Princeton Public: Math, Myths, and Inequalities

To get into a good college in those countries, it’s exclusively about your performance on standardized tests. So in their cultural repertoire, the way to get ahead is to excel academically.

Should Kids Be Cramming for Tests or Competing at Sports?, Natasha Warikoo

PART II

<< PART I

International Perspectives on Education and Careers

Parents and family members raised or educated in countries abroad may utilize a unique set of cultural repertoires to support their children academically and perhaps hold certain misconceptions about American higher education and the labor market. It is hard to pinpoint the exact number of parents in our community who were raised in a foreign country, but it is known that 29% of our residents were foreign-born and 27% of students in the district speak a non-English language at home. In terms of holding international expectations about education (not necessarily having been born there), I would estimate a full third of Princeton families fall into this category— a rather large number and one that is impacting the community’s discussion on math reform and school practices generally.

In most regions outside the U.S., top universities tend to be public institutions that are heavily supported with public tax money and are expected to act in the public good, with fair and meritocratic access through the use of entrance exams. Tuition at these schools is often subsidized and low relative to the United States. American top-tier colleges and universities, on the other hand, are most often private institutions and need not serve the public good. They are only partly meritocratic and exist to serve their own varied interests and agendas. At the same time, these private institutions portray themselves as meritocratic and acting in the public interest in order to justify the large amount of tax support they receive in the form of student loans and other forms of assistance. But in reality, these schools are better understood as private educational clubs for groups of like-minded individual students with complementary characteristics. While not very meritocratic, most would acknowledge this allows for wonderfully diverse student bodies and interests on their campuses.

Since roughly 50% of American students who enroll in college do not finish their degrees, a college’s interest in grades and other measurements of academic performance is focused on finding students who will remain for the full duration and pay healthy tuition fees for 4+ years; it is not an attempt to empirically determine the most academically fit applicants. They want a mix of legacy students, wealthy students, athletes, musicians, nerds, etc., with a range of academic interests to sustain all the various departments and activities in the school. The selection process is not fair, it is not truly meritocratic, and certain groups of applicants will be more heavily favored than others.

But in reality, these schools are better understood as private educational clubs…

One might expect a foreign-raised parent to believe tests like the SAT or ACT play a similar role in college admissions that the entrance exams played in their native country, but today such scores are only one small, and frequently optional, part of an applicant’s portfolio. Calculus (a focus of many parents’ concerns) is not even on the SAT or ACT, and imprecise AP scores in calculus act merely as indicators that a student succeeded in taking a challenging course. In contrast, all of the countries below (in rough order of test score importance) place a much greater emphasis on these standardized tests. Why? Because the structure of their educational systems require an open and ostensibly fair selection process, which ours does not.

The Role of Entrance Exams in other Nations

China: The Gaokao is an extremely high-stakes exam determining university placement. Its importance in Chinese society cannot be overstated.

India: With multiple competitive exams for engineering, medical, and other professional courses, exam performance is pivotal for many students’ career trajectories.

South Korea: The Suneung, or College Scholastic Ability Test, is a key determinant for university admissions, and the pressure around it is culturally significant.

Japan: University entrance exams are crucial, and there’s a heavy emphasis on juku (cram schools) to prepare for them.

Singapore: The GCE A-Levels and other national exams have significant influence on academic and career paths.

Taiwan: The college entrance exam holds considerable weight for university admissions.

Hong Kong: The Hong Kong Diploma of Secondary Education (HKDSE) is a high-stakes exam for university admissions.

Vietnam: University entrance exams are pivotal for higher education aspirations.

France: The Baccalauréat is a significant exam for university admissions and has been a rite of passage for French students.

United Kingdom: While the educational trajectory is more diversified than in some Asian countries, A-levels play an important role in university admissions.

Russia: The Unified State Exam (EGE) is used for both high school graduation and university admissions.

Brazil: The ENEM exam is significant for university admissions.

Nigeria: Exams like the West African Senior School Certificate Examination (WASSCE) play an essential role in academic progression.

Iran: The Konkur is a competitive, high-stakes national university entrance exam.

Turkey: The YKS is a significant university placement exam.

