Chapter 1: Student AchievementTable of Contents
Over time, the United States’ public education system has evolved from a fundamentally locally-driven enterprise to one that reflects broader goals of ensuring equality of opportunity for individuals and the country’s global economic competitiveness.
These values are mirrored in expectations and aspirations for student outcomes and in the ways student achievement is measured. Overall, American schools are doing better than in the past; but quality is highly uneven—varying among states, districts, and among groups of students. In recent decades, national focus has been on the performance of all students against state and federal standards as well as the relative performance of sub-groups of students based on race, gender, income, and other characteristics. Some tension exists among the levels of influence and control exerted by federal, state, and local goals, resulting in fragmented standards and measures of achievement across states. Nonetheless, the Nation’s Report Card, which compiles results from the National Assessment of Educational Progress (NAEP), provides an established set of metrics to gauge progress in the system as a whole.
Student achievement data discussed in this section is limited to these nationally and internationally comparable sources. However, Chapter 2 of the report presents information on state-level systems of measuring student progress and the federal structures guiding those systems.
The major message from national measures of student achievement is that the United States has much work to do. Some key findings of student achievement data are:
- Based on the most recent data, large proportions of students perform below grade level in reading and math in both elementary and secondary grades.
- Though student achievement has improved over time, the rate of improvement is slow.
- Disparities exist in achievement among student subgroups based on ethnicity and other characteristics. In spite of concentrated focus in this area in recent decades and some gains, those gaps persist and remain substantial.
- Among individual states, student achievement varies somewhat, with higher student achievement concentrated among Northeastern and some Midwestern states. However, state-level performance is generally reflective of national trends both in overall student achievement and progress toward closing achievement gaps.
- High school graduation rates are at an all-time high, exceeding 80 percent in recent years.
- On some international benchmarks, U.S. students perform at average or below-average levels among peers in other developed nations and have shown no change in achievement levels on those measures over time.
- Even the best U.S. schools underperform internationally. Analysis of some of the highest performing U.S. school districts based on state and national measures finds that performance lags behind international peers.
These statistics attest long-term and persistent problems in public education that are the driving force behind movements in recent decades for reform and increased accountability for public schools.
Based on the 2015 results of the NAEP, the average level of achievement in every grade in both reading and math rates below proficient, a standard that roughly correlates with grade-level performance (see sidebar-NAEP Facts). In reading, more than six in 10 students perform below grade level in every tested grade. In math, among the three tested grades, students in grade 4 fare the best, with the lowest percentage of students scoring below proficient at 60 percent. By grade 12, however, three-fourths are performing below grade level (See Figures 1, 2, 3.)
One of the primary policy goals of the No Child Left Behind Act (NCLB), and the inspiration for its name, has been closing achievement gaps among groups of students defined by race, ethnicity, income, and other characteristics. In spite of this concentrated effort, NAEP results show continued high relative concentrations of students within certain sub-groups at the lowest levels of achievement.
The National Assessment of Education Progress (NAEP) is administered by the U.S. Department of Education to measure student achievement across the nation with a common yardstick.
It is a sample-based assessment—testing a subset of students that reflect the student population in their states and across the country. Because the sample is statistically representative, results can estimate the student achievement of all students within a margin of error.
National results are reported through The Nations’ Report Card for all subjects assessed. State-level results are reported for select subjects. In addition to reporting average scores overall and by various student subgroups, NAEP results are presented by the following levels of achievement within subject areas and by student groups:
- Basic Achievement—partial mastery of the knowledge and skills considered fundamental for grade-level work in the subject
- Proficient Achievement—competent academic performance for grade-level
- Advanced Achievement—mastery of basic and proficient levels, representing superior academic performance
Additional information can be found at http://nces.ed.gov/nationsreportcard/about/.
Among the subgroups defined by race, black and Hispanic students are overrepresented at the lower levels of achievement and underrepresented at the higher levels relative to white peers. In each grade level and both subjects, no less than three-fourths of black and Hispanic students perform below proficiency. Over 40 percent of black students score at the lowest achievement level (“below basic”) in reading in all grades (nearly 50 percent in grades 4 and 12), indicating a failure to even partially master essential grade level material. Over half of black students score below basic in math in eighth grade, increasing to over 60 percent by grade 12. Among Hispanic students, 45 percent in fourth grade and 34 percent in eighth grade score at the lowest level in reading, and 27 percent and 40 percent score below basic in math in grades 4 and 8 respectively. In grade 12, a full 88 percent of Hispanic students perform below proficiency in math, with over half performing at the lowest achievement level.
