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The teacher is one of the key factors in the transmission of curricular objectives to their students. Their knowledge and positive attitude toward students' ethnomathematics and its pedagogical approach play an important role to make classroom teaching culture friendly. This paper is intended to explore the in-service teachers’ knowledge of ethnomathematics and perception on the integration of the ethnomathematics approach in their teaching with respect to the demographic factors of in-service teachers such as gender, academic status, teaching experience, teacher training, and nature of institution they associated. This study was conducted among 120 in-service mathematics teachers from 32 secondary schools in Kathmandu District. The explanatory sequential mix method was employed to carry out this study. The perception of in-service teachers on ethnomathematics pedagogy in their classroom teaching was measured with survey instruments in the first stage. For further justification of the results obtained from the quantitative data, six teachers with different demographic factors were interviewed in the second stage of the data collection process. The relationship between in-service teachers’ understanding on ethnomathematics and different demographic factors was investigated using the Pearson Chi-square test. From the statistical data analysis, it was found that there is no relationship between gender, academic qualifications, and teachers' training in their understanding of ethnomathematics. However, a significant relationship was found between the teachers' experience and nature of the institutions they were involved, and their understanding on ethnomathematics. In-service teachers have a similar understanding on ethnomathematics and their perception in the integration of the ethnomathematics approach in the teaching of school mathematics.

Several methods of approximate reasoning are known, and many remain to be discovered across domains. Some are tied to reasoning with uncertainty. The developments over the last fifty years or so in the development of approximate reasoning methods, and their application across multiple STEM domains, suggest that it is necessary to introduce them early in school. While efforts towards building the infrastructure for the process have been limited, the bigger question is “What should be introduced?”. If concepts are always approximated in real life, then how should they be done mathematically? If the real numbers are not always necessary to approximate concepts or even quantities, then how should they be approximated, and what should be taught in schools? Specifically, functional representations of approximate reasoning are not introduced early. This additionally impedes diversity, ethnomathematical explorations, learning from experience, and through models. The objective of this research is to explain the problem with a focus on the ethnomathematics of cooking, and associated haptic methods. Further, it is argued through the context that of the many approaches to approximate reasoning, intrusive methods are best avoided, and that general rough sets is better suited for modeling such knowledge. Intrusive methods, such as those based on fuzzy or probability theory, are those that indulge in an excess of unjustified numeric assumptions. This builds on earlier work of the present author on modeling approximate reasoning. Her axiomatic approach to granularity are additionally applicable to approximate recipes that possess desired properties. In the contexts of ethnomathematical discourse involving haptic reasoning (as in cooking), it is shown that such an approach can model the essence of context without oversimplifications or outright dismissal of the efforts involved. Further, it has the potential to help in inventing expressive structured languages for the ethnomathematics, and associated model eliciting activities. Distinct facets of three specific contexts are theoretically explored to illustrate aspects of the reasoning, and meta aspects.

The Escola da Terra Program is a State policy, involving the federal government, state and municipal governments, as well as social movements and Public Higher Education Institutions. It seeks to promote specific continuous formation of teachers to meet the needs of rural and quilombola schools. This article aims to report and analyze contributions of the Improvement Course Escola da Terra at UFT, Arraias Campus, in the formation of rural teachers in Tocantins, having as reference the Module: Mathematical Languages. We analyzed materials produced by course participants, contents and methodologies addressed in the formation. The investigation uses as a research instrument the field reports of the professionals involved in the project. The data were analyzed in the light of the theoretical framework that deals with rural education, ethnomathematics, sociocultural practices and initial and continuing teacher formation. We highlight the elaboration of the action projects of the course participants, the result of reflections on the contents discussed during online meetings and materialized in the community time in the schools where they work. Although there are many challenges, we recognize that the Project (UFT) and the Program (MEC) Escola da Terra have triggered formation processes, which seek to build spaces for dialogue and reflection on educational practices based on their contexts, in line with the principles of Rural Education.

Our purpose with this article is to analyze the meanings of contextualization in the area of ​​Mathematics and its Technology of the BNCC and its normative character. In order to achieve this objective, we rely on a qualitative and documentary research of the final version of the BNCC and the training documents: 1) “Transversal Contemporary Themes (TCTs) in the BNCC: historical context and pedagogical assumptions”; 2) “Transversal Contemporary Themes (TCTs) in the BNCC: proposals for implementation practices”. We also emphasize that the analysis was fostered from a critical discussion based on the precepts of Ethnomathematics and Decolonial Thought. The results show that the contextualization presented in the BNCC directs learning towards a labor training, based on the development of competences, with a normative character that approaches a neoliberal conception and coloniality. We consider that the meanings about the contextualization theme favor the epistemological erasure and the distancing of a critical, emancipatory formation that respects sociocultural diversities.

