In this issue of the journal, reporter Kathryn Baron writes about high-ability math students and some of the private organizations that provide them with challenges beyond what they encounter in school. Education Next editor Martin West spoke with Joshua Zucker, a veteran instructor with Art of Problem Solving, or AoPS, a for-profit company that offers online courses for young math lovers.

Martin West: How does the math instruction offered by Art of Problem Solving compare to what’s typically available in public schools? Do you simply enable students to move more quickly through a sequence of advanced courses, or is it a fundamentally different approach?

Joshua Zucker: I think it’s both. A lot of students are bored in math class. They want more, they want it faster, and they want to be pushed to think harder and discover more. So, we do give an opportunity for acceleration, but even more important, our values are different. We place a lot of value on strategic thinking, problem-solving strategies, and mathematical communication. We work on giving young kids problems that require them to express themselves and communicate about their thinking process and how they solve the problem, and we give feedback about both the mathematical content and the communication skills. Communication is often neglected in math classrooms. It’s left to the English teachers. But clear, logical communication can also be taught through mathematics, where we have well-defined signposts on what marks rigorous thinking, and we can evaluate whether students are communicating at that level.

MW: You teach courses online, but the interface you use is decidedly low tech, with no audio or video, just a screen that enables you to post problems and offer instructions and hints. What are the advantages of that low-tech approach?

JZ: In some online classes the goal is to try to replicate what it’s like to have everybody in the same room together. Instead, we ask: how can we take advantage of the fact that we’re not all in the same room? Teaching without audio and video means kids can be a little bit behind or they can be rushing ahead to go further. With the text interface, they can scroll back up and study a point they really need to think about, or they can ask a question and get individual help. And I can ask how students got an answer.

In a math classroom, there’s a tendency for the same kids to raise their hands right away, which can discourage others from trying to figure out the problem themselves. Online, we can have 20 of the 50 kids “shouting out” an answer to the problem, metaphorically speaking, but the other kids don’t know it, because only the instructors see their comments.

MW: In her article, Baron reported that in 2015, the United States won the International Mathematical Olympiad for the first time in 21 years and won again in 2016 and 2018. All 16 students on those three teams had enrolled in AoPS courses—more than a hundred courses in total. What role do national and international competitions play in the education of high-ability math students?

JZ: AoPS came into being in part to help serve the kids who have an interest in competitions. Thirty years ago, those kids had to sit alone in their rooms and prepare by themselves. Now we have hundreds of them taking courses every year and training together with really hard problems. Sometimes I wonder if I’m really helping that much, because the kids provide so many of the great ideas. The service we provide is enabling the kids to interact with each other, bringing them into one “place” where they can share the experience of struggling with these problems. That becomes their community of support.

MW: You’ve had experience as a high-school math teacher. What is an important lesson schools can learn from the success of AoPS and other such organizations?

JZ: Mathematics is fundamentally a human activity, and it’s about creativity just as much as writing a good essay is. There are rules and structure, but there’s also exploration and individuality; people’s work is not going to look exactly the same. There’s a tendency in mathematics to focus on following procedures and getting answers, but to me, that’s the part of mathematics that computers are better at than humans. So let’s focus on the parts humans are good at—the creativity, the communication.

Along with that comes a different way of asking questions—genuine questions. In a classroom or textbook, the questions are often just prompts for following the steps and getting the answer. I want to ask questions like, “How did you approach that? What did you try here?” That kind of query is much more inviting; it says, “I want to know about your thinking.” I’d like to see a lot more questions like these in classrooms throughout the country.

This is an edited excerpt from an Education Next podcast, which can be heard here.

The United States has long been the world’s most popular destination for international students studying abroad. Yet in 2017–18, American universities sustained a 6.6 percent drop in new enrollments by foreign students, continuing a trend that began in 2015–16 and causing much handwringing in higher-education circles and the media. In covering the dwindling enrollment, the Wall Street Journal quoted a college-recruitment specialist as saying that foreign “students are not feeling welcome” in some states, while the Washington Post cited “questions about whether President Trump’s nationalist rhetoric and policies have undercut overseas demand for U.S. higher education.”

Is the United States losing its edge as the go-to place for study abroad?

A first glance at the numbers might suggest so, but a closer look discloses that while growth in the international-student market has slowed, the total numbers are trending upward. In 2018, the number of foreign students studying here attained a new high, exceeding one million for the third year running, according to the Institute of International Education. Furthermore, the country has experienced, and recovered from, growth-rate dips in the past.

For colleges and universities, “internationalization”—defined, for our purposes, as the recruiting and welcoming of foreign students—brings many benefits. Students from around the globe contribute diverse perspectives and cultural values to campus life. They also enrich the academic institution and the local economy through their spending on tuition, living expenses, and travel. For research institutions, the contributions of talented scientists and engineers in training are enormous. Thus, leaders in the higher-education sector have good reason to want to recruit these students. And they know they face strong competition for them from other English-speaking countries, such as Canada, the United Kingdom, and Australia.

It’s important to underline the distinctions between the two kinds of internationalization. Universities seek to attract top graduate students for their talent, but they pursue fee-paying students, many of them undergraduates, for a very different reason: to bring in revenue. As it happens, the recent decline in enrollment is not evenly distributed between these two categories.

Talent acquisition involves selecting the best students from around the world, mainly at the doctoral level, to work with professors at research institutions. American universities have excelled at this type of internationalization over the past six decades, largely because graduate students seek the unparalleled academic opportunities our institutions have to offer. The chance to work with the world’s top professors in some of the best-equipped academic laboratories has made the United States a magnet for up-and-coming scientists of promise.

This acquisition of top-notch talent, however, costs money—and lots of it. American universities waive tuition fees for these top graduate students and pay them healthy stipends. They do this because it is a good investment: it is no exaggeration to say that the American academic research enterprise, particularly in engineering, computer science, and pharmaceutical sciences, would be impossible to maintain without the labor of foreign doctoral students. When those students manage to stay in the United States—as professors, entrepreneurs, or simply highly skilled workers—they also make substantial contributions, economic and otherwise, to their communities and the country.

The second motive for internationalization is to generate surplus cash from international students to subsidize a college or university’s operations. This is now by far the dominant form of student mobility worldwide, but it is of comparatively recent origin. The United Kingdom was the first country to engage in this kind of recruitment on a mass scale when, during the 1980s, the government began to allow universities to charge international students substantial fees (tuition for domestic students was free until 1998). The Australians built on this approach in the 1990s when the government in Canberra openly encouraged institutions to find overseas students and charge them market-based tuition fees to make up for government cutbacks in education funding.

These two forms of internationalization target different markets. Talent acquisition operates nearly exclusively at the doctoral level. Revenue-enhancing efforts focus more on undergraduates and professional-master’s-degree candidates. The United States has long enjoyed healthy international enrollment in the talent-acquisition realm, but the innovation of the last few years has been a growth in the moneymaking sector of the market.

American universities did not chase this segment until recently, perhaps because raising tuition and bolstering operating revenue were never as problematic for American institutions as they were for British and Australian ones. Private institutions here turned more seriously toward recruiting fee-paying foreign students after the recession of 2001, at the same time they began to offer more domestic students heavy tuition discounts to convince them to enroll. Major public institutions took longer to enter the market. For them, the need for “high value” undergraduates was largely met by out-of-state students, until about the 2008 recession. Then, a sudden drop in state funding created a need for additional revenue exactly when families could least afford to spend more on tuition. Recruiting international students for what amounted to commercial purposes came to be seen as an “easy way out” of budgetary problems, and within five years a number of major state universities increased their share of international students from 3–4 percent of an incoming class to 15–20 percent.

The current changes in the inter-national-student market seem to have left the talent acquisition side of the equation mostly unaffected. What we see, for the most part, is a problem with revenue generation on the moneymaking side.

By the Numbers

The countries sending the most students to the United States are, in order, China, India, South Korea, Saudi Arabia, Canada, and Vietnam (see Figure 1). Students also come here from some 200 other countries around the globe. In the decade prior to 2016, international enrollment rose by about 60 percent. During that period, the composition of that enrollment changed dramatically, shifting to students from China and India. While these two countries previously accounted for about a quarter of international students, they now contribute almost 50 percent of the total. In fact, 97 percent of all growth in international enrollments since 2006 can be attributed to increases in numbers from just four countries: China, India, Saudi Arabia, and Vietnam.

Figure 1 also shows that since 2016, enrollment growth has ceased, and now the numbers may even be declining slightly. Still, the data do not justify declaring a “crisis” in international-student enrollment. Though growth has stagnated, the numbers of international students remain substantially higher than they were a decade ago. Furthermore, drops in foreign-student enrollment are nothing new: between 2003 and 2005 the numbers fell by a little more than 8 percent, but they began to rebound a few years later.

If international-student numbers remain near all-time highs, why are the media harping on the negatives? The reason is that news outlets are focusing on total-enrollment numbers, which tell only part of the story; there are other data sets in play. The first involves the number of international applications to U.S. universities. This is not tracked at the undergraduate level, but data from an annual survey by the Council of Graduate Schools show a fall in applications of about 7 percent over the past two years, concentrated mostly at the master’s-degree level. By contrast, applications to doctoral programs actually ticked upward over the same two years. The number of applications is also related to the research-intensiveness of the institutions: the “R1” institutions (the most research-intensive type of university in the Carnegie Classification system) have actually seen a rise in applications, while at master’s-level institutions the drop has been notable.

The other relevant set of data involves the measure of new enrollments, as distinct from total enrollments. Since most degrees take more than a year to complete, new enrollments don’t need to rise for total enrollments to do so: the number of new students just needs to equal or exceed the number of students leaving the system via graduation or dropping out. These numbers do not necessarily track precisely with changes in total enrollments, which institutions can raise by simply adjusting international-student admissions standards down to maintain a steady overall student-yield rate (though of course this has some potential ramifications for perceptions of prestige and selectivity). Thus, while applications from foreign students to American graduate schools fell by 7 percent, first-time enrollments decreased by only 2 percent, with the effects again felt more severely at less-selective institutions and at the master’s level. At the undergraduate level, what we see is a major drop in enrollments of 6–7 percent in 2017, with smaller declines in both 2016 and 2018. These dips are not yet large enough to make a dent in total enrollment (which rose very quickly in the four years prior to 2016), but they will start to cascade through the system over the next few years and reduce overall numbers, even if future new enrollments stabilize.

We can conclude from all this that there is some softness in the market in terms of both international applications and new enrollments and that decreases are related to students’ perceptions of institutional quality and prestige. And even if this softening is not yet evident in total enrollment numbers, it soon will be. The downward drift might be on the same scale as we saw in the mid-2000s, or it might be worse, if the weaker enrollment trends continue or intensify.

Comparative Picture

Is this market softness unique to America, or is it happening elsewhere as well? Global enrollment growth is slowing, driven particularly by plummeting youth cohort sizes in China, which have put the brakes on two solid decades of international-student enrollment increases. Perhaps—given demographic decline in China and the increased quality of institutions throughout Asia—there just aren’t as many international students out there for any market.

The question of whether the number of international students is falling can be dealt with relatively quickly by looking at students leaving China and India, who together constitute well over half the global flow of international students. Over the period of 2013–17, students from China in five English-speaking countries (the United States, the United Kingdom, Canada, Australia, and New Zealand) increased by 40 percent, while the number of Indian students in the same countries doubled. Though China and India have both seen massive increases in access to higher education over the past two decades, the supply of student slots at their domestic institutions has not grown nearly so much andhas not kept up with demand from a burgeoning middle-class in both nations. Numbers elsewhere may not be quite so impressive, but there is no major country where the number of students studying abroad is declining.

As to whether the situation in the United States is unique, we can uncover the answer by comparing American numbers to those of the same four other English-speaking countries. Figure 2 compares the evolution of U.S. international enrollments in 2013–18 to those of Australia, Canada, New Zealand, and the United Kingdom. It shows enrollment increasing quite steadily in Canada and Australia throughout the period, staying fairly constant in the United Kingdom, and, in the United States and New Zealand, increasing until 2016 and then flattening out.

The differences among these five countries fairly jump out of the figure. Canada and Australia have gone full out in recruiting fee-paying international students. However, both the United Kingdom and New Zealand have pursued policies that made it difficult for all higher-ed institutions to follow such a strategy. In the United Kingdom, the government has put up barriers to students who want to work in the country after graduation; in New Zealand, some private universities were prevented from recruiting, owing to concerns about the quality of the institutions. Are similar forces at work here? Though one cannot with any certainty determine from these cases the cause of the growth slowdown in the United States, one can say that the magnitude of the slump here is consistent with the flagging growth that has occurred when governments have taken steps to reduce the influx of foreign students, as happened in the United Kingdom and New Zealand.

A Trump Effect?

While there is solid evidence for a mild “recession” in international-student numbers, concentrated mainly in less research-intensive institutions, the question is, why is it happening? Admissions professionals are floating two non-exclusive explanations. The first is an apparent diminution of America’s appeal in many countries and—more concretely—a harsher visa regime in the United States. The visa situation can be placed squarely at the feet of the Trump administration. The president may also bear some responsibility for the overall drop in America’s attractiveness, though there is evidence that this decline started prior to his election. The second is high tuition costs. Both explanations have merit.

Figure 3 shows the average price of one year of undergraduate tuition for international students across our five comparison countries. Based on these data, one would not say that U.S. public institutions have priced themselves out of the market (though it is worth noting that these figures are averages, and there can be wide distribution around the mean), but private institutions here have clearly chosen a very high price point. High-prestige privates can continue to generate many applications even at steep prices, but one suspects that the less research-intensive and hence less-prestigious four-year privates may struggle if indeed there is some kind of “flight to quality” on the part of international students.

As for more Trump-related causes, these are more difficult to track directly. We know from various surveys from the Pew Research Center that America’s reputation abroad has suffered under Trump. The ICEF i-graduate Agent Barometer survey has documented a marked decline in the number of international-student agents rating the United States as a “very attractive” destination (from 67 percent in 2016 to 57 percent in 2018), though in fairness, the country’s numbers had begun falling prior to Trump’s election (in 2015 it was 77 percent). That these perception indicators are tracking downward at the same time that applications are decreasing is suggestive, but not conclusive. Because the U.S. government does not publish statistics on the rejection rate for student visas, it is impossible to tell whether State Department policies are leading immigration officials to be tougher during the visa approval process. We do know, however, that university officials themselves believe that visa issues are part of the problem. In 2018, 83 percent of institutions participating in the Institute of International Education’s annual “hot topics” survey reported visa delays and denials were a factor in declining numbers of international students; in 2016, only 34 percent said this.

The Upshot

The evidence available to us suggests that there has been a modest waning in international applications to and new enrollments in American universities and colleges, perhaps on a scale equivalent to the decline seen in 2003–05. This drop has not become fully evident in the overall enrollment statistics, but it soon will. Based on international evidence, the size of the falloff here is consistent with those that have occurred elsewhere in the wake of a major government effort to let in fewer students from abroad.

The effect on talent acquisition—that is, on attracting the best students to the best universities—appears to have been minimal to nonexistent. The squeeze on institutional revenues, though, is a concern, especially for less-prestigious and less-selective institutions, where the effects have been concentrated. For private-sector institutions in this category, the comparative data on tuition fees suggest that the double whammy of lesser quality and high price point may be a problem. More generally, there is widespread concern about the Trump administration’s visa policies causing undue delays and denials of visas to prospective students.

If there is greater concern in the higher-ed sector about the decline in international-student numbers now than 15 years ago, when there was a comparable decrease, it is probably because international-student revenues make up a much larger proportion of most institutions’ budgets now. This shift has occurred not only because the foreign-student enrollments have risen; in private institutions, it is also a function of declining net revenues from domestic students after tuition discounting, and in public institutions it is also reflects declining government funding. Simply put, increasing the number of international students has been an important way for many institutions to maintain expenditure levels in the face of stagnating or declining domestic income sources.

How reasonable would it have been to presume that international-student growth might have continued indefinitely? Even if foreign-student enrollment numbers had continued to rise after 2016, eventually some public institutions would have hit levels where voters would have demanded a halt to such increases simply to preserve spaces in local universities for local students. That is what occurred in California in 2017, where the University of California board of regents adopted a set of rules capping out-of-state enrollment (including international students) at 18 percent, though campuses that were already beyond that limit were grandfathered. At some point, the relentless search for new revenue has to stop and the college-cost disease must be confronted more squarely. Perhaps this pause in international-student enrollment growth presents an occasion to do so.

Alex Usher is president of Higher Education Strategy Associates, a Toronto-based consultancy.

Have charter schools intensified the already high levels of segregation afflicting American public schools? Such was the claim advanced by the Associated Press in a December 2017 analysis showing that as of the 2014–15 school year, 17 percent of the nation’s 6,747 charter schools had enrollments consisting of 99 percent or more students of color, while just 4 percent of traditional public schools had such racially skewed student bodies. Their headline: “US charter schools put growing numbers in racial isolation.”

It is a claim that leading candidates for the Democratic presidential nomination are advancing on the campaign trail. U.S. Senator Bernie Sanders of Vermont cited the AP’s numbers in calling for a halt to public funding for charter-school expansion and a ban on for-profit charter schools. His education plan states that “the proliferation of charter schools has disproportionately affected communities of color” and notes that charters have been criticized by teachers unions and the NAACP for “intensifying racial segregation.”

The allegation is not new. As far back as 2010, the Civil Rights Project at the University of California Los Angeles asserted that “charter schools are more racially isolated than traditional public schools in virtually every state and large metropolitan area in the nation.” In an analysis for Education Next (see “A Closer Look at Charter Schools and Segregation,” check the facts, Summer 2010), researcher Gary Ritter and colleagues demonstrated the logical flaw inherent in using that kind of blanket comparison to assess whether charters increase segregation. Many charters locate in communities of color, where the education challenges and the demand for schooling alternatives are greatest. When one compares charter schools to their nearest district counterparts, Ritter and his team showed, differences in enrollment patterns virtually vanish.

Still, the question lingered: How exactly has charter schooling affected the amount of segregation in American schools? Has this ambitious school-choice experiment led families to sort into schools that are more homogeneous than those they would have been assigned to? Or, by weakening the ties between neighborhood of residence and school assignment, have charters instead fostered greater integration?