English language learner (ELL) students fare the worst of any group. It is important, however, to remember that ELL students who achieve English proficiency exit the group, and these students are likely to be among the highest performers, driving a lower average performance among the group as a whole. In reading, about 70 percent of ELL students perform at the below-basic level in grades 4 and 8, increasing to 76 percent by grade 12. Math performance is relatively better in grade 4, with 43 percent of students scoring in the below basic category. But those percentages approach 70 again for ELL eighth graders, and by grade 12, 79 percent of ELL students score below basic in math. Special education students show a similar trend, with very high concentrations of students performing below basic in both reading and math at each grade level.
Though the current level of student achievement may not meet goals and expectations, the trends over time show gradual improvement until very recently. Overall average student achievement in grades 4 and 8 in both reading and math has grown over the longer term, showing annual improvement in most years. However, as Figure 4 shows, annual changes in scores are far from dramatic. Progress has slowed over time, and in the most recent results reported, scores dipped compared to the previous administration in both reading and math among eighth and twelfth graders and in math among fourth graders. Fourth grade reading scores for 2015 were unchanged compared to the 2013 administration.
The 2015 scores mark an end to what had been a slow, steady climb in scores over about 20 years of NAEP testing. That said, the long term trend is positive—with significant gains made in both reading and math scores in grades 4 and 8 compared to the early 1990s. And while the 2015 results are disappointing, only time will tell if those single year declines are a bump in the road or evidence of a new and troubling trend.
Results for grade 12 are more mixed. Reading achievement remains fairly flat in recent years; math achievement shows some gains. But twelfth graders have only taken the NAEP math test three times since 2005, which doesn’t provide a long trend-line.
As discussed above, the performance of black, Hispanic, low income, and ELL students is below the average for all students collectively and lags behind that of white peers as a group. Though some progress has been made in closing gaps based on race and ethnicity over time, much like overall progress in student achievement, it has been slow and inconsistent.
Figure 5 provides national-level data on achievement among ethnic subgroups in reading and math in grades 4 and 8. The trend in achievement in both reading and math for black and Hispanic students as a group reflects the overall trend—with positive gains over the long term and in most years. And black and Hispanic students in grade 8 demonstrate the same declines in 2015 scores observed in math and reading. In grade 4, these students’ scores in both subjects are flat. Despite these gains, the rate of improvement in achievement among these student groups relative to white peers has not allowed for much progress in closing performance gaps. Those gaps remain substantial with black students scoring about 10 to 11 percent lower than white students in each grade and subject. Achievement gaps between Hispanic and white students range between 7 and 8 percent across grades and subjects.
For the most part, gains in closing gaps have stagnated for both black and Hispanic students. With the exception of the black-white performance gap in fourth grade math, which narrowed modestly in 2015 for the first time since 2009, measurable improvement in achievement gaps has not been posted for three to five testing cycles. And the narrowing of the gap between black and white fourth-grade math students doesn’t result from improved performance among black students relative to white students. Instead it reflects declining performance among white students and flat performance among black students. The gap in grade 12 performance between white and black students has actually grown since 1992 for reading and has not changed significantly for math since 2005 (the earliest data available). Achievement gaps between white and Hispanic twelfth graders are similarly stagnant, posting no measurable change in either subject over time.
Discussion of achievement gaps more typically focuses on race, but an alternate framework is socio-economic status. Disparities in the performance of low-income students and non-low-income students are sizable, a difference of 8 to 12 percent in reading and 9 percent in math (Figure 6). These gaps have shown no significant change in recent history in either subject or grade.1
Figure 6. NAEP Reading and Math Achievement Trends, 1998 to 2015 Eligibility for Free and Reduced Price Lunch
Because of the relationship between socio-economic status and race, trends based on income and those based on race are not mutually exclusive. NAEP does not disaggregate data within race or income categories by other factors; but the socio-economic data suggests that within the race gaps, there are likely additional disparities based on income.
At the state level, states outpacing national trends in student achievement tend to be concentrated in the Northeastern and Midwestern United States. At the other end of the spectrum, student performance in many southeastern and western states lags behind national averages. Minnesota, Massachusetts, and New Hampshire emerge among the strongest performers in math in grades 4 and 8, with Vermont joining Massachusetts and New Hampshire at the top of the list in reading in both grades. The District of Columbia, Louisiana, Mississippi, Alabama, and New Mexico are consistently among the lowest performers. But many states consistently at the bottom of score rankings also show gains in performance over time at rates higher than national averages. The District of Columbia tops the list of student performance gains over the long term across grades and subjects.
