Symmetrical freedom quilts: the ethnomathematics of ways of communication, liberation, and art

Symmetrical Freedom Quilts may be considered as links between mathematics, history, ethnomathematics, and the art of quilting. A quilt theme is a pedagogical way to integrate mathematics, art, and history in an interdisciplinary approach. This article combines an ethnomathematical-historical perspective by elaborating a history project related to the Underground Railroad. This work will allow teachers to develop classroom projects that help students to better understand geometry, especially concepts of symmetry and transformations. One of the objectives of this project is to stimulate student’s creativity and interest, because quilts may be considered as cultural and mathematical expressions of student’s daily life.

SUPPORTING LEARNING FOR NAVAJO STUDENTS THROUGH ETHNOMATHEMATICS

The purpose of this research was to address how culturally informed ethnomathematical methods of teaching can be utilized to support the learning of Navajo students in mathematics. The study was conducted over the course of four years on the Navajo Reservations at Tohatchi Middle School in Tohatchi New Mexico. The students involved in the study were all in 8th grade and were enrolled either in Algebra 1 or a Response to Intervention, RTI, class. The data collected came in the form of a student survey, student observation and student assessment. The teacher written survey, a math textbook word problem, and two original math textbook problems along with their rewritten version were the sources of these three studies. The first year of the study consisted of a math attitude survey and how Navajo students perceived math as a subject of interest. The students answered four questions pertaining to their thoughts about mathematics. The students’ responses were positive according to their written answers. The second year of the study involved the observation of how students worked through a math word problem as a group. This method tested how the students culturally interacted in order to solve a math problem. Their questions and reasoning to solve the problem were shared with peers and the teacher. The teacher supported the students in understanding and solving the problem by asking questions that kept the students focused on the goal of solving the problem. The students worked collaboratively and openly in order to complete the activity. During the iv study, the teacher was more able to notice the students’ deficiencies individually or as a group, therefore was able to support them in a more specific manner. The last study was conducted over a period of two different years. This study was used to determine how textbook bias in the form of its sentence structure or word choice affects the performance of students who are not culturally familiar with one or both. It was found that the students performed better and took less time on the rewritten problem than on the original problem. The data suggests that focusing on the culture, language and education of Navajo students can affect how the students learn and understand math.

Effect of social background on the development of probabilistic concepts

This research explores how the social backgrounds of a group of students contributed to their intuitive knowledge in probabilistic reasoning, and influenced their processing of the associated mathematics. A group of Year 11 students who came from families for whom the phenomenon of track gambling formed an important part of their cultural background was identified. Another group consisting of students in the same mathematics course (Year 11 Maths in Society) but from families for whom the phenomenon of gambling in any form was totally absent from their social backgrounds was identified. Twenty students were selected from each group. The research employed a qualitative methodology in which a phenomenographic approach was used to investigate the qualitatively different ways in which individuals within the two groups thought about concepts involving probabilistic reasoning, and processed the related mathematical skills and concepts. The cognitive processes involved in the applications of probabilistic and related mathematical concepts in a variety of both gambling and non-gambling situations were studied in order to determine whether this culturally based knowledge could be viewed as a type of ‘ethnomathematics.’ Data were obtained through individual structured interviews which enabled patterns of reasoning to be compared and contrasted. Analyses of these data enabled intuitive mathematical understandings possessed by the gamblers not only to be identified, but also to be linked with their social backgrounds. Also differences between how individuals in the two groups processed probabilistic and associated mathematical knowledge were determined. This research complements and extends existing knowledge and theories related to culturally-based mathematical knowledge. Implications for further research, for classroom teaching, and for curriculum development in the study of probability in senior secondary mathematics classes are discussed.

Investigação etnomatemática em contextos indígenas: caminhos para a reorientação da prática pedagógica

From the investigation, analysis, discussion and pondering about the activities developed by the lndians from the Porteira hamlet, members of the Xerente community, in the Tocantins state, we developed an investigative and descriptive study about the reality of this people with the aim of helping in the conceptual formation and in the reorientation of the pedagogical practice of the local teachers. In this sense, the undertaken research involved the teachers, the main representatives and experts in that cultural tradition, in order to investigate how the everyday activities (agriculture, food handling, assets distribution among the community members, etc.) and the cultural tradition (log race, body painting, clan division, Xerente numeration, Indian myths and histories, etc.), may enable the contextualization of the mathematics teaching in the lndian School Srêmtôwê of this hamlet, under a more transversal and globalizing perspective of the local and school knowledge. We based this research in the sociocultural conceptions of knowledge generation proposed by D Ambrosio (1990; 2002); Vergani (2007); Oliveras (1996); Gerdes (1991; 2002); Bishop (1999) e Sebastiani Ferreira (1997; 2004). ln the process of this study we propose some viable ways so that the Indian teachers may reorganize their classroom knowledge and actions, based in the strengthening of their history and culture. The observation of some social practices and knowledge as well as of the Xerente traditions helped us to point some possibilities of projection of a didacticalpedagogical dimension of these activities and practices, in the development of the school mathematical knowledge in this community

