, such as mean, median, maximum and minimum, amplitude, ratio analysis, percentage representation of Cartesian coordinate functions, geometry, as well as the data interpretation and images in order to generate information from a data set. Therefore, the curent work is capable to show the interaction between the two topics, the teaching of mathematics and environment education, from a l ocal air quality issue related to the region of study. [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]

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]

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]

The integration of digital games in teaching and learning processes has been assuming a relevant role in terms of contributions that offer. Considering the importance of these resources, this paper analyses the use of two digital games in mathematics classes with 5th grade students from an urban school and with 6th grade students from an indigenous school of the west region of Paraná state. The games were applied in both realities, thus requiring the creation of differentiated strategies to their use. Because of their playful and attractive form, it was verified that the educational digital games serve as stimulus to the students from different contexts and cultures, and as subsidies to improve the teaching and the learning of curricular contents. [ABSTRACT FROM AUTHOR]

This paper aims to analyze the possible influences of the Solidarity Assimilation Pedagogy (SA) in the process of teaching and learning of continuity. The SA is a proposal that aims to break with traditional mathematics teaching, allowing students to receive bonus grades for group learning work unrelated to the assessment grade. The learning work of each class is based on a activity sheets composed of problems on the topic addressed. In this article, we analyze the development of the activity sheets about the continuity of a function, applied in a class of Calculus. The data analyzed through content analysis allowed us to infer that SA allows students to develop autonomy in learning, making them co-responsible for the whole process. [ABSTRACT FROM AUTHOR]

The aim of this article is to present and analyze the trends in digital technologies in Mathematics teaching, pointed out in the XVIII, XIX, XX and XXI editions of the Brazilian Meeting of Graduate Students in Mathematics Education. As a methodological procedure, we use the state of the art and meta-analysis of 141 papers, among abstracts and complete articles, which were published in the annals of the years 2014 to 2017. Results indicate that the master's research predominates, involving mainly students of basic education. Still, in the years 2014 and 2015, the digital technology theme is a research trend. In the year 2016, the highlight was for GeoGebra, followed by the digital technologies theme and the use of videos. Finally, in 2017, GeoGebra remains in the highlight, followed by the use of videos. [ABSTRACT FROM AUTHOR]

This article aims to explain a panorama of research on continuing teacher education for teachers who teach mathematics in basic education with an emphasis on technology and it has a temporal cut from 2013 to 2017. It is a "meta-analysis" study, that is, it has a bibliographic character. The dissertations and theses were collected in the CAPES and BDTD repositories in a total of 44 papers, however, only 15 corresponded to the proposed objective. The results reveal the insertion of several technological instruments in the formative processes, with emphasis on computers. In addition, few dissertations and theses approach in their context the subjective relations existing in the formations, mainly emphasizing the activities developed throughout the formative processes. [ABSTRACT FROM AUTHOR]

Grounded on the philosophy of language of Wittgenstein and some of his commentators, this paper aims to discuss the calculation and the mathematical writting in situations of teaching and learning. In different contexts, learners must mobilize different techniques: in everyday life, on the market, for example, the student solves "calculations in his head" in their commercial relations; in school, students must learn to do calculations on paper and they learn to objectify/formalize the calculations using mathematical writing, learning, thus, a new skill. This fact shows that when the student has success with calculations in your everyday life and do not perform well in school, this means he lacks skills to work with mathematical writing. We seek to show also that in both situations, both in the calculation in the head as in the calculation on paper, it is not an internal mental process, once the student applies rules in the public domain that are learned. [ABSTRACT FROM AUTHOR]

The purpose of this research was to identify and analyze the scientific publications, national and international, about the pedagogical strategy of the flipped classroom in the teaching of Mathematics. The study retrieved 16 papers, covering investigations in the contents of Calculus, Numerical Methods and Linear Algebra. Other searches showed the inversion of the classroom in the reduction of anxiety and also in the use of this proposal by teachers of Mathematics. Such mapping indicated a limited number of publications, from 2014 to 2017, with only five journals. Therefore, it is considered necessary new searches that can discuss the flipped classroom and the influences of this one in the teaching of Mathematics. [ABSTRACT FROM AUTHOR]

