Ethnomathematics

Most of the research in CRYSTAL Atlantique investigates innovative ways of bringing science and mathematics disciplines to children in informal settings. This part of the research is the converse: it starts with students' everyday culture and brings it to the sciences. For this research, we develop conversations with communities that are not typically associated with success in academic mathematics and science (e.g. various aboriginal communities, fishing communities and artistic communities). The study draws on research in ethnomathematical conversations between scientists and disenfranchised people.

The following questions are the basis of these conversations:

1. What mathematics is already present in the disenfranchised cultures (both traditional and modern)?
2. What conflicts exist between the everyday mathematics in these cultures and Western school mathematics?
3. How can this mathematical knowledge be incorporated into the learning and teaching of mathematics in school setttings?

Progress to date:

Year 1: The first year of research began conversations with a mathematics teacher and five elders in a Mi'kmaq community in Nova Scotia.

Year 2: In the second year, this conversation evolved to include a gathering of teachers from 10 First Nations schools in Nova Scotia, and from that to develop a venue for students in their schools (and others) to engage in ethnomathematical research of their own. As part of the tradition of storytelling, elders and others share stories and other forms of knowledge with other communities across the country in 'contests', using the internet and realtime video conferencing. We gathered teachers and elders from some communities to plan a contest called "Show Me Your Math," in which children would be invited to do ethnomathematical investigations to show others the mathematics in their communities.

In order to break the school tradition of students doing work for teachers as audience, we produced a video prompt that described the parameters of the contest. It featured Aboriginal people, including an elder, a middle-aged teacher, and children, all asking the viewer (the student) to "show their math." In response to this prompt, school children interviewed elders, experts in crafts and others to explore mathematics that has been done in their communities' traditions and also more current mathematics in their communities. They published their work on the internet site used for the other 'contests' on which we modeled this contest. Students also presented their work to the region's communities in a math fair.

The contest website, which includes many student submissions, is http://schools.fnhelp.com/math/showmeyourmath/Studentwork.htm

Year 3: We continue with the "Show Me Your Math" contest and conversations with participants, drawing in more participants, including people from Maliseet communities. The complexity of the many interpersonal relationships related to the contest made the research more challenging than anticipated. Thus, this year we plan to structure situations that give us better access to these conversations better. Further, our ongoing conversations with participant teachers give us the opportunity to address questions about approaches to connecting the students' ethnomathematical work to their other work in mathematics class.

Future Years: While we intend to continue the conversations with the Mi'qmaq and Maliseet people to develop ethnomathematical resources and to better understand viable approaches to connecting community practices to classroom practices, we also intend to transfer what we are learning into non-Aboriginal communities. The aim is to expand these conversations to encompass other disenfranchised communities and to include scientific as well as mathematical practices. To do this, we will use materials from the beginning of the research to develop a course that trains and directs teachers in this kind of research. We believe that Aboriginal communities are well-positioned for modelling these kinds of conversations because the First Nations people are more aware of their cultural distinctions.

Research findings

Wagner, D. and Lunney, L. (in process). 'Conceptualizing successful mathematics education for Aboriginal students: The case of Waycobah First Nation Secondary School'. In Zevenbergen, R. and Askew, M. (ed.), Successful teaching mathematics in challenging schools: International perspectives.

• highlighting successes in this First Nation school, and considering various ways of thinking about success, considering different community values.

Wagner, D. (2008). Positioning theory and intercultural conversations about mathematics. Symposium on the Occasion of the 100th Anniversary of International Commission on Mathematical Instruction, Rome, Italy.

• mapping various models of positioning authority in ethnomathematical research
• This conference has invited only 150 scholars from around the world.

Nicol, C., Andrew-Ihrke, D., Archibald, J., Brown, L., Burton, D., Cajete, G., Commodore, J., Dawson, A., Kelleher, H., Lipka, J., Lunney Borden, L., Nielsen, W., Owuor, J., Rigney, L., Wagner, D., & Yanez, E. (2008). Creating sustainable change: Alternative perspectives on culturally responsive approaches to mathematics teaching and learning with/in Indigenous communities. Panel discussion, Annual Meeting of the American Educational Research Association, New York, New York.

• classroom implications of new models of positioning authority in ethnomathematical research

Lunney, L. and Wagner, D. (2007). 'After this research: Questioning authority when non-Aboriginal people do research in Aboriginal communities.' 24th Annual Qualitative Analysis Conference.

• locating authority in ethnomathematical research in Aboriginal communities.

Wagner, D. & Lunney, L. (2007). 'Show me your math': inviting children to do ethnomathematics. PMENA-29

• presenting ethnomathematics done by students, and showing it in the light of Aboriginal community values.

Wagner, D. & Lunney, L. (2006). Common sense, necessity, and intention in ethnomathematics. PMENA-28.

• Presenting ethnomathematics done by students, and showing it in the light of Aboriginal community values.

Lunney, L. & Wagner, D. (2006). Fostering mawkinutimatimk in research and classroom practice. Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PMENA-28).

• Outlining a methodological orientation appropriate for Aboriginal ethnomathematics.

Wagner, D. (2006). 'Critical language awareness in the mathematics classroom.' Doyle Nelson Lecture Series, Edmonton (invited lecture - not peer-reviewed though)

• Research agenda as a result of critical language awareness research, including the ethnomathematical research in this CRYSTAL project.

Lunney, L. & Wagner, D. (2006). Ethnomathematics and audience. Proceedings of the Canadian Mathematics Education Study Group Conference

• showing how typical ethnomathematics is problematic in the sense that it's intent and audience is unclear, and describing alternative approaches that could rectify this.

Autres projets

Examiner et étendre la compréhension de l'étude des sciences chez les enseignants

• Public Understanding of Science
• Outreach to Teachers

Comprendre l'incidence des technologies et des études sur l'apprentissage en ligne

• CASMI
• Ethnotechnology
• LogiAuteur
• OCOWS: Problem-based Learning Software

Ce qui se produit quand nous étendons l'apprentissage au delà des études au programme scolaire

• Ethnomathematics
• Huntsman Marine Science Centre
• Outreach to Students
• Science East
• Students Solving Environmental Problems
• Science-in-Action Project
• Research Intensive Student Experiences