Pedagogia etnomatemática : ações e reflexões em matemática do Ensino Fundamental com um grupo sócio cultural específico

mongst the trends in Mathematics Education, which have as their object a more significant and criticallearning, is the Ethnomathematics. This field of knowledge, still very recent amongst us, besides analyzing an externalist history of the sciences in a search for a relationship between the development of the scientific disciplines and the socio-cultural context, goes beyond this externalism, for it also approaches the intimate relationships betwe_n cognition and culture. In fact, the Ethnomathematics proposes an alternative epistemological approach associated with a wider historiography. It struggles to understand the reality and come to the pedagogical action by means of a cognitive approach with strong cultural basis. But the difficulty of inserting the Ethnomathematics into the educational context is met by resistance from some mathematics educators who seem indifferent to the influence of the culture on the understanding of the mathematics ideas. It was with such concerns in mind that I started this paper that had as object to develop a curricular reorientation pedagogical proposal in mathematics education, at the levei of the 5th grade of the Ensino Fundamental (Elementary School), built from the mathematical knowledge of a vegetable farmers community, 30 km away from the center of Natal/RN, but in accordance with the teaching dimensions of mathematics of the 1 st and 2nd cycles proposed by the Parâmetros Curriculares Nacionais - PCN: Numbers and Operations, Space and Form, Units and Measures, and Information Treatment. To achieve that, I developed pedagogical activities from the mathematical concepts of the vegetable farmers of that community, explained in my dissertation research in the period 2000 through 2002. The pedagogical process was developed from August through Oecember 2007 with 24 students of the 5th Grade of the Ensino Fundamental (Elementary School) of the school of that community. The qualitative analysis of the data was conducted taking into account three categories of students: one made up of students that helped their parents in the work with vegetables. Another one by students whose parents and relatives worked with vegetables, though they did not participate directly of this working process and one third category of students that never worked with vegetables, not to mention their parents, but lived adjacent to that community. From the analyses and results of the data gathered by these three distinct categories of students, I concluded that those students that assisted their parents with the daily work with vegetables solved the problem-situations with understanding, and, sometimes, with enriching contributions to the proposed problems. The other categories of students, in spite of the various field researches to the gardens of that community, before and during the pedagogical activities, did not show the same results as those students/vegetable farmers, but showed interest and motivation in ali activities of the pedagogical process in that period

Saberes e práticas etnomatemáticas na carcinicultura: o caso da Vila de Rego Moleiro-RN

This study addresses issues related to the mathematical knowledge and practices of the workers of carcinoculture (shrimp farming), associating such knowledge and practices to the conceptual aspects and the academic mathematical language. Our central aim was to investigate and discuss such knowledge and practices in order to contribute towards having the members of this group reflect upon their own working practices. The investigation took as reference the ethnographic research approach during observations and interviews, as well as the analysis and interpretation of the existing cultural aspects on the use of Mathematics in the shrimp farmers daily activities, thus composing the four chapters of this dissertation. Initially, the local-regional context was set in the area where the workers of the shrimp farm reside, also describing our methodological options. After that, the kind of work that was carried out is explained through a brief history of the shrimp-farming activity, including a short discussion on the environmental impacts that result as a consequence of shrimp-farming. We then discuss some theoretical and practical aspects of the Ethnomathematics while field of study and research. At that moment, we make a reflection upon the different kinds of Mathematics, especially stressing the kind of Mathematics being taught in Schools and that being put to practice by identifiable cultural groups. With that in mind, we show the investigated knowledge and practices e some possible systematizations accomplished during the study. In the end, we point out some conclusive propositions based on the implications of our study towards the development of an educational process within the local communities, considering a possible use of the results and conclusions of this study in the classroom activities

Pedagogia de projetos e etnomatemática: caminhos e diálogos na zona rural de Mossoró - RN

Teaching Mathematics in a contextualized and significant manner, in the world of the child and the adolescent, requires a solid theoretical and methodological basis on the part of the researcher. The present work found this foundation in two ways: teaching with projects and ethnomathematics. It is understood that these ways have points in common, such as: the real, interdisciplinarity, teaching methods, flexibility in sequencing the curriculum and interactive learning. This makes possible a theoretical cross-fertilization, which is important for the teaching/learning of Mathematics. Those points are merged in the present proposal, making possible new strategies, distinct from those of the Traditional Teaching Methodology and giving raise to an Alternative Teaching Methodology, which is to be lived in the Mathematics classrooms. This work gives a new direction to teaching, going beyond the traditional forms of education by allowing the teaching of Mathematics to become integrated with other school subjects, resulting in significant learning. In order to implement the proposal, it is necessary to form partnerships with teachers, pupils and the whole community, so that the way can be traced by continual dialogue