Mathematics Proficiency

Publication Date:

Nov 30, 2015


09_fig1After years of steady gains, mathematics scale scores decreased in 2015 for both fourth- and eighth-graders. Between 1990 and 2013, average mathematics scale scores rose from 213 to 242 for fourth-graders, and from 263 to 285 for eighth-graders. In 2015, scores had fallen to 240 among fourth-graders, and 282 among eighth-graders. For fourth-graders, there were significant increases in every year up to 2013, except between 1996 and 2000, and between 2007 and 2009, when scores stayed level. Average scores for eighth-graders increased between each test year until 2013. (Figure 1)

Math proficiency scores for twelfth-graders rose between 1990 and 2000, from 294 to 300.[1] In 2005, a new mathematics framework was developed for twelfth-grade students, using a 0-to-300 scale, instead of the 0-to-500 scale used in previous years. Despite this scoring change, a government study found that there was a probable increase in math ability for twelfth-grade students from 2000 to 2005.[2]  The average score for all twelfth-grade students increased between 2005 and 2009, from 150 to 153, but remained steady at 153 in 2013. (Figure 1)

Differences by Race and Hispanic Origin[3]

09_fig2Overall, scores have been rising for all race and ethnicity groups, although white students continue to outscore their black, Hispanic, and American Indian peers. Gaps by race/Hispanic origin are greater in eighth grade than in fourth or twelfth grades.  (Appendix 1, Appendix 2, and Appendix 3)

In the most recent year available (2013 for twelfth-graders, 2015 for younger students), Asian students had the highest math scores at all grade levels, followed by white students. Black students had the lowest math scores at all grade levels. Hispanic and American Indian students had scores between white and black students at all grade levels, and, among fourth-graders, Hispanic students had higher average scores than American Indian students. For example, among eighth-grade students, Asian students had an average scale score of 306, compared with 292 for white students, 270 and 267 for Hispanic and American Indian students, respectively, and 260 for black students. (Figure 2 and Appendix 3)

In 2015, fourth-grade scores fell significantly only among white students (two points), with no significant change for students of other races or Hispanic origin. Eighth-grade scores fell the most among black students (three points), followed by white and Hispanic students (two points, each). The eighth-grade scores for American Indian and Asian students remained steady between 2013 and 2015. (Appendix 1, Appendix 2, and Appendix 3)

Differences by Parental Education

09_fig3Children of parents with high levels of education have higher math scores than other children. In 2015, eighth-graders whose parents had graduated college had an average score 29 points higher than students whose parents had not finished high school, and 26 points higher than students whose parents had a high school degree only. (Figure 3)

In 2013, Twelfth-grade students whose parents graduated college had an average scale score of 164, compared with 139 for students of parents with a high school degree, and 137 for students of parents with less than a high school degree. (Appendix 3)

Differences by Gender

Male students in fourth grade scored slightly higher than female students (241 versus 239, respectively) in 2015. Similarly, in 2013, male students in twelfth grade scored slightly higher than female students (155 and 152, respectively). (Appendix 1 and Appendix 3)  There was no gender difference at eighth grade in 2013 or 2015.  (Appendix 2)

Other Estimates

State and Local Estimates

2015 mathematics estimates for 4th-and 8th-graders for all states are available from the National Center for Education Statistics.

2015 estimates for 4th-and 8th-graders in 22 large urban districts participating in NAEP are also available.

There are also several estimates of math proficiency available from the KIDS COUNT Data Center.

International Estimates

International estimates for fourth- and eighth-grade mathematics proficiency are available from the Trends in International Mathematics and Science Study (TIMSS) 2011 report.

Twelfth-grade assessments from TIMSS (1995) are also available.

International comparisons of mathematics literacy from the Organization for Economic Cooperation and Development’s (OECD) Program for International Student Assessment (PISA) for 15 year olds in 2009 are available in the Performance of U.S. 15-Year-Old Students in Reading, Mathematics, and Science Literacy in an International Context report.

Data and Appendices

Data Sources

U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics. National Assessment of Educational Progress Reading and Mathematics Assessments (NAEP), 2015, 2013, 2011, 2009, 2007, 2005, 2003, 2000, 1996, 1992, and 1990 Mathematics Assessments. Accessed through the NAEP Data Explorer at

Raw Data Source

National Assessment of Educational Progress Mathematics Assessments


Appendix 1 – Mathematics Scores3 Among U.S. Students in Grade 4: Selected Years, 1990-2015
Appendix 2 – Mathematics Scores3 Among U.S. Students in Grade 8: Selected Years, 1990-2015
Appendix 3 – Mathematics Scores3 Among U.S. Students in Grade 12: Selected Years, 1990-2013



Mathematics proficiency is defined as performance on the National Assessment of Educational Progress (NAEP) main assessment and is measured by average scale scores.  Scale scores range from 0 to 500, with a standard deviation of 100.  In 2005, a new mathematics framework was adopted for twelfth-graders, with scale scores ranging from 0 to 300.

Each grade level and each subject area has criteria for achievement-level, categorized as basic, proficient, or advanced. This represents what students should know.

For more information on the abilities expected for each level, see the Nation’s Report Card.

Fourth Grade

  • Basic (214-248)
  • Proficient (249-281)
  • Advanced (282-500)

Eighth Grade

  • Basic (262-298)
  • Proficient (299-332)
  • Advanced (333-500)

Twelfth Grade

  • Basic (141-175)
  • Proficient (176-215)
  • Advanced (216-300)


[1]In 1996, NAEP started allowing testing accommodations for students with disabilities and for limited English proficient students.  Accommodations may include extra time, one-on-one administration, use of magnifying equipment, translation of assessments, or the use of bilingual dictionaries and are determined by state and district policies.  Beginning in 2002, all NAEP assessments allow accommodations.

[2]Diaz, T. E., Le, H. A., and Wise, L. L. (2006).  NAEP-QA FY06 special study: 12th
grade math trend estimates. Washington, DC: U.S. Department of Education,
National Center for Education Statistics Available at:

[3]Hispanics may be any race. Note that none of the race groups in this report include Hispanics of those races, and that the Asian race group includes Pacific Islanders as well.

Suggested Citation

Child Trends Databank. (2015). Mathematics proficiency. Available at: