Tag Archives: mathematics

Entry #12: MathCentral Database


This University of Regina project has compiled a series of games drawn from a variety of Aboriginal cultures that could be played with students, including a section on games that support specific math skills. Each game page includes a very brief cultural-historical background to the culture of origin, original and adapted materials, and instructions. The source of the research for each game is also linked, providing potential extensions to one’s own research. This resource provides small ways that teachers can integrate Aboriginal culture naturally into classroom activities. There is also the potential for students to conduct their own research into additional activities not included on the website. Such games could be an excellent way to help bridge the perceived gap between cultures by including alternatives to Western approaches to learning.

Module 4 Weblog – Anne Coustalin

For this final module, I chose to continue my investigation of the intersection of (Western) Place-based education and Indigenous learning from place. I also broadened my scope to explore some models outside of the public school system – specifically band and reserve schools.

Sterenberg, G. (2013). Learning Indigenous and Western mathematics from placeMathematics Education Research Journal25(1), 91-108.

In this paper, the author explores one student’s experiences with learning mathematics from place. The paper recounts a math unit exploring triangles that was taught to grade nine students in SOMEWHERE. In the unit, place was the inroad for intertwining Western and Indigenous math learning. The author provides a useful analysis of the distinction between hands-on, place-based learning and Indigenous learning from place.  The approach taken for the unit was not so much a blending of Indigenous and Western approaches, but rather an intertwining “to increase tensile strength”. As a result of participating in the unit, students reported increased confidence in math competency as well as increased connections to the land and feelings of belonging to their culture. I found this approach to be a compliment to the idea of “Two-Eyed Seeing”, “two-way Aboriginal schooling”, and “walking in both worlds”.

NSF Includes: Envisioning Impact  – Integrating Indigenous and Western Knowledge to Transform Learning and Discovery in the Geosciences

Here is a quote from the website:

[The program] uses the principles of collective impact (CI) to create new partnerships between tribal communities and STEM institutions that promote the participation and inclusion of Native American (NA) scientists in the geosciences.

Our proposed program partners the Rising Voices: Collaborative Science for Climate Solutions (Rising Voices) member tribal colleges and communities with Haskell Indian Nations University, NCAR, Biosphere 2 (B2), and UCAR’s SOARS internship and GLOBE citizen science programs. Together, we commit to greater integration of indigenous and “traditional western” knowledge into collectively-developed climate change research projects, enhancing our collective ability to address climate change, and contributing to climate resilience in all communities.

This program is a good example of attempts to draw from the strengths of both Western and Indigenous knowledges in finding solutions to ecological problems. The fact that it is funded by the National Science Foundation indicates that such collaborations are increasingly seen to be of value within Western science organizations.

Cosmic Serpent – Bridging Native and Western Science Learning in Informal Settings

This program, which is also funded by the (U.S.) National Science Foundation, is a four-year collaboration between the Indigenous Education Institute and the University of California-Berkeley targeting informal science education professionals. This project is designed to explore the commonalities between western science and native science in the context of informal science education.

The group has produced a beautiful and informative ebook based on their project outcomes, which is available to download free on their website.  Here is a quote from that book:

Cosmic Serpent set out to explore commonalities between Western and Native science, taking into account that Native cultures have, over millennia, developed ways of knowing that are highly adapted, interconnected, and enduring. Each knowledge system informs the practice of science and its role in society in a fundamental way, and the commonalities can provide a framework for developing mutually inclusive learning experiences in STEM (science, technology, engineering, and mathematics).

Successful Practices In First Nations Schools:  They Tyee special edition (September 2011)

This special issue is part of a series hosted by the Tyee Solutions Society. In it, reporter Katie Hyslop explores several different models for BC Aboriginal education. There is great breadth of scope here from examining the context (successes and challenges faced by Aboriginal youth in BC as well as legislation and rights concerning indigenous education, and funding for indigenous education) to specific working models of Indigenous education both within BC and internationally.