Critical mathematics education can be characterized by its many concerns. I refer here to four of them connected to social justice and politics, power and mathematics, students’ future possibilities, and the socio-political structuring of education, all of which are interrelated and integrated. Those concerns are shared by much work done in ethnomathematics. However, to what extent an ethnomathematical study turns critical must be discussed in every case. I see the concerns of critical mathematics education as an important challenge to ethnomathematics.

The present work had as general objective to investigate how the work with Mathematics in the Field Education is accomplished, from a look on the Ethnomathematics. This study had as its axis the discussions about Mathematics, Ethnomathematics and Rural Education. For the development of the work, we made a bibliographic study developed from the following authors and documents: D'Ambrosio (1990, 1993, 2005b), Carvalho (1994), Almeida (2013), National Curriculum Parameters of Mathematics (BRASIL, 1998) and the Law of Guidelines and Bases of National Education (LDBEN) No. 9394/96 (BRASIL, 1996). We also made observations from the classes of two 5th grade elementary school teachers and interviewed them. We believe that the research will contribute to the formation of educators and teachers who seek to value the knowledge brought by their students and also a deepening in their teaching practice.

Abstract: This theoretical article primarily reflects upon the many points of view from an ongoing research in ethnomathematics and its connections to the responsible subversion of its pedagogical action. Furthermore, there is a discussion on mathematical ideas, procedures, and practices related to the anthropological approaches - emics (local/insiders) and etics (global/outsiders) - in order to understand the dialogic approach (emic-etic/glocal) needed for the development of an ethnomathematics research. The researchers have observed that this aspect has been theorized in anthropological research for decades, having the emic, etic, and dialogic approaches as the means to provide a deeper understanding of the mathematical ideas, procedures, and practices developed in diverse contexts. Our analysis reveals that innovative pedagogical actions need to cope with existing mathematics curricula, in order that mathematical ideas, procedures, and practices can be understood. This article aims at contributing to a holistic understanding of the mathematical ideas, procedures, and practices developed by members of distinct cultural groups.

This article aims to present a proposal of introductory activities to the concept of linear function for schools inserted in extractive regions, in which Ethnomathematics and Mathematical Modelling are related. To this end, a teaching sequence was elaborated for the 9th year of Elementary School, which aims to value the knowledge of the workers in their daily routines – hunting and selling crab in mangroves of cities located in the south of Bahia – and to relate them to the study of Mathematics contents. The work supports the idea that it is possible to construct a teaching sequence for the introduction of the concept of linear function, using the Ethnomodelling approach. It is believed that the application of the sequence may make learning more meaningful, in which students from that cultural context may see meaning for the learning of Mathematics.

El objetivo de este artículo es presentar el análisis del proceso de modelación que se da en el tallado de objetos, hechos artesanalmente en madera. En este análisis, se hizo énfasis en tres estados, que hacen visible el modelo mental que se va representando en el estado rústico del objeto, en la preforma básica y en la forma establecida, llegando así a un modelo público o privado. También, se analiza el papel que juegan las herramientas en la modelación que conlleva a los objetos tallados. El problema consistió en el desconocimiento del proceso de modelación que emplean artesanos en el tallado de la madera y su potencial educativo. La metodología fue cualitativa de corte etnográfico, se emplearon entrevistas individuales y observación participante. Por último, se presentan algunas conclusiones sobre el análisis y resultados. Una de estas conclusiones consiste en que al mostrar el paso a paso de cómo son materializados los modelos ya compartidos por todos aquellos que practican la actividad artesanal, no es necesario traducir o colocar la experiencia y los modelos de los artesanos, en función de la matemática académica.

This study discusses aspects of informal learning, evidenced in a group of women artisans living in the city Santarém / PA, Aritapera region, and how these learning styles and informal knowledge interconnect with the perspective of the Ethnomatematics Program. Their social practices, reflected in their regional craft, show particularities involving the transmission and production of knowledge, organization of communities of practice and evidenced symbolic exchanges during the preparation work of ornamental gourds. Methodological procedures used in this research were organized, according to an ethnographic approach, from observation and inference of construction processes and incisions recorded on surfaces that create the regional gourds. Research results indicate that the iconography reflected in bowls, indicate motivations especially related with social representations evidenced in the community dynamics and commercial relations involved. Possible social interactions existing in this context thus permeate a permanent flow of diversified multifaceted knowledge exchange. The production and ornamentation of gourds are closely related to a kind of technical and instrumental knowledge, which involves the community as a whole. At the same time, it adds particular elements to the practices of the artisans, closely connected with nature, revealing a dynamic knowledge integrated and balanced with the environment, without disregarding the fact that any environmental alteration threatens the cultural practice, bringing changes to its modes of production.

