In this monthly column, we speak with a notable member of the mathematics education community about their work and their perspectives on the teaching and learning of mathematics. This month, we had the pleasure of speaking with Dr. Lisa Lunney Borden, who we look forward to welcoming this fall as a SUM Conference 2017 keynote presenter.
Lisa Lunney Borden is an Associate Professor of mathematics education at St. Francis Xavier University in Canada with a particular focus on Equity in Mathematics. Having taught 7-12 mathematics in a Mi’kmaw community, she credits her students and the community for helping her to think differently about mathematics teaching and learning. She is committed to research that focuses on decolonizing mathematics education through culturally based practices and experiences that are rooted in Aboriginal languages and knowledge systems. Lisa is equally committed to mathematics outreach through programs such as Show Me Your Math that was developed with David Wagner, Newell Johnson, and a team of teachers from Mi’kmaw Kina’matnewey schools. This program invites Indigenous youth to find the mathematical reasoning inherent in their own community context. Lisa is a sought after speaker on Indigenous mathematics education, working with mathematics educators across Canada as well as internationally.
First things first: Thank you for taking the time for this interview!
Your research, coming on the heels of 10 years of teaching mathematics in a Mi’kmaw school in We’koqma’q, Cape Breton, Nova Scotia, focuses on culturally responsive mathematics curriculum and pedagogy. You have paid particular attention to the role that language plays in the teaching and learning of mathematics, and in particular, to ways in which shifting the language in our classrooms can support Aboriginal students in learning mathematics (e.g., Lunney Borden, 2011, 2013). For example, in Lunney Borden (2011), you describe the strategy of ‘verbifying’ mathematics—in other words, shifting your way of explaining concepts to be more consistent with the verb-based linguistic structures of Mi’kmaq—as a way of supporting Mi’kmaw students in mathematics learning.
How might teachers of Aboriginal students in other parts of the country (e.g., Saskatchewan), or more generally of students whose home language is not English, apply this work to their own local contexts?
[perfectpullquote align=”right” cite=”” link=”” color=”” class=”” size=””]”Mathematical reasoning is about processes and change, and verbifying captures this essence more so than the noun-dominant approach we often see being used in school.”[/perfectpullquote]Ways of knowing are embedded in language, and listening to how students talk about concepts in mathematics can help teachers think about how students are thinking about that concept. All Indigenous languages in Canada are verb-based, which means that focusing more on processes and motion can be of benefit to many Indigenous students. Leroy Littlebear talks about the sense of flux that is embedded in Indigenous languages and connected epistemologies, and this flux is more in line with a verb-based approach to learning mathematics. For this reason, verbifying school mathematics might feel more culturally consistent for Indigenous students; however, it may actually prove to be better for all students. Mathematical reasoning is about processes and change, and verbifying captures this essence more so than the noun-dominant approach we often see being used in school. I believe that most mathematicians would tell you that when they do mathematical work, they look at what is happening, what is changing, what happens when you change parameters, and so on—these explorations are all about processes.
I don’t think any mathematician set out to discover irrational numbers, quadratic functions, and so on; rather, they played with numbers and number patterns to see what they do under certain conditions, or how the patterns form; then, once they figure it out, they name it. They name it so they can do new things to it. This is very consistent with the process of verbification, and I think consistent with what real mathematicians do in their work.
In Lunney Borden and Wiseman (2016), you mention the success of Mi’kmaw Kina’matnewey (MK), a collective of Mi’kmaw communities in Nova Scotia, which has maintained a graduation rate between 87% and 89% in the past 5 years. This stands in stark contrast to the national graduation rates for Aboriginal children, which are reported to be around 48% (Assembly of First Nations, as cited in Lunney Borden & Wiseman, 2016). What has contributed to this success, and how has the Show Me Your Math program—which you developed in collaboration with teachers and elders in MK schools—played a role?
I don’t think I can assign any credit to Show Me Your Math for the high graduation rates. Rather, this program emerged in a context that supports those high graduation rates. Simply put, both things happen because of a relentless commitment amongst Mi’kmaw people to decolonize education in their own communities. Mi’kmaw Kina’matnewey has worked very hard to build capacity for jurisdictional control of education in their communities. They have worked with universities, like StFX, to prepare teachers from the community to take on the teaching jobs in community schools. There have been over 135 Mi’kmaw BEd grads from StFX alone since 1996, and the majority of these teachers are working in MK schools. Many of these teachers have completed MEd degrees, certificate programs in Mi’kmaw language and mathematics, and other graduate programs. They have moved into leadership positions in schools and at the MK office. As such, you can find Mi’kmaw educators in all levels of MK education who speak the language, know the community contexts, understand the ways of knowing, being and doing of the community, and who are deeply committed to decolonizing education through inclusion of what Orr, Paul, and Paul (2002) called cultural practical knowledge. They bring stories of community into the classroom and allow these stories to speak back to the dominant narratives in the curriculum that have, for far too long, privileged Eurocentric thought.