Australia, New Zealand: While the importance of exams like the HSC (Australia) or NCEA (New Zealand) shouldn’t be understated, the cultural emphasis might be less compared to countries like South Korea or China.

Tufts sociologist Natasha Warikoo has studied how families with different cultural backgrounds interact with school board members, administrators, and parents of other international backgrounds in a town similar to ours (Should Kids Be Cramming for Tests or Competing at Sports?). She is careful not to judge the priorities of these immigrant parents:

It’s part of what I call their cultural repertoire. Most of these immigrant Asian parents had done quite well academically in India and China, and that is what led them to be able to come to the United States, either for graduate school or college or through a highly skilled immigrant visa, and to get a high enough paying job that they could live in this town.

However, this situation can become challenging when those priorities impact the lives of other students, who become forced to compete in a race in which they had no desire to participate. If, for example, 30% of students receive private math tutoring outside of school, and a third of all students are placed in an accelerated math track, it is easy to see that students from less affluent families, or families unaccustomed to tutoring, will not be well represented in the accelerated sections. And as groups form along these lines, between so-called smart kids and regular kids, we must acknowledge that these “smart” kids grow in confidence and begin taking on an identity based on their ability to do advanced coursework. I was one of those kids, and know this type of socialization is marvelous and had a positive effect; unfortunately, the effect can work in reverse for the kids who did not make the cut.

Unlike other countries, American colleges rely on finding families and students who are willing to shoulder tuition costs that are far higher than their overseas counterparts, even when there are lower cost options available in the form of state schools, etc. One of the best ways to get students and families to pay upwards of $50,000 per year out-of-pocket (or through loans) is to perpetuate the myth that higher education is an exclusive gateway to personal and professional success. In fact they are not gate-keepers to the best and most influential positions in the nation, the way universities in foreign countries often are, such as in Japan, described by Susan Carpenter in “Why Japan Can’t Reform“:

Graduates from Tokyo University are members of a very influential clique in the ministries. This network plays a far more important role in Japanese society than does the ‘old boys’ network in the West.

Or similarly, in “France’s elite schools and their alumni networks: a flaw in the governance of French companies”:

The result is an over-representation of Polytechnique and ENA alumni at the head of large French companies. No less than 13 CEOs of CAC 40 companies come from these two schools. By contrast, only 11 CEOs of America’s top 100 listed companies were educated at an Ivy League university.

Even with such knowledge in hand, having one’s child chosen by a selective university, out of thousands of unsuccessful applicants, can be beguiling to parents and families. Moreover, those with a level of career success who have themselves attended similar schools based on merit, may have strong notions of self-worth derived from those credentials. This may make it difficult to realize they are being manipulated by colleges to pay more, because to do so would be to question their own worth.

This is not to dismiss top-tier colleges, however. The top two-dozen or so schools are not just excellent academically, but also much less expensive due to their generous financial aid programs. And even when financial aid is not forthcoming, there is of course nothing wrong with spending lavishly on education, any more than it would be wrong for a family to spend money on a fancy Mercedes when a simple Toyota would suffice. However, students should be aware that one’s choice of graduate school, unlike one’s undergraduate school, can be decisive in some career pathways, such as law, business, and medicine, and families might want to focus more on that phase of education than the college years.

As parents, we need to remember that we are often operating under outdated or inaccurate assumptions…

It’s not just immigrant parents who have different understandings and priorities, but American-raised parents as well. Many schools across the country are quite unlike our district, and public schools in the 1980s, for example, differed significantly in their practices and curricula from today. As parents, we need to remember that we are often operating under outdated or inaccurate assumptions based on our own experiences. Nationwide, schools reached the height of integration in 1988, and yet many of us have failed to notice a rise of racialized tracking that was a response to that trend. In my high school (in a small college town) the top-level math offering was Pre-Calculus. Similarly, special education was less prevalent, and standard math classes sometimes simplified material (by relying on drills, for example) and proceeded more slowly to accommodate everyone. Today, our district’s middle school, in contrast, provides separate individually tailored instruction to kids who need it, and the pace of “regular” math is actually quite brisk. A parent may have other reasons for wanting a child to take a more advanced class besides developing foundational skills, but as a pedagogical matter, schools are advancing math concepts more quickly than they have in previous decades.

