Mathematics Proficiency

Publication Date:

Nov 30, 2015

Key facts about mathematics proficiency

  • From 1990 to 2013, average scale scores[1] in mathematics for fourth and eighth graders increased steadily; but scores have declined slightly since 2013.
  • From 2003 to 2017, among fourth and eighth graders, Asian/Pacific Islander students had the highest average scores, followed by white students. Scores at twelfth grade followed similar trends.
  • In 2017, students whose parents with higher levels of education had higher math scores than students with less well-educated parents.


After years of steady gains, mathematics scale scores for both fourth and eighth graders declined in 2015 and remained stable in 2017. From 1990 to 2013, scores rose from 213 to 242 for fourth graders, and from 263 to 285 for eighth graders. In 2017, scores had fallen to 240 among fourth graders, and 283 among eighth graders. For fourth graders, there were significant increases in every successive test year up to 2013, except from 2007 to 2009, when scores remained the same. Average scores for eighth graders also increased each successive test year until 2013 (Appendices 1 & 2).

Math proficiency scores for twelfth graders rose from 1990 to 2000, from 294 to 300.[2] 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 between 2000 and 2005.[3] The average score for all twelfth grade students increased from 2005 to 2009, from 150 to 153, remained steady at 153 in 2013, and declined slightly to 152 in 2015 (Appendix 3).

Differences by Race and Hispanic Origin*

Historically, black, Hispanic, and American Indian students have had their access to high-quality educational opportunities seriously restricted. Laws, policies, and practices served to keep their families, for the most part, in conditions of poverty, unable to afford the books and other educational materials and experiences that prepare young children for academic success. Many students of color continue to attend schools that lack many of the resources and experienced teaching and support staff that are typical of schools that serve primarily white students.[4]

Overall, from 1990 to 2017, scores rose for all tabulated racial and ethnic groups, although white students continued to outscore their Hispanic, American Indian, and black peers. Gaps by race/Hispanic origin were greater in eighth grade than in fourth or twelfth grades (Appendices 1, 2, and 3).

In the most recent year available (2015 for twelfth graders, 2017 for younger students), Asian/Pacific Islander 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. For example, in 2017, among eighth grade students, Asian/Pacific Islander students had an average scale score of 310, compared with 293 for white students, 269 and 267 for Hispanic and American Indian students, respectively, and 260 for black students (Figure 2, Appendix 3). Compared to 2015 math scores, fourth grade scores in 2017 remained nearly unchanged. The scores for eighth graders followed the same trend, except that scores for Asian/Pacific Islander students increased by 4 points (Appendices 1, 2, and 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.

Differences by Parental Education

Children whose parents have greater levels of education have higher math scores than other children. In 2017, eighth graders whose parents had graduated college had an average score 29 points higher than students whose parents had not finished high school, and 27 points higher than students whose parents had a high school degree only (Figure 3). In 2015 (the latest data available), twelfth grade students whose parents graduated college had an average scale score of 163, compared with 139 for students of parents with a high school degree, and 133 for students of parents without a high school degree (Appendix 3).

Differences by Gender

In 2017, male students in fourth and eighth grades scored slightly higher than their female counterparts (241 versus 239, and 283 versus 282, respectively). Similarly, in 2015, male students in twelfth grade scored slightly higher than females (153 versus 150) (Appendices 1, 2, and 3).

Other Estimates

State and Local Estimates

International Estimates

Data and Appendices

Data Sources

U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics. National Assessment of Educational Progress (NAEP), 2017, 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



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

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] Scale scores are derived from student responses to assessment items, summarizing the overall level of performance.  While NAEP does not report scale scores for individual students, NAEP does produce summary statistics describing scale scores for groups of students.  NAEP subject-area scales typically range from 0 to 500 (reading, fourth- and eighth-grade mathematics, U.S. history, and geography) or from 0 to 300 (science, writing, twelfth-grade mathematics, and civics).

[2] 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.

[3] 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:

[4] The Annie E. Casey Foundation. (2014). Race for results: Building a path to opportunity for all children. KIDS COUNT Policy Report. Retrieved from

Suggested Citation

Child Trends DataBank. (2019). Mathematics proficiency. Available at: