## Student Learning in Mathematics and Science

Policymakers, legislators, and educators in the United States strive to increase academic achievement for *all* students. Education reform efforts focus on improving the performance of low-achieving students and on increasing the number and diversity of high-achieving students (Estrada et al. 2016; Museus 2011). Policymakers view proficiency in STEM fields as vital to the nation’s economic growth and emphasize improving student learning in STEM disciplines as a result (Atkinson and Mayo 2010; Committee on STEM Education 2018; Noonan 2017a; Peri, Shih, and Sparber 2015). This section presents indicators of U.S. students’ performance in STEM subjects in elementary and secondary school, beginning with students’ performance in mathematics and science from kindergarten through fifth grade. Next, it presents trends in mathematics performance for eighth graders from 1990 to 2017 and summarizes performance on science and technology and engineering assessments. Finally, it examines U.S. achievement in an international context and explores the certification and experience of eighth grade mathematics teachers.

### Mathematics and Science Knowledge in the Early Grades

Children begin learning STEM-related material as soon as they enter school, and their early experience and achievement in mathematics and science may affect their attitudes about, and confidence in, STEM subjects for the rest of their school careers (Maltese and Tai 2010; McClure et al. 2017). However, students typically do not begin schooling on an equal footing: kindergarten assessments reveal differences in mathematics and science achievement by SES and race or ethnicity and some of these gaps persist as students’ schooling continues (Friedman-Krauss, Barnett, and Nores 2016; García 2015). Research suggests a variety of factors contribute to the early gaps among demographic groups, including less access to informal learning opportunities and high-quality preschool (García and Weiss 2017). In a national sample of elementary school children, the mathematics score gap between low- and high-SES students was 9 points at the beginning of kindergarten and 13 points in the spring of fifth grade (Figure 1-1). The gap between white and black students was 7 points at the beginning of kindergarten and 16 points in the spring of fifth grade, and the gap between white and Hispanic students was 8 points in kindergarten and 10 points in fifth grade (Figure 1-2). Asian students scored slightly higher than white students in mathematics both in kindergarten and fifth grade.

#### Average mathematics assessment test scores of children who were in kindergarten for the first time during the 2010–11 school year and in grade 5 during the 2015–16 school year, by family poverty level

###### Note(s):

The possible range of scores for the mathematics assessment was 0–159. The fall kindergarten mathematics scores have a mean of 36.8 and a standard deviation of 11.23, and the spring grade 5 mathematics scores have a mean of 121.4 and a standard deviation of 15.90. Poverty status is based on 2010 U.S. Census poverty thresholds, which identify incomes determined to meet household needs, given family size. For example, in 2010, a family of two was below the poverty threshold if its income was lower than $14,220.

###### Source(s):

Mulligan GM, McCarroll JC, Flanagan KD, and McPhee C*, Findings From the Fifth-Grade Round of the Early Childhood Longitudinal Study, Kindergarten Class of 2010–11 (ECLS-K:2011), *NCES 2019-130 (2019). See Table S1-1.

*Science and Engineering Indicators*

#### Average mathematics assessment test scores of children who were in kindergarten for the first time during the 2010–11 school year and in grade 5 during the 2015–16 school year, by race or ethnicity

###### Note(s):

The possible range of scores for the mathematics assessment was 0–159. The fall kindergarten mathematics scores have a mean of 36.8 and a standard deviation of 11.23, and the spring grade 5 mathematics scores have a mean of 121.4 and a standard deviation of 15.90. Hispanic may be any race; race categories exclude Hispanic origin.

###### Source(s):

Mulligan GM, McCarroll JC, Flanagan KD, and McPhee C*, Findings From the Fifth-Grade Round of the Early Childhood Longitudinal Study, Kindergarten Class of 2010–11 (ECLS-K:2011), *NCES 2019-130 (2019). See Table S1-1.

