Doolittle, E. (2018). Off the grid. In S. Gerofsky (Ed.), Contemporary environmental and mathematics education: Modelling using new geometric approaches (pp. 101–121). Springer. https://doi.org/10.1007/978-3-319-72523-9_7
Introduction
In “Off the Grid,” Edward Doolittle critiques the widespread
reliance on grid-based ways of organizing space and time, arguing that
grids—rectangular plots, straight borders, fixed schedules, and Euclidean
geometry—create an illusion of order and fairness while often distorting
reality. Drawing on Indigenous knowledge (particularly Rotinonhsonni
traditions) and advanced mathematics, Doolittle shows that grids work only
under ideal conditions and frequently fail in natural, social, and educational
contexts.
Through examples from urban planning, land surveying, agriculture,
and mapping, Doolittle demonstrates how grids clash with uneven terrain, the
curvature of the earth, ecological variation, and lived experience. He links
grid thinking to control, ownership, and colonial power, noting how imposed
grids have contributed to Indigenous land dispossession and rigid schooling
practices. In contrast, Indigenous spatial and temporal frameworks emphasize relationship,
responsiveness, and place, such as defining territory by watersheds rather than
straight lines, or timing agricultural practices by animal and plant behavior
rather than calendars.
Doolittle proposes moving “off the grid” by embracing alternative
geometries—including Riemannian geometry, fractals, complexity theory, knot
theory, and weaving—which better reflect natural systems and change over time.
He concludes that these “geometries of liberation” can help free mathematics
education from rigid abstractions and reconnect it to ethics, ecology, and
lived reality.
Reflection
Reading Edward Doolittle’s Off the Grid made me think deeply
about how mapping and geometry differ across countries, cultures, and
histories. One contrast that stood out to me is the way political boundaries
are drawn. In Canada and the United States, many provincial and state
boundaries appear as straight lines, reflecting grid-based surveying systems
imposed for administrative efficiency. In contrast, in China (and similarly in
Korea and some other regions), boundaries are often nonlinear, shaped by
natural features such as rivers and mountain ranges, as well as long-standing
political and historical processes.
In addition, I remember that in Chinese history education, even
though I am not good at it, there is a commonly referenced natural division
between northern and southern China, often defined by a major mountain range
and river system. This geographic boundary is not just a line on a map; it
shapes people’s sense of belonging. Many people still identify themselves as
being “from the north” or “from the south,” and these identities correspond to
clear differences in climate, agriculture, food cultures, dialects, and
lifestyles. These differences emerged because people adapted to the land and
environment around them, rather than forcing the land into a uniform grid. This
resonates strongly with Doolittle’s argument about thinking “off the grid,” and
it also makes me wonder whether this difference reflects, at least partly, the
contrast between immigration countries and non-immigration countries in how
land is conceptualized, divided, and governed.
This chapter also reinforced my belief that bringing this kind of
knowledge into mathematics education is critical. Geometry should not be
limited to straight lines, right angles, and rectangular grids. To me,
mathematics is better understood as a discipline of reasoning, pattern
recognition, and sense-making. The way people live differently on the two sides
of a mountain or river in China is not random—it reflects patterns shaped by
geography, climate, and history. These patterns can be analyzed mathematically,
but only if mathematics is allowed to connect with geography, history, ecology,
and culture.
Doolittle’s work reminds us that mathematics is not separate from
lived reality. Teaching students to see math as a tool for understanding
human–environment relationships, rather than just a set of abstract rules,
opens powerful possibilities for cross-disciplinary learning and more just,
meaningful education.
Question
Because Off the Grid is primarily an ideological and
philosophical piece rather than an empirical study, I find it difficult to pose
a highly technical question about it. Instead, could you share an experience,
observation, or example—from teaching, learning, mapping, or everyday
life—where grid-based thinking failed to capture reality, or where thinking
“off the grid” offered a deeper or more just understanding of space, time, or
relationships? How does this example help you interpret Doolittle’s argument?
Hi Li, thanks so much for your reflection and connection to your own personal context in China. I had no idea China was divided in that way, so it seems like you are not as bad as you may think at Chinese history!
ReplyDeleteI always enjoy Edward Doolittle’s pieces, and your question immediately brought me back to our own classrooms. Teachers are often given pacing guides, syllabi, and prescribed timelines for each chapter or topic, yet these structures assume far too much about students’ readiness and progress. There are days when a class is simply not in a place to learn what has been planned. In those moments, we may find ourselves fighting tooth and nail to “teach” the content—sometimes unsuccessfully—resulting in a one-sided transmission of information rather than meaningful learning.
Thinking “off the grid” in this context occurs when lessons are allowed to slow down, shift, or veer in response to students’ questions, emotions, and needs. While these moments may appear unproductive within a grid-based framework, they often reveal what students are truly thinking and experiencing, even when it is not explicitly content-oriented. This, for me, reflects Doolittle’s argument that rigid structures can obscure relational and ethical dimensions of learning, and that deeper understanding often emerges when we attend to what lies beyond the grid.
Hi Lee, your question about the connection between how land is divided and how different countries understand and relate to their land—especially in relation to whether a country is an immigration country or not—really stood out to me. As you mentioned, Korea also has regional boundaries that are more natural and non-linear, often shaped by mountains, rivers, and long-standing historical settlement patterns rather than imposed grids. I agree that this is closely connected to Korea being a non-immigration country, where relationships to land have developed gradually over long periods of time. These boundaries are not just administrative but cultural, influencing dialects, food practices, climate adaptation, and regional identity. Thinking about this alongside Doolittle’s argument helped me see how grid-based divisions are not neutral, but deeply tied to histories of settlement, governance, and power.
ReplyDeleteAt the same time, this contrast highlights how deeply the belief that mathematics should be rigid, strict, and grid-based is ingrained in us. Even though Korea has long embraced non-linear, place-based ways of understanding land and regional boundaries, students are still much more accustomed to thinking on the grid when it comes to mathematics. In math classrooms, fixed procedures and single correct answers are often prioritized, which makes it difficult for students to think off the grid—even within a cultural context where non-linear thinking about space and place already exists. This tension reinforces Doolittle’s point that grid-based thinking in mathematics is not natural or inevitable, but something that has been systematically taught and normalized through schooling.
One example where grid-based thinking fails to capture reality comes from my experience teaching linear functions and coordinate geometry. Graph paper, axes, and evenly spaced grids suggest that relationships are uniform, predictable, and linear. However, when students try to model real-world situations—such as population growth, climate patterns, or the spread of information—the grid often obscures more than it reveals. When data does not fit neatly into straight lines or evenly spaced intervals, students struggle, and mathematics can feel disconnected from lived experience. By moving “off the grid”—through discussions of nonlinear models, variability, and contextual influences—students begin to see mathematics as a tool for understanding complexity rather than forcing reality into simplified structures.
Thanks for this fascinating discussion, everyone! It’s amazing to see how colonial administrators who most likely never visited, say, Saskatchewan or Iowa or even Bangladesh and Northern Ireland, drew straight lines with rulers on maps that ended up being the artificial, sometimes harmful boundaries between countries, lands and peoples. You can point to quite a few highly destructive conflicts and wars that were caused by this supposedly rational application of grids and straight lines to complex geographies. How interesting it is that we teachers feel pressured by similar straight lines and grids on a timetable or curriculum document! Great ideas here.
ReplyDelete