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Anthropology in the World

British Museum, London, UK; 8th - 10th June 2012


Multimathemacy: an anthropology of mathematical literacy

Location Sackler B
Date and Start Time 09 June, 2012 at 14:30


Hendrik Pinxten (Ghent University) email
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Short Abstract

This panel will focus on an anthropology of formal thinking and its contribution to the curriculum reform of mathematics education in multi-cultural societies. Based on the findings from ethnomathematics and critical-mathematics-education we will argue for a curriculum of multimathemacy.

Long Abstract

Situated Learning (J. Lave, M. Cole) recognizes that learning styles and learning processes can differ over cultures, since learning is not only in the head, but happens in and through the interaction between an individual and his/her social, historical and cultural environment.

The learning of mathematical skills and contents worked with a uniform curriculum for ages, also in developmental programs. This approach has come under fire. We propose to look at how anthropological and other social scientific research is contributing to the changes in mathematics education in the direction of multimathemacy.

Multimathemacy (Pinxten & François) recognizes that formal thinking and reasoning can take a variety of contents and of problem solution procedures. All of them have value and potential relevance. Empirical studies in this realm include ethnomathematics, but also street mathematics, radical mathematics and critical mathematics education. The diversity in social and cultural groups is recognized as a relevant dimension for the way a basic capability of formal thinking gets translated and enhanced in more sophisticated thinking which is called mathematics. Mathematics education would open up and break away from the uniform curriculum (emanating from Academic Mathematics) and seek to recognize the importance of a diversity of ways of formal thinking in the learning processes.

We invite researchers in this field to apply for the panel. We welcome empirical studies (on Romany students, on immigrants, on workers, outside school learning, ...) and more theoretical approaches.

Discussant: Karen François

This panel is closed to new paper proposals.


Ethnomodeling as an anthropological research concept on ethnomathematics and mathematical modeling

Authors: Milton Rosa (UFOP)  email
Daniel Orey (Universidade Federal de Ouro Preto)  email

Short Abstract

Using mathematics encountered outside of the school is considered constructive in developing the process of modeling rather than as a mere manipulations of ideas and procedures. The application of techniques in ethnomathematics along with the tools of modeling allows us to see a different reality and gives us insight into a holistic mathematics.

Long Abstract

Using the mathematics encountered outside of the school can be considered constructive in developing the process of modeling rather than as a mere manipulations of ideas, concepts, and procedures. The application of techniques in ethnomathematics along with the tools of modeling allows us to see a different reality and gives us insight into a holistic mathematics. In this perspective, we believe that the pedagogical approach that connects cultural aspects of mathematics with its academic aspects is named ethnomodeling, a process of translation and elaboration of problems and questions taken from systems that are part and parcel of a reality for any given cultural group.

In so doing, we propose an alternative goal for research, which is the acquisition of both anthropological concepts emic and etic knowledge for the implementation of ethnomodeling in the mathematics school curriculum. Emic knowledge is essential for an intuitive and empathic understanding of mathematical ideas of a culture and it is essential for conducting effective ethnographic fieldwork. Etic knowledge, on the other hand, is essential for cross-cultural comparison, the essential components of ethnology, because such comparison necessarily demands standard units and categories. We also offer a third perspective on ethnomodeling research, which is the dialectical approach, which makes use of both emic and etic knowledge and understandings through the processes of dialogue. Finally, we define ethnomodeling as the study of mathematical phenomena within a culture because it is a social construction and is culturally bound.

Non-literate Indian boat-builders: vernacular engineering and the rigor of reality

Author: Swapna Mukhopadhyay (Portland State University)  email

Short Abstract

Based on ethnographic work in a village on the Bay of Bengal, I describe mathematical practices in the hand-building of wooden deep-sea fishing boats using traditional tools and technologies. The boat builders are craftsmen with practically no formal schooling, minimal tools, and generally no blueprints or other specifications on paper.

Long Abstract

There is historical evidence of boat-building in India for thousands of years. The construction of these vessels has adapted to various innovations; in today's world, they are equipped with motors and technologies for communication and GPS navigation. Thus, the men who make these vessels may be using old and traditional techniques and simple tools, but the process of construction is not static. Rather than exact reproduction of techniques of construction that they have picked up in learning their trade, their success depends on problem solving around novel tasks (such as installing an engine) and on adaptive use of tools and materials available.