This article presents the state of art of ethnomathematics in North and Central America. The methodology stems from a literature review of the ethnomathematics research carried out in the region since the 1980s. This has not been an easy task, as the coordinators of each country of the region were responsible for synthesizing the projects carried out in his or her respective country, with objective criteria that limited the number of investigations referenced. The results reveal significant contributions to the development of ethnomathematics research as well as to that of diverse areas of knowledge such as history, anthropology, sociology, and mathematics education. This collaboration is evidence of a consolidation of research groups and lines of inquiry, and documents a vast participation in conferences and publications that represent a community of ethnomathematics practices in the entire region, from Panama to the United States.

Una aritmética existe por necesidad de una actividad humana y solo tiene sentido en el intercambio de los productos que genera o moviliza. El objetivo de esta investigación fue analizar las aritméticas en un sector del municipio de la Paz, departamento del Cesar, Colombia. Se identificaron, a la vez, los procesos y los algoritmos que emplean personas adultas, al hacer cálculos en algunos oficios y se determinó el grado de participación de los niños en estas actividades. He aquí justamente lo problemático, a que se hace referencia, cuando se dice que la matemática tiene sentido si se vincula con la realidad. La metodología empleada fue básicamente cualitativa de tipo etnográfica, cuyas estrategias de recolección de datos consistió en 17 entrevistas informales de periodos cortos, observaciones no participantes de actividades y el empleo del google earth, como herramienta de localización de la actividad, dentro de un mapa. Los resultados muestran que es posible determinar cuándo el niño o niña se vincula, de manera concreta, a las actividades de su entorno sociocultural próximo, en el sentido de comprender los procesos y los algoritmos de los cálculos empleados en ellas.

An important dilemma in mathematics education is its overwhelming bias against a local orientation in its research paradigm. Thus, a search for innovative methodologies such as ethnomathematics is useful for recording historical forms of mathematical ideas, procedures, and practices developed in diverse cultural contexts. It is important to highlight that an ethnomathematics program is not an attempt to replace academic mathematics. At the same time, it is necessary to acknowledge the existence of, and important contributions of local mathematical knowledge for inclusion in the mathematics curriculum. In this context, the insubordination triggered by much work in ethnomathematics is creative and often evokes a disturbance that causes a review of rules and regulations in many mathematics curriculum contexts. This process enables educators to use positive deviance to develop actions in order to deal with such norms. Thus, positive deviance involves an intentional act of breaking the rules in order to serve the greater good. This process increases the potential for continual growth in the debate about the nature of mathematics as it relates to culture since it proposes a dialogue between local and global approaches to the construction of mathematical knowledge.

This article is the result of socio-historical research on the development of ethnomathematics in Costa Rica, with an emphasis on the description of events over time, which tries to order the information along a temporal referent. This research is part of the results of the FUNDER Ethnomathematical project of the Regional Section Huetar North and Caribbean (Campus Sarapiqui) of the National University of Costa Rica. The methodology is mainly qualitative in its approach and the narrative is subdivided into theme-based topics. The results demonstrate the work that has been developed in this country to delve into ethnomathematics as a line of research from the various areas of human knowledge and work developed around it.

When thinking about mathematics, seldom does one think about culture, context, history, or diversity. Many teachers believe that there is no place for such constructs in their mathematics classrooms. As an ethnomathematician, my primary goal is to find meaningful ways to bring components of ethnomathematics into the mainstream mathematics curriculum and classrooms. In this paper, I describe key aspects of a mathematics curriculum that was designed to promote meaningful connections between ethnomathematics theory and practice and highlight how this curriculum might help address the key tenets of a critical ethnomathematics curriculum.

This article gives an account of one of the aspects dealt with in our development research on the mathematics of the Mapuche people in Chile, specifically, Mapuche arithmetic. Aiming to analyze the mathematical practices implied in the Mapunzugun language study program, we contemplate the morpho-syntactic description and analysis of morpho-mathematical structure, the numbers in Spanish and Mapunzugun. Our analysis focuses on the semiotic conflicts of a decontextualized learning, which does not consider the mathematical knowledge of the origin of Mapuche students, present in their daily mathematical practice. The main results account for the existence of Mapuche arithmetic recognized by institutions and the educational potential of numbering in mapuzungun. We conclude this study with a critical reflection on the complex stage of the teaching and learning process of the mathematical school in the Mapuche context, which evidence the need to articulate two mathematical knowledge components that converge in the mathematics classroom in the first levels of compulsory education. At the same time, we ask questions open to future research of the didactics of mathematics, that require theoretical tools that allow designing didactic proposals for an appropriate articulation between the mathematics school and mapuche mathematics.