The paper explores and analyzes the influences of game and mathematical symbols on the poetry of the Romanian modern poet Ion Barbu. The paper presents the analysis of the theories of game as a poetic art as well as the analysis of the links between science and poetry in the poeworks of Ion Barbu - links which led to the conclusion that his poetry is imbued with mathematical symbols. This was the reason why literary critics reviewed his work as original and a novelty in Romanian literature. Poet and mathematician Ion Barbu (Dan Barbilian) became known as one of the most significant modern poets of Romania, Barbus' lyric went not only through different phases distinct by various specific representations, but it also went through language modifications. Thus the motive of the game which we encounter in Barbu's poetry changes according to the literary phase through which the poet goes. The analysis of game as ars poetica by critics and other foreign and Romanian researchers represents the point of departure of this paper while the goal of this research is to identify those components which demonstrate that game is not only a cultural and literary topic but also a way of life. Literature itself is a game of time and space, a game of different eras and fashions. Poetry is a game of words and a creator of a fascinating imaginary and complex space. Life unfolds within the space of an intellectual game, in a world created by the mind where things are different from those in real life and linked with links other than the logical ones. Game is thus an element that belongs within the field of poetry and every poetic form seems closely tied to the structure of the game. [ABSTRACT FROM AUTHOR]

We conceive that teachers´ personal and professional development can (and should) be encouraged by habits of reflection and questioning about their own pedagogical practice, essential to a critical appropriation of scientific, pedagogical-didactic and contextual knowledge that outline any meaningful educational act. In this paper, we describe the formative methodology adopted in the subject Didactics of Mathematics for Preschool Context in the Master Degree in Preschool Education of a private higher education institution: from the real contexts in which the students developed the Supervised Teaching Practice and as a result of the systematization of the learning experiences developed there, this experience privileged reflexive processes of academic and professional nature and enabled a (re)definition of strategies and practices for further educational intervention. The analysis of the implemented practices and narratives produced by these students points this methodology as facilitating critical-reflective capacities development, both in terms of (re)construction of logical-mathematical knowledge as of praxis (re)configuration, and therefore, of professional development of these (future) teachers. [ABSTRACT FROM AUTHOR]

This paper is part of the process of research that the authors are making to better understand the motives s and possible methodological alternatives and teaching strategies that can be used in teaching and learning of Mathematics in Primary Education. The latest indices and sampling presented by government agencies have shown that mathematics related the results have not been very encouraging and that urgent actions need to be taken to reverse this scenario. From the term context, the authors begin the search process demystifying the term and its use. Present theoretical contributions, nurture moments of reflection to better understand the problem and offer methodological alternatives and didactic-pedagogical strategies that can be used in mathematics in compliance the request of students and in keeping with TDIC -Communication and Information Digital Technologies already present in everyday classrooms and mostly out of it. To contextualize this application and give greater significance, exemplifying through Digital Object Learning and suggest possibilities of use. [ABSTRACT FROM AUTHOR]

Based on the expectancy-value theory, the Mathematics Value Inventory (MVI) was intended to measure math value in four areas: interest, utility, achievement and personal cost. This paper presents the validation of the Spanish version among Uruguayan university students: factorial validity through confirmatory factor analysis (CFA), gender related differences and predictive validity of academic achievement. A stratified random sampling according to Mathematics achievement was performed, with a confidence level of 95% and an error margin of 5%, and 218 students (77% women) voluntarily participated. Ages ranged from 18 to 29 years (M = 20.2, SD = 1.8). Results confirm the four-factor structure as well as suggest a second order factor. The latter is recommended for continuous assessment of general attitude towards math, while the four-factor model could be a better strategy to identify problematic areas and career comparison. Higher interest and need for achievement are related to greater academic performance, while utility and personal cost seem to have no impact on it. No gender differences on math value were found. In sum, the MVI proved to be a suitable instrument to measure students' attitudes towards mathematics, which may help the design of intervention strategies. [ABSTRACT FROM AUTHOR]

This paper aims to discuss the conceptions about mathematics of the Elementary School student-teachers of a Pedagogy distance learning course, in which we performed a qualitative research while working in the disciplines related to mathematics. The virtual activities generated data which analysis revealed some aspects of mathematics conception as problem solving. It also emphasized the need to guide the teaching in the understanding and rationale of formulae, procedures, and algorithms. In addition, it pointed out that the student-teachers had reflected on and problematized their conceptions. [ABSTRACT FROM AUTHOR]