In this issue, Tomas Monarrez and Matthew Chingos of the Urban Institute and Brian Kisida of the University of Missouri provide the most compelling answer to this question to date (see “Do Charter Schools Increase Segregation?”). The authors use national data spanning nearly the entire history of the charter movement and a measure of segregation that takes into account the widely varying demographic composition of school districts and metropolitan areas across the country. To assess charters’ causal impact on school segregation, they look for any link between charter-school enrollment and racial balance across different grade levels in the same school district. If the share of charter enrollment at one grade level grew more than in other grades and there was a corresponding increase in segregation at that grade level relative to other grades, the researchers would conclude that charter schools had intensified segregation.

Their answer: charter growth has led black and Hispanic students to attend schools that are slightly more segregated, but its impact on overall segregation levels has been small.

What’s more, this modest impact of charter expansion on within-district segregation has been offset by a reduction in segregation between school districts within the same metropolitan area. Charter schools in some settings may now be playing the role originally envisioned for magnet schools, which aimed to improve racial balance by attracting suburban families to city schools. As a consequence, schools in metropolitan areas where charters have expanded the most are no more segregated than they would be without a charter presence.

These results come with important caveats. First, a state-by-state analysis shows that there are some places, such as Louisiana, New Mexico, and Oklahoma, where charters’ impact on within-district segregation has been more pronounced. Policymakers in those states would do well to bear this in mind as they consider further expansion.

Second, their study shows that any hopes that charter schools would enhance integration have not yet been fulfilled. Yes, there are a growing number of diverse-by-design charter schools that use strategic site location and carefully designed enrollment lotteries to recruit racially and economically diverse student bodies. Yet it would take far more work along these lines—not to mention a dramatic expansion of the charter sector—for this model to make a dent in the number of racially isolated schools.

The main takeaway from the study is clear, however: politicians concerned about school segregation have no good reason to single out charter schools for special criticism.

— Martin R. West

“Everything works somewhere; nothing works everywhere,” writes Dylan Wiliam in his book Creating the Schools Our Children Need. To that I would add, everything works at something; nothing works at everything.

Together, the two maxims describe what my research team found when we evaluated the Louisiana Scholarship Program, a statewide school-voucher initiative: the program satisfied some of its goals but fell well short of others, including that of raising student scores on state tests. What follows is a cautionary tale about good intentions and seemingly reasonable decisions resulting in unintended consequences.

The Louisiana Education Scene

Student performance on standardized tests in Louisiana has trailed national averages for decades. In the 2017 8th-grade reading results on the National Assessment of Educational Progress, Louisiana public schools tied for 42nd in the nation and rated significantly higher than only one jurisdiction, the District of Columbia. Only 25 percent of Louisiana 8th graders scored as proficient or above in reading, similar to the 23 percent rate in 2015 but higher than the abysmal 17 percent rate in 1998. NAEP reading scores for Louisiana 4th and 12th graders have been similarly disappointing, as have their math and science scores.

The private-school sector in the Pelican State is relatively large, for three likely reasons: the traditionally low academic performance of the state’s public schools; Louisiana’s French-Catholic heritage, which has given rise to many parochial schools; and the state’s troubled history of racial segregation. In 2011–12, when this story begins, Louisiana had 394 private schools enrolling 112,645 K–12 students, or nearly 16 percent of Louisiana K–12 students, well above the national private-school average of 11 percent. The private-school sector in Louisiana is a diverse blend of religious and secular schools, with Catholic and evangelical Christian schools dominating the scene. Annual tuition rates in 2013 ranged from $2,000 to $19,660, with a school-level average of about $6,000.

In 2005, Hurricane Katrina raged in, devastating the city of New Orleans and environs. The flood damage to more than 300 public schools was so extreme they had to be condemned. Since the storm left many area private schools intact, the Catholic Archdiocese of New Orleans, waiving tuition, initially took in thousands of students whose public schools had been ruined. Several months later, after Hurricane Rita ravaged parts of the Houston area, the federal government established hurricane vouchers for the two storm-damaged regions, temporarily covering the private-school tuitions of educationally displaced children.

In the wake of Katrina, Louisiana lawmakers established two major private-school choice programs. The first was the Elementary and Secondary School Tuition Deduction policy, enacted in 2008. This initiative allows families to deduct on their state income-tax return up to $5,000 per child in private-school educational expenses. The families of more than 106,000 of the 112,000 students attending Louisiana private schools in 2012 claimed the deduction. The second program was the Student Scholarships for Educational Excellence Program, which in 2009 began providing private-school vouchers to 624 low-income students in the parishes of Orleans and nearby Jefferson. This program served as a pilot for the larger, statewide Louisiana Scholarship Program, launched in 2012.

State policymakers also dramatically refashioned the public-school system in New Orleans. Gone were residential attendance zones, the teacher collective-bargaining agreement, and almost all of the public schools the Orleans Parish School Board directly operated. In their place arose a new kind of urban public school system, dubbed the Recovery School District. Overseen by state education officials, the new district was composed almost entirely of public charter schools that would be held accountable for student achievement on state tests. Douglas Harris at Tulane University concluded that this package of market-based reforms—expanded school choice coupled with results-based accountability—substantially improved the test scores of students attending the city’s public schools (see “Good News for New Orleans,” features, Fall 2015).

 

The Louisiana Scholarship Program

The pilot voucher program had 1,950 students enrolled in 2012 when it expanded statewide and became the Louisiana Scholarship Program. Demand for the program was strong from the start: a total of 9,736 students applied that first year, with 5,296 receiving vouchers and 4,944 using them to attend a private school. It is this 2012–13 applicant cohort, a majority of whom lived outside New Orleans, that we evaluated over the course of four years. The program enrolled 6,695 students in 2016–17, a drop of 9 percent from its enrollment peak of 7,362 in 2014–15 (see Figure 1).

Participation in the voucher program is restricted to low-income students in low-performing public schools. To qualify, the income of a child’s family must be at or below 250 percent of the federal poverty line, which in 2016–17 was $60,750 for a family of four. Applicants also must either be entering kindergarten or be attending a public school graded C, D, or F by the state’s test score-driven school accountability system. About one third of the K–12 students in Louisiana, or nearly 250,000, were eligible for the scholarship program in 2012, when 4 percent of the eligible student population applied to the program. Nearly 90 percent of the eligible applicants were African American and over 80 percent were entering grades 1–6 that year.

Applicants win spots in the program by means of a government-run lottery, and the students who did not win the lottery provided the control group for our study. Students in D or F schools receive priority in this lottery, so very few students from C schools have received scholarships. Students with disabilities also receive priority, as they are placed automatically in their private school of choice if a seat is available. The lottery simultaneously awards students with scholarships and placement in a specific private school, drawing from the school preferences listed by parents. Unlike most private-school choice programs, the scholarship award takes place after the school-shopping process, not before it.

The voucher value is limited to 90 percent of the state and local per-pupil funding in a student’s school district or the tuition rate the student’s chosen private school charges, whichever is less. Annual tuition at participating private schools ranges from $2,966 to $8,999, with an average of $5,437, compared to average state and local per-pupil funding of $8,500 in Louisiana’s public schools in 2010–11.

Why might a private school decide not to participate in the Louisiana Scholarship Program? One reason could be that participating schools must submit to regulations regarding financial practices, curriculum, student enrollment, mobility, safety, and achievement. They must provide financial audits to state officials every year and maintain a curriculum that the state Department of Education judges to be of equal or higher quality to the curriculum in public schools. Participating schools cannot select their voucher students and must instead admit them solely via the placement lottery administered by the state.

All participating private schools must administer the state’s accountability tests annually to voucher students in grades 3–8 and again in grade 10. Participating schools with at least 10 voucher students per grade are assigned school-performance ratings based on voucher-student scores on the state test.

As in the test-based accountability model applied to public charter schools in Louisiana, the state can sanction private schools participating in the voucher program. Any of three conditions leads to state sanctions. First, a school is sanctioned if the average rate of gain of voucher students on the state test is so low that the school qualifies for an F grade. Second, a school is sanctioned if less than 25 percent of its voucher students score at or above the state benchmark for proficiency. Finally, participating schools are sanctioned if their annual financial audit reveals improprieties or raises concerns about the school’s future viability.

A private school that receives a sanction is prohibited from enrolling new voucher students until it remedies the condition that led to the penalty. By 2015–16, the final year of data collection for our study, 35 of the 122 private schools in the program had been sanctioned for at least one year.

These regulations on admissions, testing, and curriculum render the Louisiana Scholarship Program one of the most highly regulated among the 58 private-school choice programs in the country. Why put so many restrictions on the private-school choices available to parents?

The history and context of education in Louisiana likely led policymakers to opt for such a highly regulated model. The Pelican State still has many racially stratified schools. Most of the D and F public schools in the state serve a majority low-income student population. Thus, restricting the voucher program to students from low-income families attending failing schools, and requiring the schools to forgo any admissions standards, was expected to prevent the program from worsening school-level racial and income segregation.

The private schools in Louisiana ranged dramatically in tuition rates, which likely serve as a rough proxy for school quality. Officials anticipated that, as is common in voucher initiatives, few of the higher-tuition private schools would elect to participate in the program, since they would have to foot a large part of the cost of educating voucher students. Moreover, the state Elementary and Secondary School Tuition Deduction policy provided the fee-paying customers of private schools with a significant cost rebate that did not require the school to take on any additional state regulations or paperwork, reducing the incentive for schools to join the voucher program and accept its regulatory requirements.

Policymakers expected the lower-quality, under-enrolled private schools in Louisiana to sign up to participate in the voucher program, so they designed a results-based accountability system that would remove schools from the program if they produced low student test scores. A similar regulatory system appeared to be working well for the public charter-school sector in New Orleans. Mandating that private schools administer the state accountability test would allow an apples-to-apples comparison of school performance. It all seemed so sensible at the time.

Private School Participation

Fewer than a third of the private schools operating in Louisiana in 2012 agreed to participate in the Louisiana Scholarship Program. That was the smallest share of schools to participate in a statewide, means-tested private-school choice program among all such programs in the country, and we sought to understand why. Brian Kisida, Evan Rhinesmith, and I implemented a survey of Louisiana private-school leaders that revealed the top factors deterring private schools from joining the voucher program. We found that these leaders feared that more regulations might arise in the future and hamper their independence or threaten their religious identity. They also worried about the integrity of their admissions policies, and they didn’t like the pressure to adhere to the state’s curriculum standards.

Evidence from a survey experiment conducted in other states suggests that the kinds of regulations in place in Louisiana may discourage private schools from participating in choice programs. Corey DeAngelis, Lindsey Burke, and I sent brief email surveys to every private-school leader in Florida, California, and New York, asking if they would be likely to participate in a private-school choice program offering a $6,000 voucher. Survey takers were randomly divided into five groups. Those in the first group were asked about their willingness to participate in the hypothetical program with “no strings attached.” Those in the other four groups were asked about participating under a specific regulatory requirement.

One third of private-school leaders who were told they would face no additional regulations said they were “certain” they would participate in such a voucher program. Among school leaders who were told the hypothetical program would mandate an open-admissions policy, just 14 percent said they would be certain to participate. Of those who were told that they would be required to administer the state accountability test to all voucher students (with the results reported publicly), 24 percent said they would be certain to participate. The remaining two conditions had no significant effect on leaders’ expressed willingness to participate: a requirement that the school administer a norm-referenced test of its choosing; and a mandate that the school accept the voucher as the full cost of educating the child.

What kinds of private schools did participate in the Louisiana Scholarship Program? Compared to non-participants, participating schools were more likely to be Catholic, have lower enrollments, and have student populations that were disproportionately made up of racial or ethnic minorities. The typical participating private school was accustomed to serving socially disadvantaged students and eager to increase its enrollment. Surprisingly, average tuition levels were not a major factor in separating participating schools from non-participating ones in Louisiana.

Students Served

The scholarship program was designed to serve a highly disadvantaged population: kids from low-income families who were attending a public school that produced consistently low test scores.

It is therefore no surprise that Yujie Sude and I found almost no evidence that the voucher program “cream-skimmed” easy-to-educate students. At the application stage, the program attracted a highly disadvantaged population of students. Louisiana public-school students were more likely to apply to the voucher program if they were low income, African American or Hispanic, and lower test performers. Students in the earlier K–12 grades were much more likely to apply than older students, suggesting that parents are more willing to switch their child from a public school to a private one when they are younger and perhaps better able to adapt to their new school environment.

Which students stayed in the program? Several factors were associated with persistent voucher use over three consecutive years. Students with lower initial test scores were more likely to persist than were students with higher scores. Girls and students who enrolled initially in earlier grades were more likely to continue than boys or students who started in later grades. Students in private schools that had lower minority enrollments and that were located a shorter distance from home were also more likely to persist, as were students residing in public-school districts that had lower per-pupil spending.

After all of these factors played out, how select was the voucher-student population three years after application? Characteristics associated with student disadvantage tended to distinguish three-year voucher users from students who never applied to the program. Compared to those who didn’t apply, students who participated and continued for three years were more likely to be female, low income, and African American. The Louisiana Scholarship Program did succeed in expanding school choice to a relatively disadvantaged population of students.

Effects on Racial Segregation

Many commentators claim that parental choice programs worsen segregation. To test that claim, Jonathan Mills and Anna Egalite analyzed the effect that initial voucher users had on the level of racial integration in both the public schools they left and the private schools they joined (see “The Louisiana Scholarship Program,” features, Winter 2014). First, the researchers established a benchmark for racial balance in each school, pegged to the racial composition of the local community. Then they determined whether each student who transferred to a private school in 2012 under the voucher program had an integrating or segregating effect. For the public school the student was leaving, the student was deemed to have had an integrating effect if the race of the student was overrepresented at that school, given the community benchmark. But a transferring-out student had a segregating effect on that school if the student’s race was under-represented there. Conversely, a transfer into a private school better integrated it if the student’s race was under-represented and further segregated it if the student’s race was overrepresented.

The researchers found that 83 percent of initial student transfers under the program had an integrating effect on the racial composition of the public schools they left. In the private schools they joined, about half of the students generated better integration and the other half lessened integration. Even in the 34 Louisiana public-school districts still under a court order to integrate by race, 74 percent of the transfers under the voucher program brought the public schools closer to the goal of racial integration. Thus, the program has operated as a voluntary school desegregation program, even though the racial integration of public schools was not its primary purpose.

Academic Outcomes

The main purpose of the scholarship program was to improve academic outcomes. On that goal, it clearly fell short. Using gold standard experimental methods, Jonathan Mills and I determined that the effects of the program on student scores on the state accountability test tended to be negative, especially in math, as long as four years after initial scholarship use.

For the students who participated in the voucher lotteries and for whom we had both baseline (2011–12) and subsequent test scores, the effects of the scholarship program on achievement varied between negative and neutral (see Figure 2). At baseline, the math test performance of the lottery winners was statistically equivalent to that of the control-group students (that is, those who did not win a voucher placement). But effects on the math performance of the scholarship students were negative and large in the first year of the program, when students were adjusting to their new schools and, likewise, the schools were adjusting to them. The voucher students recovered some of their lost ground on the state math test the second year and delivered math scores that were statistically similar to the control group in year three, when the state switched to a new accountability test and neither public nor private schools were held accountable for the results. In year four, when test-based accountability was reestablished statewide, the voucher program again produced negative impacts on math scores; these were moderately large.

The reading test-score impacts of the program followed a trend similar to the math scores but with consistently smaller effects, most of which were not significantly different from zero. For those students for whom we had baseline test scores, the reading impacts of the program were negative and moderately large the first year, and much smaller and not statistically significant in the second, third, and fourth years.

The achievement impacts of the scholarship program were not uniform for all groups of students. In the fourth year, the negative effects of the program on test scores were less than half as large for African American students as for non-African American students. Also, voucher students in grades 4 and 8 took the main state accountability test, while those in grades 3, 5, 6, and 7 took a version of the test that was scored on a different scale. For the latter group, the negative test-score effects of the program were less than half as large as for those who took the main state test.

The effects of the voucher program on student test scores also varied based on key features of the school the student most preferred. Matthew Lee, Jonathan Mills, and I determined that the achievement effects of the program were much less negative, and in some rare cases even positive, for subgroups of students whose preferred private schools ranked in the top one third of participating schools in regard to higher tuition, higher total K–12 enrollment, or a greater number of instructional hours for students.

Educational Attainment

Educational attainment—how much schooling an individual ultimately completes—greatly influences his or her later life outcomes, and researchers have increasingly turned to studying the impacts of education programs on student rates of high-school graduation and college enrollment, persistence, and completion. Too few students in our experimental sample were old enough to have graduated from college for us to examine that important outcome. However, more than 1,000 students who participated in the voucher program’s lotteries completed high school and could have enrolled in college. Did the negative test-score effects of the program decrease their rates of college going?

Heidi Holmes Erickson, Jonathan Mills, and I found that the Louisiana Scholarship Program had no effect on college entrance for students. After high school, voucher users enrolled in a two-year or four-year college at a rate of 60.0 percent, which was equivalent to the 59.5 percent enrollment rate of the control group.

Mixed Outcomes

Opponents of private-school choice may use the results of our study to argue that “free market” approaches to education have failed. However, the initiative that we evaluated was clearly not a pure free-market education reform. Free markets generally require: 1) that new suppliers can easily enter the market; 2) that prices can vary across providers and different versions of a service; and 3) that consumers are the main judge of the quality of the service. None of those conditions held for the Louisiana Scholarship Program. New suppliers were virtually prohibited from emerging, as private schools had to operate for two years with only fee-paying customers before they were allowed to participate. The price of the service was largely fixed by the voucher formula, and parents were prohibited from paying more for a higher-quality education, at least within the program. A government-run lottery placed each voucher student in a school, and government overseers determined which schools could and could not continue to enroll new voucher students. And while parents were able to communicate their preferences about school placement, it was the state, not the parents, who made the final selection.

School choice programs often seek to reduce racial segregation in schools. The Louisiana Scholarship Program succeeded in doing so. Everything is good at something. The statewide launch of the program in 2012 better integrated Louisiana’s public schools, as most voucher-program participants left public schools in which their own race was overrepresented. Persistent scholarship users were more likely to be African American and to have had lower initial test scores compared to those who didn’t apply to the program. Furthermore, the program saves the state money, because the voucher maximum of less than $6,000 is only about two thirds of the combined state and local per-pupil funding in Louisiana’s public schools.

The regulatory framework of the program rested on several ideas: that private schools accepting government vouchers are comparable to public charter schools; that low-performing schools will improve with government incentives to do so or be kicked out of the program; and that student test scores are the best single measure of school performance. All of these notions are subject to question.

