A Planting of Ideas: Important Works from My Master's Years

I'm going to cheat a little. First, I am writing a blog entry rather than a short paper. Second, I am going to present three categories of ideas that have taken root in my practice, rather than featuring three works. Yes, there will be a summary of a particular work by a particular human being (or group of humans) in each category, but I am in the mood to think about the ideas first. Finally, I am going to be myself in my writing. 

The Demystification of Mathematics

"...it shows me that the secondary high school curriculum we still teach today is, in part, grounded in a reaction to the humiliation of the English in the Anglo-Dutch War..." (Me, 2021)

I am very motivated to deepen my understanding of the history and development of western mathematics, an undertaking that I feel is necessary for understanding the modern zeal for STEM education. There are eerie parallels between our drive to ready children to compete for the future of economic development through educational STEM initiatives, the investment in "new math" and science education in Cold War North America, and the push to increase the navigational prowess of Britain through a standard math curriculum. In each of these eras, education reform--particularly in math and science--was/is fueled by existential anxiety and the desire to dominate rather than be dominated militarily and economically. If we examine the roots of our secondary math curriculum, we discover that trigonometry, logarithms, and even decimal fractions were first promoted so that the British might churn out more specialists in  navigation, fortification, and surveying back in the seventeenth century (Ellerton & Clements, 2017). I was completely blown away to discover that a sense-making approach to math, known derisively as "new math" back in the sixties and seventies, was widely promoted in the States to support the development of creative and critical thinking needed to keep the US at the fore of technological development during the Cold War (Philips, 2014). This same math was rejected by a largely conservative back-to-basics movement of the seventies and eighties. And now here we are again: worried for the future of our children and the planet and thinking STEM might hold the answers to what ails us. 

Math is one (and is arguably the most) important key to unlocking those prestigious STEM careers. Math is the language and foundation of engineering, chemistry, and physics. If your child struggles in math, the doors to higher level STEM education remain firmly locked. 

Is STEM the answer to our problems? What power has science, technology, engineering, and mathematics historically given Euro-centric cultures over others? To what extent are these disciplines implicated in the current state of our environment, our climate, our social reality?  When I speak with my Indigenous Education colleagues about ways we might combine our efforts to bring mathematics and Indigenous culture together, I am very careful to not force mathematical ideas that are a product of consumerism, mass production, engineering, ownership, and ultimately colonization on Indigenous cultural artifacts. It is a misguided and potentially harmful exercise that serves to only keep math on its current pedestal, casting its shadow on everything. Instead, it is about how Indigenous culture might shed a light on our western mathematical practices or about the useful and beautiful application of mathematical ideas that are or were truly part of Indigenous cultures (Bishop, 1990; Davis, 2009). 

So: the work that first really got me thinking about this idea was not one of the many books that I have referenced below. It was Learning to teach the M in/for STEM for Social Justice by none other than Cynthia Nicol et al (2019). It was my first step into the idea that educational leaders need to think of the harm that STEM-related fields have done historically and continue to do if engaged in only in the spirit of competition, domination, and economic development. The paper is a synopsis of the work conducted by Cynthia and five other educators from around the world as they attempted to create meaningful M in STEM problems from elementary to post-secondary levels. They learned that despite their intention to design with student interest in mind, they created problems based on their own local interests. Connections between mathematics and local, global, and STEM contexts were enhanced through collective discussion. Finally, they recommended co-creating problems with students to nurture curiosity.

After reading Cynthia's paper, I continued by journey by reading the following books and papers, all of which have been pivotal and influential for me:

Bishop, A. J. (1990). Western mathematics: The secret weapon of cultural imperialism. Race & Class, 32(2), 51-65.

Davis, W. (2009). The Wayfinders: Why ancient wisdom matters in the modern world. Toronto: House of Anansi Press.

Ellerton, N. & Clements, K. (2017). Samuel Pepys, Isaac newton, James Hodgson, and the beginnings of secondary school mathematics. Springer International Publishing.

Phillips, C. J. (2014). The new math: A political history. Chicago: The University of Chicago Press.

And here is the official reference for Cynthia's paper:

Nicol, C., Bragg, L. A., Radzimski, V., Yaro, K., Chen, A., & Amoah, E. (2019). Learning to teach the M in/for STEM for social justice. ZDM : The International Journal on Mathematics Education, 51(6), 1005-1016.