The American Workplace

With respect to the American labor market, it too, is unlike any other country with regard to its openness to diverse hires, its emphasis on experience vs. educational credentials, and the ease with which one can set up a business. This environment is another reason why the pursuit of academic credentials and accelerated learning is perhaps not the best educational strategy for children seeking careers in the United States. The Georgetown report above takes pains to note that one’s major is not wage destiny, and that the wage numbers between STEM and non-STEM workers are averages, where considerable overlap exists among individuals. For example, the top 25% of education majors end up earning more than the bottom 25% of engineering majors.

What else besides choice of college major influences earnings and career trajectory? We might reflect on the qualities that supervisors and executives have that others with the same training and background lack. As bad as some bosses are, there is usually some repertoire of social skills present, such as public speaking, formal writing, and emotional intelligence, that do not grow directly out of academic success. It goes without saying they almost always earn more money than their subordinates, and it is quite common for managers to be hired from outside an organization. This type of dynamic workplace is not at all the norm in Japan, for example, and to a lesser extent in many other countries, where management hierarchies are largely based on seniority within a company.

Thus, it is not unreasonable for American colleges to look for these qualities in their applicants, such as leadership and emotional maturity, even as their primary concern is to choose students who fit in well with the culture of the school and will finish out their degree (while paying high tuition). This author has little doubt prejudice exists in the admissions process at many schools, however, they are quite correct to select for traits that do not show up clearly in transcripts and test scores. For instance, many parents care strongly about participation in sports because it is one of the very best ways to learn about training, leadership,  and teamwork, and these are attributes that colleges and workplaces rightfully seek in their applicants.

Calculus in High School Math

We should also remember why mathematics and calculus became so prized in the first place. Throughout World War II, afterwards, and all the way through 1973, the Selective Service System required young men to register for military service. What is mostly forgotten, however, was that conscription was used not merely to draft men into the armed forces, but to persuade them to move into occupations and roles that the government valued, through the use of draft exemptions and deferments (“Rough Draft“, Rutenberg). Because the need to develop nuclear weapons and ballistic missiles was intense during the Cold War, with countless calculus problems needing to be solved, one foolproof deferment to avoid the draft was to serve as a math teacher or student. As director General Hershey of the U.S. Selective Service explained, “The only reason the Nation is not short 40,000 to 50,000 engineers is because they were deferred in 1951, 1952, and 1953.” Of course today we still have a need for such engineers, but it is lessened (fewer nuclear power plants, etc.) and the government is no longer using the threat of the draft to persuade people to pursue math careers. It thus follows we should see less emphasis placed on calculus in our high school and college curricula, and more weight given to other branches of mathematics and science, such as computing, which now plays an enormous role in our national defense but only a minor role in school curricula.

For all that, the reason why calculus in particular was added to high school curricula, along with a greater emphasis on STEM education, was that in the late 1980s and early 1990s, there was a growing concern among business leaders and policymakers in the United States about the country’s competitiveness in the global economy, particularly in the face of rising technological advancement and economic growth in East Asia. This worry proved to be largely misplaced, and by “competitiveness” what these executives really meant was inexpensive high-skilled labor, but even then the government deliberately moved much of our manufacturing base to other countries. This result highlights the folly of viewing the educational system as a tool to provide big business with workers, rather than to serve the students and families of their communities.

Starting in 1989, the report was codified into national math standards that were eventually protested by angry parents—including two particularly heated groups from Princeton, New Jersey and Palo Alto, California—who demanded more advanced math offerings. The conflict lasted years, during which time anti-reform math traditionalists, decrying what they referred to as “fuzzy math,” had organized themselves into a political force that called for changes in textbooks and lobbied national politicians.

How Math Became an Object of the Culture Wars, by Jay Caspian Kang, 11/15/2022

It is ironic that American educational reformers, who so badly wanted students to emulate the math skills of students in East Asia, were not interested in emulating their teaching methods. When American automobile manufacturers worked to improve quality in the 1980s, they didn’t merely force higher standards on to their factories, but studied the management and manufacturing processes of their foreign competitors. American math curriculum designers, on the other hand, still conceive of math study as a series of individual subjects, such as “Algebra” and “Geometry”, whereas many successful foreign educational systems take an integrated approach, incorporating a variety of math topics along the way, and not encouraging students to skip ahead.

