Chapter 1 | Elementary and Secondary Mathematics and Science Education

Highlights

The National Assessment of Educational Progress (NAEP) mathematics assessment results show that average mathematics scores for fourth, eighth, and twelfth graders declined slightly for the first time in 2015 and remained flat or showed only small gains between 2005 and 2015.

• The average NAEP mathematics score in 2015 declined by 2 points for fourth graders, 3 points for eighth graders, and 1 point for twelfth graders compared with 2013. These are the first declines since 1990 for fourth and eighth graders and since 2005 for twelfth graders.
• Although the long-term trend in average scores for fourth and eighth graders has been upward, the improvement slowed down this past decade. From 2005 to 2015, average NAEP mathematics scores increased by 2 points for fourth graders and 3 points for eighth graders; in comparison, from 1996 to 2005, the average scores increased by 14 points for fourth graders and 9 points for eighth graders.

NAEP science assessment results show that average scores increased slightly in 2015 for fourth and eighth graders but stayed similar for twelfth graders.

• The average NAEP science scores increased 4 points between 2009 and 2015 in grades 4 and 8 but did not change in grade 12.

Less than half of fourth, eighth, and twelfth grade students achieved a level of proficient (defined as “solid academic performance”) or higher on NAEP mathematics and science assessments in 2015.

• Forty percent of fourth graders, 33% of eighth graders, and 25% of twelfth graders achieved a level of proficient or higher in mathematics in 2015.
• Approximately 38% of fourth graders, 34% of eighth graders, and 22% of twelfth graders achieved a level of proficient or higher on the NAEP science assessment in 2015.

Performance disparities in mathematics and science were evident among different demographic groups at all grade levels.

• Average scores on 2015 NAEP mathematics and science assessments for fourth, eighth, and twelfth grade students who were eligible for free or reduced-price lunch (an indicator of socioeconomic status) were 23 to 29 points lower than the scores of their peers who were not eligible for the program.
• Performance gaps between white students and black and Hispanic students showed similar patterns across all NAEP assessments and grade levels, with average scores of white students at least 18 points higher than those of Hispanic students and at least 24 points higher than those of black students.
• Score differences between students eligible for free or reduced-price lunch and those who were not persisted within racial or ethnic groups. For example, the gaps between eligible and non-eligible students in grade 4 mathematics were 18 points among white students, 17 points among Hispanic students, and 16 points among black students. Similar gaps held among eighth and twelfth grade students and across all grade levels in science.
• Gaps between male and female students on NAEP mathematics and science assessments were small, with average score differences of two to five points in favor of male students. There was no difference in average scores by sex for grade 8 mathematics or grade 4 science.

Performance disparities in mathematics and science begin as early as kindergarten and persist through subsequent school years.

• A study based on the mathematics and science assessment scores among the kindergarten class of 2010–11 shows that gaps in average scores by race or ethnicity and family income level evident in kindergarten do not narrow by the end of third grade.
• The gap in average mathematics scores between students in families with income below the federal poverty level and those in families with income at or above 200% of the federal poverty level was 9 points at the beginning of kindergarten and 10 points by the spring of third grade; the science score gap was 5 points at the beginning of first grade and 8 points by the spring of third grade.
• The gap in average mathematics scores between white and black students was 6 points at the beginning of kindergarten and 13 points in the spring of third grade; the science score gap was 5 points at the beginning of first grade and 9 points by the spring of third grade.

In the international arena, the Trends in International Mathematics and Science Study (TIMSS) and the Program for International Student Assessment (PISA) 2015 data show that the U.S. average mathematics assessment scores were well below the average scores of the top-performing education systems.

• On the TIMSS mathematics assessment, average scores for the top five performers—Singapore, Hong Kong, South Korea, Taiwan, and Japan—were at least 54 points higher than the United States at grade 4 (593–618 versus 539) and at least 68 points higher than the United States at grade 8 (586–621 versus 518).
• The United States’ average score of 470 on the PISA mathematics literacy assessment for 15-year-olds was at least 62 points below the average scores (532–564) of the top five performers—Singapore, Hong Kong, Macau, Taiwan, and Japan.

TIMSS data show that U.S. fourth and eighth graders have raised their scores over the 20 years since administration of the first TIMSS mathematics assessment in 1995.

• Between 1995 and 2015, the average mathematics score increased by 21 points for fourth graders and by 26 points for eighth graders.

The 2015 data from PISA indicate that the United States performs better internationally in science literacy than it does in mathematics literacy.

• The United States’ average science literacy score of 493 was not significantly different from the Organisation for Economic Co-operation and Development (OECD) average and put the United States behind 18 other education systems. In contrast, the mathematics literacy score was below the OECD average and put the United States behind 36 other education systems.

Among ninth graders who entered high school in 2009 and completed high school in 2013, the vast majority (89%) completed algebra 2 or higher in mathematics, and nearly all (98%) completed biology in science.

