Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction

Abstract

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-...

A Hitchhiker's Guide to Thinking about Literacy, Learning Progressions, and Instruction

“…Working groups of experts in those two fields produced reports that concluded that there was empirical and theoretical support for the idea that the ways children learn some of the concepts and practices of science and mathematics could be characterized as typically advancing through identifiable levels or steps of growing understanding and skill (see Daro, Mosher, & Corcoran, 2011;Corcoran, Mosher, & Rogat, 2009). There also was support for the notion that children typically encounter identifiable difficulties or problems along the way which may hinder their movement from level to level on the progression.…”

Investigación en educación matemática : [actas del XXI Simposio de la Sociedad Española de Investigación en Educación Matemática : Zaragoza, 6-9 de septiembre de 2017]

“…En este sentido, la información sobre una trayectoria de aprendizaje, entendida como contenido a ser aprendido por los estudiantes para maestro, puede ser usada como un instrumento conceptual para comprender y tratar situaciones de enseñanza y aprendizaje de las matemáticas (Llinares, 2004). Aprender a usar la información sobre las trayectorias de aprendizaje como un instrumento conceptual para desarrollar la competencia "mirar profesionalmente" el pensamiento matemático de los estudiantes, puede interpretarse en términos de su "instrumentalización" (entendido como el desarrollo de la capacidad del estudiante para maestro de usar la trayectoria de aprendizaje para interpretar la comprensión de los alumnos y tomar las correspondientes decisiones instruccionales que favorezcan su aprendizaje) (Daro, Mosher y Corcoran, 2011;. El análisis de este proceso de instrumentalización aporta información sobre la manera en la que los estudiantes para maestro aprenden a usar el conocimiento de matemáticas y sobre el aprendizaje de las matemáticas para apoyar sus decisiones en la enseñanza.…”

The Role of Learning Progressions in Standards-Based Education Reform

“…As a result of these deliberations, CCII produced two reports, one for science and one for mathematics (Corcoran, Mosher, & Rogat, 2009;Daro, Mosher, & Corcoran, 2011). This policy brief reviews their conclusions and the implications of their findings for policy and for future research and development.…”