Comparing and networking theoretical frameworks is a topic treated by various authors and discussion forums, as a source of enrichment and starting point for advancing theory development. In this paper we present a study about this topic, establishing a relationship between ethnomathematics and the onto-semiotic approach (OSA) to mathematical knowledge and instruction. Ethnomathematics is a research program with a consolidated international presence that proposes an expanded vision of mathematics and mathematics education. The OSA is a theoretical framework, which is widespread and valued in the community of scholars in mathematics education. A reciprocal glance of both theoretical frameworks can provide mutual enrichment. Specifically the basic features and the paradigmatic issues addressed by both theoretical frameworks are presented and compared. Some commonalities and complementarities are also identified.

The teaching experience we present is closely linked to research, considered part of the action of training teachers. In the new curriculum, adapted to the European Higher Education Area and valid throughout the European continent, a Final Degree Work (TFG) was introduced to the last semester of training, which must demonstrate a received comprehensive training in all subjects. We planned a TFG model in which students interrelate knowledge, professional practice and research. This type of TFG is based on the Emergent Educational Model that we have elaborated. In the current course we have carried out and analyzed four examples in which ethnomathematics is introduced as a foundation, microprojects focusing on different cultural signs are elaborated, and the interrelationship of the various sciences are reflected upon, creating awareness that research is a necessary element in teacher education. We describe the MED model of teacher education, the didactic teaching construct called micro-project, and the type of TFG designed, along with four examples thereof.

Ethnomathematical research, together with digital technologies (WebQuest) and Drama-in-Education (DiE) techniques, can create a fruitful learning environment in a mathematics classroom—a hybrid/third space—enabling increased student participation and higher levels of cognitive engagement. This article examines how ethnomathematical ideas processed within the experiential environment established by the Drama-in-Education techniques challenged students‘ conceptions of the nature of mathematics, the ways in which students engaged with mathematics learning using mind and body, and the ‗dialogue‘ that was developed between the Discourse situated in a particular practice and the classroom Discourse of mathematics teaching. The analysis focuses on an interdisciplinary project based on an ethnomathematical study of a designing tradition carried out by the researchers themselves, involving a search for informal mathematics and the connections with context and culture; 10th grade students in a public school in Athens were introduced to the mathematics content via an original WebQuest based on this previous ethnomathematical study; Geometry content was further introduced and mediated using the Drama-in-Education (DiE) techniques. Students contributed in an unfolding dialogue between formal and informal knowledge, renegotiating both mathematical concepts and their perception of mathematics as a discipline.

The Herero/Helelo people of southern Angola, still keep their daily traditions alive . This study is guided through interviews with the elderly, visits to the group and also by the study of theories of Ubiratan D'Ambrosio’s Ethnomatematics program. It was possible through the observation of Mucubais and Himba subgroups allied to urge the preservation of the people’s roots and thinking of new ways and techniques for teachers to approach school knowledge within a contextualized framework closer to the reality of both groups. In particular, an emphasis was given to thinking about the relations between Art, Culture and Mathematics that the teacher can create and weave together in order to approach the reality experienced by young people and in the school. In this sense the research is justified by the need to learn about the current knowledge surrounding the group, in order to ensure their survival today without losing the culture.

The document is about the history of the development of the author’s PhD thesis. At the beginning, by understanding Ethnomathematics as the study of mathematical practices of specific cultural groups, the research focuses on the mathematical practices of a craft environment and a specified methodology is created as an instrument for the analysis of braids in two different crafts. The field work provides the evidence to distinguish that in the first braid craft the generated mathematical modeling can be considered as a situated interpretation since the artisans themselves manage it, but in the second braid craft the modeling is not situated as the artisans did not know it. A following ethnographic study provides the way these craftsmen think mathematically their own practice.The reflection above is the key point for the development of the following part of the PhD work. Ethnomathematics is re-conceptualized as the way of social thinking and understanding the quantitative, relational and spacial aspects of reality, making the author sensitive to the deep epistemological changes about the conception of mathematics as a social and cultural construct that taking on an ethnomathematics perspective involves. So we carried out a workshop addressed to teacher education with the objective of making the participants aware of their conceptions about the nature of mathematics through the direct and creative experience of a consensual modeling of braid crafts. Finally we recognize three dimensions in the ethnomathematical perspective that enable us to analyze the observations of a group of pre-service and in-service teachers after their participation in the workshop.

Since ancient times human beings, particularly the merchants, used mathematical knowledge enabling them to solve problems related to trade, which the least skilled in the business or the mathematics context, thought to have no solution or to be too difficult to solve.Problems involving proportional reasoning were considered of medium to high complexity. However, the merchants, many centuries ago, without formal schooling, ingeniously solved some problems of relative complexity.Even today, some professions, despite their low levels of education, have a very close relationship with problems involving proportional reasoning. Such is the case of fishing communities that use informal mathematical knowledge in their daily lives, although sometimes this becomes difficult to translate into the classroom language and vice versa. This study, of a qualitative nature with Ethnomathematics as a reference, was developed in two fishing communities (Câmara de Lobos - Madeira and Caxinas) by collecting information on mathematical elements used in everyday life (boat building). At a later stage, tasks in the context of proportional reasoning were applied with students (of 10-12 years) of two schools of different contexts: with the fishing community of Caxinas and with the more urban context of Vila Nova de Famalicão. Data will be presented in a descriptive and interpretative form, including both students' strategies and difficulties. Also we will present a brief analysis on the possible influence or interference of school mathematics on the performance of students in these two very different social contexts while faced with the same mathematical tasks.

