Updated: Mathematics Proficiency
Average mathematics scale scores 1 for students in grades four and eight improved almost every year between 2000 and 2013, but decreased between 2013 and 2015. Twelfth-graders scores improved slightly between 2005 and 2009, but remained the same for 2013 as they were in 2009. Importance Competence in mathematics is essential for functioning in everyday life, as well as for success in our increasingly technology-based workplace. Students who take higher-level mathematics and science courses which require strong fundamental skills in mathematics are more likely to attend and to complete college. 2,3 One study of high school females found that one difference between those who later dropped out of high school and those who graduated was lower math scores among the former group. 4 The importance of mathematics extends beyond the academic domain. Young people who transition to adulthood with limited mathematics skills are likely to find it difficult to function in society. Basic arithmetic skills are required for everyday computations, and sometimes for job applications. 5 Additionally, competence in mathematics skills is related to higher levels of employability. 6,7,8,9 Since 1976, the influence of high school students mathematics skills on later earnings has grown steadily. 10,11 2 P a g e
Average scale score Mathematics Proficiency Trends After years of steady gains, mathematics scale scores decreased in 2015 for both fourth- and eighthgraders. Between 1990 and 2013, average mathematics scale scores rose from 213 to 242 for fourthgraders, 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. 12 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. 13 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) Figure 1 350 Average Scale Scores in Mathematics for Fourth-, Eighth-, and Twelfth-Grade Students: 1990-2015 300 250 200 150 100 294 304 285 Twelfth Grade* 302 300 263 272 Eighth Grade 270 279 282 213 224 Fourth Grade 224 238 242 240 Twelfth Grade* 150 153 153 50 No Accommodations permitted Accommodations Permitted 0 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 *Note: In 2005, a new mathematics framework was developed for twelfth -grade scores on a 0-to-300 scale, instead of the 0-to- 500 scale which was used in previous years, therefore, scores between the two periods are not comparable. Source: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics. National Assessment of Educational Progress Mathematics Assessments (NAEP), 2009, 2007, 2005, 2003, 2000, 1996, 1992, and 1990 Mathematics Assessments. Accessed through the NAEP Data Explorer, at http://nces.ed.gov/nationsreportcard/naepdata/. 3 P a g e
Average Scale Score Mathematics Proficiency Differences by Race and Hispanic Origin 14 Overall, 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. (Appendices 1, 2, and 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, Appendix 3) Figure 2 500 Average Scale Scores in Mathematics for Fourth- and Eighth-Grade Students, by Race and Hispanic Origin: 2015 400 White Black Hispanic Asian American Indian 300 248 224 230 257 227 292 260 270 306 267 200 100 0 Fourth Grade Eighth Grade Source: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics. National Assessment of Educational Progress Mathematics Assessments (NAEP), 2015 Mathematics Assessments. Accessed through the NAEP Data Explorer, at http://nces.ed.gov/nationsreportcard/naepdata/ 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 4 P a g e
Average Scale Score Mathematics Proficiency 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. (Appendices 1, 2, and 3) Differences by Parental Education Children 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) Figure 3 400 Average Mathematics Scale Scores of Eighth-Grade Students, by Parent's Education: 2015 320 265 268 282 294 240 160 80 0 Less than high school Graduated high school Some education after high school Graduated college Source: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics. National Assessment of Educational Progress Mathematics Assessments (NAEP), 2009 Mathematics Assessments. Accessed through the NAEP Data Explorer, at http://nces.ed.gov/nationsreportcard/naepdata/ 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 5 P a g e