Private schools differ from public charter schools in two critical ways that affect how they might be effectively regulated. First, private schools have a choice in whether to participate in voucher programs, accepting government funding and the regulations that come with it. In Louisiana, where tax policies indirectly subsidize families who pay tuition out of pocket, private schools have lots of paying customers and thus greater latitude to turn down the chance to serve disadvantaged students on state scholarships if the offer is not attractive to them. Public charter schools have no such choice, as the government is their only reliable funding source.

There is little evidence that education overseers can help schools improve by using regulatory carrots and sticks. Student test-score performance is a product of many complex factors, including family background (see “How Family Background Influences Student Achievement,” features, Spring 2016), school culture, teacher quality, child nutrition, test preparation, and curricular alignment with the test. Actual levels of student learning are in there somewhere, but it is a crowded room of factors that most private schools with established educational programs and cultures cannot change over the course of a few years, even if a regulatory system incentivizes them to do so. The evaluation literature on aggressive efforts at systematic school turnaround reinforces this point: school improvement is a slow, difficult, evolutionary process.

Removing private schools from the program if they fail to boost student test scores might seem like an automatic method for improving outcomes by “chopping off the lower tail of the performance distribution,” but where do the affected students go instead? If the existing private schools already are full and new ones are prohibited from serving voucher students during a long probationary period, the state sanctioning system merely serves to limit the educational options of parents and students.

Finally, student scores and annual gains on the state-mandated accountability test are only one measure of school performance. They capture only a portion of what we would consider actual student learning, and advancing student learning is only one of many goals of publicly financed education. We also charge schools with instilling civic values in students and developing positive character traits of persistence, conscientiousness, and respect for others and the norms of society. When Thomas Stewart and I polled a room of 40 parents participating in the D.C. Opportunity Scholarship Program on how they assess the academic progress of their child in school, none of them selected “standardized test scores” as the metric. Instead, they said they used “student motivation to learn,” “student grades,” “positive student attitudes toward school,” and “positive student behaviors toward schools” as measures of whether their child was succeeding. The private schools participating in the Louisiana Scholarship Program may be delivering these more nuanced but vital outcomes to their voucher students, but determining that would require a more comprehensive assessment of school performance.

In order to accomplish anything, schools must keep their students safe. Recent surveys suggest that school safety now rivals academic concerns as the main reason parents seek private-school choice. Public regulators would be wise to work indicators of school safety and an orderly school environment into their measures of whether a school is performing at a satisfactory level.

The Louisiana Scholarship Program did not succeed in raising student scores on the state accountability test. In fact, it had a clear negative effect on math scores and a possible, though less severe, negative effect on reading scores. Nothing is good at everything. Our evidence suggests that about half of the negative test-score effect is likely due to public schools more carefully aligning their curriculum to the tested material and systematically implementing techniques for preparing students for the test. Still, it is clear that the program did not positively affect scores on the state test. Insofar as state accountability test scores are used as the litmus test for effectiveness, the Louisiana voucher program did not let the good times roll down in the Bayou.

Patrick J. Wolf is a distinguished professor and 21st Century Endowed Chair in School Choice in the Department of Education Reform at the University of Arkansas College of Education and Health Professions.

For families living in neighborhoods with low-performing schools, choice-friendly policies open up an array of options. Students can seek out district or charter schools with stronger academic programs, or look for schools that match their unique interests or needs. The concept is simple, but families who want to take the school-choice route may find that getting students to and from school presents a significant roadblock.

Considering a school some distance from home means weighing the costs and benefits to student and family. Traveling outside the neighborhood can entail earlier wake-ups, lost time en route, unruly fellow travelers, and missed transit connections. For choice to be worthwhile, the payoff has to outweigh the drawbacks. Transportation must be affordable and safe so that all students, regardless of their location or resources, can attend their school of choice. And on the municipality’s end, the cost of providing transportation must be sustainable. All of these factors play into the discussion on the benefits of choice.

In 2017, Matthew Chingos and Kristin Blagg of the Urban Institute convened a group of researchers to analyze students’ school choices and travel to school in five cities—Denver, Detroit, New Orleans, New York, and Washington, D.C.—where families are able to select from among many charter and district schools (see Table 1). Our team found that a large number of students in these cities take advantage of school choice, and that it often provides them with important academic benefits. Traveling for these benefits, however, does come with some costs to students and their cities’ education systems and at times reveals conditions of unequal access. Cities are hungry for innovative solutions to the transportation challenge.

Transportation Policies

State legislatures throughout the country anticipated that student transportation would play a role in the success or failure of school choice. Of the 44 states and D.C. that have enacted charter laws, 14 included provisions specifying whether the charter school, school district, or some other entity would be responsible for providing transportation. Another 13 states require prospective charter schools to submit a plan describing how they would furnish transportation to their students. Laws in three additional states require local districts to provide the same service to local charter-school students that they provide to students enrolled in district schools. These laws, however, rarely spell out the details of the mandated support and, as a result, approaches vary across cities.

The five cities we examined have adopted a number of different policies for providing transportation for students who opt out of their neighborhood school. In New Orleans, New York, and D.C., students who choose another school can still receive district-provided transportation. In D.C., all students, regardless of their distance from the school, receive free transportation to school on public-school buses or via free access to public transit. In New Orleans and New York, transportation support depends on how far away students live. In Denver, students who exercise choice and live and enroll in any school in specific transportation zones served by Success Express, a dedicated shuttle-bus service, receive free transportation. In addition, most charter schools offer public school-bus transportation to students. In Detroit, students who select a different district school or a charter school are not guaranteed transportation, but some charter schools do offer it.

 

CHOICE POLICIES IN FIVE CITIES (Table 1)
City	Available School Choices
Denver	• Interdistrict choice • Zoned schools plus open enrollment • 60 charter schools
Detroit	• Interdistrict choice • Zoned schools plus open enrollment • Charter schools
New Orleans	• 100 percent charter schools
New York	• Zoned schools plus open enrollment for elementary and middle schools • Mandatory choice for high schools • Charter schools
Washington, D.C.	• Zoned schools plus open enrollment for elementary and middle schools • Charter schools

 

The Road to School

In all five cities, many children are opting for schools other than the one assigned to them, but these choices have not, for the most part, entailed long commutes.

In D.C., nearly 75 percent of the city’s students opt out of their assigned school, and in Detroit, more than 75 percent decline to attend their closest school. In Denver, among students applying to high school, less than half select the school closest to home as their first choice. The median first choice for Denver students is actually the fourth-closest school to home. In New York, only 12 percent of high-school students enroll in the closest school. Despite the high number of students who are exercising choice, the median drive time to school for 9th graders across all five cities ranges from 10 minutes in Denver and Detroit to 15 minutes in New York. (Times were estimated via Google driving directions for the typical morning commuting hours.) Actual commute times for students are likely longer if they are traveling by public transit or school bus. For example, in New York, the median commute time rises to 29 minutes when students use public transit, the more common method of getting to school in that city. That said, a 2017 survey of parents in Denver, Detroit, New Orleans, and D.C. found that driving was the most common mode of transport to school in each of these cities. As many as 67 percent of Denver parents drive their kids to school. Even in D.C., which has a strong public-transit system, 43 percent of parents drive their children to school.

African American students face somewhat longer commutes to school than white students and more-affluent students. In each of the cities except New Orleans, the drive to school for African American 9th-grade students is between two and five minutes longer than the drive for their white counterparts. Even so, the longest average drive—that of African American students in New York—is only 20 minutes. Interestingly, our analysis also finds that students from less-affluent households do not, on average, travel farther to school than their peers from more-affluent households.

For elementary and middle-school grades, our research team only calculated drive times in New Orleans, New York, and D.C., but in these cities, drive times are even shorter for families of younger students. These shorter drive times may simply reflect the fact that there are more elementary schools than high schools and that they are more widely distributed across neighborhoods, but it may also suggest that parents of younger children place a particularly high premium on having a school close to home—or perhaps that they view the school options available to them as more interchangeable, and therefore see less reason to sacrifice convenience.

It should not be surprising that students who exercise school choice still enroll in schools that are a relatively short drive from home. Research clearly indicates that parents and students weigh the trade-offs between distance and quality when selecting a school, favoring a closer one when all else is equal.

Analysis from the five cities, however, suggests that balancing the trade-off between quality and distance may not be exceedingly difficult for many families. We examined how long it would take 9th graders in these cities to drive to the closest high-quality school (defined as one having high graduation rates, employing a high percentage of veteran teachers, and offering calculus). We found that student time en route varies across cities, but the average drive time to a high-quality school does not exceed 15 minutes for any quality measure. More typically, the drive time to the closest high-quality school falls below 10 minutes.

The drive time to the closest high-quality school varies somewhat among white, African American, and Hispanic students, but the gaps do not always disadvantage students of color. In fact, only Hispanic students in Denver and Detroit have to travel farther than white students to reach a school with a high graduation rate. In all other cities and for all other quality measures, Hispanic students are closer to high-quality schools than their white counterparts. Only in New Orleans and D.C. do African American students have to go farther than their white counterparts to reach a high-quality school.

In sum, our analyses suggest that, for most school choosers in these cities, the drive to school is not exceptionally long, although there are some students who enroll in schools that are farther from home. Ten percent of 9th-grade students in Denver, Detroit, New York, and D.C., are willing to travel more than twice the median distance to school.

Students Reap Benefits

Even a small travel burden would be pointless if students did not gain any benefits for it. Examining three of the five cities—Denver, Detroit, and New York—we explored the extent to which students who exercise choice tend to select schools with higher performance or attractive academic offerings. In each of these cities, we found that students who choose to travel for school do get something for their effort.

In Detroit, students who opt for schools of choice select those with somewhat higher accountability ratings, lower absentee rates, and, for students who started at the school in 9th grade, higher graduation rates. For example, 9th-grade students in Detroit who opt out of the closest school end up selecting one that has an accountability rating that is, on average, 5 points (out of 100) higher, a graduation rate that is 9 percentage points higher, and an absenteeism rate that is 3 percentage points lower, relative to the other schools in the city. In Denver, incoming 9th-grade students who demonstrate the greatest willingness to travel for school, a group we call “super-travelers,” choose schools that have graduation rates that are, on average, 23 percentage points higher and that have seven fewer incidents of discipline per 100 students. They are also more likely to opt for schools that offer advanced curricula (Advanced Placement courses, International Baccalaureate programs, and calculus) as well as dual-language or immersion programs. We found that these super-travelers typically could find closer-to-home schools that had one, but not all of these traits, suggesting that the schools that necessitated long commutes offer a “package” of benefits that the neighborhood schools lack.

In New York, our analysis of choice enrollment in elementary grades found that students opting out of their assigned schools choose schools with proficiency rates that are, on average, 6 percentage points higher on the state English language arts and math exams than the schools that “non-choosing” students in their neighborhood attend. Students in grades K–2 enroll in schools with higher student-achievement growth. We found that these benefits increase when students attending choice schools have access to free transportation, suggesting that providing for this service can enhance the potential benefits of choice to students.

Costs to Students and Cities

Students may not necessarily have to endure overly long commutes to their chosen schools, but they still face real costs—as do their cities and school systems.

The prospect of a long ride to school has long led to worries about students’ ability to access before- and afterschool activities, as well as the unsupervised and unproductive time spent en route. Our analysis from New York and D.C. also notes potentially important academic and social costs for students.

Longer commutes can be difficult for students and families to sustain. In D.C. we found that the longer students had to travel to school the more likely they were to miss school and transfer out—two circumstances that can disrupt student learning. Specifically, kindergarten and 6th-grade students with long commutes (that is, whose commutes were longer than 75 percent of all students) missed about one more day a year and were 2 percentage points more likely to transfer schools than students with relatively short commutes (shorter than 75 percent of all students). Ninth-grade students with long commutes missed about two more days and were 1 percentage point more likely to transfer schools than their counterparts with short commutes. We did not find, however, that longer commutes alone led to lower academic outcomes for students.

Going to school in another neighborhood can also involve social costs. Our analysis from New York found that the farther students traveled to school, the less likely there were to attend a school with another child from their own neighborhood, potentially fraying important social networks.

For public-school systems, providing transportation to students can consume considerable resources. Transportation is a costly and volatile business, subject to fluctuating fuel costs, road construction, and labor shortages. Transporting students introduces a host of additional issues that amplify the costs dramatically.

There are immense logistical demands involved in safely moving students from their homes to a vast number of different school locations. These logistics are further complicated by the fact that many students will change schools (and thus their route to school) some months into the school year, as spots open up on waitlists. When a city lacks a centralized policy managing the student-transfer process, an official at a charter authorizer in Detroit explained, the churn of students can be overwhelming. She noted, “Kids come and go with no transfer policies and no kind of accountabilities in place around who’s moving where. Kids are just constantly moving. [For schools] it would be out of control, the amount of jostling you would have to do to even try to operate a bus schedule.” In addition, schools in choice-rich cities often operate with different start and end times that must be accommodated in the bus schedules.

Two other factors that escalate costs are the requirement to provide transportation accommodations, such as door-to-door service or smaller vehicles for students with disabilities, and the need to hire bus monitors to protect students and maintain order.

Choice may involve higher spending on transportation, but not necessarily. In New Orleans, Tulane University researchers learned that transportation costs increased by almost $200 per pupil, an increase of 34 percent, after the city shifted to a full-choice system. According to charter-school leaders in that city, where individual schools carry the costs of transportation, school leaders are forced to make difficult trade-offs between classroom and transportation spending. In Denver, the public school system provides transportation services for most district and charter schools. Federal data for the 2015–16 school year show that the district spent $25 million on delivering these services—almost 2 percent of total district spending. (Charter schools contribute funds from their own budgets for the use of this district service.) Denver’s spending is well in line with that of comparably sized districts nationwide, which devoted, on average, 3.6 percent of their budget to transportation.

Innovation Needed

No single solution will address the costs and challenges of providing transportation in choice-rich cities. So far, school officials in the five cities cited here have turned to public transportation, decentralizing transportation, creating transportation zones and enrollment zones, and using small rideshare enterprises.

Public transportation. Cities often rely heavily on public transit to get students to and from school. But, with notable exceptions such as in New York and D.C., public-transit networks tend to fall short in this capacity. On top of causing worries about safety and unsupervised travel, the public-transit option increases students’ travel time, especially in cities without extensive transit networks. In Denver, Detroit, and New Orleans, for example, the typical 10-minute drive turns into more than 30 minutes by public transit, and a 30-minute drive morphs into a 70–80 minute transit ride. Predictably, public-transit options are least efficient for students in lower-rent neighborhoods.

Decentralization. Rather than relying on a centralized school-transportation system, New Orleans has assigned responsibility to the individual schools, with the goals of distributing the burden of cost and giving all students access to any of the city’s schools. This policy has guaranteed such access for most students but it has also created considerable inefficiencies in getting them to school. Bus routes serving individual schools are often long and circuitous. The median school-bus commute for students is 35 minutes (more than twice the drive time), with some students on the bus for upward of 90 minutes one way. Schools and networks have tried to improve efficiency by staggering start times and sharing bus routes with other schools, but costs in funding and student time remain high.

Enrollment zones. Some cities, such as Denver, have tried to balance choice and the costs of transportation by establishing enrollment zones, geographic areas whose residents are eligible to receive free transit to in-zone schools, regardless of whether the school is closest to their home. Students may still be free to enroll in schools outside the zone but would forgo free transportation.

Transportation zones. Among the most innovative efforts to expand service and manage cost are transportation zones where shuttle buses travel a set circuit of stops at neighborhood locations and schools in the zone. Buses operate for a certain number of hours in the morning and afternoon, and students hop on and off as needed. This approach accommodates different start and end times, facilitates student participation in before- and afterschool activities, and captures some economies of scale. Denver’s Success Express, for example, overlays these transportation zones upon two of the city’s enrollment zones and in so doing provides free transportation to students living and enrolling in two of Denver’s most difficult-to-access and underserved communities. Detroit is poised to adopt Denver’s approach and expand on it by including childcare and afterschool activity centers in the bus circuit.

Ridesharing. More recently, small rideshare companies dedicated to transporting children have emerged. These services, which feature highly vetted drivers and extensive safety examinations for vehicles, allow parents to request rides for their children through a phone app and furnish them with point-to-point transportation. While cities are unlikely to use these relatively high-cost providers at scale, their flexible, custom service has worked for highly vulnerable students living in homelessness or in the foster-care system.

The Start of a Journey

For many students, choice without transportation is not much of a choice, and transportation in high-choice cities remains a vexing concern. Analyses from the five high-choice cities in our study show that most students select schools that are within a short drive from home and, despite challenges, many families are sorting out how to get their children there. Still, the leaders we spoke with in high-choice cities want to serve families better, especially families with limited resources and those living in less-accessible neighborhoods. The challenge lies in the execution.

So far, cities have tried to shoehorn their transportation services for schools of choice into traditional systems. But to move forward, cities will likely have to shift their perspective on providing transportation to match the one they have been taking with schools—that is, being open to a greater diversity of providers and approaches to meet student needs. As the director of transportation for Denver’s public schools put it, “We are trying to figure out how to migrate to a system that can support the complexity of offerings that the district has created for families.” Accomplishing that in choice-rich cities will take innovation and a willingness to go beyond long-established practices.

Betheny Gross is associate director at the Center on Reinventing Public Education (CRPE) and affiliate faculty, School of Interdisciplinary Arts and Sciences, at the University of Washington Bothell.

Since the publication of A Nation at Risk in 1983, policymakers and politicians have worked to stave off a perceived decline in the academic preparation of American students. Stubbornly low scores on international exams and signs that many U.S. graduates are ill-equipped for college and the workforce have lent urgency to this perception, and many states have made high-school graduation requirements more rigorous in response. As a result, American high-school graduates today complete more academic courses and more advanced coursework than they did three decades ago. At first glance, this seems clear evidence of progress.

But much of those gains have come at the expense of student participation in vocational, or career and technical education, classes—a broad category of coursework that encompasses everything from welding, to sports management, to computer science. Many praise this shift, arguing that vocational education in high school deters capable students from college and prepares them for “dead-end” jobs. Yet an opposing camp points to shortages in the skilled professions, noting that not all students are college-bound and that for some, vocational training may be the difference between high- and low-paying jobs. Pushing all students to concentrate on core academic classes at the expense of vocational study, advocates say, takes the focus off the occupationally relevant skills and credentials graduates need for a smooth transition to adulthood.