This paper narrates facts and consequences of a course focused on Interculturality and Ethnomathematics developed in a Venezuelan Pedagogical University. The reflection is centered on Ethnomathematics and the development of "curricular ethnomathematics micro-projects". The form of the group work was cooperative, with each team chosing a culture and an important cultural symbol in it, to allow for the reconstruction of this cultural practice in the classroom. This was materialized through a forum and supplemented with visits to schools in indigenous populations, which have been developing the Intercultural Bilingual Education Program (PEIB) of that University. During the course various aspects associated with the idea of mathematics in different cultures were developed, which allowed us to initiate research on Teacher Education and Ethnomathematics, emphasizing the identification, evaluation and description of mathematical practices that take place outside school (mathematics in the design and construction of: blowguns, indigenous baskets, musical instruments, houses). In the medium-term (5 years), the products emerging because of the impulse of the course are: Ethnomathematics training courses, MA and PhD postgraduate work, research projects and numerous publications in conferences and scientific journals.

In this article we describe and interpret ethnomathematical theorizing about the institutionalization of mathematical knowledge, and we present the socio-educational challenges that arise from these thoughts. Our approach is to take two sociopolitical contexts as a reference, exemplifying how Ethnomathematics faces and tackles the difficulties and challenges that arise in each of them. This dual analysis of both theoretical and empirical studies lets us deepen our understanding of how the sociopolitical context in which an investigation is situated affects the relationships it establishes between scholarly and/or academic mathematics, and other ethnomathematics. We also describe the methodological tool used for the systematic analysis of the ethnomathematical works (scientific articles, books and book chapters) that comprise the sample studied.

Mathematics, as a social and cultural construct, is not an ahistorical and enduring entity, but is subject to developments and vicissitudes of human communities from which they arose. Therefore, for its historiographical reconstruction, the task of interpretation of the historian is necessary. In this paper, we propose an interpretation of mathematics in Ancient Egypt based in the theoretical assumptions of cultural history and anthropology of mathematics, which together characterize the research program of Ethnomathematics. For this, we will take as a documentary source of reference to Moscow Mathematical Papyrus. Given the great diversity of problems that arise there, we will focus on one particular type: No. 10, concerning the calculation of the area of a solid figure that in the Egyptian language is designated as nbt.

Ethnomathematics is the mathematics of cultural groups, but often those cultural groups are “others” and “elsewhere”. However, it is also valuable to look inward to see the interaction of mathematics and one’s own culture. An assignment in a graduate course offers this opportunity to students. The assignment is to find an area of the student’s personal “culture” (sometimes defined rather broadly) and find its use of mathematics. Students are asked to write about (a) the cultural area; (b) how they are personally tied to it; and (c) how and where it uses mathematics. In addition to the paper, students make an oral presentation. Thus, all students learn (often surprising) aspects of their classmates’ non-professional life, and the presenter digs into areas of family and heritage that may not have been reviewed before. Since all students are classroom mathematics teachers, finding their own cultural mathematics is not only enlightening for themselves, but also offers opportunities to include new mathematics applications in their teaching. This paper includes much personal background that led to this assignment and is a report on more than a decade of using it, including brief student examples.

A current challenge in the Ethnomathematics research is the characterization of its role in the field of mathematics education. Here we present some experiences with primary school teachers in Argentina and Costa Rica, where we propose to apply Ethnomathematics as a tool for teacher education. We wonder if the study of the ethnomathematics of cultural environments in teacher education could promote reflection on mathematical knowledge -with special care given to the influence of cultural aspects in the development of this- and could provide significant contextualization for designing activities for elementary education. In both countries we organize a course that promotes the research of ethnomathematics of cultural signs and the design of contextualized activities by the participant teachers. We present some results of the ethnomathematics studied and the application of this in the design of activities for primary education. Finally we show the impact that Ethnomathematics has on these teachers and we emphasize the implication of this in the acquisition of a reflective attitude about the universality and contextualization of mathematical knowledge. Working with Ethnomathematics promotes teacher creativity when developing a curriculum of mathematics in connection with the sociocultural environment.

