A Learning Progression for Geometrical Measurement in One, Two, and Three Dimensions

As part of the CBAL® learning and assessment initiative in mathematics, we developed a hypothesized learning progression (LP) for geometrical measurement in 1, 2, and 3 dimensions based on a synthesis of empirical literature in this field and through expert review. The geometrical measurement LP is intended to represent a developmental progression of students' understandings and learning for 1-, 2-, and 3-dimensional measurement in terms of transitions along levels within a dimension and connections across the 3 dimensions. In addition, we designed cognitive laboratory tasks associated with the levels of the geometrical measurement LP. The development process of the geometrical measurement LP and cognitive laboratory tasks presented here provide guidance for future development of LPs and task design that would provide the evidence supporting the proposed LPs.