Exploring the topic of reserve/band schools

In exploring education models that chose to focus more intensely on Indigenous knowledges and ways of knowing, I came across several interesting newspaper articles on reserve/band schools in BC. These articles shone a light on various aspects of the schools, from how they operate to how they are funded and fit within the provincial system. Here are some of the more relevant articles I encountered.

  1. How Chief Atahm Elementary School Became a Success Story (The Tyee, September 6, 2011)
  2. First Nations School teaches “all that culture stuff” (Globe and Mail, October 13, 2012)
  3. Low graduation rates at reserve schools put aboriginals in jeopardy: report (Globe and Mail, January 24, 2-16)


Module 1 Weblog Entry – Anne Coustalin

BCTF Aboriginal Education Teaching Resources


This site is an excellent resource for British Columbia educators wanting to integrate Aboriginal Ways of Knowing into their practice. It provides a comprehensive (but not exhaustive) list of links connecting teachers to relevant resources that provide essential background and perspective on: the treaty process; the historical timeline of European contact and colonization (pre-contact to 2015); Indian Residential Schools and their legacy; and creating an inclusive, racism free classroom community. Of particular note is the BCTF-created document Beyond Words: Creating Racism-Free Schools for Aboriginal Learners. This resource offers practical information that speaks directly to issues teachers may confront in the classroom, with a focus on racism, understanding the rules of culture and how they may present in the classroom, and creating an inclusive community.


Two-Eyed Seeing

Two-Eyed Seeing (Etuaptmumk in Mi’kmaw) is a concept introduced by Mi’kmaw Elder Albert Marshall in 2004. It is described as the guiding principles of how one should live on this Earth and is discussed by Elder Albert Marshall and Cheryl Bartlett. The concept was developed in response to the lack of representation of Indigenous students in the sciences and mathematics, particularly at the university level. It recognizes that there are different ways of looking at the world. The two ways that are particularly relevant in Canada are through the lens of Western science and through an Indigenous lens.  Two-eyed seeing refers to finding the strengths in both paradigms and mindfully bringing them together – drawing upon the deep understandings that each represents. When we employ two-eyed seeing, we very quickly realize that science alone is not going to save the natural world. Instead, a change of mindset must occur and the Indigenous way of seeing must simultaneously be employed so that people have a path to move forward on the planet together. The video describes the concept and provides the context of its introduction.


Two-Eyed Seeing – A Different Vision for Teaching Aboriginal Learners Science and Mathematics

This lecture, delivered by Dr. Michelle Hogue as part of the 2015 PUBlic Professor Series at the University of Lethbridge Alberta, further expands on the concept of two-eyed seeing and describes specific ways that it has been successfully applied to teach math and science to Aboriginal and non-Aboriginal learners at the secondary and post-secondary level. Dr. Hogue describes her own teaching and research as being “focused on the space between Aboriginal ways of knowing and learning and the white western education system . . . the space I call the liminal space” (3:52). She describes this space as a space of possibility rather than a gap. The concept of learning through performing is discussed at length, as are a variety of other multi-layered education opportunities that move through different performance, experiential and theoretical stages.


First Peoples’ Cultural Council


This site provides a wealth of resources to assist in the revitalizations of First Peoples’ heritage, language and culture. For each of those areas, the website lists a number of valuable resources including maps, toolkits, events, programs. Of particular note is the FirstVoices Indigenous language archiving and teaching resource “that allows Indigenous communities to document their language for future generations”. Part of this program is the FirstVoices language tutor (an online interactive First voices language learning program). There are also links to specific language tutor mobile apps in a number of Indigenous languages as well as Aboriginal fonts that may be downloaded to your computer.  While much of the content is geared towards Indigenous communities, there are also resources and information useful to classroom teachers.


