Student Learning in Mathematics and Science

1 Grade 12 mathematics data are presented from 2005 only because the grade 12 mathematics framework was substantially revised in 2005, making prior assessment results not comparable with those in or after 2005.

2 Science data are presented beginning in 2009 only because the science framework was substantially revised in 2009, making prior assessment results not comparable with those in or after 2009.

3 The NAGB, as directed by NAEP legislation, has been developing achievement levels for NAEP since 1990. A broadly representative panel of teachers, education specialists, and the public help define and review achievement levels. As provided by law, the achievement levels are to be used on a trial basis and should be interpreted and used with caution. More information about NAEP achievement levels is available at

4 TIMSS required participating countries and other education systems to draw probability samples of students who were nearing the end of their fourth or eighth year of formal schooling. In the United States, one sample was drawn to represent the nation at grade 4 and another at grade 8. The U.S. national sample included public and private schools, randomly selected and weighted to be representative of the nation at grade 4 and at grade 8.

5 TIMSS Advanced required participating countries and other education systems to draw probability samples of students in their final year of secondary school who were taking or had taken courses in advanced mathematics or physics. In the United States, two samples of twelfth graders were drawn to represent the nation—one for advanced mathematics and one for physics. The courses that defined the target populations had to cover most, if not all, of the advanced mathematics and physics topics that were outlined in the assessment frameworks. In the United States, this was defined as a calculus course for eligibility for the advanced mathematics population and an advanced physics course, such as AP physics, for the physics population. The U.S. national samples included public and private schools, randomly selected and weighted to be representative of the nation’s advanced mathematics and physics coursetakers at the end of high school.

6 Non-national entities that are not IEA member countries (e.g., Abu Dhabi, Buenos Aires) may participate in TIMSS to assess their comparative international standing. These entities are designated as “benchmarking participants.”

7 Results presented here are for 48 education systems at grade 4 and 37 at grade 8 because Armenia is excluded. Although Armenia did participate in TIMSS 2015 at grades 4 and 8, the country's results are not reported by TIMSS because the data are not comparable for trend analysis.

8 The scores are reported on a scale from 0 to 1,000, with the TIMSS scale average set at 500 and the standard deviation set at 100.

9 The TIMSS results presented in this report exclude individual U.S. states, Canadian provinces, Abu Dhabi, Buenos Aires, and Dubai. These states and provinces participated in 2015 TIMSS as “benchmarking participants” to assess the comparative international standing of their students’ achievement and to view their curriculum and instruction in an international context.

10 For additional details, see the Technical Notes available at

11 Of the 73 education systems that participated in PISA 2015, results for three of these—Argentina, Kazakhstan, and Malaysia—are not included due to technical issues with their samples that prevent results from being discussed in this report.

12 Developing countries in this report are any countries that do not appear on the International Monetary Fund list of “advanced economies.”

13 The PISA mathematics assessment was also conducted in 2000 but, because the framework for the mathematics assessment was revised in 2003, it is not appropriate to compare results from the 2000 assessment with subsequent PISA mathematics assessments. Similarly, the framework for the PISA science assessment was changed in 2000 and in 2003, preventing comparisons of results in 2000 or 2003 with science literacy scores from subsequent years.

High School Coursetaking in Mathematics and Science

1 One credit is equivalent to a 1-year course of instruction.

2 The cost of taking an AP exam was $93 per exam in 2017, a fee that might be prohibitive for low-income families and may affect equity of access to the exams. ESSA ended a federal grant program that had subsidized the cost of AP exams for students from low-income families for 17 years, adding to concerns about financial barriers to AP exam access. For more information, see

3 “High/low black and Latino enrollment” refers to schools with more than 75% and less than 25% black and Latino student enrollment, respectively, as defined and reported by the U.S. Department of Education’s Office for Civil Rights.

Teachers of Mathematics and Science

1 The Teachers of Mathematics and Science section from Science and Engineering Indicators 2016 can be accessed at

2 Special tabulations (2016) using Schools and Staffing Survey PowerStats tool are available at

Instructional Technology and Digital Learning

1 The Federal Communication Commission short-term goal is 100 Mbps per 1,000 students. The long-term goal is 1 Gbps per 1,000 students.

2 The global education nonprofit, Project Tomorrow, conducts the annual Speak Up Research Project, which polls K–12 students, parents, and educators about the role of technology in learning in and out of school. In fall 2014, Project Tomorrow surveyed 431,231 K–12 students, 35,337 parents, 41,805 teachers, 680 district administrators, and 3,207 school administrators representing 8,216 public and private schools from 2,676 districts. Schools from urban (30%), suburban (30%), and rural (40%) communities were represented. Just over one-half of the schools (56%) that participated in Speak Up 2014 were Title I eligible schools (an indicator of student population poverty). In fall 2015, Project Tomorrow surveyed 415,686 K–12 students, 38,613 teachers and librarians, 4,536 administrators, and 40,218 parents representing more than 7,600 public and private schools and 2,600 districts. Schools from urban (25%), suburban (40%), and rural (35%) communities were represented. Just over one-half of the schools (58%) that participated in Speak Up 2015 were Title I–eligible schools.

Transition to Higher Education

1 To calculate the ACGR, states identify the “cohort” of first-time ninth graders in a particular school year and adjust this number by adding any students who transfer into the cohort after ninth grade and subtracting any students who transfer out, emigrate to another country, or die. The ACGR is the percentage of the students in this cohort who graduate with a high school diploma within 4 years. The AFGR uses aggregate student enrollment data to estimate the size of an incoming freshman class, which is the sum of eighth grade enrollment in the first year, ninth grade enrollment for the next year, and tenth grade enrollment for the year after, and then dividing by three. The AFGR is the number of high school diplomas awarded 4 years later divided by the estimated incoming freshman class size.

2 The earlier editions of Science and Engineering Indicators reported U.S. high school graduation rates based on AFGR because the student-level records needed to calculate the ACGR were not available at a state level until recent years.

3 See for a definition of economically disadvantaged.

4 Upper secondary education, as defined by the OECD, corresponds to high school education in the United States. In calculating the U.S. graduation rates, the OECD included only students who earned a regular diploma and excluded those who completed a GED certificate program or other alternative forms of upper secondary education. The OECD defines the typical graduation age as the age of the students at the beginning of the school year: when they graduate at the end of the school year, students will generally be 1 year older than the age indicated. According to the OECD, the typical graduation age in the United States is 17 years old. The U.S. high school graduation rates calculated by the OECD cannot be directly compared with U.S. on-time graduation rates because of the different population bases and calculation methods for the two measures.

5 International comparisons are often difficult because of differences among education systems, types of degrees awarded across countries, and definitions used in different countries. Some researchers have pinpointed various problems and limitations of international comparisons and warned readers to interpret data, including those published by the OECD, with caution (Adelman 2008; Wellman 2007).