Although variability and structure are often considered as antonyms in many<br>everyday settings, a mathematically disciplined view contradicts this<br>opposition. To initiate fifth- (10 years old) and sixth-grade (11 years old)<br>students in this disciplinary view, we engaged students in practices of<br>modeling data. These practices included inventing and revising data displays,<br>inventing and revising measures of centre and variability, and inventing and<br>revising models of chance to account for variability. Here we focus on<br>prospective correspondences between students' invented measures (statistics)<br>of variability and those favoured by the discipline. We suggest that inventing<br>measures positions students to transform their vision of variability from mere<br>difference to more structured forms, some of which coordinate centre and<br>spread. By tracing interactions among an inventor, her classmates, and the<br>teacher, we trace how structuring variability and constituting its measure co-<br>originated during the course of negotiations about the meaning of the measure.<br>Consideration of the coherency, transparency and generalisability of a statistic,<br>all of which are valued by the discipline of statistics, emerged during the course<br>of invention.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education