Authentic First Peoples Resources (FNESC, FNSA. 2016)


This document provides background into the way resources dealing with Aboriginal content have, in the past, contained false information and inaccurate representations of the unique experiences and world views of Aboriginal peoples. It provides teachers with the rationale for using only authentic Aboriginal resources, as well as guidelines for recognizing for how to recognize those resources. As outlined on the site, authentic First Peoples texts are historical or contemporary texts that

  • Present authentic First Peoples voices (i.e., are created by First Peoples or through the substantial contributions of First Peoples)
  • Depict themes and issues that are important within First Peoples cultures (e.g., loss of identity and affirmation of identity, tradition, healing, role of family, importance of Elders, connection to the land, the nature and place of spirituality as an aspect of wisdom, the relationships between individual and community, the importance of oral tradition, the experience of colonization and decolonization)
  • Incorporate First Peoples story-telling techniques and features as applicable (e.g., circular structure, repetition, weaving in of spirituality, humour).

Connecting Mathematics To BC Curriculum — Kimberly

For this weblog entry, I decided to share some of the research I have been collecting for my final project on connecting Aboriginal knowledge and the BC math curriculum.  Of particular interest to me, is creating cultural and meaningful contexts when teaching Mathematics, with the intention that the learners will develop a personal connection and relevance to the learning.

Teaching Mathematics in a First Peoples Context screen-shot-2016-11-05-at-10-06-49-amis a resource written and published by the First Nations Education Steering Committee.  It is a resource targeted for educators teaching the grade 8 and 9 curriculum. The targeted lesson plans reflect the First Peoples Principles of Learning while promoting engagement and inclusiveness of aboriginal culture in the area of Mathematics.

Of particular interest to me, is the explanation and description of the pedagogy and principles of the Math First Peoples which is an extension to the First Peoples Principles of Learning.  The First Peoples Principles of Mathematical Teaching specifies how teachers should implement the First Peoples Principles of Learning in the area of Mathematics.


screen-shot-2016-11-05-at-9-47-22-amThe Aboriginal Mathematics K-12 Network is a web gathering space where teachers, students, parents and academics share and investigate ideas on how to improve mathematics learning for Aboriginal students.

Within this webspace is a connection to the Aboriginal Math Symposiums which is a gathering held annually where students, educators and community members join together to discuss how Mathematics can be connected to Aboriginal students in more meaningful ways.


Various Universities have created websites for sharing Aboriginal Education content.  The UBC library website has a link to lesson plans and other portals organized by subject area, including Aboriginal Education.  A link from the University of Toronto website, connects viewers to resources and lesson plans from the webpage titled, Deepening Knowledge: Resources for and about Aboriginal Education.  Here, students and teachers are able to access resources, tools and lesson plans that fuse Aboriginal Education with various subject areas.  A sample lesson plan from this site includes:  Haida Legends: Culturally Responsive Mathematics.


Various districts across Canada have also created their own collection of resources for teachers and students to use around Math content.  screen-shot-2016-11-05-at-12-39-15-pmThe Port Alberni School District (SD70) for example, have created a resource called Integrating Aboriginal Culture With Mathematics K-12.  Although this resource was developed with curriculum that is now outdated, the concepts and ideas of using various Aboriginal artifacts and contexts are highly valuable.  The project that initiated this document centred around the creation of a button blanket, and various mathematical concepts from various grade levels reflected each step of the process of its creation.


The Alaskan Native Knowledge Network is a great site which includes various resources which contextualize Aboriginal Education and Mathematics.  This site includes a database searchable by content, cultural standards, cultural region, and grade level.  screen-shot-2016-11-05-at-1-38-26-pm A example of a resource found on the site, which demonstrates the use of Aboriginal context when teaching Mathematics is called, Math In A Cultural Context.  University of Alaska Fairbanks collaborated with Yup’ik elders, teachers, and Alaskan school districts to develop culturally based curricular materials.  The resource consists of modules/teaching guides for grades 2-7 of various contexts such as berry picking, kayak building, and salmon fishing, which are accompanied with CDs, and DVDs, that demonstrate elder’s knowledge.