152, respectively). (Appendices 1 and 3) There was no gender difference at eighth grade in 2013 or 2015. (Appendix 2) State and Local Estimates 2015 mathematics estimates for 4 th -and 8 th -graders for all states are available at: http://nces.ed.gov/nationsreportcard/states/ 2015 estimates for 4 th -and 8 th -graders in 22 large urban districts participating in NAEP are available at http://nces.ed.gov/nationsreportcard/districts/ There are also several estimates of math proficiency available from the KIDS COUNT Data Center: http://datacenter.kidscount.org/data#usa/2/8/13 International Estimates International estimates for fourth- and eighth-grade mathematics proficiency from the Trends in International Mathematics and Science Study (TIMSS) 2011 report are available at: http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2013009 Twelfth-grade assessments from TIMSS (1995) are available at: http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=98049 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 at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2011004 6 P a g e
National Goals The No Child Left Behind Act, signed into law in January 2002, requires states to set performance standards for multiple subjects, including mathematics, and requires that each state measure students progress in mathematics and reading every year from grades 3 to 8, and at least once in grades 10 to 12. Each state is expected to make adequate yearly progress toward meeting standards, and all children are expected to meet or exceed minimum proficiency standards, as defined by the state, within twelve years (by 2014). For more information visit: http://www.ed.gov/nclb/methods/math/math.html Related Indicators Reading proficiency: www.childtrends.org/?indicators=reading-proficiency Science proficiency: www.childtrends.org/?indicators=science-proficiency Writing proficiency: www.childtrends.org/?indicators=writing-proficiency Definition 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 http://nces.ed.gov/nationsreportcard/mathematics/achieveall.asp. 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) 7 P a g e
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 http://nces.ed.gov/nationsreportcard/naepdata/ Raw Data Source National Assessment of Educational Progress Mathematics Assessments http://nces.ed.gov/nationsreportcard/mathematics/ 8 P a g e
Appendix 1 - Mathematics Scores 3 Among U.S. Students in Grade 4: Selected Years, 1990-2015 1990 1992 1996 1996 2000 2003 2005 2007 2009 2011 2013 2015 No Accommodations Permitted 1 Accommodations Permitted 1 Total 213 220 224 224 226 235 238 240 240 241 242 240 Gender Male 214 221 226 224 227 236 239 241 241 241 242 241 Female 213 219 222 223 224 233 237 239 239 240 241 239 Race/Hispanic Origin 2 White 220 227 232 231 234 243 246 248 248 249 250 248 Black 188 193 199 198 203 216 220 222 222 224 224 224 Hispanic 200 202 205 207 208 222 226 227 227 229 231 230 Asian/Pacific Islander * 231 226 229 * 246 251 253 255 256 258 257 American Indian * * * * * 223 226 228 225 225 227 227 Free/Reduced-Price School Lunch Program Eligibility Eligible - - 207 207 208 222 225 227 227 229 230 229 Not eligible - - 231 232 235 244 248 249 250 252 254 253 Information not available - - 233 231 237 241 244 246 246 249 249 248 Type of School Public 212 219 222 222 224 234 237 239 239 240 241 240 Nonpublic 224 228 237 235 238 244-246 246 247 246-9 P a g e
1990 1992 1996 1996 2000 2003 2005 2007 2009 2011 2013 2015 No Accommodations Permitted 1 Accommodations Permitted 1 Type of Location City - - - - - - - 235 235 236 237 237 Suburb - - - - - - - 244 243 244 245 243 Town - - - - - - - 238 238 237 241 238 Rural - - - - - - - 240 241 243 243 241 Percentile 10 th 171 177 182 182 184 197 200 202 202 203 203 202 25 th 193 199 204 203 205 216 220 222 221 222 222 221 50 th 214 221 226 225 227 236 239 242 241 242 243 242 75 th 235 242 246 245 248 255 258 260 260 261 262 261 90 th 253 259 262 262 265 270 273 275 275 276 278 277 "-" Indicates data not available *Sample size was insufficient to permit reliable estimates. 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. 2 Note that none of the race groups include Hispanics of those races. 3 Scale scores range from 0 to 500, with a standard deviation of 100. Source: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics. National Assessment of Educational Progress Mathematics Assessments (NAEP), 2015, 2013, 2011, 2009, 2007, 2005, 2003, 2000, 1996, 1992, and 1990 Mathematics Assessments. Accessed through the NAEP Data Explorer, at http://nces.ed.gov/nationsreportcard/naepdata/ 10 P a g e