*Science and Engineering Indicators*

The patterns for science achievement gaps were largely similar to those of mathematics (Table 1-1). The science score gap between low- and high-poverty students was 7 points in kindergarten and 10 points in fifth grade (Figure 1-3). White students’ science scores were higher than black and Hispanic students’ scores in both kindergarten (by 6 points and 7 points, respectively) and fifth grade (by 11 points and 7 points, respectively), although the gap between Hispanic and white students did not change during that time, remaining at 7 points (Figure 1-4). Unlike patterns seen in mathematics, Asian students’ science scores were lower than those of white students in kindergarten (32 versus 37); by fifth grade, however, Asian students had caught up to white students, with both groups scoring 78 points.

#### Average mathematics and science assessment test scores of children who were in kindergarten for the first time during the 2010–11 school year and in grade 5 during the 2015–16 school year, by child and family characteristics

^{a} Hispanic may be any race; race categories exclude Hispanic origin.

^{b} Poverty status is based on 2010 U.S. Census poverty thresholds, which identify incomes determined to meet household needs, given family size. For example, in 2010, a family of two was below the poverty threshold if its income was lower than $14,220.

###### Note(s):

Mathematics was first assessed in kindergarten in fall 2010. Science was first assessed in kindergarten in spring 2011. The possible range of scores for the mathematics assessment was 0–159. The fall kindergarten mathematics scores have a mean of 36.8 and a standard deviation of 11.23, and the spring fifth-grade mathematics scores have a mean of 121.4 and a standard deviation of 15.90. The possible range of scores for the science assessment was 0–100. The spring kindergarten science scores have a mean of 34.4 and a standard deviation of 7.28, and the spring grade 5 science scores have a mean of 74.7 and a standard deviation of 11.76.

###### Source(s):

Mulligan GM, McCarroll JC, Flanagan KD, and McPhee C, *Findings From the Fifth-Grade Round of the Early Childhood Longitudinal Study, Kindergarten Class of 2010–11 (ECLS-K:2011)*, NCES 2019-130 (2019). See Table S1-1.

*Science and Engineering Indicators*

#### Average science assessment test scores of children who were in kindergarten for the first time during the 2010–11 school year and in grade 5 during the 2015–16 school year, by family poverty level

###### Note(s):

The possible range of scores for the science assessment was 0–100. The spring kindergarten science scores have a mean of 34.4 and a standard deviation of 7.28, and the spring grade 5 science scores have a mean of 74.7 and a standard deviation of 11.76. Poverty status is based on 2010 U.S. Census poverty thresholds, which identify incomes determined to meet household needs, given family size. For example, in 2010, a family of two was below the poverty threshold if its income was lower than $14,220.

###### Source(s):

Mulligan GM, McCarroll JC, Flanagan KD, and McPhee C*, Findings From the Fifth-Grade Round of the Early Childhood Longitudinal Study, Kindergarten Class of 2010–11 (ECLS-K:2011)*,* *NCES 2019-130 (2019). See Table S1-1.

*Science and Engineering Indicators*

#### Average science assessment test scores of children who were in kindergarten for the first time during the 2010–11 school year and in grade 5 during the 2015–16 school year, by race or ethnicity

###### Note(s):

The possible range of scores for the science assessment was 0–100. The spring kindergarten science scores have a mean of 34.4 and a standard deviation of 7.28, and the spring grade 5 science scores have a mean of 74.7 and a standard deviation of 11.76. Hispanic may be any race; race categories exclude Hispanic origin.

###### Source(s):

Mulligan GM, McCarroll JC, Flanagan KD, and McPhee C*, Findings From the Fifth-Grade Round of the Early Childhood Longitudinal Study, Kindergarten Class of 2010–11 (ECLS-K:2011), *NCES 2019-130 (2019). See Table S1-2.