Module 3, Post 4- Inquiry Based Learning

Screen Shot 2015-07-11 at 4.34.35 PM

Alaska Native Knowledge Network


By teaching mathematics through an inquiry approach to learning, students will be involved in hands on engaging experiences applying critical thinking and problem solving skills.

The Alaska Native Knowledge Network has a diagram on their website (see above) representing the ‘iceberg’ model of thinking about Aboriginal culture. This is an effective visual when developing culturally responsive math curriculum with reminders about a variety of ways of making connections to deep culture as opposed to only what’s above the surface level. This ties in well with also considering the math concepts being taught and ensuring that math concepts are taught in more depth for greater understanding than at a surface level. By engaging students in authentic, relevant learning engagements, students’ conceptual understandings should also be enhanced. These were the findings in the research done with Canadian Aboriginal youth (Nicol, Archibald & Baker. Designing a model of culturally responsive mathematics education: place,relationships and storywork).  

Below, I have included a diagram from the International Baccalaureate (http://www.ibo.org/) showing how Math practices are changing in mainstream classrooms. The curriculum is based on ‘best practices’ such as starting with students’ prior knowledge, making connections between different subject areas and learning through authentic experiences.

How are Mathematics Practices Changing

How are Mathematics Practices Changing- Making the PYP Happen, page 84). retrieved from http://tecnosanfran.wikispaces.com/file/view/Making+the+PYP+Happen.pdf

The article and link to curriculum below show some wonderful ways of integrating Aboriginal culture into our teaching practices.

Lipka, Jerry & Andrew-Irhke, Dora. Ethnomathematics Applied to Classrooms in Alaska retreived from https://www.uaf.edu/files/mcc/Articles/Ethnomathematics-Applied-to-Classrooms-in-Alaska-Math-in-a-Cultural-Context.pdf

Village Math (draft)- http://ankn.uaf.edu/publications/VillageMath/village_math.html


McGregor, H. E. (2012). Curriculum change in Nunavut: towards Inuit Qaujimajatuqangit.McGill Journal of Education, 47(3), 285-302.

Nicol, C., Archibald, J., Baker, J. (2013), Designing a Model of Culturally Responsive Mathematics Education: Place, Relationships and Storywork. Mathematics Education Research Journal. 25(1), 73-89.

Module 3.5: First Nations’ Games of Chance

Post 5: First Nations’ Games of Chance


I found a site housed by the University of Victoria outlining a couple of traditional games played by First Nations’ peoples: dice games and guessing games. The website outlines the rules and point systems for the games, as well as provides worksheets and images that could be used in the classroom alongside the games. These games would be ideal to incorporate into a culturally responsive mathematics lesson concerning counting, comparisons, or probability.

Module 3 Post 1 – Culturally Responsive Mathematics

One of the greatest barriers to implementing more culturally-responsive activities into my math lessons is my lack of local Indigenous knowledge and resources.

The First Nations Education Steering Committee has created the Math First Peoples resource that Math 8 and 9 teachers in BC can use to become more responsive to the cultural perspectives of First Peoples. This resource is intended to:

1. Help all students appreciate the universal presence and importance of mathematics

2.Help all students appreciate the significant role First Peoples play in BC

3. Help Aboriginal students feel more comfortable in mathematics and more motivated to participate.

In addition to describing First Peoples perspectives of mathematics, this resource suggests several ways that educators can form meaningful connections between mathematics, students, community members and Indigenous knowledge. The resource also provides several sample unit plans for teaching mathematics in a culturally responsive way.

The University of Toronto has also provided a blog post with a list of culturally-responsive mathematical lesson plans and games.


First Nations Education Steering Committee. (2011).  Teaching mathematics in a first peoples context – Grade 8 and 9. Retrieved from www.fnesc.ca/curriculum/math

University of Toronto. (2015, July 6). Deepening knowledge: Resources for an about Aboriginal education. [Blog post]. Retrieved from http://www.oise.utoronto.ca/deepeningknowledge/Teacher_Resources/Curriculum_Resources_%28by_subjects%29/Math/index.html#Lessons