Reading Response: Off the grid.

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

Summary

In the chapter "Off the Grid " Edward Doolittle looks at the things that the grid's not good at and the things it does wrong. He writes this from the point of view of a mathematician. Edward Doolittle says that the grid is a tool for people, in the West who do math and for people who run colonies. The grid often does not do a good job of showing how the natural world really is. The natural world is not always straight and simple it is often. Complicated. The grid fails to show these things. Edward Doolittle is talking about the grid. How it does not work well for everything, especially the natural world. Through a series of diverse examples—including the mathematical distortions of map projections, the self-organizing behavior of bees, and the devastating real-world impact of applying flat grid-based surveying to Indigenous treaty territories—Doolittle suggests that a truly comprehensive mathematics education must move beyond rigid Western paradigms. He advocates for "off the grid" thinking that embraces Indigenous traditions, chaos theory, and the anomalies that arise when we try to force a curved reality into a straight-lined system.

Stop 1: My first "stop" occurred on page 102 when Doolittle discusses how the grid is used to "rectify" the world. This term stopped me because it implies that the world is somehow "wrong" or "crooked" until we apply our coordinate systems to it. In my own teaching, I realize I have often presented the Cartesian plane as a neutral, perfect truth rather than a specific cultural tool used to flatten and control space. Doolittle’s analysis "tugs on my sleeve" by forcing me to reconsider the underlying power dynamics of the geometry I teach every day.

Stop 2: I paused again on page 112 at the description of how flowers and bees coordinate their actions without a central master plan or grid. In secondary mathematics, we spend so much time teaching students how to find points on a grid to model behavior. Doolittle reminds us that highly complex "math" happens in nature through proximity, curvature, and organic interaction. This is a "stop" for me because it suggests that our curriculum might be overlooking "emergent" mathematics—systems that organize themselves from the bottom up rather than being imposed from the top down.

Stop 3: The most significant "stop" was on page 107, regarding the miscalculation of Indigenous treaty territories. Doolittle explains that applying a flat, rectangular grid to the curved surface of the Earth isn't just a technical error; it resulted in the physical loss of land for Indigenous people. As a math educator, this moment arrested my habits of engagement. We often treat spherical geometry as an "advanced" elective topic, but Doolittle shows that failing to understand the curvature of the Earth has deep moral and political consequences. It highlights that math is never truly "off the hook" from social justice.

A Question I Wonder

Doolittle argues that the grid eventually "falls apart" when faced with the complexity of the real world. How can we adapt our secondary math pedagogy to teach the "standard" grid-based skills required by the curriculum while simultaneously honoring the "off the grid" Indigenous and organic mathematical perspectives that Doolittle proves are so vital?