Few states buck the national trend of stronger progress in improving overall student achievement around the turn of the millennium followed by ebbing rates of progress in subsequent years. Exceptions to that trend include the District of Columbia and Mississippi, each of which continues to show above average improvement in student achievement in both reading and math in grade 4. A number of other states continued to show above average gains in grade 4 reading in 2015. But the majority of states posted flat or declining scores across grades and subjects, reflecting the national trend. Over the longer term, more states show continual improvement in grade 4 than in grade 8, with fourth-grade math showing the most continued progress.
Though in a handful of states, achievement gaps in select subjects or grades are narrower than the national averages, few states actually reflect trends that are significantly different than those of the nation as a whole — sizable, persistent gaps in performance among students in different demographics. In some cases, states’ scores show smaller gaps in performance among students in different demographics, but in a context of middling or poor student performance overall. In other words, there may be less disparity among student groups, but few students are excelling. That is the case in Louisiana, which serves high proportions of minority students in its public schools and posts narrower-than-average achievement gaps between white and black students and between white and Hispanic students across grades and subjects in the 2015 results. But, overall, Louisiana students perform below national averages across grades and subjects. And, in fact, some places where overall student achievement is relatively higher, such as in Massachusetts and Connecticut, exhibit some of the biggest gaps based on race and ethnicity.
In other cases where overall performance is at least average, several states with narrower-than-average achievement gaps serve student populations that are less diverse compared to the make-up of the student population nationally. For example, Kentucky students score average or above average in each grade and subject except for eighth-grade math in 2015 and exhibit narrower gaps in performance among white and black and Hispanic students across grades and subjects. However, Kentucky’s public schools also serve fewer minority students as a proportion of the total student population. Similarly, Oklahoma students demonstrate smaller performance gaps across the board in the context of overall performance at national averages. Oklahoma serves relatively fewer black and Hispanic students; that said, Oklahoma’s public schools serve an above-average sized population of Native American students. And the gap between the performance of Oklahoma’s Native American students relative to white students is significantly smaller than national averages.
Few examples exist in states with diverse student populations where strong overall performance pairs with better-than-average achievement gaps. And where that occurs, performance is uneven across grades and subjects. For instance, Florida, which serves a large proportion of Hispanic students in its public schools, posts narrower gaps in performance between white and Hispanic students in some grades and subjects. But though Florida students overall score at or above national averages in the fourth grade, student achievement diminishes on the grade 8 assessments. Delaware, which serves a proportionally larger population of black students than the nation serves as a whole, exhibits a similar pattern with respect to the white-black achievement gap in reading—stronger early-grades performance, but below-average overall performance by eighth graders. These examples illustrate that although pockets of positive trends in closing achievement gaps exist, there are no exemplars of student achievement among all students and student groups across the board.
Some of the states serving the most diverse student populations appear on the opposite end of the spectrum, exhibiting achievement gaps that exceed national averages. For example, across grades and subjects, the District of Columbia has the widest gaps in performance between white and black students and serves the highest concentration of black students in the nation. Similarly, California has among the widest white-Hispanic achievement gaps and serves a student population that is 52 percent Hispanic — second only to New Mexico.2
One limitation in comparing scores across states is that such comparison fails to account for demographic differences among states and the impact those demographics may have on NAEP performance. A recent analysis examined 2013 NAEP scores among states after adjusting for various demographic characteristics of each states’ student population, such as eligibility for free and reduced price lunch, status as ELLs, and other factors. The resulting adjusted scores revealed that some states’ student achievement looked much stronger when students were compared to similar students elsewhere. For instance, the ranking of student achievement among students in Texas and Florida rose from average among states to scoring among the top four states in the nation after controlling for demographic differences. Massachusetts and New Jersey remained at the top of the heap, but in both cases demographic adjustments diminished the distance between student performance in those states and states further down the rankings. Applying the same adjustments to measures of gains in NAEP scores over time also brought a different crop of states to the top of the list, highlighting gains in scores in Nevada, Maryland, and Hawaii, with Massachusetts and New Jersey remaining near the top as well.3 The variation in relative student achievement among states highlighted by this analysis demonstrates the caution necessary when interpreting state-level NAEP. The best use of state-level NAEP data may be in marking performance within a given state over time and among student demographic groups within that state. But the lack of demographic adjustments in the published data that can ensure apples to apples comparison among states limit its value as a tool for determining which states perform more or less well than other states or as a means of analyzing performance in the context of differing state education policies.