Reverence, Respect, Responsibility, and Reciprocity

"When your mind grasps the relationship between these stumps and Indigenous people, you realize a crucial truth: the story of what happened to Indigenous people is held in the land itself. These stumps know the impact of colonialism. They are not dead and buried. They hold the stories and are waiting to tell them." (Me, 2020)

I have been very fortunate to have learned from Dr. Jo-ann Archibald Q'um Q'um Xiiem through out my time in the program. Cynthia invited anyone who was interested to join a focus group on the potential use of the principles of Indigenous Storywork in a mathematics context. Jo-Ann provided us with feedback and new insights on possible ideas.

Of course, the book that shaped this journey was Indigenous Storywork: Educating the Heart, Mind, Body, and Spirit (Archibald, 2008)

The book itself documents Jo-ann's journey as she consulted with Stó:lō elders and elders from throughout the province on the role of story in teaching and learning in Indigenous communities. From this learning journey, she distilled the 4 R's of Indigenous Storywork--respect, reverence, responsibility, and reciprocity--as well as synergy, holism, and interrelatedness. These ideas serve to not simply explain the way that learning might happen from the oral storytelling tradition, they also guide and shape the behaviours of the listener and the storyteller through an awareness of the respectful engagement with protocols, the responsibilities of the participants, the necessary reverence for both story and storyteller, and the ongoing learning relationship through reciprocity.

After reading the book, I wondered if the storyteller could be more than human--water, stumps, air, soil? My thought was that such storytellers need a language for communication of important ideas and that mathematics might be a just such a language. How might stumps tell their stories, for example? The listener/observer can look for patterns, count, collect data, measure, conjecture. Jo-ann thought the idea was beautiful and so I set about making a series of videos and lessons. 

First, I created the Stump Stories inquiry. Here is the starting video:

You might also notice the influence of Kieran Egan's Cognitive Tools of Imagination (particularly somatic, mythic, and romantic understandings) inherent in this work as well. The rest of the lessons and videos can be found here. 

Over the last couple of terms, Joy Fast and I worked together on water as the storyteller. We created two out of four videos explaining the 4 R's of Indigenous Storywork in the this context under the direct guidance of Jo-ann and Cynthia. Here is our first film on the R of reverence:

Archibald, J. Q’um Q’um Xiiem. (2008). Indigenous Storywork: Educating the Heart, Mind, Body, and Spirit. UBC Press.

Teachers and Students Can Shape the Future for Themselves and Their Communities

"Love is commitment to others. It exists in dailogue and requires humility, be you teacher or student. It is an understanding that you can learn more together in praxis." (Me, 2020)

This quote is from a summary of the important learning I took from Paulo Freire's Pedagogy of the Oppressed. This book is on many people's shelves of important works, I am sure. It is Freire's articulation of how people might transcend oppression and lift themselves up into a place of freedom through dialogue, praxis, conscientization, and problem-posing. The ideas are connected directly to Freire's experience as a Brazilian knowing, loving, and attempting to help other Brazilians. However, I think of them and find them useful when working with teachers and students. 

I am in a position of relative power and influence in my district as the Numeracy Coordinator (a brand-new role for me). I can push ideas, resources, and assessments onto teachers, but I am fortunate to be a creative individual who believes that others know their situations and certainly their students better than I do. And even if I knew them to be desperate for resources, I also know that they don't appreciate having their sense of agency and dignity chipped away at by receiving condescending advice and crappy materials that don't work for their context from the likes of me. 

At the core of my belief system sits the idea that any thing I offer teachers can and should be improved through dialogue and praxis, regardless of whether their teaching styles differ from mine. This idea is empowering for teachers and for me. Humbling, too, but mostly empowering because of the feelings of autonomy and responsibility that Freire identifies as core to true freedom. 

Finally, I think of math itself as a social justice issue. It is a terrible thing that the paths of many students are constrained and shaped by their avoidance of math. Math is the gateway to powerful and influential careers that not only provide personal security and satisfaction, but also serve communities as well. They can be a force for good, providing citizens with the opportunity to solve problems their communities face rather than relying on outside forces. I think it is critical that the mathematical experiences we provide for students serve them well and empower them to become the leaders their communities need.

Freire, Paulo, 1921-1997. (2000). Pedagogy of the Oppressed. New York: Continuum. 

Conclusion:

There were important and inspiring ideas from all of my courses, but not all of them have taken root in quite the same way as the ideas I mentioned above and others were already flowering before I began my studies. In this course, I hope to research one of the assessments I designed to increase teacher dialogue, provide teachers with a picture of student strengths and needs, and empower students rather than demoralize them. In other words, I am hoping for the assessment to be an example of the kind of practice that is in line with the values and ideas I articulated above. It has been tested in many schools across the district already and yielding promising results. I am hoping that the use of proper methodologies and research practices will provide me with clearer insights and help me better understand what might come next. I really want to dig into this one.