*Science and Engineering Indicators*

These mathematics and science test results come from the Early Childhood Longitudinal Study, Kindergarten Class of 2010-11 (ECLS-K:2011), a nationally representative, longitudinal study of children’s development, early learning, and school progress. ECLS-K:2011 assessed mathematics and science knowledge and skills in a cohort of kindergarteners and followed them through fifth grade.^{The ECLS-K sample is not nationally representative of all fifth graders. Statistics cited here are nationally representative of the population of students who were first-time kindergarteners in the 2010–11 school year and who were in fifth grade in 2016. It does not include students who may have repeated or skipped a grade.} Data were first collected in fall 2010 from approximately 18,200 kindergarten students who were followed and tested each year through spring 2016. Results are reported as scale scores, which are used for comparisons among demographic groups and for capturing growth over time. Students’ mathematics and science assessment results cannot be compared with each other because scales are developed independently for each academic subject.

ECLS-K:2011 used 2010 U.S. Census poverty thresholds to identify students’ SES. Low-SES students are those whose families have incomes below the federal poverty level, and high-SES students are those whose families have incomes at or above 200% of the federal poverty level. The most recent available ECLS-K:2011 data revealed that fifth graders who were from high-SES families in kindergarten scored higher than students from lower-SES families by approximately 13 points in mathematics (126 versus 114) and approximately 10 points in science (78 versus 69) (Table 1-1).^{Family poverty level was determined in spring 2011 when students were in kindergarten. Family income data were not collected in subsequent years of the study.} Significant discrepancies were also seen by race or ethnicity and sex. White fifth grade students had an average score of 126 on the mathematics assessment, compared with scores of 129 for Asian students, 110 for black students, and 116 for Hispanic students. Fifth grade male students’ scores were slightly higher than female students’ scores in mathematics (122 versus 120). There was no statistical difference between male and female students’ fifth grade scores in science.

### National Trends in K–12 Student Achievement

Patterns of student achievement in grade 8 largely mirror those in kindergarten and fifth grade, based on the demographic characteristics discussed in this report. This section focuses on grade 8 results, which in turn are similar to those for grade 12 (results for grades 4, 8, and 12 can be seen in Table S1-3). This section presents estimates from the National Assessment of Educational Progress (NAEP), the largest nationally representative and continuing assessment of what America’s students know and can do in various subject areas. After examining eighth grade performance in 2017 and over time, the section provides a brief summary of student performance in science, last assessed in 2015, and then discusses the results from the 2018 technology and engineering assessment.

NAEP reports student performance in two ways: scale scores, and student achievement levels.^{Scale scores convert the total number of correct answers (raw score) to a standardized score, which allows comparison of test scores across different editions of the test over time. Scale scores are used for comparative purposes among demographic groups and to examine changes in scores over time.} Regarding scale scores, NAEP states that “a statistically significant scale score that is higher or lower in comparison to an earlier assessment year is reliable evidence that student performance has changed” (NAEP 2018). Although mathematics was assessed for both fourth and eighth graders in 2017, this section focuses on eighth graders’ results because the patterns of performance are similar for both grade levels. Results for grades 4, 8, and 12 can be seen in Table S1-3. The *Science and Engineering Indicators* State Indicators data tool provides NAEP performance and proficiency data for students in each state.

#### Mathematics Performance of Grade 8 Students: Average Scores

Average mathematics scores for eighth graders have trended upward since 1990, but improvement has slowed in the past decade (Figure 1-5). Before 2007, the average score increased 16 points, from 263 points in 1990 to 279 points in 2005. The average NAEP mathematics score for eighth graders was 281 in 2007 and 283 in 2017. The 2017 score represents a slight decline from the 2013 score of 285 (Table 1-2).^{The scale for the main NAEP mathematics assessment is 0–500 for grade 8. In 2017, 80% of students scored between 233 and 333 (Table 1-2).}

#### Average NAEP mathematics scores of students in grade 8: 1990–2017

NAEP = National Assessment of Educational Progress.

