The National Assessment of Educational Progress (NAEP) is the nation’s best source of data on the mathematics performance of pre-college students.  The National Center for Education Statistics (NCES) provides overall results each time an assessment is administered but the analyses provided are too general to have direct impact on teaching and curriculum development.  This symposium will focus on trends in achievement on specific items and topics in the mathematics curriculum for elementary and middle school students.  With respect to format, the symposium will consist of four 12-minute presentations followed by 12 minutes of commentary by a discussant and then 30 minutes for comments and questions from the audience.  Analyses presented will include examples of changes in performance on items that have been released to the public as well as on secure items that are still in use.  As with previous item-level research using NAEP data (e.g. Kloosterman & Lester, 2007; Silver & Kenney, 2000), the research presented in this symposium is focused on documenting what a broad national sample of students are able to do from the perspective that understanding performance is necessary to decide where mathematics instruction seems to be working well and where changes might be needed.  Specific research questions are (1) What mathematics do elementary and middle school students in the United States know and how has performance changed over time? And (2) Do trends in achievement vary by grade/age level, complexity of the items used to assess achievement, or other background variables?

The first presentation will focus on trends in achievement on specific items and sets of related items (e.g., items that require finding patterns) between 1996 and 2007 at grade 4. These years were selected because the same criteria were used for selecting the NAEP sample across these years and most of the items were used in multiple years.  As of this writing, the 2009 secure NAEP data set had not been released to researchers; but assuming it is released before the end of 2011, data from 2009 will also be included. Sets of related items were identified based on inspection of the items and trends over time were based on the proportion of students answering each item correctly for each year an item was administered.  The second presentation will be analogous to the first except that it will be based on the grade 8 data.  The third presentation will focus on the age 13 NAEP Long-Term Trend (LTT) data between 1982 and 2004.  This period was chosen because almost all of the LTT items used during this period were exactly the same for every administration.  Note that while we have provided general descriptions of age 9 and age 17 LTT secure items used over this period elsewhere (Authors, 2010; in press), this symposium will be the first time that descriptions of the secure age 13 items will be presented.  In the fourth presentation, the first three presenters will join together to outline where the trends are the same across the three data sets and where trends in one data set are not seen in the other data sets.  The discussant, who was selected because of her extensive knowledge of NAEP, will then comment on each of the papers with additional focus on what the three NAEP data sets indicate about trends in mathematics achievement.

Because the findings across the data sets are too broad to be summarized beyond the fact that there are general upward trends in achievement, we offer the following as examples of the types of conclusions that will be presented in the symposium. At grade 4, one of the secure items is a one-step story problem (item number M010831) that requires students to find the correct numbers in the problem and then select and perform the correct operation with those numbers.  In 1996, 58% of students wrote down the correct answer.  By 2007, however, the percentage of students answering correctly dropped to 52%.  In contrast, a 2009 released item (number 12 in block 5) required grade 4 students to write the next two numbers in the pattern 1, 6, 4, 9, 7, 12, 10 and write the rule for that pattern.  Performance on this item improved from 21% answering correctly in 1996 to 37% answering correctly in 2007.  The audience will be challenged to explain why the trends on these items are so different.  Is emphasis on traditional story problems declining and, if so, is that cause for concern?  Is performance on the pattern item the result of increased emphasis on algebraic thinking and, if so, will improved performance on pattern items lead to improved performance in a traditional algebra course?  A more general question will be the relevance of the NAEP data and the appropriateness of the items NAEP uses in light of the adoption by most states of the Common Core State Standards.

 A broader example of the results that will be presented involves fractions.  The LTT data indicate that were statistically significant gains by 13-year-olds between 1982 and 2004 on 13 of the 15 fractions and decimals items used, including gains of more than 10% on 10 of the items.  There was also significant improvement on almost all grade 4 Main NAEP fractions items between 1996 and 2007.  Given these findings in relation to the claim made in the National Mathematics Advisory Panel Report (2008) that weak fraction skills are a major impediment when students are studying algebra, we must ask how much more can be can be accomplished with respect to the teaching of fractions.

In brief, this symposium will provide data on the health of mathematics instruction in the United States.  Audience members will be challenged to speculate on the extent to which changes in curriculum or instruction can explain the changes in performance, and to reflect on what new directions in mathematics teaching might mean for NAEP results in years to come.

References

Kloosterman, P., & Lester, F. K., Jr. (Eds.) (2007).  Results and interpretations of the 2003 mathematics assessment of the National Assessment of Educational Progress. Reston, VA: National Council of Teachers of Mathematics.

National Mathematics Advisory Panel (2008).  Foundations for success: Final report of the National Mathematics Advisory Panel.  Washington, DC: U.S. Department of Education.

Silver, E. A., & Kenney, P. A. (Eds.). (2000). Results from the seventh mathematics assessment of the National Assessment of Education Progress. Reston, VA: National Council of Teachers of Mathematics.