The acquisition of both emic (local) and etic (global) knowledge is an alternative goal for the implementation of ethnomodeling research. Emic knowledge is essential for an intuitive and empathic understanding of mathematical ideas, procedures, and practices developed by the members of distinct cultural groups. It is essential for conducting effective ethnographic fieldwork. Furthermore, emic knowledge is a valuable source of inspiration for etic hypotheses. Etic knowledge is essential for cross-cultural comparisons, which are based on the components of ethnology. In this regard, such comparisons demand standard units and categories to facilitate communication. Dialogical (glocal) is a third approach for ethnomodeling research that makes use of both emic and etic knowledge traditions through processes of dialogue and interaction. Ethnomodeling is defined as the study of mathematical phenomena within a culture because it is a social construct and is culturally bound. Finally, the objective of this article is to show how we have come to use a combination of emic, etic and dialogical (glocal) approaches in our work in the area of ethnomodeling, which contributes to the acquisition of a more complete understanding of mathematical practices developed by the members of distinct cultural groups.

Emmerging from the confluence of the history of mathematics and of mathematics education, with strong connections to anthropology and cognitive sciences, ethnomathematics is seen consolidated as a field of research with great concern, in particular, to the school context. Within this framework the present article has as its objective to identify the main tendencies of the national research related to this program and centered on the context of education through the analysis of two works published in the annals of the Brazilian Conference of Ethnomathematics (Congressos Brasileiros de Etnomatemática - CBEm). Dealing with a “state of the art” kind of research, we begin with a reading of two hundred and two abstracts of works presented in the annals of the four editions of the CBEm. Using previously established criteria, sixteen works were selected and read in their entirety, that were later categorized according to general aspects. In general, the plurality of theoretical concepts of Ethnomathematics reflects the diversity of aspects such as: geographic distribution, subjects and levels of eduction, contents addressed and promotion strategies of Ethnomathematics. In this way, it follows that Ethnomathematics assumes an important committment to questions of teaching and learning mathematics, and that the tendencies of the research analyzed suggests a promising future for an even deeper connection between the ideas of this field of research and the school context.

Mathematical thoughts are in interaction with culture and they, together, form an indivisible whole. Therefore, Ethnomathematics both helps us understanding the nature of mathematics and contributes to understanding of one’s self as well as the other people sharing the same planet. Ethnomathematics reflects the studies of mathematical thoughts of multicultural or traditional societies. Mathematical thought is an approach in which people try to find quick and systematic solutions to a problem in many ways. The role of Ethnomathematics, which studies mathematical thoughts, cannot be ignored in a historical-cultural context. This paper examines some reflections of Ethnomathematics in Anatolian culture through geometry perception in engineering field, carpet, rug motifs and intelligence games.

This paper starts from two statements based on a literature review. The first one concerns the learning process and states that learning is situated and socioculturally contextualized. Learning happens in the space of the background and the foreground of the learner in his or her particular environment of experience. This statement is based on the Vygotsky and the Cultural psychology approach (Cole, 1996) and on the work of Vithal & Skovsmose (1997).The second statement concerns the deficient theory of the learning process (instead of the deficiently of the learner). Based on the international comparative research on mathematical skills we claim that the drop out of school of many groups of children (OECD, 2010) has to do with the insufficient learning system at school that fail to fit with the daily background knowledge of the children.In the final part of the paper we will present three different ethnomathematical cases based on the educational practices that the authors developed in recent years.

The paper presents the results of a research Project, which aims to analyzing the truths about mathematics education that circulate in Teacher Education courses (of the Southernmost state of Brazil) and how cultural difference operates in the constitution of such truths. The empirical data are composed by interviews done with teachers who work in the first years of schooling and have completed their Teacher Education courses. Using Ethnomathematics theoretical tools, linked to Foucault and Later Wittgenstein‟s theorizations, data analysis showed that Teacher Education courses enable students to reflect on their past experiences with school mathematics; the Teacher Education courses allow the appropriation of language games associated with diverse mathematics, instituted by different forms of life; and the boys are positioned as those who perform better in school mathematics and the girls as those who are obedient and able to follow rules in mathematics classes.

Researchers who have carried out studies pertaining to mental computation and everyday mathematics point out that adults and children reason intuitively based upon experiences within specific contexts; they use invented strategies of their own to solve real-life problems. We draw upon research areas of mental computation and everyday mathematics to report on a study that investigated adults’ use of mental mathematics in everyday settings. In this paper, we report on one adult’s use of mental computation at work and highlight the role of context and context related parameters in his mental mathematical activities.Los investigadores que han realizado estudios relacionados con el cálculo mental y las matemáticas cotidianas señalan que los adultos y los niños razonan intuitivamente basándose en las experiencias de contextos específicos; usan estrategias inventadas por sí mismos para resolver problemas de la vida real. Nos basamos en las áreas de investigación del cálculo mental y las matemáticas cotidianas para informar sobre un estudio que investigó el uso que hacen los adultos de la matemática mental en el entorno cotidiano. En este artículo, informamos sobre el uso que hace un adulto del cálculo mental en su trabajo y destacamos el papel del contexto y de los parámetros relacionados con el contexto en sus actividades matemáticas mentales.