The paper presents a study about the frequency and purpose of use Information and Communication Technologies (ICT) in undergraduate courses in Mathematics. We conducted a field research and data were collected through questions applied to students of undergraduate Mathematics courses in presence and distance modes. We take for field research two institutions in the region of Ariquemes (RO). We highlight conclusions as: ICT is not used regularly to work out specific content in both modes of graduation; in the distance mode the use intended to provide interaction and communication and does not to improve the quality of teaching; in the presence mode are more used for homework. [ABSTRACT FROM AUTHOR]

In this paper we present a report of an experience with a qualitative character, which aimed to examine the use of different activities through a didactic sequence for teaching non-Euclidean geometry, in particular Spherical and Hyperbolic. To this end, we conducted a participatory research with 14 students of the 2nd year of High School in a public school of Tijucas, Santa Catarina. The research relied upon the Theory of Meaningful Learning by Ausubel. The research was divided into three phases: in the first one, a pretest was applied, in the second moment, it occurred the implementation of the didactic sequence, and finally a post-test was applied. The results show that, after the didactic sequence, most students were able to assimilate, differentiate and reconcile concepts of Euclidean, Spherical and Hyperbolic Geometry. For it still is a new subject in school databanks, there were students who remained with a Euclidean positioning facing a non-Euclidean problem. [ABSTRACT FROM AUTHOR]

Based on the study of some philosophical schools -- such as the Cartesian Racionalism, the Empiricism of Hume and Kant's Criticism -- and of some brief remarks on Mathematics in ancient world -- particularly the greek Mathematics -- this paper intends to understand how the euclidean ideas have been taken for a long time as a model of how to geometrize and of what Mathematics is. [ABSTRACT FROM AUTHOR]

Our goal in this paper is to propose an interpretation different from that which usually has been given on the subject 'mathematics or simultaneous mathematics', namely, that there would be different mathematics: the mathematics of the day-to-day, school mathematics, academic mathematics etc. This assertion is often made from reflections of the mature philosophy of Ludwig Wittgenstein. Thus, we intend to develop this work as follow: we will discuss some general issues in the first phase of Wittgenstein's thought. These issues help to understand the discussion that will follow; we will explain how is based the asserting of the existence of several mathematics, according to our understanding, and discussing concepts of Wittgenstein - with special attention to the concept of family resemblances - we propose our interpretation on the theme 'mathematics or simultaneous mathematics'. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to analyze the mathematical knowledge obtained as a result of work activities developed by subjects with little schooling in social exclusion contexts. This study belongs to the research field 'Culture and Cognition', which includes gender issues, research developed by the Recife Group (Carraher, Nunes, Schliemann and collaborators) and the ethnomathematics research program, which is led by Ubiratan D'Ambrosio. The study was based on ethnographic observation of different contexts of work (garbage collectors, seamstresses, mechanic turners) and video recorded interviews, inspired by the self-confrontation interview, in order to understand the mathematical knowledge that is implicit to the different activities. The results show that mathematical specific knowledge has been developed as a consequence of survival needs as well as contexts that favored the development of such professional activities. It was also observed the development or inhibition of cognitive competencies due to the social values that encouraged or prevented these activities as a result of gender issues. [ABSTRACT FROM AUTHOR]

The easiness by which we use language to communicate with others and to interpret what others say leads us to believe that language is transparent and of immediate comprehension. Linguistic studies, however, show that such transparency is illusory since the mother language is rife with indeterminations, ambiguities and dual meanings. Such reflections become even more important when we consider the classroom and the interactions that take place through language. This is because in school communication, the differences between the subjects involved, as long as mother language and specific knowledge are concerned, are part and parcel of every day situations. Therefore, it is important for the Math teacher to listen to the students and leave them at ease to expound their doubts and formulate their questions. Grounded on the results of research in mathematical education field, the objective of this paper is to discuss whether the communication which takes place in the classroom between the subjects in the educational process by means of language favors or not the building of mathematical knowledge by the students. [ABSTRACT FROM AUTHOR]

The financing of unfunded actuarial liabilities in pension funds, whether resulting from insufficient asset constitution, revision of actuarial premises or inclusion of participants in the plan with non capitalized interests, generally remains restricted to the use of m-year period certain annuity, ignoring a set of possibilities offered by financial or actuarial mathematics. This paper aims to demonstrate and systemize three groups of (financial and actuarial) methods, available to actuaries, managers and sponsors to capitalize such insufficiencies. Finally, we will demonstrate the different speed of temporal resource accumulation for the coverage made possible by the analyzed methods. [ABSTRACT FROM AUTHOR]