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ERIC Number: ED519792
Record Type: Non-Journal
Publication Date: 2011-Jan
Pages: 84
Abstractor: ERIC
Reference Count: 58
Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction. CPRE Research Report # RR-68
Daro, Phil; Mosher, Frederic A.; Corcoran, Tom
Consortium for Policy Research in Education
The concept of learning progressions offers one promising approach to developing the knowledge needed to define the "track" that students may be on, or should be on Learning progressions can inform teachers about what to expect from their students. They provide an empirical basis for choices about when to teach what to whom Learning progressions identify key waypoints along the path in which students' knowledge and skills are likely to grow and develop in school subjects. Such waypoints could form the backbone for curriculum and instructionally meaningful assessments and performance standards. In mathematics education, these progressions are more commonly labeled learning trajectories. These trajectories are empirically supported hypotheses about the levels or waypoints of thinking, knowledge, and skill in using knowledge, that students are likely to go through as they learn mathematics and, one hopes, reach or exceed the common goals set for their learning. Trajectories involve hypotheses both about the order and nature of the steps in the growth of students' mathematical understanding, and about the nature of the instructional experiences that might support them in moving step by step toward the goals of school mathematics. This report aims to provide a useful introduction to current work and thinking about learning trajectories for mathematics education; why everyone should care about these questions; and how to think about what is being attempted, 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 authors and their colleagues in this work. Appended are: (1) A Sample of Mathematics Learning Trajectories; and (2) OGAP Multiplicative Reasoning Framework-Multiplication. (Contains 2 figures, 1 table and 18 footnotes.) [This report was prepared with Jeffrey Barrett, Jere Confrey, Wakasa Nagakura, Michael Battista, Vinci Daro, Marge Petit, Douglas Clements, Alan Maloney and Julie Sarama.]
Consortium for Policy Research in Education. University of Pennsylvania, 3440 Market Street Suite 560, Philadelphia, PA 19104. Tel: 215-593-0700; Fax: 215-573-7914; e-mail:; Web site:
Publication Type: Reports - Descriptive
Education Level: Elementary Education; Elementary Secondary Education; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: Consortium for Policy Research in Education
Identifiers - Location: Alabama; New York; Vermont
Identifiers - Laws, Policies, & Programs: No Child Left Behind Act 2001