This raises a central question: What is the relationship between modern-day vocational or career and technical coursework and high-school graduates’ success in college or in the workforce? Is vocational education an off ramp to college foisted upon lackluster students, or a different and less costly path toward adult success? We examined high-school and college transcripts and labor-market outcomes for about 4,000 adults to find out.

Our study, making use of a nationally representative sample of early-career Americans, shows that students tend to enroll in vocational classes based on whether such options are available to them, suggesting that the commonly held belief that marginal students are funneled into such classes is untrue. Further, we find that not all vocational classes are equal: students earn about 2 percent more annually for each advanced or upper-level vocational class they take, but enjoy no wage premium for having completed lower-level or introductory vocational study. In terms of college enrollment, while lower-level vocational courses may deter marginal students from college, they have no impact on net graduation rates; advanced courses at worst do no harm.

The implications are considerable. First, students most likely to benefit from vocational coursework seem to be self-selecting into those courses, implying that policies that limit their ability to do so, such as increased course requirements in academic subjects, may not be in all students’ best interests. Second, we find that vocational courses may pull students out of college who are the least likely to graduate if they enroll. Finally, the benefits of vocational coursework accrue to students who specialize rather than those who take multiple vocational courses in several areas; therefore, programs should allow for depth in any topic offered. Recent trends toward more specialized concentrations or “pathways” and away from general, non-specialized coursework appear to be smart policy.

A curriculum continuum

In recent decades, vocational study in high school has been on the decline, in tandem with a 32 percent drop since 1985 in federal funding for such programs. Between 1990 and 2009, as the average number of academic credits high-school students earned increased, the number of vocational credits dropped by 14 percent, or roughly two thirds of a year of vocational studies (see Figure 1).

However, the vast majority of American students still take at least one vocational course during high school, and roughly 50 percent take the equivalent of one full course each year. This contradicts the mainstream image of vocational study as an alternative “track” in which students do not complete a full complement of academic classes. We should instead think of the high-school curriculum as a continuum, in which the real question is just how many vocational classes students select. Our study takes this perspective.

To trace students’ choices to enroll in vocational courses and their effects, we examine schooling and labor-market activity for participants in the 1997 National Longitudinal Survey of Youth, collected by the U.S. Bureau of Labor Statistics. These data cover a nationally representative group of 8,984 individuals who were ages 12 to 18 when first interviewed, and include detailed information from the high-school transcripts of 6,009 of them. Importantly, the study collects detailed information on each individual, including scores on the Armed Forces Qualification Test, family background data, and annual records of college going and work histories.

In reviewing those records, we focus our attention on the 4,414 participants who have transcripts in all years of high school and relevant college-outcome records. When studying earnings, we use the 3,708 students whom we determined had completed schooling and entered the labor market. (We define labor-market entry as the first of four consecutive semesters an individual is not enrolled in any educational institution followed by no more than one enrolled semester thereafter.) The median age of our sample in the most recent round of data collection, which occurred in 2010, is 29.

In looking at high-school transcripts, we consider classes to be “vocational” if they focus on general or specific labor-market preparation under the Perkins Act according to the National Center for Education Statistics, excluding family and consumer sciences. The most common types of vocational courses taken are transportation and industry, business and management, computer technology and keyboarding, and general labor-market preparation classes such as industrial arts or work experience opportunities. Courses classified as “first course” in a sequence are considered low level, while courses listed as “second or later,” “specialty course,” or “co-op/work experience” are considered advanced or upper level. This distinction allows us to analyze the benefits of breadth (taking many courses in different fields) and of depth (specializing in a particular vocational field). We also conduct an analogous disaggregation for the core academic courses of English, math, science, and social studies, based on the transcript labels of “basic,” “regular,” “advanced and honors,” “specialized,” and Advanced Placement or International Baccalaureate.

Approximately 95 percent of the students in our sample took at least one vocational class. One third of the students in the sample obtained a four-year college degree, one third attended college without earning a degree, 8 percent earned a two-year degree, 19 percent obtained a high-school diploma but no postsecondary education, and 3 percent did not graduate from high school (recall that we limit our data to students with four years of high-school records, so we exclude most dropouts).

Who takes vocational courses?

To learn which student take the most vocational classes, we examine course-taking patterns by a variety of student characteristics, including year in school, gender, race, grade-point average in 9th grade, and parental education. Consistent with prior research, we find that males, students from disadvantaged backgrounds, and students in rural and southern states are more likely to take vocational classes. We also see notable relationships between course taking and ability as measured by the Armed Forces Qualification Test, which assesses reading and math skills. Students with high scores take about two thirds as many vocational courses but also take more science classes and about three times as many foreign-language courses as do students with lower scores.

On the whole, students enroll in vocational courses with much greater frequency in 11th and 12th grade as they approach graduation and ostensibly have more control over their schedules (see Figure 2). This highlights the tradeoff students face in high school between what are traditionally seen as “college prep” courses and learning workforce skills. Social studies classes exhibit a similar though weaker trend, while math and science course taking drops considerably in 12th grade. In other words, specialization in vocational coursework has a distinct temporal aspect, and students’ experiences early in high school may inform their later course choices.

This line of thinking suggests that information revealed to students during high school could influence their course selections over time: students’ grades in academic courses taken as freshmen, for example, could provide information about their perceived “fit” with academic vs. vocational curricula and thus influence their decisions. Economists have shown that students’ course performance early in college helps to explain their choice of major. Consistent with this logic, we find that students who performed poorly in math and English in the 9th grade are more likely to take vocational courses later in high school. A one-point increase in 9th-grade math and English grade-point average decreases total vocational course taking by 15 percent of a one-year course, a decrease of roughly 5 percent off the average of approximately three total vocational courses.

We also examine which students enrolled in only introductory courses, and which enrolled in advanced courses. We find that students with poor performance in math and English in 9th grade were more likely to enroll in introductory-level vocational courses in grades 10–12. Yet the same is not true for advanced vocational coursework. Students with weaker academic performance were no more likely than those with strong academic performance to enroll in more-advanced vocational courses.

College and labor-market outcomes

What do these patterns mean for college going and labor-market performance? To understand this, we follow students through college and into the labor market, observing the relationship between vocational)course taking in high school and college enrollment, graduation, and labor-market outcomes. We limit our comparisons to students who graduated from high school in the same state and year, ensuring that any relationships that we document will not reflect differences in state graduation requirements or local labor markets. Our analysis reveals that while lower-level vocational courses may deter students who are on the fence about enrolling in college from doing so, upper-level courses are not strongly predictive of college enrollment. But we find no negative impact of lower-level courses on college graduation, and some positive impact of advanced vocational courses. And while upper-level vocational courses benefit students in the labor market, low-level vocational courses have no effect.

College enrollment and completion: On the whole, we find only weak relationships between the number of vocational courses students take and their likelihood of attending college. Students who take a larger number of low-level or advanced vocational courses have similar college-enrollment rates at both two- and four-year colleges as students who take fewer such courses.

Among students who do enroll in college, however, each additional course credit from an advanced vocational class increases their chances of graduating by nearly 2 percentage points. As expected, we also find a relationship between academic course credits and graduation among college enrollees. Each additional academic course credit is associated with an increase of 2 percentage points in graduation rates for low-level academic courses and 4 percentage points for advanced academic courses.

Taken together, these results suggest that vocational courses may deter the marginal student from college but have little aggregate impact on graduation rates among college matriculants. Put differently, vocational courses may pull those students out of college who are least likely to graduate if they enroll.

This evidence is again suggestive of a learning process in which vocational coursework provides students with information about what flavor of education best fits their talents. An alternative explanation is that the opportunity to take vocational coursework compels some students who otherwise would have dropped out to graduate from high school, but that these students are the least likely to attend college. This would result in lower college-enrollment rates and higher college-graduation rates among those who enroll, consistent with the data we see.

Wages: To examine the labor-market consequences of vocational course taking, we measure the relationship between enrollment in low-level and advanced vocational classes and students’ hourly wages, which we observe at multiple ages. As before, our analysis takes into account other student characteristics, such as parental education, family income, race, ability as measured by the armed-forces qualifying exam, and the state and year of high-school graduation. In some analyses, we also account for the composition of students’ non-vocational courses. This is a subtle yet important adjustment, which takes into consideration that an additional vocational course may come at the expense of an additional college-prep class.

We find no relationship between taking low-level vocational classes and wages after accounting for these factors (see Figure 3). But we do find that taking upper-level vocational classes has a positive impact on wages, with an increase of 2 percent for every high-level class. We obtain similar results regardless of whether we control for the number of non-vocational courses taken, which suggests that vocational courses are not crowding out more-academic classes. This is important, because we also find evidence that high-level academic courses are associated with higher earnings.

We also calculate the relationship between vocational courses and wages after controlling for whether students attended and completed college. The earnings advantage associated with core academic coursework declines by more than half after controlling for college attendance and graduation, implying that the majority of wage gains associated with core academic coursework are explained by the fact that such students are more likely to succeed in college. The courses may in fact have little direct value in the labor market. But the positive wage gains associated with upper-level vocational courses are largely unaffected by the inclusion of these factors, suggesting a premium of 1.8 percent for each additional year of upper-level vocational coursework, even conditional on whether students enroll in or graduate from college. This reveals what we view as the unique impact of advanced vocational study, above and beyond any effect on college going.

There may be other factors affecting these results, and we cannot be certain that we have identified a causal relationship. However, we take this as prima facie evidence that the labor-market value of vocational coursework accrues largely to non-college graduates, while the labor-market value of non-vocational coursework is largely if not entirely explained by its contribution to postsecondary attainment.

These results hold true in a variety of analyses, such as looking only at adults older than age 23 or only at those working more than 35 hours per week. We also find that students taking more-advanced vocational courses are less likely to be “idle,” defined as being not in work and also not in school. Hence, benefits are not simply in terms of wages. We also see that wage gains associated with advanced vocational coursework are more evident in certain industries, such as transportation, construction trades, health care, and business management.

Policy implications

Our analysis reveals several subtle yet sharp distinctions with direct policy implications. First, we find that vocational coursework may enable students to make more informed choices about their likely fit with college. Taking more advanced vocational coursework is associated with lower four-year college-enrollment rates but no reduction in college completion, suggesting that students nudged away from four-year colleges by their exposure to a vocational secondary curriculum were unlikely to earn a degree had they enrolled. Early exposure to a vocational curriculum may thus facilitate better post-secondary enrollment decisions before students make potentially expensive mistakes—an important priority amid concerns about the number of college dropouts burdened with student debt.

Second, we demonstrate that students who complete more specialized vocational coursework earn higher wages in their early careers. We attribute this to students positively sorting into coursework that aligns with their talents and preferences, unlike the common perception that less-able students are pushed into vocational coursework. This is an important distinction, one that denotes that limiting students’ ability to take these courses, such as through more prescriptive graduation requirements, may make many of them worse-off.

Third, we show the value of depth over breadth, with the biggest wage premiums going to students who complete a series of industry-specific advanced classes. There are of course caveats to these conclusions, such as the relatively young age of our sample. Recent work by Eric A. Hanushek and Ludger Woessman, for example, suggests that overly specialized training in high school may limit workers’ ability to adapt to changing labor-market conditions later in life. The extent to which that phenomenon affects U.S. workers would be wise to address in future research.

Last, we demonstrate that while wage gains associated with core and elective academic courses are largely explained by college enrollment and graduation, wage gains from advanced vocational courses are unaffected by controlling for college enrollment and completion, suggesting that these courses have value in the labor market. This evidence speaks directly to criticisms that vocational education is “preparing students for jobs that don’t exist,” or that it is a catchall for low-ability students. Our results support neither of these conclusions.

How high schools should prepare students for life after graduation—college, the workforce, citizenship—is an enduring policy question. This is nowhere more evident than in the recent shift from “college for all” to “college and career” and in the simultaneous drive toward increased academic rigor and workforce preparedness in high-quality vocational programs that use a career pathways approach. The research presented here makes a strong case for not only keeping vocational education an accessible part of the high-school curriculum, but also for ensuring such programs provide opportunities for the sort of in-depth study that our research shows has positive effects on students’ lives after high school.

Daniel Kreisman is assistant professor of economics at Georgia State University and director of CTEx. Kevin Stange is associate professor of public policy at the University of Michigan.

In Search of Deeper Learning: The Quest to Remake the American High School
by Jal Mehta and Sarah Fine
Harvard University Press, 2019, $29.95; 448 pages.

As reviewed by Eric Kalenze

Attempts to remake the public schools have been with us almost as long as the schools themselves. Regardless of the reinvention being pitched, the education “remakers” paint pictures of ideal learning environments where teachers empower students and ignite new interests, students relish challenges, and classrooms buzz with meaningful discussion and novel problem solving. If only schools would adapt themselves according to the would-be remakers’ recommendations, they would produce kids who both genuinely value their school experience and are better prepared for the world later.

Inspiring as these visions may be,history has shown that bringing them to fruition is more difficult than the reformers might envisage, in part because it is so difficult to define “success” in education. Measurement is even thornier. Confirming that kids are indeed growing into “better human beings,” for example, is far trickier than demonstrating that they’re growing academically. And attempts to make learning tasks more engaging can end up devouring time but doing nothing to improve results. Again and again, the education enterprise has turned back to practices whose desired outcomes are easier to define and target—and eventually, this retreat leads to a new cycle of education remaking.

In their new book, In Search of Deeper Learning, education professors Jal Mehta and Sarah Fine explore these tensions—though such an examination wasn’t their original goal. They started out hoping to study, understand, and showcase high schools that were bringing the visions of education remakers into reality: schools “that were not merely achieving academic minimums but helping students to flourish—to think critically, to become engaged in their learning, and, in a variety of ways, to prepare for the demands of twenty-first-century life.”

Mehta, of the Harvard Graduate School of Education, and Fine, of High Tech High Graduate School of Education, went looking for “break-the-mold schools” where students were consistently experiencing “deep learning.” This they define as learning that emerges “at the intersection of . . . mastery (acquiring knowledge and skills), identity (learning that is seen as vitally connected to one’s self), and creativity (producing something new within a field).” The authors wanted to visit high schools that embraced different pedagogical approaches, governance styles, and designs. When they struck particularly rich veins of deep learning, they would try to understand how the school produced them, and share their insights with others.

The authors soon observed, however, that deep learning wasn’t happening very often or widely. Even when they investigated schools that were known for excellence and innovation, the authors “found gaps between aspirations and realities,” and “big ambitions” matched by “significant struggles”—teachers who did not fully understand, or just plain disagreed with, their charge within the innovative model; administrators who were unsure how to communicate expectations and build capacity around the new approaches; conflicting ideas about what school leaders were trying to accomplish; too much oversight from management, or not enough of it.

As the authors put it: “We were seeking inspiration; we found complexity.” So they decided to shift direction. Instead of searching for exemplary schools, they would explore those gaps between aspiration and reality. What obstacles to change arose, and why? Who had succeeded in overcoming some of them, and how?

Four High-School Models

Mehta and Fine looked closely at four distinct high-school models, which they present under the pseudonyms “Dewey High,” a progressive, project-based school; “No Excuses High,” emphasizing high academic standards and strict behavior rules; “IB High,” centered on the International Baccalaureate concept; and “Attainment High,” a comprehensive-model school. The authors devote a chapter to each approach, exploring how the model attempts to generate deep learning. Readers see into classrooms and extracurricular activities and hear administrators, teachers, and students talk about their professional and scholastic experiences: what works for them, what they struggle with, which classes and tasks they enjoy.

The authors succeed in creating a vivid picture of what goes on in many high schools, but one thing they de-emphasize is academic performance data. That’s because Mehta and Fine view this kind of assessment as but a small, and sometimes obscuring, way of measuring school quality. Yet the lack of data can’t help but detract from our understanding of “deep learning” and how it can be produced.

Still, the authors present the four school settings fully and fairly (though they clearly prefer more student-centered and progressive methods), acknowledging the pros and cons of each model. They note, for instance, that the project-based school achieves high student engagement but gets uneven results in developing basic skills. And they report that students from the no-excuses school say they appreciate what the school is doing for them but that “no one actually likes it here.”

They also dedicate significant space to describing student experiences and teacher methods that they judged had potential for facilitating deep learning. They spend several chapters exploring “instructional peripheries” (that is, electives, clubs, and extracurriculars) and zooming in on seven teachers they identified as doing some of the “deepest” teaching they observed. While these chapters have compelling elements, they suffer from logical flaws. For example, in the chapter on “instructional peripheries,” titled “Deeper Learning at the Margins,” they describe students willingly devoting time and energy to their various chosen activities and classes. But by definition, students follow their interests, passions, talents, and friends into those ventures. Student engagement is effectively built-in; thus, one cannot draw clean analogies between these elective pursuits and the required, often taxing subjects of the academic classroom.

Also, only one extracurricular activity is examined closely in this chapter: itis theater, at a school with a reputation for an outstanding theater program and director. Yet the skills and qualities that might be developed in drama class likely differ from what might be expected and cultivated in other “peripheral” activities. For example, expressing one’s self creatively is probably not valued as highly in athletics or news writing or the marching band as it is on the theater stage. The “authentic product that will matter to the student” looks different, depending on the activity, and sometimes the desired “product” is more related to precision, order, and, yes, rule following than are the theater experiences described in this chapter. Do other, more-structured peripheral experiences also provide “deep learning” opportunities, or just theater? Because these activities vary so widely, it’s difficult, if not impossible, to extrapolate.

Finally, the authors make some puzzling choices when it comes to singling out teachers for their ability to make deep learning experiences come to life. For instance, they describe “Ms. Peterson,” a science teacher at “Attainment High,” who is skilled at providing her students with highly engaging and exploratory engineering activities. The authors note that she came by this gift, in part, through a “seminal learning experience” that fundamentally changed how she thought about her domain and her students—an experience they say is common among teachers who enable deep learning. But Peterson’s seminal learning experience came via her work as an engineer, preceded by a master’s degree from Northwestern and a PhD from MIT. It therefore seems curious that the authors (and, indeed, Peterson) would turn up their noses at “traditional” teaching and learning. And there are several others like Peterson, from “Dr. Duchin,” a doctorate-holding constructivist science teacher, to “Mr. Fields,” a Zen priest and English teacher. In light of these teachers’ backgrounds, it is perplexing that the authors—and the teachers themselves—are as dedicated as they are to remaking traditional education.