Earning a high school diploma is a milestone that correlates with many positive outcomes. High school graduation opens doors to post-secondary opportunities for training and further education that are increasingly required in the job market. Further, high school graduates are estimated to earn about one-third more than non-graduates and are less likely to be unemployed.4 5 In recognition of the inherent value of a high school diploma, high school graduation rates have become a primary feature of federal and state accountability systems.
And public schools have responded. High school graduation rates continue to climb, peaking at 81 percent nationally for the Class of 2013 (the most recent year for which nationally aggregated data is available). Among the 48 states for which graduation rates were reported since 2011, 45 showed positive growth in graduation rates over a four-year period. Figure 7 below shows graduation rates for all 50 states, the District of Columbia, and the nation since 2011. In each year, the District of Columbia posts the lowest graduation rates, peaking at 62 percent in 2013. Iowa posts the highest—at 91 percent in 2014.6 The majority of states report rates in excess of 80 percent in each year, and all but two states post rates above 70 percent in 2014 (Figure 8).
|Graduation Rate||Number of States 2010-2011||Number of States 2011-2012||Number of States 2012-2013|
|50 to 60%||1||1||0
|60 to 70%||5||2||2|
|70 to 80%||18||18||16|
These high graduation rates seem at odds with the high proportions of students demonstrating performance below proficient or even basic levels of achievement in reading and math on the NAEP. This disconnect may occur because, although the methodology for calculating high school graduation rates is consistent among states, the requirements for earning a diploma are not. So while high school graduation rates provide comparable measures of the degree to which students in various states are achieving state standards, the standards themselves are not comparable and may not be indicative of a high level of achievement.
Administered since 2000 by the Organisation for Economic Co-operation and Development (OECD), the Programme for International Student Assessment (PISA) tests 15-year old students once every three years in reading, math, and science and may include other subjects periodically.
The most recent administration was conducted in 2012 and included assessments in reading, math, science, financial literacy, and creative problem solving. Sixty-five countries participated in the reading, math, and science assessments. Of those,44 participated in the creative problem solving assessment, and 18 participated in the financial literacy assessment.
Administered since 1995 by the International Association for the Evaluation of Educational Achievement housed at Boston College (IEA), the Trends in International Mathematics and Science Study (TIMSS) tests students in grades 4 and 8 (or international equivalents) in mathematics and science every four years. Countries volunteer to participate and in the most recent administration in 2011, 65 nations participated in total, though not all nations participated in all assessments offered.
Similar to NAEP at the national level, there are a couple of internationally-administered exam programs that enable comparisons of educational achievement among nations. The Programme for International Student Assessment (PISA) is a set of sample-based assessments administered by the Organisation for Economic Co-operation (OECD) to 15-year-old students around the world for the purpose of analyzing and comparing education programs in different countries. The Trends in Mathematics and Science Study (TIMSS) assesses math and science among students in grades 4 and 8 every four years. To be clear, PISA and TIMSS are two distinct assessments that measure different sets of skills in different ways among students in different grades and in different groups of participating nations. PISA focuses on applying math and science knowledge to “real world” problems, whereas TIMSS is curriculum-based, assessing skills and knowledge as they are often taught in schools.7 Comparing results of the two, in some cases countries that perform well on one, fare worse on the other and vice versa. The United States’s TIMSS performance is stronger overall than its performance on the PISA; the U.S. TIMSS math performance in 2011, for example, ranks twelfth for grade 4 and ninth in grade 8 —performing on par with Finland and ahead of several countries that perform better on the PISA.
Figure 9 provides the overall PISA performance for participating countries in the primary assessments in reading, math, and science.
|Nation||PISA Math||PISA Science||PISA Reading||TIMMS Math Grade 4||TIMMS Math Grade 8||TIMMS Science Grade 4||TIMMS Science Grade 8|
|United Arab Emirates - Ex. Dubai||49||48||50||40||23||42||23|
Among the 34 OECD-member countries (highlighted), the United States ranks 27th in math performance, 17th in reading, and 20th in science. Math performance in the United States corresponds with a below-average level among OECD-member nations. U.S. students perform about average among OECD-member countries in reading and science.