I share an ethnographic investigation of this vernacular engineering of boat building in coastal Bengal. Typically, a team of eight to ten men, varying in age and experience, works together for four months of the dry season to make boats some 60 feet in length. Teaching and learning are based on informal apprenticeship. The men, often related or from the same village, work in teams with clear understandings of their roles. They share simple tools, help one another, and offer friendly criticism. Most are functionally illiterate, having had little schooling. I have seen no evidence of recorded drawings, plans, formulae, or indeed book-keeping. They report that everything is kept in the head and transmitted orally.

The rigor that a formally trained engineer might consider lacking in their work contrasts with another form of rigorous validation; the boats are exceptionally functional and strong, and used for extended oceanic travel.

Activity systems of mathematics and mathematics education

Author: Brian Greer  email

Short Abstract

Mathematics schooling as an Activity System should be related to three other Activity Systems, namely mathematics as a discipline, mathematics in action, and non-academic mathematical practices, and not exclusively the first, with direct implications for celebration of cultural diversity, and for diversity of forms of mathematical education.

Long Abstract

To situate arguments about mathematics education, a framework is proposed in terms of four Activity Systems (more accurately, families of Activity Systems) of mathematics, namely: mathematics-as-a-discipline, mathematics in action, non-academic mathematical practices, and mathematics-as-school subject.

The dominant view is that mathematics-as-school-subject can be unproblematically derived from mathematics-as-a-discipline. Planning mathematics education is a matter of setting out content within a developmental structure, influenced by theories of developmental psychology. This (typically unexamined) assumption has been problematized in a line of analysis beginning with Bernstein's work, and by persistent critiques that school mathematics fails to connect with children's lived experience, including the social and cultural diversity of that experience (the program of ethnomathematics being an important contributor to this critique). A further critique stems from the concept of "mathematics in action" elaborated by Skovsmose and others, which refers to the mathematical formatting of more and more aspects of our lives, often beyond our control or even influence. These considerations lead to the stance that mathematics education should pay more attention to the nature and limitations of mathematical modeling of physical and social phenomena, in order to prepare people for democratic citizenship with a disposition towards critique and agency (reflection and action, in Freire's dialectic).

The argument, then, is that the Activity System of mathematical schooling should be framed in terms of all three other Activity Systems described. Such an enhancement obviously implies celebration of diversity in forms of life and culturally situated mathematical practices, and diversity in the modes of mathematical education.

Comparing use and learning of early maths skills in a first and a second language

Author: Esther Goody (Cambridge University)  email

Short Abstract

My paper for the mathematics panel would use this material in two ways. Drawing on experiments with maths club examples in the Baale classroom, suggestions could be made about teaching modes that could make bridges between local and formal school maths. Less concretely, it would be interesting to look at both the similarities and differences between transfer of L1 literacy skills and L1 maths skills to later school work.

Long Abstract

The reading research began when sitting in on grade four classes in several government schools made it obvious that children were not really learning there. This was not surprising, since children learned to read only in the national language, English.

Observations, grounded in video filming, were the main form of data collected from classrooms, and from their communities. During one observation in the Birifour upper primary classroom in Baale, the pupils clearly understood little of the mathematics lesson on how to calculate profit and loss. The parallel with the failure to understand enough English to learn to read was striking. With reading, the longitudinal scheme for LLIL classrooms clearly showed that reading skills learned in L1 transferred effectively to the second language, English. It seems you only have to learn to read once . The problem was whether, and in what ways, children's already established local maths skills would assist them to understand formal maths.

In order to get some idea of how these boys and girls thought about school mathematics problems, a 'maths club' was started on Saturdays (following Mike Cole's research model). Each pupil identified a market-influenced activity that s/he was actively involved in. Later, selected Maths club cases were used to construct 'Profit and loss' problems in the English-language maths class.

Anthropology of space and the urban boundaries: a study centred in the communitarian education.

Authors: Monica Mesquita (Lisbon University)  email
Ana Caetano (Instituto de Educação da Universidade de Lisboa)  email
Filipa Ramalhete (Universidade Autónoma de Lisboa)  email
Karen François (Free University Brussels)  email

Short Abstract

A study of urban spaces where the presence of the invisible beings and the gap of act reveal themselves as a transverse wave has been requiring an interdisciplinary research on the concept of space. The proposal is to share fieldwork experiences in two invisible communities (Portugal) following the Curriculum Trivium.