###### Note(s):

The scale for NAEP mathematics assessment scores is 0–500 for grade 8.

###### Source(s):

National Center for Science and Engineering Statistics, National Science Foundation, special tabulations (2018) of the 1990–2017 NAEP mathematics assessments, National Center for Education Statistics, Department of Education. See Table S1-3.

*Science and Engineering Indicators*

#### Average scores of students in grade 8 on the NAEP mathematics assessment, by student characteristics: 1990–2017

NA = not available; s = suppressed for reasons of confidentiality and/or reliability.

NAEP = National Assessment of Educational Progress.

^{a} Other racial and ethnic groups are included in the rows for All students in grade 8 but are not shown separately in the table.

^{b} Hispanic may be any race; race categories exclude Hispanic origin.

^{c }Parents' highest level of education is defined by the highest level reported by eighth graders and twelfth graders for either parent. Fourth graders were not asked to indicate their parents' highest level of education because their responses in previous studies were highly variable, and a large percentage of them chose the "I don't know" option.

^{d} NAEP uses eligibility for the federal National School Lunch Program (NSLP) as a measure of socioeconomic status. NSLP is a federally assisted meal program that provides low-cost or free lunches to eligible students. It is often referred to as the free or reduced-price lunch program. Information on students' eligibility for free or reduced-price lunch was first collected in 1996.

^{e} From 1996 on, students with a disability and English language learners were allowed to use testing accommodations (e.g., extended time, one-on-one testing, bilingual dictionary). More information about testing accommodation is available at https://nces.ed.gov/nationsreportcard/about/inclusion.asp.

^{f} A percentile is a score location below which a specified percentage of the population falls.

###### Note(s):

The scale for NAEP mathematics assessment scores is 0–500 for grade 8. From 1996 on, data shown here are for students allowed to use testing accommodations.

###### Source(s):

National Center for Science and Engineering Statistics, National Science Foundation, special tabulations (2018) of the 1990–2017 NAEP mathematics assessments, National Center for Education Statistics, Department of Education.

*Science and Engineering Indicators*

NAEP mathematics scores in 2017 varied widely by student demographic characteristics, including race or ethnicity and SES, as indicated by a student’s eligibility for the National School Lunch Program (NSLP).^{Student eligibility for a free lunch program is a less-than-perfect measure of SES (Harwell and LeBeau 2010).} In 2017, low-SES eighth graders (those eligible for free or reduced-price lunch) scored below their high-SES peers by 29 points (267 versus 296) (Figure 1-6). Since 1996, the gap between low- and high-SES eighth graders’ scores has consistently been from 26 to 30 points (Figure 1-7).

Scores also varied by race or ethnicity and sex. Among groups defined by race or ethnicity, Asian or Pacific Islander students achieved the highest average score, 310 points, in 2017 (Figure 1-6). In comparison, white students scored an average of 293 points, higher than black students’ average of 260 points and Hispanic students’ average of 269 points. Male students slightly outscored female students in 2017, with 283 points for male students versus 282 points for female students. (Although small, the difference is statistically significant.)

#### Average scores of students in grade 8 on the NAEP mathematics assessment, by student characteristics: 2017

NAEP = National Assessment of Educational Progress.

###### Note(s):

The scale for NAEP mathematics assessment scores is 0–500 for grade 8. Hispanic may be any race; race categories exclude Hispanic origin.

###### Source(s):

National Center for Science and Engineering Statistics, National Science Foundation, special tabulations (2018) of the 2017 NAEP mathematics assessment, National Center for Education Statistics, Department of Education. See Table S1-3.

*Science and Engineering Indicators*

#### Average NAEP mathematics scores of students in grade 8, by eligibility for National School Lunch Program: 1996–2017

NAEP = National Assessment of Educational Progress.