The OECD establishes performance levels analogous to the achievement levels for NAEP, where Level 2 corresponds to a basic level of achievement and Level 5 corresponds to a proficient level of achievement. In mathematics, the United States has an above-average share of students scoring below Level 2 (26 percent) and a below-average share of students achieving at the highest levels. In contrast, the top-achieving countries each have 10 percent or less students at the lowest levels. For both reading and science, the U.S. share of students at both the lowest and highest performance levels are near the OECD averages.
U.S. student performance on PISA reading, math, and science assessments has not changed significantly over time, despite being advantaged financially relative to other nations, outspent on a per-student basis only by Switzerland.
But in the ad hoc assessment of creative problem solving, U.S. students fared better than average —ranking 10th among the 28 participating OECD nations and 14th among all participating nations. Further, U.S. students performed better on creative problem solving than other nations that had similar performance on the math, reading, and science assessments.9
In addition to reporting overall scores, with each administration OECD conducts a focused analysis on a single subject area, which for 2012 was math. OECD’s analysis of U.S. mathematics results finds that students perform well on lower-order mathematical skills such as extracting information from diagrams and performing simple calculations. However, U.S. students exhibit weak performance on higher-order tasks such as applying mathematical concepts to real-world scenarios and geometric reasoning.10
American students rank higher among participating nations on the TIMSS, ranking 10th and 9th in math and 7th and 9th in science in grades 4 and 8 respectively (Figure 9). In contrast to PISA results, U.S. students have shown some improvement over time in both math and science as assessed by TIMSS. In fourth grade math, they gained 22 points since 2003. Gains in eighth grade math have been more modest, with U.S. students gaining 17 points since 1995, but only five since 2003. This trend is consistent with national trends in math performance on the NAEP, which also show stronger gains over time in grade 4 than in grade 8.11 Gains in science scores on TIMSS are modest, with fourth graders gaining a net two points since 1995 — improving by eight points between 2003 and 2011 after a decline in the early 2000s. Eighth-grade science results have been more mixed over time with stronger gains between the 1995 and 2003 administrations, followed by a slight decline. American student performance improved with the 2011 administration, but still lags behind the high point in 2003 by two points.12
As this report indicates, the performance of several nations between PISA and TIMSS, including the United States, varies. This raises questions regarding the cultivation of the different skills being assessed by each assessment. Methodological differences between the two assessments — testing different aged students in different ways — explain some of the variance. And, of course, the participating nations differ, with many of the higher-performing PISA nations engaging in more limited or no TIMSS participation to date, which also accounts for some variation in rankings.
Additionally, structural and societal differences in approaches to education skew results when comparisons are based entirely on averages. In particular, while the overall socio-economic status of U.S. students is higher than average among OECD nations, the proportion of economically disadvantaged students is about average. This statistic is reflective both of the disparity of wealth in the United States and the inclusiveness of its education system.
OECD analysis finds that about 15 percent of variability in the performance of American students is explained by socio-economic factors; the OECD average is 10 percent.13 Research suggests that if the PISA results of U.S. students are adjusted such that the distribution of low-income students is more similar to other countries with comparable post-industrial economies, both math and reading results would look significantly higher.14 This does not mean the United States should not be concerned about international comparisons of educational achievement, but it suggests that the conclusions drawn from rankings based on national averages are limited and that reality is more nuanced.
More detailed analysis of state- and district-level performance finds that a very small proportion of school districts perform well relative to other countries. Based on 2007 data, 94 percent of school districts performed below the 67th percentile in math, and none of the 20 largest districts in the nation (responsible for educating 10 percent of the nation’s students) exceed the 50th percentile in math. Even performance in affluent and pre-dominantly white suburban school districts in this analysis is profoundly average, affirming past research findings that even among advantaged students low proportions of U.S. students perform at advanced levels relative to students in other developed nations.15 This research not only supports the overall negative international indicators, but also suggests that many schools perceived to be among the best in the United States fail to produce students with globally competitive levels of achievement.