The authors describe classrooms that are “alive with creativity and energy and enthusiasm,” and they cite students who say they feel validated as they get to “think like scientists.” But if mastery, identity, and creativity are the three sides of the deep-learning triangle, the authors leave too many unanswered questions about the “mastery” aspect. Nor do we discover whether or how students’ identities and creative abilities are being shaped.

These residual questions suggest a need for future research. They also imply that a longitudinal approach may be more effective in studying deep learning and what enables it. Classroom observation over periods of a few days coupled with student interviews constitutes a limited research method. Going forward, researchers may want to follow students who were taught in classrooms where they deem deep learning happened (preferably, as verified empirically or by multiple observers) to see how they fare in subsequent years—academically, socially, and emotionally.

The problem is, how do we verify that “deeper learning” has taken place? Until we can answer that question, it stands to reason that individual educators will interpret the concept differently and will only inconsistently produce the classroom conditions and experiences that can foster it. Future research could shed light on the matter by backward mapping from graduates who thrive in adulthood, and works like In Search of Deeper Learning at least provide a compelling set of places where education leaders and practitioners can start.

Eric Kalenze is the U.S. organizer of researchED, an international organization dedicated to building educators’ research literacy. His latest book, What the Academy Taught Us: Improving Schools from the Bottom Up in a Top-Down Transformation Era, will be released in fall 2019.

From a political perspective that values equality and diversity, integrated schools are inherently good. Research also supports the notion that exposure to individuals from a diverse set of backgrounds has positive social and political benefits for a pluralistic society, and an expanding body of research attests to the positive consequences of school integration for academic outcomes.

Yet schools remain highly segregated by race and class, in part because of the segregation of neighborhoods, which largely determine where students enroll. Public charter schools, which have dramatically expanded their reach since they were first established in 1992, now occupy a central role in the public debate over racial isolation in school, with advocates and critics pitching the schools as either a potential cure for, or a key contributor to, segregation.

Charter advocates argue that decoupling school assignment from already intensely segregated residential neighborhoods should lead to more integrated schools. Charter critics, however, allege that these public schools of choice are instead driving resegregation. They worry that if socioeconomically advantaged families take advantage of school-choice opportunities and leave the most disadvantaged students behind in the worst schools, choice could exacerbate segregation.

Which of these camps is correct? How do charter schools affect segregation? The current empirical evidence fails to provide a definitive answer. In this study, we attempt to close that gap with the first nationally comprehensive examination of this question. We use detailed annual records on school enrollment by race spanning a period of 17 years, from 1998 to 2015, and a research design that isolates the causal effect of the charter share of enrollment on the segregation of American school systems.

We find that, on average, an increase in the percentage of students going to charter schools leads to a small increase in the segregation of black and Hispanic students within the school districts in which charters open. Our analysis suggests that an increase of 1 percentage point in the fraction of students attending charter schools in a district causes segregation in that district to increase by 0.11 percentage points. For the average district nationwide, this implies that eliminating charter schools would lead to a modest 5 percent decrease in the segregation of black and Hispanic students.

However, we uncover considerable variation in the size of this effect, particularly depending on how we define a school system. The presence of charter schools slightly increases segregation when it is measured at the level of the town or county, similar to the effect at the school district level. But in metropolitan areas, the net effect is not distinguishable from zero, as the increase in segregation within districts tends to be offset by a decrease in segregation between them. We also find dramatic differences in the charter effect on segregation in different states: in some it is close to zero, and in others it is much larger than the national average.

Taken together, we find compelling evidence that the rise of charter schools over the last 20 years has led to slightly higher levels of racial and ethnic segregation, on average. However, these results need to be interpreted in the context of the purpose of charter schools. A large number of charter schools were founded and specifically tailored to serve students from vulnerable backgrounds, out of which a good number have been successful at improving student outcomes. Patterns resulting from black and Hispanic families choosing schools that they feel meet their children’s needs should not be interpreted with the same lens as the government-mandated segregation that was outlawed by the U.S. Supreme Court in Brown v. Board of Education.

A long history of separate schools

Students in U.S. schools were racially isolated for decades before the Supreme Court declared separate facilities to be constitutional in its 1896 Plessy v. Ferguson ruling, which was not successfully challenged until the court’s Brown decision in 1954. It was only in the mid-1970s that rates of school segregation began to fall substantially, as the result of court-ordered desegregation plans for districts. However, segregation between districts was difficult to address after a 1974 court decision, Milliken v. Bradley, struck down desegregation plans that sought to address segregation across district boundaries.

Hastened by so-called “white flight” and racist housing-market practices, race-based residential patterns at the municipal level continued and segregation between school districts increased. Across the United States, segregation between districts is now higher than segregation within districts, though this trend is somewhat less pronounced in the South and West, where districts tend to be larger and encompass many communities.

Research has found the effects of racial segregation on students are far-reaching, though the precise mechanisms that produce these effects are less clear. Analysis of the desegregation plans that followed the Brown ruling found black students were less likely to drop out of high school or be incarcerated, were more likely to be healthy and employed, and earned better wages. When desegregation orders were terminated, dropout and incarceration rates among students of color increased.

Researchers Sean F. Reardon and Ann Owens suggest that there are two primary ways by which integration might improve student outcomes: by ensuring educational resources are more equitably available to all students, and by increasing the total pool of available resources (because, for example, the political capital of parents in an integrated system may be more directed at acquiring higher total resources for the entire system rather than for specific schools). Thus far, studies have tended to focus on the distribution of available resources, which varies greatly as a function of segregation and seems to be a driving mechanism of the benefits of integration.

Enter public charter schools. Existing research says little about how charter schools affect the distribution of students in school systems. In 2017, for instance, the Associated Press conducted an analysis that compared charter schools to traditional public schools and found that charters were more likely to demonstrate high levels of racial isolation, which was quickly interpreted as more segregated. The reaction to the story exemplified the divisiveness of the issue and the importance of sound measurement.

The president of the American Federation of Teachers, Randi Weingarten, called the data “damning,” and argued that “America’s children deserve better.” The National Education Association announced “Racial Isolation of Charter School Students Exacerbating Resegregation.” Charter proponents pushed back, calling the Associated Press analysis “irresponsible” and asserting that charter schools merely reflect the neighborhoods in which they operate. Charter schools, they argued, were being unfairly criticized for doing exactly what they had set out to do—serve students who are most in need of better education.

What has been lacking is a large-scale study of the effects of charters on school segregation in the United States using a credible research design. Simply comparing the share of charter and traditional public schools that are racially isolated is insufficient, as charter schools are not spread evenly across the educational landscape and their introduction may affect the composition of students in traditional public schools. Rather, what is needed is a strategy to determine how the emergence of charter schools has influenced patterns of school enrollment in the specific systems in which they operate. We provide such an overview here with a longitudinal analysis of the universe of public school systems from 1998 to 2015.

Measuring segregation

Our primary data source is the National Center for Education Statistics’ Common Core of Data, which includes school enrollment counts by grade level, race, and ethnicity, as well as each school’s type (charter or traditional public) and location. Our study period begins in 1998, the first year the charter category was available, but we obtain similar results if we exclude data from 1998 to 2002, when national data on charter schools were of lower quality.

We match school locations to different districts, counties, cities and towns, and metropolitan areas, which we treat as distinct definitions of school systems when computing school segregation. This is particularly important, as it allows us to geo-locate charter schools in the school systems that they affect. For school districts, we use the 2015 definition of school-district boundary maps from the National Center for Education Statistics’ Education Demographic and Geographic Estimates. We also use U.S. Census data to locate all schools within tracts, which provides us with residential population counts by age, race and ethnicity, adult educational attainment, and median household income.

We focus on annual school-district enrollments by grade level: for each year in 1998 through 2015, we observe the racial composition at each grade level from kindergarten to 12th grade for all schools located in U.S. mainland states. We limit our analysis to district-grade combinations with at least two schools throughout this period, so that segregation measures can be computed. Our final sample includes 4,574 school districts, observed for each grade in K–12 across 1998–2015, for a total number of observations that exceeds 500,000.

Nationally, charter schools increased their share of total enrollment from less than 1 percent to nearly 7 percent over this time span (see Figure 1). Among districts that had at least one charter school at some point during this period, the charter enrollment share grew to more than 11 percent.

Charter schools, on average, serve different populations of students from traditional public schools: they enroll higher proportions of black students than white students in elementary and middle schools, and tend to enroll higher proportions of Hispanic students in middle and high schools. These enrollment characteristics largely reflect their locations; charter elementary and middle schools are more likely to be located in census tracts with higher proportions of black residents, while charter middle and high schools are found in areas with higher proportions of Hispanic residents compared to white residents. Charter schools also tend to be located in tracts with lower median income and adult educational attainment.

Determining the effect of charter-school growth on school-system segregation has proved vexing, in part because different methods of measuring segregation can lead to different conclusions. Absolute measures, often referred to as measures of exposure or isolation, determine the extent to which students from one demographic group are exposed to or isolated from another demographic group within individual schools. For example, some researchers have adopted terms such as “hypersegregated” or “intensely segregated” to describe schools that enroll more than 90 percent of students with the same demographic characteristic, and have employed these methods to claim charter schools are more segregated.

While descriptively useful, a drawback of these measures is that they are partly driven by the underlying racial composition of the school system. Schools in high-minority areas may be labeled as segregated simply for reflecting the underlying pool from which they draw students. Recent claims in the media that schools have been resegregating have tended to rely on absolute measures, which do not account for the fact that white students make up a shrinking share of all students in the United States. As a result, it is misleading to compare absolute measures of segregation across time or geography.

Relative measures of imbalance or unevenness adjust for the underlying composition of students, making them comparable across different locations and over time. They are also conceptually different in that they measure how evenly a given population of students is distributed across a school system.

One commonly used metric in this family of relative segregation measures is the variance-ratio index, which we employ here. The variance-ratio index builds from the isolation index but includes a simple adjustment for system-wide composition that allows for accurate comparisons across time or place. It indicates how segregated a system is relative to how segregated it could be, given the demographic mix of students, and can also be interpreted as how predictive a student’s own race is of the racial composition of her school peers. The variance-ratio index ranges from zero (complete integration) to 100 percent (complete segregation).

Still, to be sure that our results are not driven by our choice of segregation measure, we conduct a parallel analysis using another common metric, the index of dissimilarity. The dissimilarity index measures the proportion of a group’s population who would have to change schools to reach an even distribution across each school in the system. We obtain similar results when we use the dissimilarity index instead of the variance-ratio index.

We focus on the segregation of black and Hispanic students from other students, as prior research shows that most segregation occurs between whites and minority groups. In general, we find similar results when we separately measure the segregation of black, Hispanic, and white students from students in all other groups, and we note any exceptions.

We first employ the variance-ratio index to determine trends in average segregation nationally using four different definitions of a “school system”: school districts, cities and towns, counties, and metropolitan areas (see Figure 2). We find the segregation of black and Hispanic students relative to other groups has remained remarkably stable over the last 15 years, and has even declined modestly for metropolitan areas.

These national trends show that the growth of charters has not been accompanied by rising levels of segregation, but they do not indicate whether the presence of charter schools has influenced segregation in specific communities. We thus employ a more localized approach, and compute charter enrollment and segregation for each grade (kindergarten through 12th) in each school system over time. Our analysis identifies the causal effect of the percentage of students attending charter schools by comparing changes in segregation across grade levels within the same system that have experienced differing intensity in charter penetration. For example, if in 2010 the share of 9th-grade charter-school enrollment in Washington, D.C., grew more than in other grades and there was a corresponding increase in 9th-grade segregation relative to other grade levels, our methodology would attribute this to charters having increased segregation. Our national estimate of the effect of charters on segregation is an weighted average of these types of comparisons across all school systems and grade levels over the period 1998–2015.

Results

Charter schools have led to small increases in school-district segregation for each of the racial groups that make up the majority of the student body in most U.S. school systems. An increase of 1 percentage point in the share of enrollment in charter schools leads to an increase of segregation of black and Hispanic students within districts of 0.11 percentage points. Put a different way, if the average district in the sample shut down all of its charter schools, we would expect its overall segregation of black and Hispanic students to decline from 15.0 to 14.2 percent, a decrease of 5 percent. Excluding districts that have never had a charter school, we would expect average segregation to fall from 19.1 to 17.8 percent, a decrease of 7 percent.

Thus, this average effect of charters, while statistically significant, is of modest magnitude—likely due both to charters’ relatively small share of total enrollment and to heterogeneity in the effect of charter schools across different types of districts.

This is important because local school districts are the governing units with the most influence over student-assignment policies. From a geographical perspective, however, charter schools are not constrained from enrolling students from multiple districts. Moreover, the bulk of school segregation in the United States occurs between different districts, not within the same district. Because charter schools can draw students from beyond the school district in which they are geographically located, how we define the geographical school systems may be an important driver of our results.

To test this theory, we group schools into four types of settings—geographic school districts, cities and towns, counties, and metropolitan areas—and examine the effects of charter schools on the segregation of black and Hispanic students in each grouping (see Figure 3). We find that charters have a statistically significant segregative effect at each level of aggregation, with the exception of metropolitan areas. At this broadest level of aggregation, the impact on segregation is positive but neither large nor precisely estimated enough to be statistically significant. When we look at each racial and ethnic group separately, the charter impact on segregation at the metropolitan area level is statistically significant for blacks but not for Hispanics or whites.

We dig deeper into segregation at the metropolitan-area level by dividing it into two components: segregation within districts and between districts (see Figure 4). Between-district segregation reflects differences in the average racial composition of school districts in the same metropolitan area, while within-district segregation is that which occurs due to differences in the composition of schools within the same district. For black and Hispanic students combined, we find that charter schools have counteracting effects on segregation at the metropolitan-area level. As we established before, charters increase segregation inside school districts, but they tend to decrease segregation between districts in the same metropolitan area. When we examine individual racial groups, however, this pattern holds for white and Hispanic students but not for black students.

One interpretation of these results is that charter schools echo the role of magnet schools during the era of court-ordered desegregation plans. Magnet schools were hoped to counteract white flight to suburban school districts by offering programs in urban districts that would attract white families. They were thus meant to partly sacrifice the within-district integration objective in order to limit the more severe problem of growing segregation between districts. Charter schools today appear to have this type of dual effect—but while they alleviate certain demographic imbalances across district lines, this has not resulted in greater school integration overall.

We also compare how charters have affected within-district segregation across the country by looking at enrollment in all U.S. states where at least 1 percent of students attend charter schools (see Figure 5). We find substantial variation, with evidence of notable effects on segregation in Louisiana, New Mexico, North Carolina, Oklahoma, and Rhode Island. And there are several states where charters appear to have little or no effect on segregation, such as Arizona, Florida, Georgia, New Jersey, and Oregon. For a number of other states, the results are too imprecise to come to a definitive conclusion either way.

Implications

Our study shows that critics are incorrect when they say that charters are driving a resegregation of American schools. Their impact on segregation is small, and appears to be somewhat offset by improvements in racial balance across districts in the same metro area. But it also shows that charter proponents are incorrect to assume that freeing public schools from neighborhood boundaries will necessarily enhance racial integration. The evidence in our study shows that charter schools lead to slightly higher levels of racial and ethnic segregation, on average, with wide variation across states.

Is such segregation comparable to the separate and unequal circumstances of the past? Segregation that occurs as a result of a family choosing a charter school designed to meet the particular needs of their children is fundamentally different from the type of school segregation that took place during the pre-Brown era of de jure segregation. Still, there are compelling reasons to enhance school integration, both as an ideal and as a proven path to better outcomes for minority students.

Charters may better serve this purpose through more intentional recruitment policies that are attentive to how relative advantages across families can lead to increased stratification. One promising strategy comes from policies that centralize school-choice options into common enrollment systems, which research has found reduce the burden of choosing a school and increase the proportion of disadvantaged students entering charter schools. Designing these common enrollment systems to intentionally increase diversity (such as by making school-assignment decisions in part based on students’ socioeconomic background) may also be a worthy tactic.

Other promising strategies involve so-called diverse-by-design charter schools—a small but growing trend. Because charter schools are free to target their recruitment strategies from broader geographical areas, such designs have the promise of using charters as agents for integration. While little research has evaluated the effectiveness of such policies, strategies to encourage diversity, such as weighted admission lotteries and targeted recruitment efforts, show promise. For example, San Antonio, Texas, is pursuing a holistic enrollment approach that includes district-authorized charter schools, magnet schools, and traditional public schools in common enrollment systems and weighted admission lotteries, while also strategically locating new schools of choice and increasing funding for transportation for participating students. With the right design features, the promise of school choice as an agent of integration may yet be realized.

Tomas Monarrez is a research associate in the Center on Education Data and Policy at the Urban Institute; Brian Kisida is assistant professor in the Truman School of Public Affairs at the University of Missouri; and Matthew Chingos is vice president for education data and policy at the Urban Institute.

For an unabridged version of this study, visit Urban.org.

When the New York Times ran an article headlined “Do Children Get a Subpar Education in Yeshivas? New York Says It Will Finally Find Out,” the newspaper illustrated the piece with a photo of a Jewish school in Queens.

An administrator from that school promptly complained to the Times about its photo selection, pointing out that six of the school’s recent graduates had attended Harvard Law School.

So the Times website swapped out the photo, replacing it with one of a Jewish school in Brooklyn. An administrator there complained too—noting that the school offers 24 Advanced Placement courses, including ones in physics, computer science, and calculus.

The Times then took down this second photo, replacing it online with a picture of an advocate whose organization sued the governor of New York in an attempt to force more secular instruction in Jewish private religious schools.

This episode from December 2018 neatly reflects the years-long policy battle over the curricula in Jewish schools in New York and the government’s role in overseeing them. High-quality educational offerings and outcomes are met with accusations of inferiority. And the Times is paying close, if clumsy, attention.

One can understand why. It’s a good story, of interest well beyond the Jewish community. Jewish schools educated more than 151,000 students in New York State in 2013, the last year a careful count was done. That’s more than the number enrolled in the Philadelphia City or San Diego Unified public-school districts. And taxpayers have a stake in how well the yeshivas are doing their jobs. The Jewish schools absorb more than $100 million a year in city government funds for things such as textbooks, special education, security, and transportation. What’s more, if yeshiva students don’t get the skills necessary to participate in the economy, other taxpayers may be stuck supporting them with subsidized housing and medical care, the schools’ critics contend.

