American education policy seems poised to escalate and shift its two decade long commitment to standards and outcome-based reform. That commitment has involved a set of "grand bargains", in which the federal government provides Title I (The "No Child Left Behind Act" or NCLB) disadvantaged education funds in return for the states' agreeing to set ambitious content standards, and define performance or "proficiency" standards associated with them that all students in the states' schools will be expected to meet by the 2013/ 2014 school year. The disadvantaged children targeted by Title I are expected to meet the same standards as all of the rest of the children in each state. In return for agreeing to hold their schools accountable for meeting these expectations, the states are left free to set their standards and their related measures of proficiency as they wish, within some broadly defined parameters. And the local school systems and schools in each state, in return for their share of the Title I/NCLB money are left free, for the most part, to choose their preferred approaches to instruction as long as they agree to be held accountable for ensuring that all their students are making adequate progress towards meeting the state's proficiency goals. So, the general form of each bargain is an agreement to reduce or forgo regulation of inputs in return for a commitment to define, and meet, outcome expectations.But, having agreed to do something they had never before tried to do-to succeed with essentially all students-schools and educators face the problem that they don't know how to meet their side of the bargain. Proponents and observers of reform claim to be shocked that some states are setting their performance standards in ways that minimize or disguise the degree to which their students are likely to fail to meet the hopes of reform. In addition, schools and teachers are resorting to approaches, such as relentless test preparation and focusing on students who are just at the edge of meeting proficiency requirements, that try to meet the letter of the bargains' requirements while leaving the more ambitious spirit of the reforms' hopes well behind, along with all too many children. Established in 1985, CPRE unites researchers from seven of the nation's leading research institutions in e orts to improve elementary and secondary education through practical research on policy, nance, school reform, and school governance. CPRE studies alternative approaches to education reform to determine how state and local policies can promote student learning. e Consortium's member institutions are the

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-...

American education policy seems poised to escalate and shift its two decade long commitment to standards and outcome-based reform. That commitment has involved a set of "grand bargains", in which the federal government provides Title I (The "No Child Left Behind Act" or NCLB) disadvantaged education funds in return for the states' agreeing to set ambitious content standards, and define performance or "proficiency" standards associated with them that all students in the states' schools will be expected to meet by the 2013/ 2014 school year. The disadvantaged children targeted by Title I are expected to meet the same standards as all of the rest of the children in each state. In return for agreeing to hold their schools accountable for meeting these expectations, the states are left free to set their standards and their related measures of proficiency as they wish, within some broadly defined parameters. And the local school systems and schools in each state, in return for their share of the Title I/NCLB money are left free, for the most part, to choose their preferred approaches to instruction as long as they agree to be held accountable for ensuring that all their students are making adequate progress towards meeting the state's proficiency goals. So, the general form of each bargain is an agreement to reduce or forgo regulation of inputs in return for a commitment to define, and meet, outcome expectations.But, having agreed to do something they had never before tried to do-to succeed with essentially all students-schools and educators face the problem that they don't know how to meet their side of the bargain. Proponents and observers of reform claim to be shocked that some states are setting their performance standards in ways that minimize or disguise the degree to which their students are likely to fail to meet the hopes of reform. In addition, schools and teachers are resorting to approaches, such as relentless test preparation and focusing on students who are just at the edge of meeting proficiency requirements, that try to meet the letter of the bargains' requirements while leaving the more ambitious spirit of the reforms' hopes well behind, along with all too many children. Established in 1985, CPRE unites researchers from seven of the nation's leading research institutions in e orts to improve elementary and secondary education through practical research on policy, nance, school reform, and school governance. CPRE studies alternative approaches to education reform to determine how state and local policies can promote student learning. e Consortium's member institutions are the

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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