The secret life of mathematical concepts

Abstract This article features a theoretical example—a seemingly simple example that possesses, nonetheless, the potential to advance theory. Since the example radiates with the glow of silence and movement, it resists conventional analysis. Using words and images to trouble the grammar of an orderly world with hierarchal relations and depersonalized language commonly found in conventional analyses, the article aligns with a grammar of animacy to follow the agentive, sensorial, and relational encounter between an elementary student and the secret life of fractions and geometry concepts. The article offers two-way implications for research and practice, namely: (a) “what’s in it that could have an effect on my research” and (b) “how am I implicated in the effect of my own research.”