The proposed project is an initial step toward solving a compelling problem that has received insufficient research attention in mathematics education: Why do U.S. students perform and understand measurement so poorly, in contrast to other content domains and students' in other developed countries? The problem is well-documented, but no comprehensive, empirically-grounded explanation has been advanced. Absent such an explanation, efforts to redress the problem via changes in curricula, professional development, or teacher education will remain unfocused and ineffective. The research literature (e.g., Clements, 1999; Lehrer, 2003, Strom, Kemeny, Lehrer, & Forman, 2001) suggests that four factors shape the problem, directly and in interaction: (1) deficits in published elementary and middle school curricula, (2) problems in teachers' enactments of those curricula, (3) problems in the character of classroom discourse about measurement, and (4) teachers' own knowledge of measurement. Recognizing this interactive complexity, this project will assess the capacity of elementary and middle school curricula to support robust student learning of measurement of length, area, and volume. Drawing on the existing research literature, the project will (a) assess the deficits and strengths of elementary and middle school curricula, and (b) characterize how key topics in these curricula are enacted by teachers in their classrooms. Four elementary and three middle school curricula were selected based on market-share, differences in design (publisher-developed vs. NSF-funded) and local adoption patterns. Their complete content for length, area, and volume will be evaluated using a framework, built from research, that details the elements of robust understanding. That content includes (1) basic approach, (2) explicit content statements, e.g., definition of area, and (3) all problems, tasks, and activities linked to the target measures. Each evaluation will yield a curriculum profile that will be communicated to each author team and revised, if appropriate, from their feedback. Teachers' presentation of lesson sequences in key topic areas (introduction to length, complex lengths, introduction to area, perimeter & area, and surface area & volume) will then be analyzed using the same framework. The primary objective is to estimate the extent to which written curricula contribute to the problem of weak student learning; a secondary objective is to trace how teachers enact these measurement topics in their classrooms, as a step toward modeling the contributions of all major factors listed above. Intellectual Merit. This project will provide a detailed, research-based analysis of the capacity of current published curricula to support robust student learning of core measurement content. Analyses of teachers' enacted curricula will characterize how written materials combine with other factors to shape students' learning, productively or not. The conceptual frame and the curricular profiles will support analyses of other written curricula (e.g., those in high-performing countries), teachers' enacted curricula, and students' learning. Broad Impact. Length, area, and volume are taught in all elementary and middle grades, but too often instruction is ineffective. Failing to learn the conceptual foundations of measurement undermines subsequent STEM learning across a wide spectrum of content. The project will expand and enrich the work of the current NSF-funded Center for the Study of Mathematics Curriculum where analyses have primarily focused on number, algebra, and reasoning.