Long Abstract

The research project Urban Boundaries was designed to attend needs from three different cultural groups and includes members of each group. The academic group focuses on the necessity of an emancipatory educational policy while the Bairro group is centred on the urge of having water supply in their territory and the Fishing group wishes strengthening their professional and social voice.

Therefore, Urban Boundaries focus is on diversity: actors with different social, geographic, history, cultural, and school backgrounds. In face of this diversity, the structure of this project is based on a flexible sketch, where different voices can be heard, having as a common stage the fieldwork data collected in two urban communities.

We will explore on this paper, looking to the Concept of Act from Slavoj Zizek, the encounter of these communities, which two of them (Bairro and Fishing) have as main characteristic the presence of the cultural groups that are materially and symbolically marginalized in the urban central area, and the mathematical literacy of them as a tool to work the situcionalidade of these communities, on Paulo Freire' sense.

The Curriculum Trivium, developed by Ubiratan D'Ambrosio, appears on this project as category of the dialogue among the three involved groups and as category of analysis in the understanding, recognition, and empowerment of the communitarian educational processes as tools of survival

Applied anthropological research project on math, environmental science education in china's poverty and border minority regions

Author: Ga Wu (Yunnan Academy of Social Sciences)  email

Short Abstract

The first part of my presentation will discuss different stages of minority educational reforming process, both bilingual and curriculum reforming educational policy will be discussed in detail. Second part of my presentation will discuss why our newly initiated, insightful, innovative, and visionary project proposed by Dr. Professor Chair Rik Pinxten from Ghent University, is urgently needed for studying China’s national minority’s natural science education policy and related legal theories and practises, especially in China’s poverty regions. The debate between Bonnie Johnson (exclusionary policies and practises in Chinese minority education) and Wang CZ / Zhou QH (from state preferential policies to dislocated Tibetan schools) Chen Yangbin’s (Uyghur boarding school) writings all touched important issues for today’s minority education question both for china and for our global world: Existing literature on ethnic minority’s education reform in western language mainly focused on national minority education with identity issues, (Hansen M H C 1999; identity limited in an exclusive old fashion European Nation state sense and framework – issues raised and studies are limited 21st century’s globalisation process requires China’s leaders and global scholars plan and learn from each other, from isolation to constructive dialogue). Finally I will discuss the practical implication of the project: The main fruits of this project should centered to eight aspects: the Ghent University’s educational language policy, especially its both learning and teaching language policy in its science department in early 1930s, one of the beautiful result - was the university's historical Nobel winner scholar from its science department.

Long Abstract

Applied Anthropological Research Project on Math, Environmental Science Education in China's Poverty and Border Minority Regions

--- Some Improvement Suggestion and Thoughts

Wu Ga

YASS Yunnan Academy of Social Sciences Kunming Yunnan China


Visiting Post-Doctor Fellow and Scholar Ghent University Ghent Belgium


Key words

Multicultural ethnic Country ; minority science education and ethnomathematics Curriculum ; Escaping-poverty in the Countryside of the Poor


All these related problems leads the third stage and current minority educational reform for the 21st century, ----the math and science curricula reform project, 数学与自然科学课程改革计划in this new project, suggestedquestions should be addressed are: all reasons related to why either type school did not provide genuine bilingual education; or they did provide in some schools but have not summerized and concluded? the research project should show and try to provide an example of how bilingual education should connect with local native science system curriculum constructing and building efforts, math and science education should reflect local minority wisdom and local culture history and new textbook should list and discuss local minority people's science concepts and special mountain enviomental names and terms, minority schools with extra minority knowledge or native textbooks as reference materials might address issues of educational outcomes.

Reference: Wu Ga: 2001 Issues in Female Minority Higher Education in 21scentury China; Special Report for the Ford Foundation New York and Beijing Office; 伍呷.彝族的经典与族群认同.YI nationality's classics and identity transformation project见:周大鸣编.中国的族群与族群关系[C].南宁:广西民族出版社,2002.291-292.

This panel is closed to new paper proposals.

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