Some Jewish schools serve essentially like other private schools, as feeders to secular higher education or the workplace. The critics, though, are focused on the education in ultra-Orthodox schools, especially Hasidic institutions. Hasidim are Orthodox Jews loyal to a particular charismatic rabbi; they live in tight-knit communities, dress in traditional garb, and closely follow the teachings of the Torah and Talmud. Boys spend most of their school day studying these sacred texts and related writings, often to the near exclusion—critics contend—of traditional school subjects such as English and math.

The mayor of New York, its city schools chancellor, the state and federal courts, and even Governor Andrew Cuomo have been drawn into the dispute, which at one point was used by a state senator to hold up negotiations over the Empire State’s entire $168 billion annual budget.

It’s also a story that extends beyond education outcomes and New York politics to deeper philosophical and legal issues: religious liberty, state power, and family freedom. How much authority should the city and state have to impose the government’s vision of an education on a religious minority that would prefer to be left alone? How much power should parents have to send their children to schools that emphasize religious subjects at the expense of topics such as science or math? Does society have a responsibility to ensure that all children receive an education that enables them to participate in democracy and the workplace? And who determines the answers to these questions—parents, politicians, courts, bureaucrats, advocacy groups, or some complicated combination thereof?

The advocate whose photo the Times finally settled upon, Naftuli Moster, was dissatisfied with the education he received at the yeshivas he attended as a child. In a federal civil complaint his advocacy group filed in 2018 against Cuomo and the state commissioner of education, he cited a New York Post headline contending “Jewish schools are dooming young men to poverty.” The complaint—which in January 2019 was dismissed in district court for lack of standing—charged that “although non-public schools are required by state law to provide a substantially equivalent secular education, almost no secular education is provided at most Hasidic ultra-Orthodox Jewish non-public schools. . . . The language of instruction is almost exclusively Yiddish, the same language the students speak at home, and sometimes includes some Hebrew and/or Aramaic texts.”

Then in March 2019, a Jewish advocacy group that supports the religious schools, Parents for Educational and Religious Liberty in Schools, along with five of the schools and some individual parents, filed a lawsuit in state court. That suit challenged guidelines the state of New York announced late last year, which had called for onsite evaluation of all non-public schools every five years. Schools that failed those evaluations risked losing public funding for textbooks and transportation, and parents at failing schools potentially faced liability under truancy laws.

The complaint contends that the guidelines “violate both the United States Constitution and the New York Constitution,” invoking the free exercise of religion, a free-speech right to determine what to teach, and a “constitutionally protected due process right to control the upbringing and education of their children.” On April 18, a state judge overruled the new guidelines on procedural grounds, but the issue remains a live one; the state has said that it “will determine the appropriate next steps.”

The whole fight hinges on language in New York’s state education law requiring that non-public schools offer an education that is “substantially equivalent” to that of the public schools. The origins of that language help uncover the issues at stake.

1894

If the current controversy is to some degree an intra-Jewish dispute, it’s being fought against the backdrop of education law that was largely shaped by a conflict between Catholics and Protestants in the second half of the 19th century—a battle over control of tax dollars for education.

Nationally, the key figure in that fight was James G. Blaine. The son of a Presbyterian father and a Catholic mother, Blaine served as a congressman from Maine, Speaker of the House, a U.S. senator, secretary of state, and, in 1884, the Republican Party’s presidential nominee. Today, though, he is best known for championing a constitutional amendment in 1875 stipulating that “no money raised by taxation in any State for the support of public schools, or derived from any public fund therefor, nor any public lands devoted thereto, shall ever be under the control of any religious sect.”

The federal Blaine Amendment failed, but the effort moved to the states, 38 of which adopted some form of it in their own constitutions (see “Answered Prayer?” legal beat). In a 2000 opinion, Mitchell v. Helms, four justices of the U.S. Supreme Court noted what they called the “shameful pedigree” of the Blaine Amendments, adding that the national one was considered “at a time of pervasive hostility to the Catholic Church and to Catholics in general, and it was an open secret that ‘sectarian’ was code for ‘Catholic.’”

In New York, a key figure in the story of the Empire State’s Blaine Amendment was Joseph Hodges Choate. Choate, a graduate of Harvard College and Harvard Law School, was from Salem, Massachusetts, a member of the same family whose name has survived on the Choate Rosemary Hall School in Connecticut and the Choate Hall & Stewart law firm in Boston. A portrait of him, an oil painting by John Singer Sargent, hangs today in a prominent location at the Harvard Club of New York.

Choate was known for his “lasting distrust of the New York Irish as a political force,” as D. M. Marshman Jr. wrote in a 1975 American Heritage profile of the man. The author put the kindest possible face on this bias, attributing it to Choate’s reaction to racist Irish violence against blacks in the 1863 New York draft riots: “He considered them largely responsible for the hangings and tortures that caused hundreds of black men and women to die violently and was bitter because neither Governor [Horatio] Seymour, elected with Irish votes, nor Archbishop [John] Hughes himself made any real effort to stop them.”

In March 1893, in New York City, Choate delivered an after-dinner speech on St. Patrick’s Day to an Irish American social and charitable group. With many Irish Americans supporting the campaign overseas for Irish sovereignty, Choate—the “embodiment of pure English stock and the Republican Party, that is, of what his audience most opposed,” as Marshman put it—told the group that the best thing for them to do was “with your wives and your children, and your children’s children, with the spoils you have taken from America in your hands, set your faces homeward, land there and strike the blow. . . . Think what it would mean for both countries if all the Irishmen of America . . . should march to the relief of their native land! Then, indeed, would Ireland be for Irishmen and America for Americans!” The remarks didn’t earn laughs, though Choate maintained he jested.

A year later, Choate, speaking at a Republican meeting at Cooper Union on the topic of “Tammany Rule,” declared, “We are tired of being submitted to the despotic control of a handful of foreigners who have no stake in the soil.” Catching himself, he quickly asserted that the Republicans “should be just as tired of it if they were not foreigners.”

In May of that year, Choate, then 62, was elected president of the New York State Constitutional Convention. At the time, the New York Times was on high alert for anti-Catholic bigotry. The newspaper reported on a cartoon that the anti-Catholic American Protective Association had mailed to each convention delegate. The drawing depicted a monstrous snake labeled “Catholic Church,” and the Times called it a “rabid and vicious” attack, comparing its vitriol to the hatred exhibited by the New England witch burners in Choate’s hometown. In the same article, a Protestant minister was quoted as saying: “They [the Catholics] only teach the children in their parochial schools to sing ‘Hail Marys.’ That doesn’t benefit them any. . . . We don’t want such systems in our public schools.”

The delegates gathered in the assembly chamber in Albany were there to tackle not just the pressing matter of defunding Catholic schools, but a range of other hot-button issues of the late 19th century: Canals. Railroads. Indians. Prohibition. Women’s suffrage. All 175 delegates were men, and largely opposed to granting women the right to vote, though they did hear from Susan B. Anthony and Jean Brooks Greenleaf, whose husband was a congressman from Rochester.

The convention’s work continued for months. It concluded with a compromise between the aims of Catholics, who hoped to secure funding for their schools and charities, and those who opposed all such support from tax dollars. The Catholics got funding for their charities but not their schools. The convention’s education committee arrived at the following text: “Neither the state nor any sub-division thereof shall use its property or credit or any public money, or authorize or permit either to be used, directly or indirectly, in aid or maintenance, other than for examination or inspection, of any school or institution of learning wholly
or in part under the control or direction of any religious denomination or in which any denominational tenet or doctrine is taught.” New York’s Blaine Amendment was born.

At the same time, the state also added to its education law the requirement that the non-public schools offer an education that is “substantially equivalent” to that of the public schools. That measure was known as the Pound compulsory education law, after its primary sponsor, Cuthbert Winfred Pound, a Republican lawyer from Lockport, in western New York, and the second cousin, once removed, of Roscoe Pound, who would become dean of Harvard Law School. In reporting the legislation’s passage, the New York Tribune wrote that “the measure has been defeated in former years, owing to the fears of Roman Catholics that a compulsory education law would interfere with their parochial schools.” Between the state Blaine Amendment and the Pound law, the overall mood for religious education was embattled, and defensive. Trying to reshape the narrative, the same week that the Pound law was enacted, New York’s Archbishop Michael Augustine Corrigan invited an audience of 2,000 to the opening of a display of parochial-school student art at the Grand Central Palace, a Manhattan exhibition hall. Under the page-one headline “Catholics Are Patriots,” the New York Sun reported the event by noting that William Bourke Cockran, an Irish-born Democratic congressman, “said that he was amazed that at this part of the nineteenth century it was found necessary to repel the charge that the Catholic Church was hostile to republican institutions.”

In mid-October of the same year—1894—a Jewish French army captain, Alfred Dreyfus, was accused of treason. By December 22, he had been convicted with a life sentence. What became known as the Dreyfus affair was covered by a Viennese journalist, Theodor Herzl, who later credited it with inspiring him to become the founder of modern political Zionism. Although the false charges against Dreyfus were ultimately dropped, the affair, and other manifestations of anti-Semitism in Europe in subsequent years, spurred a wave of Jewish immigration to the United States. New York City was the primary arrival point for these immigrants, many of them religiously Orthodox, who soon began to develop religious schools, synagogues, and other community institutions.

Regulatory Wrangling

From 1894 to 2012, the Jewish schools flourished under a relatively non-intrusive New York regulatory regime. The schools, at times allied with Catholic ones, pressed with limited success for additional funding and even at times for repeal of the Blaine Amendment. In 1973, the U.S. Supreme Court struck down a New York State program designed to fund school building repairs and reimburse parents for religious school tuition, ruling in Committee for Public Education & Religious Liberty v. Nyquist that the program violated the First Amendment’s establishment clause.

Some of the bitterest legal flare-ups involved not Jewish private schools but public-school districts, including that of Kiryas Joel, a Hasidic village about 50 miles northwest of Manhattan. In 1994, the U.S. Supreme Court struck down as unconstitutional the state’s creation of a school district whose boundaries corresponded with those of the village. But the “substantially equivalent” language wasn’t much tested.

In 2001, the state established guidelines suggesting that local education officials make site inspections of non-public schools to investigate compliance only after “a serious concern arises,” and then only after having an informal discussion with the school officials.

The legislative language from 1894, though, was key to the complaint issued by Naftuli Moster in 2015. Moster grew up in Brooklyn as one of 17 children in a family of Hasidic Jews of the Belz sect, which is named after the town in Ukraine where the rabbinic dynasty that leads the group was founded in the 19th century. Moster attended New York Hasidic schools until age 16, when he went to Israel to study. He told the Rockland/Westchester Journal News that from about the time he turned 13, he received no secular education at all. He couldn’t do long division or write an essay; he didn’t know what a molecule or cell was; and he hadn’t heard of the American Revolution, he told the New York Jewish Week.

In July 2015, Moster’s group, Young Advocates for Fair Education, wrote to seven New York school superintendents alleging that yeshivas in their educational districts offered “poor quality and scant amount of secular education, particularly English instruction.” The writers identified themselves as parents, students, and teachers at the schools who were “seriously concerned that these yeshivas are not providing an education that meets the requirement of substantial equivalence.” For the most part, they alleged, yeshiva students may expect to learn a combined 90 minutes of English and math four times weekly, and other secular studies are ignored. This all stops at age 13 for boys, and although Hasidic girls receive more secular instruction than the boys do, the letter’s authors said they were also concerned about whether Hasidic schools sufficiently prepare girls for their futures.

The group’s complaint called for the investigation of 38 schools in Brooklyn and one in Queens. A state probe ensued, and then in early August, Mayor Bill de Blasio launched a city investigation of the schools. His spokesperson told the Jewish Week that “there is zero tolerance for the kind of educational failure alleged.”

By March 2018, after city investigators had visited more than a dozen of the Jewish schools, state senator Simcha Felder held up the state budget until his colleagues agreed to amend the state law by further specifying what the state would consider in determining “substantial equivalence.” Felder, an Orthodox Jew who represents Brooklyn’s heavily Orthodox neighborhood of Borough Park, is a Democrat who often votes with Republicans and thus wields an influential swing vote in the narrowly divided senate.

Felder’s amendment set out two standards for nonprofit schools with bilingual programs: for elementary and middle schools, the state would consider whether

the curriculum provides academically rigorous instruction that develops critical thinking skills in the school’s students, . . . including instruction in English that will prepare pupils to read fiction and nonfiction text for information and to use that information to construct written essays that state a point of view or support an argument; instruction in mathematics that will prepare pupils to solve real world problems using both number sense and fluency with mathematical functions and operations; instruction in history by being able to interpret and analyze primary text to identify and explore important events in history, to construct written arguments using the supporting information they get from primary source material, demonstrate an understating of the role of geography and economics in the actions of world civilizations, and an understanding of civics and the responsibilities of citizens in world communities; and instruction in science by learning how to gather, analyze and interpret observable data to make informed decisions and solve problems mathematically, using deductive and inductive reasoning to support a hypothesis,
and how to differentiate between correlational and causal relationships.

And for high schools, the amendment said, state officials were to consider whether “the curriculum provides academically rigorous instruction that develops critical thinking skills in the school’s students, the outcomes of which, taking into account the entirety of the curriculum, result in a sound basic education.”

Felder’s amendment was seen as a defense of the Jewish schools. “Parents should have the ability to decide what sort of education their children receive,” he told the New York Times in April 2018. But his success soon appeared to be a Pyrrhic victory.

In November 2018, state education commissioner MaryEllen Elia released guidelines for more extensive general-studies offerings at private schools. The guidelines, which included consequences for noncompliance, called on yeshivas to teach seven subjects to students in grades 1 to 4 and 11 subjects to 5th- to 8th-graders.

“Adding up all of the subjects and time requirements, a yeshiva will have to devote more than six hours every day, five days a week to secular studies,” reported the Yeshiva World. The guidelines also called for the state to inspect the schools and warned that parents would face possible prosecution under truancy laws if they didn’t withdraw their children from schools found to be failing. Those truancy laws call for fines and jail terms for parents found in violation; they could also trigger “educational neglect” charges that could culminate in children being taken away from their parents and placed in foster care, a group home, or a court-ordered guardianship.

That same month, Rabbi Aaron Teitelbaum, the leader of the Kiryas Joel community of Satmar Hasidim, publicly denounced Elia, saying that she had “conspired with traitors and the wicked to persecute” a Jewish community “which only wants to educate its children in accordance to Torah and tradition as has been from generation to generation.”

Teitelbaum, speaking days before the onset of Hanukkah, compared Elia to the villains of the Maccabees’ era in the second century BCE, accusing her of wanting to “remove us from our religion exactly as the Greeks wanted in their time, to destroy the education institutions, a decree of extermination.”

Said Teitelbaum, “in a democratic country there is freedom of religion and they have no right to interfere.” He added, in remarks reported by the Yeshiva World, that if Elia wanted to improve education in the state she should focus on the public schools.

In February 2019, shortly before filing suit, Parents for Educational and Religious Liberty in Schools noted that the New York City education department was advertising two job positions devoted to enforcing the substantial-equivalency law: an executive director and a senior operations director. The duties of the operations position, with a salary of $125,256 and up, included determining whether 250,000 students at 800 religious or independent city schools receive a substantially equivalent education and managing a team for school visits, monitoring curricula, and reconnaissance work. The executive post calls for someone with a “solid understanding” of state educational standards and practices but mentions nothing about fluency in the diverse values, culture, and languages of the schools.

Contrasting Views

With the state’s new guidelines now on hold, it remains to be seen whether those positions will ever be filled. If they are, and the new hires walk through the doors of the yeshivas, what will they see?

The answer can depend on whom you ask.

Rabbi Ysoscher Katz, chair of the Talmud department at the Modern Orthodox (sometimes called “Open Orthodox”) rabbinical school Yeshivat Chovevei Torah, grew up in the Satmar Hasidic sect but now identifies as Modern Orthodox. He called the secular studies of his childhood “literally abysmal,” and said his impression was that teachers were concerned that such training would expose students to the secular world, which they saw as morally corrupt.

A significant number of those classmates graduated unable to write a sound English sentence and without knowing the words “medieval” and “Renaissance,” let alone the difference between the two, Katz said. “I knew nothing about science,” he added.

Inspectors today, Katz said, would likely find that the secular education offered by the Hasidic schools has deteriorated even from the level he and his classmates experienced. In recent years, Hasidic schools have replaced non-Orthodox teachers and the occasional non-Jewish one with Hasidic instructors, Katz said, contending that these non-credentialed, untrained Hasidic teachers leave today’s students even less prepared for work and higher education than their parents and grandparents were.

A contrasting view comes from Moshe Krakowski, an associate professor at Yeshiva University and director of the Jewish education master’s program at its Azrieli Graduate School of Jewish Education and Administration. Krakowski’s research has taken him on visits to schools of several different Hasidic varieties.

“One of the biggest misconceptions is that [students] don’t get any secular education. That’s not true,” Krakowski said. “There isn’t a single Hasidic school that doesn’t offer secular education at least through 8th or 9th grade. We’re not talking about zero secular education for anybody.” After this article was published online, Krakowski contacted Education Next to clarify that there is one school that does not offer formal instruction in English writing, grammar, or spelling but said that it was an outlier.

Not only are schools offering secular studies, Krakowski said, but the training is more than sufficient for students’ needs. The secret kosher sauce, he said, is study of the Talmud, the Hebrew and Aramaic writings on the Jewish Bible codified between the second and sixth centuries. Rabbis teaching Talmud don’t quite ask the same sorts of questions that university professors do, but they often cold-call upon their young students to probe sophisticated questions about ancient and medieval texts. And like law professors, they frequently ask follow-up questions that require students to articulate arguments in a way that demonstrates their grasp of essential points.

“These are things that, honestly, college kids and even graduate students have trouble with,” Krakowski said. “They can’t really do the sorts of things that these kids can do pretty well.” (With a doctorate from Northwestern University and a bachelor’s degree from the University of Chicago, Krakowski is familiar with some of the nation’s most elite schools.)

Krakowski said that, ironically, the state pressure may be counterproductive, because it came at a time when, in his estimation, some Hasidic communities were organically nudging schools in a direction of offering more-substantial secular studies. “When you start pushing from the outside and imposing regulations from the outside, then it becomes treyf,” non-kosher, he said. Even people in the community who want more secular education “are not going to pursue it, because it’s associated now with the ex-Hasidim and the government and the evil outside people who are pushing against us. Ironically, you end up harming the development of a more-robust secular education by doing that.”

