Alternative Administrative Geometries of Learning

In their article, “Dancing teachers into being with a garden, or how to swing or parkour the strict grid of schooling,” Susan Gerofsky and Julia Ostertag show how grids are everywhere in education. It is so ubiquitous it can become invisible: tiled floors, rows of desks, schedules, worksheets, tables, rubrics, gradebooks. “Grid thinking” supports a certain kind of productivity, but it also limits administrative imagination—restricting learning to parceled boxes, slicing time into units, and flattening the complexities of identity, interest, and curiosity into prefab categories.

The article’s best move is that it doesn’t demand we “escape” the grid. Instead, the authors suggest learning to be beside it; like jazz swing beside a strict beat. Swing doesn’t abolish discipline; it leans on it: chord progression, harmony, tempo. The point isn’t to erase constraints, but to cultivate ways of moving through them that leave room for breath, surprise, and embodied presence. Think, for example, of Johann Sebastian Bach’s Invention in A minor.

Jazz and classical pianist Hazel Scott reinterprets that piece by compressing, bending, and stretching it while keeping it recognizable. Her reframing, without quite breaking the composition, made something click for me: what we need is not anti-structure pedagogy, but alternative administrative geometries.

Western science already lives this pluralism. We switch coordinate systems depending on what we’re trying to see. Rectangular coordinates are natural for some problems; polar coordinates for others. Neither is “more true.” Each is a disciplined way of making certain relationships legible; and every act of showing is also, strategically, an act of hiding. The danger isn’t the existence of a grid; it’s when the grid becomes the only authorized way to represent learning. That monopoly privileges some people, cultures, and perspectives, while leaving others at the fringe. Coordinate systems suggest we can have it both ways; music shows us how.

So what might alternative administrative geometries of learning look like, concretely, in classrooms and assignments?

Keep the schedule, but design deliberate openings where clock-time takes the back seat: reflective pauses, restorative breaks, and habit-forming repetition. Not as self-indulgence, but as cognitive ecology.

Prefer spiral pathways to linear checklists, staying open to unexpected lines of “progress” that allow learners to re-encounter a problem—and a solution—from ever-deepening angles.

Build in improvisation to distinguish metronome compliance from musicality. This encourages both students and teachers not to blindly follow steps, but to notice invariants, recognize opportunities for choice, and name the tradeoffs those choices introduce.

If we take the article seriously, we can teach students, and ourselves, that structure is something we can inhabit, choose, and sometimes redesign.

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Gerofsky, S., & Ostertag, J. (2018). Dancing teachers into being with a garden, or how to swing or parkour the strict grid of schooling. Australian Journal of Environmental Education, 34(2), 172–188.