On the complex geometry of individuality and growth: Cook’s 1914 “Curves of Life” and reading measurement

Abstract

Growth in reading ability varies across individuals in terms of starting points, velocities, and decelerations. Reading assessments vary in the texts they include, the questions asked about those texts, and in the way responses are scored. Complex conceptual and operational challenges must be addressed if we are to coherently assess reading ability, so that learning outcomes are comparable within students over time, across classrooms, and across formative, interim, and accountability assessments. A philosophical and historical context in which to situate the problems emerges via analogies from scientific, aesthetic, and democratic values. In a work now over 100 years old, Cook’s study of the geometry of proportions in art, architecture, and nature focuses more on individual variation than on average general patterns. Cook anticipates the point made by Kuhn and Rasch that the goal of research is the discovery of anomalies—not the discovery of scientific laws. Bluecher extends Cook’s points by drawing an analogy between the beauty of individual variations in the Parthenon’s pillars and the democratic resilience of unique citizen soldiers in Pericles’ Athenian army. Lessons for how to approach reading measurement follow from the beauty and strength of stochastically integrated variations and uniformities in architectural, natural, and democratic principles.