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

Abstract

Since its 1947 founding, ETS has conducted and disseminated scientific research to support its products and services, and to advance the measurement and education fields. In keeping with these goals, ETS is committed to making its research freely available to the professional community and to the general public. Published accounts of ETS research, including papers in the ETS Research Report series, undergo a formal peer-review process by ETS staff to ensure that they meet established scientific and professional standards. All such ETS-conducted peer reviews are in addition to any reviews that outside organizations may provide as part of their own publication processes. Peer review notwithstanding, the positions expressed in the ETS Research Report series and other published accounts of ETS research are those of the authors and not necessarily those of the Officers and Trustees of Educational Testing Service.The Daniel Eignor Editorship is named in honor of Dr. Daniel R. Eignor, who from 2001 until 2011 served the Research and Development division as Editor for the ETS Research Report series. The Eignor Editorship has been created to recognize the pivotal leadership role that Dr. Eignor played in the research publication process at ETS. ETS Research Report Series ISSN 2330-8516 R E S E A R C H R E P O R T A Learning Progression for Geometrical Measurement in One, Two, and Three DimensionsEun Mi Kim, Jeff Haberstroh, Stephanie Peters, Heather Howell, & Leslie Nabors Oláh Educational Testing Service, Princeton, NJ 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.Keywords Geometrical measurement; learning progression; task design; mathematics doi:10.1002/ets2.12189 At Educational Testing Service (ETS) the CBAL ® learning and assessment research initiative aims to construct "a model for an innovative K-12 assessment system that documents what students have achieved (of learning); facilitates instructional planning (for learning); and is considered by students and teachers to be a worthwhile educational experience in and of itself (as learning)" (Bennett, 2010, pp. 71-72). This model comprises domain-specific competency models (for reading writing and mathematics), summative and formative assessments, and pr...

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