###### Note(s):

NAEP uses eligibility for the federal National School Lunch Program (NSLP) as a measure of socioeconomic status. NSLP is a federally assisted meal program that provides low-cost or free lunches to eligible students. It is sometimes referred to as the free or reduced-price lunch program. Information on students' eligibility for free or reduced-price lunch was first collected in 1996. The scale for NAEP mathematics assessment scores is 0–500 for grade 8.

###### Source(s):

National Center for Science and Engineering Statistics, National Science Foundation, special tabulations (2018) of the 1996–2017 NAEP mathematics assessments, National Center for Education Statistics, Department of Education.

*Science and Engineering Indicators*

#### Mathematics Performance of Grade 8 Students: Achievement Levels

The National Assessment Governing Board (NAGB), an independent board that sets policy for NAEP, has developed three achievement levels, which are determined by score ranges that indicate students’ achievement relative to expected achievement for each grade level. These score levels are: *basic—*partial mastery of knowledge and skills; *proficient—*solid academic performance at grade level; and *advanced*—superior academic performance. NAGB suggests that these levels are subject to refinement, and the results should be interpreted with caution.^{NAGB, as directed by NAEP legislation, has developed achievement levels for NAEP since 1990. A broadly representative panel of teachers, education specialists, and the public helps to 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 until the NCES commissioner determines that the levels are reasonable, valid, and informative to the public. This determination will be based on a congressionally mandated, rigorous, and independent evaluation. More information about NAEP achievement levels is available at https://nces.ed.gov/nationsreportcard/achievement.aspx.}

In 2017, about one-third (34%) of eighth graders scored at or above the proficient level in mathematics (Table S1-4), a slight but statistically significant decrease since 2013 (when 36% of students scored at that level). Demographic differences in students’ proficiency levels are similar to those noted in the discussion of scale scores. For example, 48% of high-SES eighth graders scored at or above proficiency, compared with 18% of low-SES students. In addition, 62% of Asian or Pacific Islander students scored at or above proficient, compared with 44% of white students, 13% of black students, and 20% of Hispanic students. Finally, 35% of male students scored at or above proficient, compared with 33% of female students.

#### Science Performance of Grade 8 Students: Average Scores

Science was most recently assessed in 2015; thus, updated data are not available for this edition of *Science and Engineering Indicators**.*^{NAEP administered a new science assessment beginning in 2009 to keep pace with advances in both science and cognitive research, the growth in national and international science assessments, advances in innovative assessment approaches, and the need to incorporate accommodations so that the widest possible range of students could be fairly assessed. This assessment was not comparable to prior assessments administered beginning in 1996. As a result, it is not possible to report long-term trends for science achievement.}* **Indicators **2018* presents a detailed discussion of 2015 NAEP science achievement results (NSB *Indicators 2018*:* *National Trends in K–12 Student Achievement).The average score for eighth grade students was about 4 points higher in 2015, compared with the previous science assessment in 2009. Socioeconomic and demographic patterns seen in grade 8 NAEP science performance in 2015 are largely similar to the patterns seen in 2017 mathematics performance.

#### Technology and Engineering Performance of Grade 8 Students

NAEP administered the first Technology and Engineering Literacy (TEL) assessment for eighth graders in 2014 and again in 2018. Eighth grade students scored 2 points higher in TEL overall in 2018 compared with 2014 (152 versus 150) (Table 1-3).^{Although technology and engineering are important aspects of STEM, they receive less coverage in this report because of the lack of national data sources covering these topics. The NAEP TEL assessment began providing national data for eighth graders when it was first administered in 2014.} Female students scored higher than male students by 5 points in 2018 (155 versus 150) and by 2 points in 2014 (151 versus 149^{Actual scores for male and female students in 2014 were 148.6 and 151.4, respectively, a difference of 2.8 points, which rounds up to 3 points.}). As in 2014, white and Asian students scored higher than black and Hispanic students in 2018, with scores of 169 for Asian students, 163 for white students, 139 for Hispanic students, and 132 for black students. The TEL score gap between students eligible for free or reduced-price lunch and those not eligible did not change significantly from 2014 (28 points) to 2018 (26 points). Patterns for NAEP TEL student achievement levels (percentage scoring proficient or above) were similar to those for average scores (Table S1-5).