Ethnomathematics studies the cultural aspects of mathematics. It presents mathematical concepts of the school curriculum in a way in which these concepts are related to the students’ cultural and daily experiences, thereby enhancing their abilities to elaborate meaningful connections and deepening their understanding ofmathematics. Ethnomathematical approaches to mathematics curriculum are intended to make school mathematics more relevant and meaningful for students and to promote the overall quality of their education.In this context, the implementation of an ethnomathematical perspective in the school mathematics curriculum helps to develop students’ intellectual, social, emotional, and political learning by using their own unique cultural referents to impart their knowledge, skills, and attitudes. This kind of curriculum providesways for students to maintain their identity while succeeding academically.

El presente artículo recopila el conocimiento geométrico plasmado a través de diseños textiles de diferentes pueblos nativos de América. Puede verse cómo en el arte del tejido en telar, se transmiten distintos conocimientos, muchos de ellos asociados a sus creencias, a ideas religiosas, estatus social o político. El marco, en el cual se ha realizado la presente investigación, es la etnomatemática, estudiando así los conocimientos matemáticos transmitidos en forma oral y plasmados en las prendas tejidas. Es así como seestudiarán los tejidos guatemaltecos, realizados por descendientes del pueblo Maya, transmitiendo en ellos parte de su cultura, también se incluirá un análisis de la obra textil incaica, para luego finalizar con los diseños realizados por el pueblo Mapuche que habitan el sur del territorio argentino

Este artículo presenta algunos procedimientos y estrategias geométricas utilizadas por un grupo de artesanos del municipio de Guacamayas en Boyacá, Colombia. Así mismo, se expone un análisis geométrico de algunosdiseños presentes en la cestería que elabora la comunidad y, finalmente se hace una reflexión sobre la importancia de la integración de conocimientos matemáticos extraescolares al currículo escolar.

El presente artículo es el resultado de una investigación, cuya actividad de campo se desarrolló alrededor de seis meses, en el Distrito de Agua Blanca de Cali y en el barrio de las Américas de Palmira, Valle del Cauca, Colombia. El propósito fue determinar cómo eran algunos procesos de medición y de estimación en los albañiles. Se presentan algunas reflexiones sobre los aportes de este grupo de trabajadores a la Educación Matemática. Doce albañiles, con bajo grado de escolaridad y no coordinados por Ingenieros, colaboraron con la información. Las edificaciones que se visitaron fueron construcciones para vivienda (construcción de dos pisos o un segundo piso) y la construcción de una iglesia. Para analizar dichos procesos cognitivos, se hicieron pruebas controladas, se experimentaron situaciones reales en el oficio y conversaciones reales entre Oficiales y Ayudantes y, se estudiaron algunas herramientas artesanales, propias del ejercicio de la albañilería, como la flejadora, la grifa, la cimbra y la manguera de nivel. Solo se presenta una pequeña parte de ese ambiente de construcción etnomatemática, importante para el desarrollo arquitectónico de un pueblo, fecundo de discursos lógicos y gestuales y herramientas dispersas por doquier.This article is the result of a research activity realized during six months at the district of Agua Blanca (Cali) and in the suburb Americas (Palmira), Valle del Cauca, Colombia. The purpose was to determine some mason´s measurements and estimation processes. Reflections about the contributions of this working group to the Mathematical Education are presented. Twelve masons, with low schooling levels and not coordinated by engineers, helped with information. The constructions visited were houses (two-story buildings or the structure of a second floor) and a church. To analyze these cognitive processes controlled trials were executed; real situations in the office and actual conversations between officers and assistants were witnessed, and some proper masonry craft tools such as the strap, the faucet, the form and plummet were studied. Only a small part of building environment related to ethnomatemathics, important for the architectural development of a, fertile of logical speeches and gestures and tools scattered everywhere, nation.

In this review, we present the ethnomathematics investigations undertaken in the last three decades by Paulus Gerdes, a Mozambique mathematics educator. The author presents a variety of discussions with several examples that explains the relationship of mathematics to human activities. We present, among other things, the cyclic matrices and its interrelationships with the African cultural contexts, undoing the erroneous impression that mathematics can be seen disconnected from the feature, which makes the individuals in their socio-cultural environments. Gerdes shows us that there's mathematics in different cultures and this helps us to realize the beauty of the symmetries and patterns, in addition to allowing depth between mathematics and human actions in the art.

Este proyecto indagó sobre las relaciones de género entre las y los profesores y las y los estudiantes en el aulade matemáticas, y cómo éstas influyen en el desempeño académico de ellos y ellas. Esta investigación se realizó en dos instituciones mixtas de la ciudad de San Juan de Pasto, y la información fue recolectada por medio de entrevistas y observaciones dentro del aula de clase, las cuales se analizaron desde un punto de vista cualitativo y cuantitativo.Finalmente, se espera que esta investigación contribuya a crear conciencia sobre esta problemática y a mejorar las relaciones en el salón de clase de matemáticas entre docentes y estudiantes, tomando en cuenta las diferencias de género.