• Approximately one-quarter of students stopped with algebra 2 as their highest mathematics course, another quarter stopped with trigonometry or other advanced mathematics, 22% advanced to pre-calculus, and 19% finished with calculus or higher.
• In addition to taking biology, 76% of ninth graders who began high school in 2009 took chemistry and 42% took physics by the time they completed high school in 2013.

The number of high school students who take Advanced Placement (AP) exams in mathematics and science continues to rise.

• Calculus AB is the most common mathematics AP exam. The number of students who took an AP exam in calculus AB increased from 197,000 in 2006 to more than 308,000 in 2016.
• Biology is the most common science AP exam. The number of students who took an AP exam in biology increased from nearly 132,000 in 2006 to 238,000 in 2016.
• Computer science A is the fastest-growing AP exam, with the number of students taking the exam growing nearly four-fold from just under 15,000 in 2006 to nearly 58,000 in 2016.
• Passing rates for the mathematics and science AP exams in 2016 ranged from lows of 40% for physics 1 and 46% for environmental science to highs of 77% for physics C: mechanics and 81% for calculus BC.

The majority of K−12 mathematics and science teachers held a teaching certificate and had taught their subjects for 3 years or more.

• In 2011, the vast majority of public middle and high school mathematics (91%) and science (92%) teachers were fully certified (i.e., held regular or advanced state certification).
• In 2011, 85% of public middle and high school mathematics teachers and 90% of science teachers had more than 3 years of teaching experience.

Fully certified, well-prepared, and experienced teachers were not evenly distributed across schools or classes.

• Fully certified mathematics and science teachers were less prevalent in high-minority and high-poverty schools when compared with schools with students from higher-income families. For example, in 2011, 88% of mathematics teachers in high-poverty schools were fully certified, compared with 95% of those in low-poverty schools.
• At the middle school level, in 2011, 75% of mathematics teachers in low-poverty schools had in-field degrees, compared with 63% of teachers at high-poverty schools.
• At the high school level, 95% of mathematics teachers at low-poverty schools had in-field degrees, compared with 87% at high-poverty schools.
• The percentage of mathematics teachers with fewer than 3 years of experience was higher at high-poverty schools (18%) than at low-poverty schools (10%). The pattern was similar for science teachers.

In 2011, the average base salary of middle and high school teachers was approximately $53,000 for mathematics teachers and $54,000 for science teachers.

• Compensation for U.S. mathematics and science teachers was nearly equivalent to that of teachers of other subjects in 2011.
• In the international arena, the United States ranks low among developed countries with respect to teachers’ salaries relative to the salaries of other college-educated workers. For primary school teachers, the U.S. ranking is 20th of 23 countries. For lower and upper secondary school teachers, the United States is 21st of 23 countries.

The use of instructional technology in K−12 classrooms has grown, and the number of schools with adequate bandwidth for accessing the Internet has increased.

• In 2009, 97% of K–12 public school teachers reported that they had one or more computers in their classroom, and 69% said that they or their students often or sometimes used computers during class time.
• In 2016, more than two-thirds of school district technology administrators indicated that all the schools in their district fully met the Federal Communication Commission’s Internet bandwidth recommendations for public schools, up from 19% in 2012.
• National data available to address the quality and effectiveness of technology-based educational programs delivered in classrooms remain limited; available research has generally shown only modest positive effects of technology on learning.

The number of students participating in online learning has also risen.

• In the 2014–15 school year, 24 states operated virtual schools that offered supplemental online courses for students. These schools served more than 462,000 students, who took a total of 815,000 online semester-long courses. Although still a small fraction of the approximately 50 million students enrolled in K–12 public schools, this was a substantial increase since 2012–13, when 721,149 semester course enrollments were recorded.
• High school students took most of these courses (85%). Math courses made up nearly 23% of the courses taken, and science courses made up 14%.

U.S. on-time high school graduation rates have improved steadily.

• In 2011, 79% of public high school students graduated on time with a regular diploma; by 2015, the figure had climbed to 83%.
• Although on-time graduation rates for economically disadvantaged students have improved by 6 percentage points since 2011, these students continue to graduate at lower rates than the general population (76% versus 83% in 2015).

Significant racial and ethnic differences persisted, with white and Asian or Pacific Islander students having higher graduation rates than other racial or ethnic subgroups.

• In 2015, the on-time high school graduation rates for Asian or Pacific Islander and white students were 90% and 88%, respectively; and both rates surpassed those of black, Hispanic, and American Indian or Alaska Native students (72%–78%) by at least 10 percentage points.

Immediate college enrollment rates have increased for all students from 1975 to 2015, although differences remain for demographic groups.

• Between 1975 and 2015, the percentage of high school graduates making an immediate transition to college increased from 51% to 69%.
• In 2015, the immediate college enrollment rate of students from low-income families was 14 percentage points lower than the rate of those from high-income families (69% versus 83%).
• Enrollment rates also varied widely with parental education, ranging in 2015 from 56% for students whose parents had less than a high school education to 82% for students whose parents had a bachelor’s degree or higher.