A Look at Two Schools

One day earlier this year, I spent nearly three and a half hours touring about a dozen classes—grades 3 to 7—and talking to administrators, students, teachers, parents, and alumni at two Hasidic schools in Brooklyn. One of them was on the list of 39 schools that Young Advocates for Fair Education flagged as failing. Both asked not to be named in this article.

In one of the schools, the students stood respectfully when my guide—an Orthodox but non-Hasidic rabbi and chair of the secular studies program, who holds a graduate degree from Yeshiva University—entered the room. In a 7th-grade class, an infectiously enthusiastic teacher saw 25 hands shoot up when he sought two volunteers. Two lucky kids came to the front of the room, where the teacher had hung a world map. He acknowledged that the map, which he’d reclaimed from a public-school discard pile, still included the Soviet Union.

“It still works,” he quipped.

The teacher quizzed the boys in an apparently impromptu competition, asking them to locate Sri Lanka; a place where the United States lost a war; the most populous nation in the world; and the Horn of Africa. The duo handled each task with ease—faster than I probably could have. One student erred when the teacher asked the class to name a major Sri Lankan export, but another had a correct response: tea.

“When I see a class like this, and the kids are engaged, and I read an article to the contrary, it breaks my heart,” the secular studies coordinator said to me as we left the room.

In most ways, the classrooms and facilities I saw were no different from any of thousands of others one might visit across the nation. The halls had water fountains, and backpacks, school supplies, and colorful signage abounded. The only details that seemed to set these schools apart were the students’ (and many teachers’) skullcaps, side curls, and ritual fringes. When Gerry Albarelli, a non-Jew, was considering a job offer from the Brooklyn Hasidic school where he would teach for five years, he was warned by the hiring principal to think of it as going to Mars. “These boys live in a very insular world. Not one of them has a television set,” he was told, as he later recorded in his book Teacha! Stories from a Yeshiva. “They speak Yiddish at home; some don’t speak any English at all. We’re up against the impossible.” Albarelli did face challenges, but he also made a lot of progress teaching the boys.

An alumnus of one of the schools I visited, a lawyer, told me that studying for the bar was easier for someone used to spending long days poring over books. And when fellow law students became frustrated trying to tease meaning out of impossibly complicated tax-law codes, he was reminded of studying certain Talmudic volumes that address laws akin to torts.

Rabbi Chaim Dovid Zwiebel, executive vice president of Agudath Israel of America, a nearly century-old advocacy organization for U.S. Orthodox Jewry, also said that his Talmud instruction growing up helped him in law school. “I would not say that about trigonometry or the history of the Ming dynasty, which I learned in high school and never used,” he said.

At both yeshivas, I observed and heard nothing in my interviews suggesting anything but two communities striving to instruct young people as best they knew how, within the context of the religious values they hold dear. “We’re not in the business of wasting people’s time, and whether that is Judaic studies or secular studies, we absolutely believe that it needs to be done well,” a principal told me. “It’s not like secular studies is a secondhand activity that happens at the end of the day, like some kind of afterschool program.” Yet that is exactly what critics allege.

Any school could stage a two-hour charade for a journalist’s benefit, and it’s certainly not uncommon for schools and colleges to closely guide a reporter’s visit. But my impression was that what I heard and witnessed at these two schools was genuine. At one of the Hasidic schools, I was able to talk to any students I chose, and at the other, I didn’t speak directly with students but talked with parents and alumni without restriction.

I talked to 3rd graders writing essays in English about the upcoming Jewish holiday of Purim, and I found their writing to be clear and largely error-free. Students I selected at random happily answered my questions, and when I feigned ignorance about the holiday’s story, they explained to me what they were writing about.

In a teachers’ lounge, an administrator talked me through an elaborate, color-coded computer program, which the school uses to track students’ progress in every subject on a highly granular level.

I spoke at length with a mother, Sarah, whose son is a 3rd grader at the Hasidic yeshiva from which his father graduated. “My son is an active, cute, rambunctious thing. The fact that his teachers can keep this guy engaged somehow until 5 p.m. is a miracle,” she said. Her son is reading Andrew Clements’s children’s novels, which at a public school would be on his grade level. Sarah said she didn’t teach him to read in English. “He’s able to read it and repeat the story back to me and describe the plot and the characters in detail,” she said.

The secular studies coordinator told me that in his first years on the job, boys would demand to know why they needed to learn certain general-studies information. “There’s always a good answer, because if I can’t answer it, it shouldn’t be taught,” he said. Then a group of mothers asked for a meeting to discuss curriculum. They demanded to know: “What are you doing to ensure that my child has a better chance at supporting his family than my husband does?” The coordinator explained what he was trying to accomplish with the secular studies curriculum, noting that preparing the boys for jobs was to be his focus.

These sorts of questions from parents, said Sarah, come amid a shifting tide in the Hasidic world, where many parents increasingly want their children to have better general-studies skills than they have themselves. Yet clearly, many families still value the faith-based education offered at Jewish schools, even though, like most private education, it can be expensive. Tuition at the schools is generally $16,000 nationwide, but can exceed $35,000 at some New York yeshivas, according to the Avi Chai Foundation, which has done research on financing Jewish education; New York City’s annual per-pupil spending in public schools was $25,199 in 2017, according to the U.S. Census Bureau.

Fundamental Questions

What has changed since 1894? Perhaps not some of the religious instruction in the Jewish schools, and certainly not the Jewish texts being studied, some of which date back hundreds, even thousands of years. What is different, though, is who makes the laws of New York State. Whereas in 1894 it was Protestants like Choate and Pound who wielded power, today the state has a Catholic governor, Andrew Cuomo, and its legislature includes the influential Orthodox senator, Simcha Felder.

But if Jewish and Catholic politicians have gained power in the past 125 years, the hold that traditional religion has on Americans, as measured by regular attendance at religious services, has eroded recently. In 2015, the Pew Research Center noted that 36 percent of Americans report weekly religious service attendance, down three percentage points from 2007; between 2007 and 2014, the percentage of U.S. adults who never or rarely attend religious services rose to 30 percent from 27 percent.

Given this decline in religious observance, some see the New York probe of yeshivas in the context of broader infringements by secular or liberal society on traditional religious institutions. In that analysis, the current regulatory effort to evaluate the educational offerings of Hasidic schools seems like just the latest development in a long government push against minority religious education. In 1894, authorities took away funding. In 2019, they’re sending inspectors into schools to check up on them.

Zwiebel, of the Orthodox Agudah, sees the current criticism of Hasidim in the context of a recent surge in anti-Semitism reported by the Anti-Defamation League. Referring to Hasidim as “insular” implies suspicion about what takes place behind closed doors, he said. “There’s a general perception out there that somehow children who grow up in this community are being kept in the dark and the Dark Ages to control them,” Zwiebel said of the Hasidim.

It’s possible that the current conflict could trigger further revision of New York education law, or perhaps even repeal of New York’s Blaine Amendment. A showdown over the state amendments could happen soon in the U.S. Supreme Court, as the court has agreed to hear a Montana case centered on their constitutionality.

As for substantial equivalence, the limits of state authority over private schools have yet to be fully tested. Most likely, that battle will play out in the courts. In Wisconsin v. Yoder, the Supreme Court ruled in 1972 that Amish families had a First Amendment right to end their children’s formal education at the 8th grade, but the ruling was somewhat narrowly tailored.

Zwiebel said the fracas over New York’s Jewish schools should lead the educational establishment to reexamine some fundamental questions, like the purpose of education.

“I hope the commissioner of education is asking herself that today,” he said. Education shouldn’t be about what law books have said it should be for a century, or substantial equivalence, he said. “It’s a dumb way to do it.” Instead, educational institutions should strive to create lifelong learners. That’s something many of the yeshivas do quite well, Zwiebel noted, and of which they are very proud. Whatever their graduates’ English-language skills are, many continue to pore over religious texts daily, long after they’ve graduated from yeshiva.

It’s enough to raise the question: If the state does revisit its education laws, maybe it should consider reversing them—requiring the public schools to be substantially equivalent to the religious ones rather than the other way around.

Menachem Wecker is a freelance journalist based in Washington, D.C. He wrote for the Spring 2019 issue of Education Next about Turkey’s fight against a network of U.S. charter schools.

Megan Joshi has always loved math— and excelled at it. When she was seven, her parents would reward her for doing chores around the house with algebra and geometry workbooks. Joshi capped her senior year in high school by winning the Math Prize for Girls, an annual competition for high-schoolers from the United States and Canada, and earning a silver medal at the European Girls’ Mathematical Olympiad.

Even though Joshi grew up in a wealthy Southern California community, her public schools played little role in these achievements or in nurturing her passion for math. In elementary school, she was a standout. As a 3rd grader, she was placed in 5th-grade math and still outperformed the other students. She found ways to keep herself “less bored” by helping classmates, grading papers for the teacher, and, when there was nothing else to do, reading novels. “I don’t especially remember paying attention,” said Joshi, now an undergraduate at Massachusetts Institute of Technology.

Tens of thousands of students languish in similar mathematical monotony in schools that are unable to fully support them. Despite the overall limp scores of U.S. students on state, national, and international math exams, the number of high-achieving math students in the country has soared during the past 20 years. During those two decades, the number of schools offering Advanced Placement classes in Calculus AB and Calculus BC grew by about 50 percent. The number of students taking those courses jumped to nearly half a million—an increase of 161 percent—and pass rates are rising. In 2018, twice as many 8th graders and 50 percent more 4th graders scored as advanced in math on the National Assessment of Educational Progress, as compared to their counterparts in the year 2000.

A 2017 study in the journal Gifted Child Quarterly found that between 16 percent and 37 percent of students in California, Texas, and Wisconsin scored at least one grade level ahead in math—and as many as four—on state standardized exams.

In the years since Congress passed the No Child Left Behind Act of 2001, which held schools accountable for each student’s proficiency in core academic subjects, policymakers and educators have put significant effort into getting all students up to minimum standards. But there is no comparable effort to meet the unique needs of the nation’s highly gifted math students in the public schools.

“The country needs to develop talented, visionary problem solvers,” said Jonathan Plucker, an education professor at Johns Hopkins University and president-elect of the National Association for Gifted Children, “yet we’re not finding ways to get enough of that talent,” especially among low-income and traditionally underserved students. “We have a very diverse student population that gets more and more diverse every year; those are a lot of talented kids that are totally sidelined.”

Global competitiveness and the U.S. workplace increasingly require skills in science, technology, engineering, and math, known collectively as STEM. The U.S. Bureau of Labor Statistics projects more than 5 million new STEM jobs by 2024, with the largest growth rate expected in mathematical-science occupations. Yet, of all the 2018 U.S. high-school graduates headed to college, only 20 percent were prepared for college-level STEM work, according to college entrance-exam developer ACT.

Data from the Program for International Student Assessment reveal that, by the time U.S. kids are 15, the nation ranks sixth from last in the share of students achieving at an elite level (see Figure 1). But the deficit begins earlier than that. American 4th- and 8th-graders fall below Singapore, South Korea, Russia, Northern Ireland, England, and other developed nations in math achievement, based on scores from the competency exam Trends in International Mathematics and Science Study.

While U.S. public schools are falling short in serving high-achieving math students, several programs in the private sector have stepped up to meet their needs. Art of Problem Solving, or AoPS, Math Circles, Mathcounts, the Center for Talented Youth, and Math Kangaroo are among the best-known private math-enrichment programs. These are not the ubiquitous tutoring centers that dot strip malls; they are online and in-person courses designed for students who thrive on the challenge of mathematical puzzles and need a welcoming community of kindred spirits they can’t find at school.

The programs—minus Math Circles, which doesn’t track student numbers nationally—enroll nearly 125,000 students annually. Another 350,000 people worldwide are registered with Art of Problem Solving’s free online community that lets kids share math problems and hosts forums and study groups on everything from Euclidean geometry in mathematics Olympiads to lighter fare about the latest movies.

But there’s a drawback to the approach: the students in the courses are overwhelmingly white, affluent, and male. Educators and advocates have begun to develop ways to extend these enrichment opportunities to the gifted students on the sidelines, but there’s a long way to go.

Programs for Math Whiz Kids

Sitting alone at a corner table in his neighborhood coffee shop in Menlo Park, California, Joshua Zucker leaned toward his laptop and typed, “Welcome to week 16, our final week together.”

“I love math,” responded a student with the user name Mat-h-ero.

“Math is amazing,” wrote another.

During the next 75 minutes, Zucker taught pre-algebra to about 50 students—in this particular course, about evenly split between girls and boys, hailing from all 50 states, and ranging in age from 8 to 12—through an online course developed by Art of Problem Solving. AoPS is a for-profit company that offers in-person and online courses for high-ability math students. It is accredited by the Western Association of Schools and Colleges commission.

The week’s topic was conversions, and Zucker started the class with a straightforward problem to assess the students’ understanding of the concept: If a car is traveling 64 mph for four hours, how far will it go? The students typed in their answers and nearly everyone got it right.

The problems became successively more difficult and required students to convert units, say hours to minutes, or to solve for speed instead of distance. For example: A police officer is chasing a bank robber on foot. The officer runs 12 miles per hour, while the robber runs 10 miles per hour. If the robber starts with a 1/10-mile lead, how long will it take the officer to catch him?

“Let’s think about this problem,” Zucker typed to his online students. “Is it asking us to solve for a distance, a time, or a speed? This is the same equation we already know expressed in a different way” (see sidebar).

There is no audio or video, just a screen on which Zucker deftly multitasks: posting problems, offering hints and explanations, and directing remote teaching assistants to work with students requiring more attention.

Since 2007, Zucker has taught more than 50 AoPS online courses. Before that, he taught high-school math, cofounded a math festival, and also started the San Jose Math Circle, part of a network of afterschool and weekend enrichment programs. Zucker has always loved math and wishes programs like AoPS existed when he was growing up. Although he was on the high-school math team, none of the students were at his level, said Zucker. “I was very isolated. There wasn’t anyone to bounce ideas back and forth. It was just me and some books sitting in my room by myself.”

Richard Rusczyk also remembers that feeling, but he was fortunate that a teacher told his parents about Mathcounts, a nonprofit that runs the largest middle-school math competition in the country. That was the first time he met other kids like himself. Years later, after serving as an alternate to the 1989 U.S. team to the International Mathematical Olympiad, graduating from Princeton, and making brief forays into teaching and bond trading, he created an online community for math geeks, a term he proudly wears himself. In 2003, he founded AoPS. It’s a “bootstrapped” organization, said Rusczyk. He and his wife used their personal savings to launch AoPS and still own a majority stake. Nearly all other shareholders are employees. While he won’t disclose revenue figures, Rusczyk said AoPS has “been profitable for over a decade.”

In the beginning, it offered two online summer courses that enrolled a total of 24 students, and an online forum that drew several hundred students to share and discuss difficult math problems and chat. Today, the program runs 200 online courses a year, attracting nearly 15,000 students internationally. AoPS opened its first brick-and-mortar classrooms in North Carolina and Virginia in 2016 and has since added centers in Maryland, Washington, California, New Jersey, Georgia, and Texas. Together, they serve 4,200 students in grades 2 through 12. Several more sites are scheduled to open this year.

Rusczyk attributes the company’s success to staying true to the mission of designing a place where young people can do interesting, challenging math. “I’d say the guiding light for a lot of what we do is building the things that we wish we had when we were kids.”

Math Circles have also taken off, growing to at least 100 circles in 39 states. Each is independent, so it’s not known how many students participate nationwide, but many of them have substantial waiting lists.

The last place most teenagers want to be on a Friday night is in another math class. But 28 of them have gathered in a classroom of the math and statistics department at San Jose State University, giddily bent on beating their instructor, Alon Amit, at a game of probability, otherwise known as cheating by calculating. Well, not actual cheating. Amit is giving them a lesson on hustlers’ odds using a coin toss and math.

“Guys, here’s something absolutely mind-blowing. Instead of flipping coins until we find a pattern, we’re going to be playing a game,” he said, and explained the strategy carnies use to win at so-called games of chance.

“Now, because I’m in a generous mood today, I’m going to let you pick the pattern first,” Amit continued. “Which pattern do you want?”

“Heads, tails, tails,” they shouted. He picks heads, heads, tails and demonstrates how probability is on his side (see sidebar).

By day, Amit is vice president of products at Origami Logic, a marketing analytics and data startup that he cofounded. But the San Jose Math Circle is his first love.

“For many kids, the math program is the highlight of their week,” Amit said. “You can see this in their eyes. They come in here and they’re over the moon.”

That’s true for Jeremy Pettitt, 18, who plans to major in computer science at college. Pettitt is home schooled by his mother but outstripped her math ability and is learning calculus on his own by reading textbooks. He began coming to the San Jose Math Circle about three years ago.

“It’s really nice, because I don’t have to be the only one supplying ideas. If there’s something I’m not getting, I can turn and ask, ‘hey, am I doing this right?’” Pettitt said. “It’s nice being among my peers.”

Three of Amit’s students have won gold medals in the International Mathematical Olympiad and several have earned PhDs in math. AoPS students have had similar triumphs. In 2015, the United States won the International Mathematical Olympiad for the first time in 21 years, and followed with two more first-place triumphs in 2016 and 2018. All 16 students on those teams had enrolled in more than 100 AoPS classes, collectively. The six students on this year’s team have collectively taken more than 50 classes.

 

Cops and Robbers The cop-and-robber problem is asking students to solve for time (t), specifically, how long it will take the officer to catch the robber. The equation is formed from the distance the officer travels, 12t (miles per hour multiplied by t) being equal to the robber’s head start of 1/10 mile plus the robber’s distance traveled, 10t: 12t = 1/10 + 10t Subtract 10t from both sides to simplify: 2t = 1/10 Divide both sides by 2 to find t: t = 1/20 of an hour, or 3 minutes for the officer to catch the robber Students often get sidetracked looking for total distance traveled, which isn’t necessary, said Joshua Zucker. To solve this problem, we only need to know how fast the officer is narrowing the gap. When students master the idea of relative rates, Zucker will give the problem another twist. For instance: What if they were running toward each other? How long would it take for them to collide? The value of learning new tools and strategies is that students can group several steps into a single chunk that’s easier for them to remember and use. This is important when moving on to more difficult problems, said Zucker. He believes it’s one of the reasons that people hit the wall in their math studies: “They’ve dealt with everything up to then by memorizing procedural steps instead of building understanding and building up better tools for handling the problem, and they become overwhelmed by all the things they have to keep in their head at once.”