#### Average scores of students in grade 8 on the NAEP technology and engineering literacy assessment, by student characteristics: 2014 and 2018

NAEP = National Assessment of Educational Progress.

^{a} Other racial and ethnic groups are included but are not shown separately.

^{b} Hispanic may be any race; race categories exclude Hispanic origin.

^{c} NAEP uses eligibility for the federal National School Lunch Program (NSLP) as a measure of socioeconomic status. NSLP is a federally assisted meal program that provides low-cost or free lunches to eligible students. It is sometimes referred to as the free or reduced-price lunch program.

###### Note(s):

The scale for NAEP technology and engineering literacy assessment scores is 0–300.

###### Source(s):

National Center for Science and Engineering Statistics, National Science Foundation, special tabulations (2018) of the 2014 and 2018 NAEP Technology and Engineering Literacy assessment, National Center for Education Statistics, Department of Education.

*Science** and Engineering Indicators*

NAEP TEL also asked students about technology and engineering coursetaking in grade 8. In 2018, 57% of students at grade 8 reported that they had taken or were taking at least one of the following technology- or engineering-related classes: industrial technology; engineering; classes that involve learning to use, program, or build computers; or any other type of technology-related class.^{NAEP TEL data are available at https://www.nationsreportcard.gov/tel/student-questionnaires/.} The percentage of students who reported taking a technology- or engineering-related class in 2018 was 5 percentage points higher compared to 2014.

Students who reported taking at least one technology- or engineering-related class in 2018 had a higher TEL score on average than those who reported not taking any technology- or engineering-related classes.

### International Comparisons of Mathematics and Science Performance

Governments view their population’s STEM education levels and skills as national resources and use them to assess their status in a broader international context. In the United States, policymakers and educators aim to produce more high-achieving STEM students to ensure that the United States has the knowledge and skills needed to innovate in a rapidly changing world economy and remain a world leader in STEM fields (Chatterji 2018; Committee on STEM Education 2018). The Trends in International Mathematics and Science Study (TIMSS) provides data on the mathematics and science achievement of U.S. students compared to that of students in other advanced economies, as defined by the International Monetary Fund (IMF) (IMF 2018). TIMSS, conducted every 4 years beginning in 1995 and most recently in 2015, is sponsored by the International Association for the Evaluation of Educational Achievement (IEA), an international nonprofit organization consisting of research institutions and government research agencies from member countries and economies. The IEA member countries include countries—defined as complete, independent political entities—and non-national entities (e.g., Hong Kong). The term *education systems* is used here to acknowledge that not all TIMSS participants are countries, and this should be kept in mind when comparing U.S. students’ performance with that of their peers in other education systems. Also, the United States may be larger or more diverse than other participating education systems (e.g., Singapore, Japan), which may affect its rankings.

Another international assessment, the Program for International Student Assessment (PISA), measures the performance of 15-year-old students in science and mathematics literacy every 3 years. *Indicators 2018* discusses the 2015 PISA results; new data were not available in time for the current *Indicators* report (NSB *Indicators 2018*: International Comparisons of Mathematics and Science Performance).

#### Average Scores

Among 19 advanced economies participating in TIMSS for grade 8 in 2015,^{Although the IMF does not include Russia among the world’s advanced economies, this analysis includes it because it is a large economy with high levels of student achievement and high levels of science and technology capability. Other countries with high and rising levels of science and technology capability, such as India or China, are not included because they do not participate in the TIMSS assessment.} the United States placed ninth in both mathematics and science, when examining average scores. In 2015, the average score for U.S. eighth graders was 518 for mathematics (Table 1-4) and 530 for science (Table 1-5). Singapore was the highest-scoring country in both mathematics and science, with scores of 621 and 597, respectively.