Appendix 2 - Mathematics Scores 3 Among U.S. Students in Grade 8: Selected Years, 1990-2015 1990 1992 1996 1996 2000 2003 2005 2007 2009 2011 2013 2015 No Accommodations Accommodations Permitted 1 Permitted 1 Total 263 268 272 270 273 278 279 281 283 284 285 282 Gender Male 263 268 272 271 274 278 280 282 284 284 285 282 Female 262 269 272 269 272 277 278 280 282 283 284 282 Race/Hispanic Origin 2 White 270 277 281 281 284 288 289 291 293 293 294 292 Black 237 237 242 240 244 252 255 260 261 262 263 260 Hispanic 246 249 251 251 253 259 262 265 266 270 272 270 Asian/Pacific Islander * 290 * * 288 291 295 297 301 303 306 306 American Indian * * * * * 263 264 264 266 265 269 267 Free/Reduced-Price School Lunch Program Eligibility Eligible - - 252 250 253 259 262 265 266 269 270 268 Not eligible - - 280 277 283 287 288 291 294 296 297 296 Information not available - - 280 285 276 285 289 291 295 296 297 294 Parent's Education Did not finish high school Graduated high school Some education after high school 242 249 254 250 253 257 259 263 265 265 267 265 255 257 261 260 261 267 267 270 270 271 270 268 267 271 279 277 277 280 280 283 284 285 285 282 Graduated college 274 281 282 281 286 288 290 292 295 295 296 294 Unknown 241 252 254 252 254 259 260 263 264 265 266 263 Type of School Public 262 267 271 269 272 276 278 280 282 283 284 281 Nonpublic 271 281 284 285 286 292-293 296 296 296-11 P a g e
Type of Location 1990 1992 1996 1996 2000 2003 2005 2007 2009 2011 2013 2015 No Accommodations Accommodations Permitted 1 Permitted 1 City - - - - - - - 275 279 279 280 278 Suburb - - - - - - - 286 287 287 289 286 Town - - - - - - - 280 279 282 282 279 Rural - - - - - - - 282 284 286 286 282 Percentile 10 th 215 221 224 221 223 230 231 235 236 237 237 235 25 th 239 243 248 245 249 254 255 258 259 260 261 258 50 th 264 269 273 273 275 279 280 283 284 285 286 283 75 th 288 294 298 297 300 303 304 306 308 309 310 308 90 th 307 315 317 316 320 323 324 327 329 329 331 329 "-" Indicates data not available *Sample size was insufficient to permit reliable estimates. 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. 2 Note that none of the race groups include Hispanics of those races. 3 Scale scores range from 0 to 500, with a standard deviation of 100. Source: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics. National Assessment of Educational Progress Mathematics Assessments (NAEP), 2015, 2013, 2011, 2009, 2007, 2005, 2003, 2000, 1996, 1992, and 1990 Mathematics Assessments. Accessed through the NAEP Data Explorer, at http://nces.ed.gov/nationsreportcard/naepdata/ 12 P a g e
Appendix 3 - Mathematics Scores 3 Among U.S. Students in Grade 12: Selected Years, 1990-2013 1990 1992 1996 1996 2000 2005** 2009 2013 No Accommodations Accommodations Permitted 1 Permitted 1 Total 294 299 304 302 300 150 153 153 Gender Male 297 301 305 303 302 151 155 155 Female 291 298 303 300 299 149 152 152 Race/Hispanic Origin 2 White 300 305 311 309 307 157 161 162 Black 268 275 280 275 273 127 131 132 Hispanic 276 286 287 284 282 133 138 141 Asian/Pacific Islander 311 312 312 305 315 163 175 172 American Indian - - 284* - 294* 134 144 142 Free/Reduced-Price School Lunch Program Eligibility Eligible - - 281 280 279 132 137 139 Not eligible - - 307 306 304 155 160 162 Information not available Parent's Education Did not finish high school - - 308 303 303 162 159 163 272 278 282 280 278 130 135 137 Graduated high school 283 288 294 290 287 138 142 139 Some education after high school 297 299 302 302 299 148 150 152 Graduated college 306 311 314 313 312 161 164 164 Unknown 269 277 275 269 274 123 129 127 Type of School Public 294 297 303 301 300 149 152 152 Nonpublic 300 314 314 310 315 - - - 13 P a g e