 

The Power of Problem Solving

Competitions aren’t for everyone, but just taking part in the practice sessions can bolster students’ problem-solving skills.

Kasia Kim, a 6th grader in Alameda, California, spends her Monday evenings during the school year at the University of California, Berkeley, taking classes through Math Taught the Right Way. The program’s approach offers a sharp contrast to what happens in school, she says, where teachers say, “OK, here’s this topic, here’s the formula, we’re going to make you do this for like, three months. Then they have a quiz on it, and then move on.”

Building a creative, analytic math muscle in kids requires that the subject matter be taught slowly, with each lesson building on the previous one, said Zvezdelina Stankova, a Berkeley math professor and director of Math Taught the Right Way. “It’s like learning how to play the piano,” she explained. “You cannot in one year learn what you should learn in six.”

Stankova based the program’s curriculum on the Bulgarian math she learned growing up in the former Soviet Union—a method she also used when coaching the U.S. team to the International Mathematical Olympiad. (She herself competed twice at the Olympiad on the Bulgarian team, winning two silver medals.) Math Taught the Right Way grew out of the Berkeley Math Circle, which Stankova cofounded in 1998. Math Taught the Right Way runs four sequences of courses a semester for students in grades 6 through 9; courses fill up quickly and there is always a waiting list.

Students must show and explain every step of their work—listing the variables, drawing a picture or diagram, identifying the technique used, and then explaining other situations in which that technique would work.

Elysee Wilson-Egolf, a teacher at Math Taught the Right Way, calls this the “struggle strategy” that every student needs to develop, one “that allows them to try problems in new contexts, to apply the things that they know in different scenarios.”

The strategy isn’t just useful in math but in all subjects and all arenas of life. The essence of mathematics is being able “to solve a problem that nobody told you how to solve,” said Stankova’s colleague Tatiana Shubin, who cofounded the San Jose Math Circle and is a math professor at San Jose State University. “I don’t believe that everyone in their adulthood needs to know how to factor a quadratic expression, but everyone needs to be able to confront difficult problems without fear and just fight those problems with the power of their own mind.”

Addressing the Equity Gaps

Families in middle-class and affluent communities learn about private math-enrichment programs from teachers, on neighborhood listservs, and by word of mouth. But word may never reach families in underserved schools and communities and, even if it does, impediments abound. The programs are expensive, often have limited space and, at the higher end, require entrance exams that favor students in wealthier schools with well-educated parents.

Similarly, public-school offerings for students of high potential do not reach all groups equally. Nearly 70 percent of public elementary and middle schools offer gifted and talented programs and, except for schools serving nearly 100 percent students of color, such programs are evenly spread among high- and low-wealth schools, according to a study by the Thomas B. Fordham Institute. However, students in low-wealth schools are less than half as likely to participate in a gifted program than their counterparts at high-wealth schools (see Figure 2). Likewise, about 90 percent of students attend schools with Advanced Placement courses, but the Education Trust found that schools less likely to offer AP tend to be those in high-poverty and rural areas.

Enrollment in advanced math courses shows an even wider gap by race, ethnicity, and income. The College Board, which administers AP exams, reports that despite a steady increase in the number of schools offering AP courses in calculus, more than half the students taking the Calculus AB exams are white. This is not particularly surprising, since white students make up nearly half (about 45 percent) of the K–12 population. But by contrast, only about 5 percent of the students who took the exam in 2018 were black, even though black students represent about 16 percent of the K–12 population.

American girls now outpace boys in academic achievement, even in math, but they remain underrepresented in high-end math programs. In the 44 years that the United States has participated in the International Mathematical Olympiad, only three girls have been selected for the team. Megan Joshi noticed the gender gap at the Mathematical Olympiad Summer Program, the training camp for international competitions. One summer, she counted just 12 girls out of 54 students participating. That inspired Joshi, who had just completed her freshman year in high school, to start the STEM for Girls group at her former middle school. Four years later, it’s still going strong, taking girls on field trips to local STEM companies and introducing them to successful women in STEM.

A smattering of nonprofits are aimed at closing these gaps, especially those related to income, race, and ethnicity. New York Edge runs free afterschool and summer programs in academics, athletics, and the arts for low-income students in New York City. In addition to starting the San Jose Math Circle—which is fee-based but offers scholarships—Tatiana Shubin also founded Navajo Math Circles in 2012, and trains teachers on the reservation to run them in their schools.

One of the largest outreach programs is Bridge to Enter Advanced Mathematics. Located in New York City and Los Angeles, the program is run by the AoPS Initiative, Inc., an independent nonprofit launched by Art of Problem Solving to address the income gap in math achievement. Bridge to Enter Advanced Mathematics partners with 35 schools in New York and 14 in Los Angeles, where at least 75 percent of the students are eligible for free or reduced-price lunch.

“The kids who are not connected are getting farther and farther behind, and we’re responsible for part of that gap,” said Rusczyk. “So, we felt a responsibility to try to reach, try to educate, try to serve, try to bring into this community people who wouldn’t naturally find it, people who don’t have parents who were engineers or scientists, people who don’t already go to schools that have math teams [and] math clubs.”

One Saturday in Greenwich Village, nearly 200 high-ability math students in the 8th through the 11th grade have come to New York University to participate in classes offered by Bridge to Enter Advanced Mathematics. Eighth graders take algebra and a high-school preparation course called “Things You Need to Know.” One of the program’s goals is for these kids to meet the competitive academic standards for admission to one of the city’s top-tier public high schools.

Youmna Nasr, 13, a first-generation American whose family emigrated from Egypt, took the high-school entrance exam and will be attending Bard High School Early College Queens, where students graduate with both a high-school diploma and an associate degree. Other 8th-grade students in the Bridge to Enter Advanced Mathematics program were admitted to highly selective New York City high schools, including Stuyvesant, Bronx Science, Brooklyn Technical, Manhattan Center for Science and Mathematics, and LaGuardia High School of Music & Art and Performing Arts.

Diversity is a pillar of Bridge to Enter Advanced Mathematics. Students are evenly split by gender, 56 percent identify as Latino or Hispanic, 39 percent as African American, 14 percent as white, 9 percent as Asian American, and 1 percent each as Native American or Alaskan Native and Native Hawaiian or other Pacific Islander. The median family income is $31,000; more than two thirds of students are eligible for federally subsidized school lunch.

Nasr likes that Bridge to Enter Advanced Mathematics supports students through the entire process, with test preparation for the Specialized High School Admissions Test; essay-writing workshops for the schools that require them; and counselors available in person, by text and through e-mail.

High-school juniors and seniors receive similar assistance for their college applications. Students also have access to emotional, financial, and social supports. The program serves lunch, provides eyeglasses for students who can’t afford them, and has a social worker available.

The heart of Bridge to Enter Advanced Mathematics is its summer program for students entering 6th and 7th grade. Staff members help teachers identify students who are likely to prosper in the program—not just those who excel at math, said Lynn Cartwright-Punnett, senior director of programs for Bridge to Enter Advanced Mathematics, but also those who enjoy solving problems and persist in the face of challenge. She tells teachers to look for students who are bored and get As with little effort, and asks them to keep in mind that “the strongest student in your room is lonely.” Sometimes such students are ostracized.

“In middle school everyone thought I was a little bit weird, since I liked math so much, so I was singled out,” said 15-year-old Agata Regula, who credits her immigrant parents with encouraging and helping her to succeed. In Bridge to Enter Advanced Mathematics, though, she encountered lots of other kids who “had a thing for math.”

Her involvement in the program served her well. When Regula entered Stuyvesant High School, one of the highest-ranked public schools in the city, she felt that she “had to play a little bit of catch-up,” but that participating in Bridge to Enter Advanced Mathematics gave her the confidence to persevere. Without it, she said, “it would have been so much worse. It would have been truly horrible.”

In Maryland, AoPS has a partnership with the Montgomery Blair High School Magnet Foundation, Inc., to run a pilot program called the Pipeline Project. This initiative places strong math students from low-income families into the Gaithersburg AoPS center’s Beast Academy, its program for kids in 3rd through 5th grade.

The nonprofit foundation was created in 2008 to raise funds for the science, mathematics, and computer-science magnet program at Montgomery Blair High School in Silver Spring after it was hit with budget cuts. The foundation selected 40 public-school students in Montgomery County—based on interest, grades, and teacher recommendations—to attend Beast Academy, and covered most or all of the $150-per-month tuition.

AoPS separated 3rd-grade Pipeline students from the other Beast Academy students to get them up to speed. This year, in 4th grade, they’re intermingled, and Pipeline students are doing so well the teachers have no idea who’s who, said Kelcie Bartley, the AoPS Academy national director of outreach.

The goal is to intervene while talented students are still in elementary school to put them on the advanced math track through high school. A key measure of its success will be how many Pipeline students are admitted to the highly selective math, science, and computer-science magnet program at Montgomery County’s Takoma Park Middle School, said computer-science teacher Samir Paul, a foundation board member and driving force behind the program.

In 2017, under 16 percent of the 860 5th-grade students who applied for admission to the Takoma Park magnet program were accepted. Only 15 of the accepted students were Hispanic, fewer than 10 were black, and boys outnumbered girls by almost two to one.

This imbalance becomes self-perpetuating because the Takoma Park magnet is the primary feeder program for the Montgomery Blair High School magnet program.

In an effort to counter the inequity, Montgomery County Public Schools revised the application process. Instead of leaving it to parents and teachers to refer students, the district automatically reviewed the education records of the entire 5th-grade class and notified parents of every student performing above grade level that, unless the parents objected, their children would sit for the magnet entrance exam. The selection process quadrupled the number of students in the 2018 application pool. It nearly closed the male-to-female gap, but there was a barely a blip in the number of black students selected, and admission for Hispanic students fell.

The change didn’t achieve the district’s goals of increasing minority-student participation in the magnet program because students were still selected on test performance, and high-stakes tests often undercut students who haven’t had the opportunity to attend high-performing elite schools. The district is again working to alter the selection criteria for the middle-school magnet program to make the application process less dependent on a standardized test.

The Center for Talented Youth at Johns Hopkins University has already been tackling this issue. The idea for the center began in the late 1970s with a Johns Hopkins psychology professor and one 7th grader from Baltimore who had taken every math class his school offered. Today, the nonprofit academic center runs summer, online, and family programs for gifted and talented students in grades 2 to 12 from around the world.

Typically, 75 to 85 percent of students who take the center’s verbal and math screening exams score high enough to qualify for its enrichment programs. But when the organization sought to create a program specifically for under-resourced Baltimore City Public Schools, only about 30 percent of students met the cutoff.

Amy Shelton, director of research and interim executive director of the program, thought it implausible that Baltimore students truly fell short on aptitude, so the center developed a research project to test other skills and abilities that predict success in math, such as spatial and working-memory ability and critical and divergent thinking. That began the Baltimore Emerging Scholars initiative for the brightest students in 16 of the district’s lowest-performing elementary schools. By the end of the 25-week curriculum, the “emerging scholars” matched students from wealthier schools in qualifying for the center’s regular programs. (A $300,000 endowment, bankrolled by gifts and grants, funds the Emerging Scholars program; another $5 million annually, from tuition and philanthropy, goes toward financial aid for students in the center’s other programs.)

Initially, when the center asked Baltimore schools to identify students for the Emerging Scholars program, it ran into pervasive bias, said Plucker, the Hopkins education professor, who is affiliated with the center. Teachers and principals were intrigued but told him, “We don’t have any gifted students here because we’re a mostly black, Hispanic, or low-income school.”

Plucker said such bias is common in schools, even among people who truly want these students to succeed. To try to counter it, he supports broader universal screening for gifted and talented programs and assessing students within the context of their school rather than the entire district.

“What we find is that if you skip the nomination phase and you just assess everybody, you find many more low-income students who are already performing at higher levels,” Plucker said.

Gadsden Elementary School District in southwest Arizona provides a small but powerful example of how schools can identify and nurture talented students who might otherwise fall through the cracks. The poor, rural district on the Mexican border serves 100 percent minority students, mostly Hispanic, and nearly every student is eligible for free or reduced-price lunch. Yet more students from Gadsden qualify for the Hopkins center’s summer programs than from any other district in the country.

When the district started a gifted program 13 years ago, it reviewed data for every student in grades 2 through 4, expanded tutoring in math and science, created a partnership with the local community college for high-performing middle-school students, and redesigned its professional-development programs for teachers. Counselors and teachers regularly communicate with parents, generally in Spanish, and help them fill out applications for enrichment programs. In other words, the district does everything possible to identify strong math students and develop their skills over the long term.

 

Winning at Heads and Tails It may seem that flipping a coin is fair; after all, there’s a 50-50 chance of getting heads or tails on each flip. But if the game calls for a specific pattern of heads and tails to emerge in continuous succession over a series of flips, math strategy matters. Let’s say that Sansa and Bran agree to flip a coin for the Iron Throne. Sansa predicts that three heads in a row (HHH) will emerge first, while Bran selects tails, heads, heads (THH) as his pattern. If the first three flips are HHH, then Sansa wins, but if tails comes up in any of the first three flips, she has no chance of winning. Why? “Because once we have a T, we can never get three heads in a row without there being a T beforehand,” explains Alon Amit, a teacher at the San Jose Math Circle. “We get THH before the HHH pattern has a chance to show up.” Sansa’s chances of winning the throne are 12.5 percent, but Bran will win about 87.5 percent of the time. Bran decides to give Sansa another chance. Since tails, heads, heads (THH) worked so well for Bran, Sansa picks that pattern in the next round. Bran then picks tails, tails, heads (TTH) and, again, is more likely to succeed. The reason is this: both of them need to wait for a T to show up because both patterns start with a T. Once the first T comes up, the next two flips may be any one of these four combinations: • HH: Sansa wins with THH. • HT: The sequence is now THT, so neither player wins. The final T becomes the beginning of the chain, and they have to wait for the next two flips.  • TH: Bran wins with TTH. • TT: The pattern is now TTT. Bran is now guaranteed to win, because Sansa’s THH pattern will never come up. Whenever the next H is thrown, there will always be a TT preceding it.

 

 

Lessons for Schools

The folks who run the private enrichment programs say their goal isn’t to create a separate school system for top students but to fill a void. Could the public schools ever evolve to meet this need? The story of the Gadsden district hints that they could, and a few other initiatives provide encouraging signs. AoPS is piloting the Beast Academy curriculum in a Minnesota school district and working out a partnership with a large, urban district. If results of the Pipeline program in Montgomery County continue to go well, Paul said, he will probably ask the school district to fund an expansion.

As Stankova put it, “The Math Taught the Right Way program was really not intended to replace what’s happening in school. It was intended to be an example of what should happen in schools.”

Some schools are moving toward that approach, but usually only for the students who already excel in math and, even among those students, competition is fierce. Of a little more than 12,000 8th-grade students in Montgomery County Public Schools, about 600 apply for the 100 Blair science-and-math magnet spots. Since 1999, the program has had more finalists in the Intel Science Talent Search (now sponsored by Regeneron) than any school in the nation. Everyone on Blair’s math team has qualified for the American Invitational Mathematics Examination, one in a series of progressively challenging tests on the road to selection for the U.S. team to the International Mathematical Olympiad, and this year, student Daniel Zhu earned a spot on the U.S. team. At one of Blair’s weekly math-team meetings last fall, fresh from the school’s third consecutive win at the Princeton University math competition for high schools, senior Haydn Gwyn, a co-captain of the math team, discussed a research project on graph theory that he and a teammate conducted at the University of Maryland the previous summer.

He spoke with no notes and no hesitation in a half-hour presentation that was equal parts lecture, problem-solving lesson, and standup routine for an audience of mathematicians. Gwyn seems born for math. On Pi Day when he was 10, his dad recorded him saying 220 digits of pi in under a minute and posted it on YouTube.

There would be a sizable void in his life without the magnet, said Haydn. He credits the teachers for the high quality of the program, especially math-team adviser and magnet teacher Jeremy Schwartz.

Many of the math-team members enroll in Schwartz’s multivariable calculus and differential equations class. One day last fall, students were working on a series of problems using Lagrange multipliers, named after 18th-century mathematician and astronomer Joseph Louis Lagrange. Schwartz moved from group to group answering questions and asking a few of his own, prompting students to defend their work. Reviewing the equations of four girls who had hit an impasse, Schwartz offered a clue: “We have three variables and only two equations, if only there was a third equation.” After a moment’s thought, one girl exclaimed: “There is!”

Schwartz takes issue with the idea that math “is this big, complicated, difficult thing.” People use algebra, fractions, and probability every day; they just don’t necessarily make the connection. “If you can tell me that 20 minutes is a third of an hour, you can do fractions,” he reasoned.

Unfortunately, math phobia can even affect math teachers. A 2018 survey of 7,600 math, science, and computer-science teachers by Horizon Research found that 39 percent of elementary-school teachers felt they were inadequately prepared to teach math, and 25 percent admitted not being very interested in the subject.

Recent neuroscience research has challenged the idea that some of us are “math people” and some not. As with any other subject, math can be “learned through hard work and practice,” wrote researchers Robin Keturah Anderson, Jo Boaler, and Jack A. Dieckmann in a 2018 report. “A range of studies have demonstrated the neuroplasticity of the brain and the potential of all students to grow brain pathways that enable mathematics learning.”

Driven by Common Core standards, which require students to learn to justify and explain their answers, research is underway to identify more-effective methods of teaching math, especially for underperforming and underserved students. The nonprofit Education Development Center and its partners are analyzing findings of a five-year, nearly $8 million grant from the National Science Foundation to support Pittsburgh Public Schools in this effort.

But even if schools learn from these efforts and increase their focus on math education, will such changes help the whiz kids, or only those who are performing below standard?

“We’re obligated to do a good job for both,” said Jon Star, a Harvard University education professor whose research focuses on how students learn math, but he adds that high-achieving kids are going to succeed even if they’re not challenged enough. On the other hand, “if a teacher does a bad job with the kids who are struggling, then those kids are just falling out and they have no other way to succeed.”

Plucker said the data don’t bear out the notion that bright kids will take care of themselves. He also believes that setting the bar at minimum standards does a disservice to all students. Instead, the goal should be that every student continues to grow. “I just want a public school system where getting them to grade level is not the finish line. It’s a mile marker in a much longer journey.”

Kathryn Baron is a freelance education writer based in California.