#### Average TIMSS mathematics scores of students in grade 8 and percentage of students in the highest and lowest percentiles among participating developed economies, by education system: 2015

* = estimate is significantly different from U.S. estimate at the 0.05 level of statistical significance.

TIMSS = Trends in International Mathematics and Science Study.

###### Note(s):

Education systems are listed in descending order by the percentage of students scoring at or above the 90th percentile. TIMSS participants include both countries, which are complete, independent political entities, and non-national entities (e.g., Hong Kong). Developed economies are based on the International Monetary Fund (IMF) designation of advanced economies (Table A, pg. 132 in* World Economic Outlook: Challenges to Steady Growth*, 2018). IMF classifies Russia as a developing economy, but it is included in this analysis because it is a large economy with high levels of student achievement.

###### Source(s):

National Center for Science and Engineering Statistics, National Science Foundation, special tabulations (2018) of the 2015 TIMSS; Mullis IVS, Martin MO, Foy P, and Hooper M, *TIMSS 2015 International Results in Mathematics *(2016).

*Science and Engineering Indicators*

#### Average TIMSS science scores of students in grade 8 and percentage of students in highest and lowest percentiles among participating developed economies, by education system: 2015

* = estimate is significantly different from U.S. estimate at the 0.05 level of statistical significance.

TIMSS = Trends in International Mathematics and Science Study.

###### Note(s):

Education systems are listed in descending order by the percentage of students scoring at or above the 90th percentile. TIMSS participants include both countries, which are complete, independent political entities, and non-national entities (e.g., Hong Kong). Developed economies are based on the International Monetary Fund (IMF) designation of advanced economies (Table A, pg. 132 in *World Economic Outlook: Challenges to Steady Growth*, 2018). IMF classifies Russia as a developing economy, but it is included in this analysis because it is a large economy with high levels of student achievement.

###### Source(s):

National Center for Science and Engineering Statistics, National Science Foundation, special tabulations (2018) of the 2015 TIMSS; Martin MO, Mullis IVS, Foy P, and Hooper M, *TIMSS 2015 International Results in Science *(2016).

*Science and Engineering** Indicators*

For a detailed examination of U.S. average scores and demographic differences among U.S. students from TIMSS 2015, see NSB *Indicators 2018*: Mathematics Performance of U.S. Students in Grades 4 and 8 on TIMSS.

#### Comparison of High and Low Percentile Groupings

In addition to providing the opportunity to rank advanced economies by average scores, TIMSS data also allow for analysis of the distribution of scores within and across countries. Large percentages of students scoring at the high end of a distribution (e.g., scores at or above the 90th percentile) indicate the presence of higher-achieving students in that education system, whereas large percentages at the low end of a distribution (e.g., scores below the 10th percentile) indicate the presence of lower-achieving students.

Using a database of only student scores in the 19 advanced economies that participated in TIMSS 2015, this report estimates high (90th and 95th) and low (5th and 10th) percentile cut scores across all students in these specific education systems (referred to as the aggregate high or low percentile scores); then, the report examines the percentage of students in each of these advanced economies who scored above the aggregate cut scores for the higher-achievement group (i.e., above the aggregate 95th and 90th percentiles) and lower achievement group (i.e., below the aggregate 5th and 10th percentiles). For example, 41% of Singapore’s student scores in mathematics were in the aggregate 90th percentile group, whereas only 5% of the U.S. student scores were in that group (Figure 1-8). Other education systems with relatively large percentages of students scoring at or above the aggregate 90th percentile include Taiwan (33%), South Korea (31%), Japan (23%), and Hong Kong (23%).

#### Students in grade 8 with TIMSS mathematics test scores in the highest and lowest percentiles among participating developed economies, by education system: 2015

TIMSS = Trends in International Mathematics and Science Study.

