# Mathematics and Education

A slow blog

## Grade 4 and 8 NAEP Objectives Outside the Common Core

This is a guest post by Jason Zimba.

Created in the late 1960s, the National Assessment of Educational Progress (NAEP) today measures U.S. achievement in mathematics, reading, science, U.S. history, and other subjects. The most recent framework for the mathematics assessment is described in a document published in 2014 by the National Assessment Governing Board and entitled Mathematics Framework for the 2015 National Assessment of Educational Progress. Below, I list assessment targets from the NAEP Mathematics Framework that are outside the expectations in the Common Core State Standards for Mathematics (CCSS-M). Here, “outside” means “located in CCSS-M after the grade level tested in NAEP, or not in the Common Core.” NAEP objectives meeting this description are listed in Table 1.

Table 1 does not aim to include all differences between NAEP objectives and CCSS-M expectations. In particular, it considers NAEP objectives that are outside CCSS-M but not CCSS-M expectations that are outside of the NAEP framework. Note that for some NAEP objectives, the likelihood of the associated items assessing skills from outside of CCSS-M is difficult to analyze based only on the language of the objective. For example, with reference to the grade 4 NAEP objective “Solve problems involving conversions within the same measurement system” (not listed in Table 1), converting from a larger unit to a smaller unit would fall in CCSS-M grade 4, but some other conversions would fall in higher grades. A more global example of a content-related question would be the different treatments of estimation in the two documents.

Table 1 does not give a comprehensive analysis of the relationship between the NAEP framework and CCSS-M. Such an analysis would have to consider many factors, ranging from content focus and content balancing schemes to the role of calculators. Nor is it the purpose here to make recommendations (note, a 2013 NAEP–CCSS study that did offer recommendations can be found here). Table 1 only lists NAEP objectives that at face value lie outside of CCSS-M.

The existence of such differences should not be surprising. For one thing, CCSS-M’s expressed goal of addressing the “mile wide, inch deep” problem (CCSS-M, p. 3) necessarily implies that some long-traditional topics are no longer part of intended content, while other topics such as functions, congruence, statistics and probability are moved from elementary to middle grades where they are treated in more depth. These features of the content progressions in CCSS-M contribute to the standards’ close match to standards in high performing countries.

Another difference is simply historical. As noted in the NAEP framework (pp. 1, 3; Exhibit 1), “The 2015 Mathematics Framework reflects changes from 2005 in grade 12 only; mathematics content objectives for grades 4 and 8 have not changed.” In other words, for grades 4 and 8, the most recent revision of the NAEP mathematics framework occurred five years prior to the publication of the Common Core State Standards.

Table 1. NAEP grade 4 and grade 8 mathematics objectives not in CCSS-M or located in later grades.

Key:

• NA means that the content isn’t in CCSS-M.
• +1, +2, +3, and +4 indicate how many grades later the content appears in CCSS-M. For NAEP Grade 8, an offset of +1 means that the content appears in the CCSS-M high school standards.
• Square brackets indicate portions of an objective that fall outside of CCSS-M. In such cases, information in the CCSS-M column refers to the bracketed portion(s).

References

Hughes, G., Daro, P., Holtzman, D., & Middleton, K. (2013). A Study of the Alignment Between the NAEP Mathematics Framework and the Common Core State Standards for Mathematics (CCSS-M). Washington, DC: American Institutes for Research. http://www.air.org/resource/examining-content-and-context-common-core-state-standards-first-look-implications-national

National Assessment Governing Board. (2014). Mathematics Framework for the 2015 National Assessment of Educational Progress. Washington, DC: U.S. Department of Education. https://www.nagb.org/publications/frameworks/mathematics/2015-mathematics-framework.html

National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Author. http://www.corestandards.org/Math/

Schmidt, W. H., Houang, R. T., & Cogan, L. A. (2002). Coherent Curriculum: The Case of Mathematics. American Educator, 1-18. https://www.aft.org/sites/default/files/periodicals/curriculum.pdf

Schmidt, W. H., & Houang, R. T. (2012). Curricular Coherence and the Common Core State Standards for Mathematics. Educational Researcher, 41(8), 294–308. http://edr.sagepub.com/content/41/8/294.abstract