Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction aims to provide:• A useful introduction to current work and thinking about learning trajectories for mathematics education • An explanation for why we should care about these questions • A strategy for how to think about what is being attempted in the field, casting some light on the varying, and perhaps confusing, ways in which the terms trajectory, progression, learning, teaching, and so on, are being used by the education community.Specifically, the report builds on arguments published elsewhere to offer a working definition of the concept of learning trajectories in mathematics and to reflect on the intellectual status of the concept and its usefulness for policy and practice. It considers the potential of trajectories and progressions for informing the development of more useful assessments and supporting more effective formative assessment practices, for informing the on-going redesign of mathematics content and performance standards, and for supporting teachers' understanding of students' learning in ways that can strengthen their capability for providing adaptive instruction. The authors conclude with a set of recommended next steps for research and development, and for policy. LearnInG TraJeCTOrIeS In MaTHeMaTICSA Foundation for Standards, Curriculum, Assessment, and instructionEstablished in 1985, CPRE unites researchers from seven of the nation's leading research institutions in efforts to improve elementary and secondary education through practical research on policy, finance, school reform, and school governance. CPRE studies alternative approaches to education reform to determine how state and local policies can promote student learning. The Consortium's member institutions are the University of Pennsylvania, Teachers College-Columbia University, Harvard University, Stanford University, the University of Michigan, University of Wisconsin-Madison, and Northwestern University.In March 2006, CPRE launched the Center on Continuous Instructional Improvement (CCII), a center engaged in research and development on tools, processes, and policies intended to promote the continuous improvement of instructional practice. CCII also aspires to be a forum for sharing, discussing, and strengthening the work of leading researchers, developers and practitioners, both in the United States and across the globe.To learn more about CPRE and our research centers, visit the following web sites: Visit our website at http://www.cpre.org or sign up for our e-newsletter, In-Sites, at insites@gse.upenn.edu.Research Reports are issued by CPRE to facilitate the exchange of ideas among policymakers, practitioners, and researchers who share an interest in education policy. The views expressed in the reports are those of individual authors, and not necessarily shared by CPRE or its institutional partners. About the Consortium for PoliCy reseArCh in eduCAtion (CPre)CPre reseArCh rePort series CPRE Research Report # RR-...

Goals for literacy, math, and science education may increase citizens' capacity to argue from evidence.

1 NAEP also maintains a long-term trend line in mathematics that goes back to 1972-73. It is the main NAEP mathematics assessment, however, that is the focus of this validity study.

Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction aims to provide:• A useful introduction to current work and thinking about learning trajectories for mathematics education • An explanation for why we should care about these questions • A strategy for how to think about what is being attempted in the field, casting some light on the varying, and perhaps confusing, ways in which the terms trajectory, progression, learning, teaching, and so on, are being used by the education community.Specifically, the report builds on arguments published elsewhere to offer a working definition of the concept of learning trajectories in mathematics and to reflect on the intellectual status of the concept and its usefulness for policy and practice. It considers the potential of trajectories and progressions for informing the development of more useful assessments and supporting more effective formative assessment practices, for informing the on-going redesign of mathematics content and performance standards, and for supporting teachers' understanding of students' learning in ways that can strengthen their capability for providing adaptive instruction. The authors conclude with a set of recommended next steps for research and development, and for policy. LearnInG TraJeCTOrIeS In MaTHeMaTICSA Foundation for Standards, Curriculum, Assessment, and instructionEstablished in 1985, CPRE unites researchers from seven of the nation's leading research institutions in efforts to improve elementary and secondary education through practical research on policy, finance, school reform, and school governance. CPRE studies alternative approaches to education reform to determine how state and local policies can promote student learning. The Consortium's member institutions are the University of Pennsylvania, Teachers College-Columbia University, Harvard University, Stanford University, the University of Michigan, University of Wisconsin-Madison, and Northwestern University.In March 2006, CPRE launched the Center on Continuous Instructional Improvement (CCII), a center engaged in research and development on tools, processes, and policies intended to promote the continuous improvement of instructional practice. CCII also aspires to be a forum for sharing, discussing, and strengthening the work of leading researchers, developers and practitioners, both in the United States and across the globe.To learn more about CPRE and our research centers, visit the following web sites: Visit our website at http://www.cpre.org or sign up for our e-newsletter, In-Sites, at insites@gse.upenn.edu.Research Reports are issued by CPRE to facilitate the exchange of ideas among policymakers, practitioners, and researchers who share an interest in education policy. The views expressed in the reports are those of individual authors, and not necessarily shared by CPRE or its institutional partners. About the Consortium for PoliCy reseArCh in eduCAtion (CPre)CPre reseArCh rePort series CPRE Research Report # RR-...

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