"Learning progressions" are one of the most important assessment design ideas to be introduced in the past decade. In the United States, several committees of the National Research Council (NRC) have argued for the use of learning progressions as a means to foster both deeper mastery of subject-matter content and higher level reasoning abilities. Consideration of learning progressions is especially important in the context of the new Common Core State Standards (CCSS) and Next Generation Science Standards (NGSS) that attend specifically to the sequencing of topics and skills across grades to ensure attainment of college and career expectations by the end of high school. In this paper we address the question: Should more formally developed learning progressions be considered for the future design of the National Assessment of Educational Progress (NAEP)? After a brief overview of the research on learning progressions, we describe the idealized model whereby shared, instructionally grounded learning progressions--once developed--could be used to link classroom-level assessments with large-scale assessments such as NAEP. At the same time, we also consider potential problems. In particular, learning progressions--which require agreed-upon instructional sequences--could be problematic in the context of a national assessment program intended to be curriculum neutral (i.e., not favoring one state's or district's curriculum over another). Finally, we use a sample of NAEP and Balanced Assessment in Mathematics (BAM; Mathematics Assessment Resource Service, 2002, 2003) items to explore the possibility of constructing "quasi learning progressions" that could be used to illuminate the substantive meaning of the NAEP achievement results. An appendix presents: Items in Learning Progressions. [For the main report, "Examining the Content and Context of the Common Core State Standards: A First Look at Implications for the National Assessment of Educational Progress," see ED545237.]