When David Wagner and I invited MK teachers to a planning session to talk about Show Me Your Math in the fall of 2006, the room had teachers who spoke the language, who were deeply connected to community cultural practices, and who knew exactly where this idea could go. What keeps Show Me Your Math going is this commitment and a desire amongst these teachers to learn about ways of reasoning that are embedded in cultural practices and align with what we teach as mathematics in schools. This passion is also what helps students succeed in schools where they get to be themselves, learn in culturally consistent ways, and be proud of being Mi’kmaq. There are many interconnected factors that bring about these high graduation rates, but they all are rooted in the capacity development that has been such a central focus of MK.
Much of your work has been drawn from your experiences and work in small Mi’kmaw communities in Nova Scotia, and has emphasized the importance of respecting and supporting children’s culture and language as a key factor in improving outcomes for Aboriginal students (e.g., Munroe, Lunney Borden, Murray Orr, Toney, & Meader, 2013). You have presented compelling examples of how mathematics can emerge from Indigenous contexts, rather than simply being imposed upon Indigenous artefacts (e.g., Lunney Borden & Wiseman, 2016; Munroe et al., 2013). However, this is clearly a particular challenge for teachers in urban settings, where a classroom typically includes students with a variety of cultural backgrounds and cultural experiences.
How might (mathematics) teachers in such settings honour students’ culture and language without resorting to sweeping generalizations and/or tokenization of Aboriginal cultures, perspectives, and ways of knowing—that is, to the oversimplification of complex ideas that Edward Doolittle has dubbed the “cone on the range” approach (2006, p. 20)?
There are school districts in New Brunswick that are doing Show Me Your Math with all students, so every student is expected to learn about ways of reasoning that might be mathematical in their own cultural context; then, they share across cultural contexts. This has proven to be successful in promoting cross-cultural conversations that allow all students to see what we might call mathematical reasoning as a part of their cultural heritage. It also helps all students to see that mathematics is a human endeavour and that mathematical reasoning has emerged in many contexts. So that is one way to avoid trivialization—let all children explore their own interests and share their own stories.
[perfectpullquote align=”right” cite=”” link=”” color=”” class=”” size=””]”Whether we are in an urban or rural setting, there is merit in learning about the Indigenous knowledges and technologies that existed long before settlers arrived on these lands.”[/perfectpullquote]That being said, I believe that whether we are in an urban or rural setting, there is merit in learning about the Indigenous knowledges and technologies that existed long before settlers arrived on these lands. Both Indigenous and non-Indigenous students would benefit greatly from learning about the Indigenous knowledges and how these ways of knowing, being, and doing allowed for settlers to survive in these lands. A big part of reconciliation is helping non-Indigenous Canadians learn about Indigenous peoples and knowledge systems, treaties that govern this land, and so on. When we center Indigenous knowledges and practices in our classroom as a starting point for learning mathematics, we are honouring the knowledge that springs from this place, and all children can benefit from this decolonized approach to learning.
For example, when I begin with a story about the late Dianne Toney who made quill boxes and knew that to make a ring for a circular top, she would measure with the wood strip three times across the circle and add a thumb width to make the ring, I can introduce an investigation for learning about pi that begins with Indigenous knowledge, rather than beginning by privileging a Eurocentric voice. All students see that this knowledge was passed down through generations of Mi’kmaw people and did not come from a Greek mathematician. Sure, the Greeks were interested in this relationship, too, but this lesson shows that they were not the only ones who knew this relationship. Eurocentric approaches have privileged only Eurocentric knowledge and have attempted to erase evidence of similar knowledge in non-European cultures.
The Truth and Reconciliation Commission has said that reconciliation is about respect, which requires all Canadians to challenge the notions of European superiority and Aboriginal Inferiority that shaped the colonization of these lands. When we take opportunities to raise up Indigenous knowledges and counter the discourse of European superiority that still permeates our system, we are doing decolonizing work and that benefits everyone and moves us closer to reconciliation. How we do that without trivializing is by being committed to first unpacking our own privilege, examining our own place in the history of colonialism, and then being open to learning in honest and sincere ways. I think teachers need to build good relationships with Indigenous communities in their local area, whether urban or rural, and make a point to learn with their students.
Your work has frequently dealt with the issues of how mathematics curriculum and instruction can be more aligned with Aboriginal perspectives and ways of knowing. How might classroom assessment, too, be more aligned with Aboriginal perspectives on education? (This seems to be a particular challenge, given that Aboriginal worldviews emphasize holistic and interconnected knowledge, while Western assessments have often tested discrete skills in situations that are decontextualized from context.)
[perfectpullquote align=”right” cite=”” link=”” color=”” class=”” size=””]”Machines can do calculations, but humans need to tell them what calculation is needed in what context.”[/perfectpullquote]Well, I would again say that a move toward more holistic and applied knowledge would be a better way to assess every student. I don’t think such a narrow focus on assessment is helpful for anyone. We want to educate a generation of children who can think and solve problems. We want them to be able to apply their learning in meaningful ways so that they are prepared to tackle the real problems of the world. Personally, I am much more interested in knowing whether or not a student can explain what multiplication means and show how it might be represented in multiple ways than I am in whether or not they can recite facts. Machines can do calculations, but humans need to tell them what calculation is needed in what context. That comes from meaningful experiences with various contexts and representations and not from memorization. Inviting a student to explain how a calculation might be used in a situational story will tell you more about their understanding of that calculation than giving a quick answer.