Type of Location 1990 1992 1996 1996 2000 2005** 2009 2013 No Accommodations Accommodations Permitted 1 Permitted 1 City - - - - - - 152 149 Suburb - - - - - - 157 158 Town - - - - - - 151 151 Rural - - - - - - 151 153 Percentile 10 th 247 254 261 257 254 105 110 111 25 th 270 276 282 279 276 127 130 131 50 th 296 301 305 302 301 151 154 154 75 th 319 324 327 326 325 174 177 177 90 th 339 343 345 344 346 194 197 197 "-" Indicates data not available. *The nature of the sample does not allow accurate determination of the variability of the statistic. **In 2005, a new mathematics framework was developed on a 0 to 300 scale, instead of the 0 to 500 scale which was used in previous years, therefore, scores are incomparable. 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. 2 Note that none of the race groups include Hispanics of those races. 3 Scale scores range from 0 to 500, with a standard deviation of 100. Source: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics. National Assessment of Educational Progress Mathematics Assessments (NAEP), 2013, 2009, 2005, 2003, 2000, 1996, 1992, and 1990 Mathematics Assessments. Accessed through the NAEP Data Explorer, at http://nces.ed.gov/nationsreportcard/naepdata/ 14 P a g e
Endnotes 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 Adelman, C. (1999). Answers in the Tool Box: Academic Intensity, Attendance Patterns, and Bachelor's Degree Attainment. Washington, DC: Office of Education Research and Improvement, U.S. Department of Education. Available at: http://www.ed.gov/pubs/toolbox/index.html 3 Attawell, P., & Domina, T. (2008). Raising the bar: Curricular intensity and academic performance. Educational Evaluation and Policy Analysis, 30(1), 51-71 4 Tyler, John H., Murname, R. J., and Willett, J. B. (2002). Who benefits from a GED? Evidence for females from High School and Beyond. Economics of Education Review, 22, 237-247. 5 Kirsch, I., Jungeblut, A., Jenkins, L. & Kolstad, A. (1993). Adult literacy in America: A first look at the findings of the National Adult Literacy Survey. Washington, DC: National Center for Education Statistics. [On-line]. Available at: http://nces.ed.gov/pubs93/93275.pdf 6 Riley, R. W. (1998). The state of mathematics education: Building a strong foundation for the 21 st century. Speech given at the Conference of the American Mathematical Society and the Mathematical Association of America, January 8,1998. 7 Murname, R. J., Willett, J. B., Braatz, M. J., and Duhaldeborde, Y. (2001). Do different dimensions of male high school students skills predict labor market success a decade later? Evidence from the NLSY. Economics of Education Review 20, 311-320. 8 Finnie, R. & Meng, R. (2006). The importance of functional literacy: Reading and math skills and labour market outcomes of high school drop-outs. Statistics Canada. Available at: http://www.statcan.gc.ca/pub/11f0019m/11f0019m2006275-eng.pdf. 9 Tyler, J. H. (2004). Basic skills and the earnings of dropouts. Economics of Education Review, 23(3), 221-235. 10 Murnane, R., Wilett, J., and Levy, F. (1995). The growing importance of cognitive skills in wage determination. The Review of Economics and Statistics, 77(2): 251-266. 11 Reyna, V. F. & Brainerd, C. J. (2007). The importance of mathematics in health and human judgment: Numeracy, risk communication, and medical decision making. Learning and Individual Differences, 17(2), 147-159. 12 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 15 P a g e
of assessments, or the use of bilingual dictionaries and are determined by state and district policies. Beginning in 2002, all NAEP assessments allow accommodations. 13 Diaz, T. E., Le, H. A., and Wise, L. L. (2006). NAEP-QA FY06 special study: 12 th grade math trend estimates. Washington, DC: U.S. Department of Education, National Center for Education Statistics Available at: http://new.humrro.org/finalreports/naep12mathtrends.pdf 14 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. 16 P a g e