###### Note(s):

TIMSS participants include both countries, which are complete, independent political entities, and non-national entities (e.g., Hong Kong). Developed economies are based on the International Monetary Fund (IMF) designation of advanced economies (Table A, pg. 132 in* World Economic Outlook: Challenges to Steady Growth*, 2018). IMF classifies Russia as a developing economy, but it is included here because it is a large economy with high levels of student achievement.

###### Source(s):

National Center for Science and Engineering Statistics, National Science Foundation, special tabulations (2018) of the 2015 TIMSS; Mullis IVS, Martin MO, Foy P, and Hooper M, *TIMSS 2015 International Results in **Mathematics *(2016).

*Science and Engineering Indicators*

Singapore, Taiwan, South Korea, Japan, and Hong Kong far outpaced the rest of the advanced economies in producing student scores at or above the aggregate 90th percentile in mathematics. The next closest are Russia at 8% and Israel at 7%. Overall, the United States placed eighth in terms of the percentage of student scores at or above the aggregate 90th percentile in mathematics. Education systems with the lowest percentage of student scores at this level include Italy and Sweden, with just 1% of their student scores in that range. In some cases, the United States achieved lower average scores than other advanced economies but produced a higher percentage of scores at or above the aggregate 90th percentile. For example, Canada had a higher average mathematics score on TIMSS than the United States (527 versus 518) but a lower percentage of student scores at or above the aggregate 90th percentile (3% versus 5%) (Table 1-4).

Similarly, in science, the United States ranked in the middle (9 out of 19) when examining the percentages of student scores in advanced economies at or above the 90th percentile. In the United States, 8% of students scored at or above the 90th percentile in science (Figure 1-9), compared with 34% of students in Singapore, 20% in Taiwan, 18% in Japan, and 14% in South Korea. Italy (3%) and Norway (4%) produced the lowest percentages of student scores at or above the 90th percentile. Hong Kong had a higher mean science score than the United States (546 versus 530), but 8% of both education systems’ students scored at or above the 90th percentile (Table 1-5).

#### Students in grade 8 with TIMSS science scores in the highest and lowest percentiles among participating developed economies, by education system: 2015

TIMSS = Trends in International Mathematics and Science Study.

###### Note(s):

TIMSS participants include both countries, which are complete, independent political entities, and non-national entities (e.g., Hong Kong). Developed economies are based on the International Monetary Fund (IMF) designation of advanced economies (Table A, pg. 132 in* World Economic Outlook: Challenges to Steady Growth*, 2018.). IMF classifies Russia as a developing economy, but it is included here because it is a large economy with high levels of student achievement.

###### Source(s):

National Center for Science and Engineering Statistics, National Science Foundation, special tabulations (2018) of the 2015 TIMSS; Martin MO, Mullis IVS, Foy P, and Hooper M, *TIMSS 2015 International Results in Science** *(2016).

*Science and Engineering Indicators*

Looking at percentages of student scores in the lowest 10th percentile shows which advanced economies have relatively larger percentages of student scores at the low end of mathematics achievement. In the United States, 13% of students scored at or below the aggregate 10th percentile, compared with just 2% of students in Singapore and South Korea (Figure 1-8). New Zealand, Malta, and Israel produced the largest percentage of student scores below the aggregate 10th percentile, approximately 20%. Again, examination of percentiles yields information not available from examining average scores alone. The average scores for the United States and Israel, for example, were not significantly different, but Israel produced a higher percentage of student scores below the 10th percentile than the United States did (20% and 13%, respectively).

Science results for the United States were similar to those observed in mathematics for student scores below the 10th percentile: 12% of U.S. students scored below the 10th percentile, compared with 4% in Japan and 5% in Singapore (Figure 1-9). Israel and Malta produced the largest percentage of student scores at the low end of science achievement, with 22% and 29%, respectively, of their student scores below the 10th percentile.