I’m not saying we don’t want students to have fluency with numbers—of course we do, but fluency doesn’t come from memorizing facts you do not understand. Consider, for example, a task where students are given 24 squares and are asked to make all the rectangular areas they can make using all 24 squares. Students will begin to see that 24 can be represented by 2 rows of 12 or 3 rows of 8 or 4 rows of 6 and so on. This is a holistic approach to working with quantity in a multiplicative way that allows students to see the factors of 24, and this is what will allow them in year to come to think flexibly about 24 in multiplicative contexts. This is how fluency develops. This is how we should be assessing.
In Lunney Borden and Wiseman (2016, p. 143), you write: “We have learned from Aboriginal colleagues that teaching and learning are fundamentally about relationships—an idea also deeply embedded in mathematics and science.” And yet, Western mathematics and science have also been instrumental in concealing the relationship between people and the natural world via knowledge and tools that allow humans to control certain natural phenomena and dissociate themselves from their environment.
In light of this, could you elaborate on the connection between mathematics and Aboriginal philosophies?
As a non-Indigenous person, I don’t think I can do justice to discussing Indigenous philosophies—I would invite folks to read work from Greg Cajete, Leroy Littlebear, Marie Battiste and others—but what I know for sure is that we would all benefit from being more connected to our world and to one another. It is easier to destroy the land when we feel no kinship connection to it. It is easier to commit atrocities against another nation when we do not see a kinship relationship with the people of that nation. Connecting with one another can certainly benefit our world and help us to think more deeply and responsibly about how we live with the land and ensure its survival for generations to come.
[perfectpullquote align=”right” cite=”” link=”” color=”” class=”” size=””]”Being mindful of connections to our world will ensure that more students see the potential power of mathematics to support their own communities.”[/perfectpullquote]I think there are aspects of mathematics that can help children to see and value these connections. For example, mathematical modelling of complex problems is one way we can help students connect mathematics with the world around them. I work with colleagues on an outreach program called Connecting Math to Our Lives and Communities, where we engage Mi’kmaw and African Nova Scotian youth in activities that help them connect math to things going on in communities right now. For example, we have done work on water security in First Nations communities in Canada. One of our communities was under a boil-water order at the time, which has been an ongoing issue in that community. We used water security to learn about this issue and see how math can be used to model some of the issues related to water security in communities.
Much of mathematics emerged in contexts where humans were seeking to solve real problems in their communities. When we teach that math is not connected, we deny this human activity and make math seem mysterious and magical, and that doesn’t help students to learn it and use it meaningfully. Being mindful of connections to our world will ensure that more students see the potential power of mathematics to support their own communities.
Lastly, our readers are likely aware that you will in Saskatoon this November to present as a keynote speaker at our very own Saskatchewan Understands Math (SUM) Conference. (We can’t wait!) We don’t want to spoil the surprise, but could you give our readers some insight into what you will be discussing during your sessions?
I will be doing a lot, based on the number of descriptions I sent in! ☺ My keynote will focus on the role of mathematics education in reconciliation, so I will share ideas about how we decolonize mathematics teaching and learning. I will also do a featured session where I will talk about a framework I developed in my doctoral work that draws upon Indigenous language to inform pedagogy—in particular, we will talk about verbifying and spatial reasoning. Two follow-up sessions will focus on what this looks like in early number work and in multiplication and division. I will also have a session about the Show Me Your Math program.
Thank you for taking the time for this conversation. We look forward to continuing the discussion at SUM 2017!
Ilona Vashchyshyn
References
Doolittle, E. (2006). Mathematics as medicine. In P. Liljedahl (Ed.), Proceedings of the 2006 Annual Meeting of the Canadian Mathematics Education Study Group (pp. 17-25). Available at http://www.cmesg.org/wp-content/uploads/2015/01/CMESG2006.pdf
Lunney Borden, L. (2011). The ‘verbification’ of mathematics: Using the grammatical structures of Mi’kmaq to support student learning. For the Learning of Mathematics, 31(3), 8-13.
Lunney Borden, L. (2013). What’s the word for…? Is there a word for…? How understanding Mi’kmaw language can help support Mi’kmaw learners in mathematics. Mathematics Education Research Journal, 25, 5-22.
Lunney Borden, L., & Wiseman, D. (2016). Considerations from places where Indigenous and Western ways of knowing, being, and doing circulate together: STEM as artifact of teaching and learning. Canadian Journal of Science, Mathematics and Technology Education, 16(2), 140-152.
Munroe, E. A., Lunney Borden, L., Murray Orr, A., Toney, D., & Meader, J. (2013). Decolonizing Aboriginal education in the 21st century. McGill Journal of Education / Revue des sciences de l’éducation de McGill, 48(2), 317-337.