- NAEP measures gaps between students eligible for the National School Lunch Program and those students not eligible. Eligibility for the program is determined by family income. ↩
- “What States are Closing the Achievement Gap?” Nation’s Report Card, accessed February 8, 2015, http://www.nationsreportcard.gov/reading_math_2013/#/state-gaps. ↩
- Matthew M. Chingos, “Breaking the Curve: Promises and Pitfalls of Using NAEP Data to Assess the State Role in Student Achievement,” Urban Institute, October 2015, accessed November 23, 2015, http://www.urban.org/sites/default/files/alfresco/publication-pdfs/2000484-Breaking-the-Curve-Promises-and-Pitfalls-of-Using-NAEP-Data-to-Assess-the-State-Role-in-Student-Achievement.pdf. ↩
- Anthony Carnevale, Stephen Rose, and Ban Cheah, “The College Payoff,” Georgetown Center on Education and the Workforce (2011): 3, accessed February 8, 2015, https://www2.ed.gov/policy/highered/reg/hearulemaking/2011/collegepayoff.pdf. ↩
- “Digest of Education Statistics: 2013, Table 501.80,” National Center for Education Statistics, accessed February 8, 2015. http://nces.ed.gov/programs/digest/d13/tables/dt13_501.80.asp. ↩
- “EDFacts/Consolidated State Performance Report, School Years 2010-11, 2011-12, and 2012-13, and 2013-14,” U.S. Department of Education, accessed November 16, 2015, http://www2.ed.gov/admins/lead/account/consolidated/index.html. ↩
- Tom Loveless, “International Tests Are Not All the Same,” Brookings Institution, January 9, 2013, accessed February 4, 2015, http://www.brookings.edu/research/papers/2013/01/09-timss-pisa-loveless. ↩
- :PISA 2012 Results: What Students Know and Can Do (Volume I, Revised edition, February 2014) Copyright © OECD 2014 and TIMSS 2011 Assessment. Copyright © 2012 International Association for the Evaluation of Educational Achievement (IEA). Publisher: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College, accessed November 6, 2014, http://www.keepeek.com/Digital-Asset-Management/oecd/education/pisa-2012-results-what-students-know-and-can-do-volume-i-revised-edition-february-2014/united-states_9789264208780-22-en#page7. ↩
- “PISA 2012 Results: Creative Problem Solving: Students’ Skills in Tackling Real-Life Problems, Volume V,” PISA, OECD Publishing, 2014, accessed December 13, 2015, http://www.oecd.org/pisa/keyfindings/PISA-2012-results-volume-V.pdf. ↩
- “PISA 2012 Results: What Students Know and Can Do, (Volume I, Revised Edition, February 2014): Student Performance in Mathematics, Reading, and Science,” PISA, OECD Publishing, 2014, accessed November 6, 2014, http://www.keepeek.com/Digital-Asset-Management/oecd/education/pisa-2012-results-what-students-know-and-can-do-volume-i-revised-edition-february-2014/united-states_9789264208780-22-en#page5. ↩
- TIMSS 2011 Assessment. Copyright © 2012 International Association for the Evaluation of Educational Achievement (IEA). Publisher: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College, Chestnut Hill, MA and International Association for the Evaluation of Educational Achievement (IEA), IEA Secretariat, Amsterdam, the Netherlands, accessed February 4, 2015, http://timssandpirls.bc.edu/timss2011/downloads/T11_IR_M_Chapter1.pdf, ↩
- TIMSS 2011 Assessment. Copyright © 2012 International Association for the Evaluation of Educational Achievement (IEA). Publisher: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College, Chestnut Hill, MA and International Association for the Evaluation of Educational Achievement (IEA), IEA Secretariat, Amsterdam, the Netherlands, accessed February 4, 2015, http://timssandpirls.bc.edu/timss2011/downloads/T11_IR_S_Chapter1.pdf, ↩
- “PISA 2012 Results: What Students Know and Can Do (Volume I, Revised Edition, February 2014): Student Performance in Mathematics, Reading, and Science,” PISA, OECD Publishing 2014, accessed November 6, 2014, http://www.keepeek.com/Digital-Asset-Management/oecd/education/pisa-2012-results-what-students-know-and-can-do-volume-i-revised-edition-february-2014/united-states_9789264208780-22-en#page5. ↩
- Martin Carnoy and Richard Rothstein, “What Do International Tests Really Show about U.S. Student Performance?” Economic Policy Institute, 2013, accessed February 4, 2015, http://www.epi.org/publication/us-student-performance-testing/. ↩
- Jay P. Greene and Josh B. McGee,”When the Best is Mediocre,” Education Next, accessed February 4, 2015, http://educationnext.org/when-the-best-is-mediocre/. ↩