Mathematics used outside of the school may be considered as a process of ethnomodeling rather than a mere process of manipulation of numbers and procedures. The application of ethnomathematical techniques and the tools of modeling allow us to see a different reality and give us insight into mathematics done in a holisticway. In this perspective, the pedagogical approach that connects the cultural aspects of mathematics with its academic aspects is denominated ethnomodeling, which is a process of translation and elaboration of problems and questions taken from systems that are part of the students’ reality.

El actual trabajo, considera varios aspectos teóricos que involucran temáticas de las matemáticas como de la Etnomatemática, las cuales al ser abordadas dentro del análisis de las prácticas de un albañil, permitieron desplegar una serie de acciones que posibilitaron una pequeña investigación en torno a evidenciar los procesos matemáticos referentes a la conversión de medidas, la construcción de circunferencias y la medición de ángulos que se dan de manera implícita en las prácticas laborales de un grupo social determinado(albañiles).

La presente investigación se realizó durante los años 2008 y 2009 en el Parque Arqueológico de San Agustín, Huila y en la Universidad del Valle, Cali, Valle del Cauca, ambos departamentos de Colombia. El propósito de esta investigación fue identificar el desarrollo que alcanzó el grupo escultor sobre sus propias concepciones de las transformaciones isométricas. El medio que se utilizó para potencializar la decodificación de esta lógica de construcción fue el programa Cabri Geometry II Plus. Es decir, lo que se hizo fue tratar de acercarnos a los procesos de abstracción de dichos escultores visualizando algunas transformaciones en el plano, hechas en laestatuaria de San Agustín, de las cuales ellos eran conscientes en su uso. Para el análisis se tomaron fotografías a las esculturas que fueron editadas y así ser usadas como fondo de pantalla en Cabri, estopermitió verificar que los escultores manejaban las transformaciones de traslación, rotación, simetría, figuras geométricas y ejes perpendiculares que utilizaron en la planeación y elaboración de los monumentos.

En este documento se describen y analizan algunas habilidades, pensamientos y estrategias matemáticas referentes a la maximización de áreas utilizadas por un grupo de ocho (8) modistas que actualmente trabajan en una fábrica de confección de ropa en Bogotá Colombia. Inicialmente se hace una búsqueda de referentes de investigaciones de este tipo, posteriormente se hace una recolección de información por medio de entrevistas, observación no participante, diario de campo y la resolución a situaciones problemáticas del trabajo asociadas con la maximización de áreas, finalmente se hace un análisis y una reflexión de la información recolectada y el proceso llevado a cabo con la población.

Neste artigo, problematizamos as narrativas da nação brasileira que mascaram a identidade múltipla do País e ressaltamos mecanismos de exclusão presentes nas escolas. Lembramos que o Brasil, devido à sua formação histórico-social, é multirracial e pluriétnico, mas a escola continua a desconsiderar essa realidade, o que tem contribuído para elevar os índices de evasão e repetência de crianças provenientes de alguns grupos socioculturais. Então, remetendo-nos à aprovação da Lei 11.645/08, que inclui no currículo oficial dos estabelecimentos de ensino básico das redes pública e privada a obrigatoriedade do estudo da história e culturas africana, afro-brasileira e indígena, encaminhamos nossas discussões para o ensino de Matemática. Nesse contexto, discorremos sobre algumas das formas por meio das quais as pesquisas em Etnomatemática podem contribuir para discutir e destacar, no espaço escolar, os conhecimentos que possuem essas matrizes culturais. A partir daí, apresentamos algumas reflexões suscitadas por pesquisas que temos realizado na região de Pirituba, no município de São Paulo, onde atua o segundo autor e junto aos índios A'uwe-xavante do Mato Grosso, onde atua a primeira autora.In this article, narratives from the Brazilian nation are problematized, which disguise the country multiple identity and we emphasize mechanisms of exclusion present in schools. We remind that Brazil, because of its historical and social organization is multiracial and pluriethnical, but school continues to ignore this reality, which has contributed to raise the dropout and repetition rates of children from some socio-cultural groups. Then, concerning the 11.645/08 Law approval, which includes the compulsory study of the history and culture from Africans, Brazilian Africans and indigenous added in the official curriculum of private and public elementary schools, we guided our discussions for the teaching of Mathematics. In this context, talking about how research in Ethnomathematics can help enhancing, at school, the knowledge from those cultural matrix. From there, we present some thoughts raised by the research we have conducted in Pirituba, in Sao Paulo city, where the second author works, and close to the A'uwe-Xavante Indians of Mato Grosso state, the subject of doctoral research by the first author.