Today, calculus is much more prevalent in high school curricula than it was in the 1980s, but still only about 19% of U.S. graduates have completed a course in the subject. While math education experts have advised in recent years to place less emphasis on calculus in high school curricula, many admissions officers still view its presence on a transcript favorably, even as most top schools have dropped calculus as a requirement (“Even as Caltech Drops Calculus Requirement, Other Competitive Colleges Continue to Expect Hard-to-Find Course“).

Colleges with a strong preference for calculus should be viewed with some skepticism, since turning away applicants without calculus is a great way to filter out African American, Hispanic, and students on the lower end of the socioeconomic scale. Only 38% of public high schools with 75%+ Black and Hispanic populations offer calculus as a class, and even when it is offered, white students take calculus at over twice the rate of Black students, and skews heavily towards kids from wealthier families (US News).

Thus, in the Princeton environment, ironically, it is in the savvy and affluent parent’s interest for overall standards to be “lower”.

The Upsides of Flexible Math Standards

Families who worry that curriculum reform will result in lower math standards and fewer math opportunities, may not have considered there are advantages. For example, if math savvy parents are able to provide enrichment opportunities for their kids like tutoring and summer math instruction, they will stand out more from those who do not have such opportunities. Top American colleges do not look only at academic accomplishments on an absolute scale (like test scores), but how well a student took advantage of whatever opportunities were available to them (as part of a “holistic review process”). It is also unfortunately true that a high school student’s competitors are sometimes their own classmates, as colleges strive for geographical diversity and school counselors are forced to play favorites with recommendations. Thus, in the Princeton environment, ironically, it is in the savvy and affluent parent’s interest for overall standards to be “lower”.

Similarly, if calculus were merely a single course offering next to other math courses in the high school curriculum—such as Statistics, Data Science, or Computing—that would only serve to better highlight those relatively few students who persevered in calculus, and mark them as being truly interested in pursuing majors in physics, math, and engineering, benefiting them as well.

Students opting for calculus may ask themselves, however, whether focusing on those areas makes the most sense when Princeton University—typically the 2nd most common destination for PHS students—offers as its most popular majors Computer Science and Public Policy. For such valued majors, their sub-fields and disciplines are not major components of the high school curriculum.

A factor working against college-savvy and affluent families is that college admission officers around the country know that our district has a poor reputation with regard to racial equity, which has been printed in mainstream media outlets for decades. These colleges aren’t typically looking for more privileged students from wealthy suburban public schools to fill their enrollments. I suspect they would be more likely to recruit students of all backgrounds from PHS if they knew the success of our best students was not being achieved at the expense of Black, Hispanic, and socioeconomically-disadvantaged kids.

Parents, educators, and community members with academic careers and STEM backgrounds tend to value academic credentials and exam scores more than most groups, and Princeton is saturated with such individuals. However, one cannot dispute there are other values, other careers, other hierarchies, that are equally valid and lead to just as much success, whatever that means. If that is financial success, well yes, Princeton is relatively affluent, but it doesn’t even crack the top-50 towns in New Jersey for median income.

Clearly, academic skills and achievements are important to one’s life and career success. However, if we think about who is really successful among us, those with strong social skills often seem to do very well. As described in Harvard Business Review, one study found that men having a combination of both math and social skills have increasingly earned more than those with only one of those skills. HBR concludes,

The data suggests that today’s economy rewards the balance of quantitative and social skills more than ever. That has ramifications for how we educate children – calling into question schools’ heightened focus on standardized testing, as opposed to a broader view of skills development – as well as for our own careers. In an era even more defined by rapid technological innovation, we’re increasingly expected to bring technical savvy and interpersonal know-how to the table. Quantitative reasoning is understandably in high demand, but so too are the skills learned on the sports field.

Moreover, many supporters of universal high math standards seem to ignore the supply vs. demand dynamics of the labor market. If more and more students take calculus in high school, it follows that the skill that will be valued less when applying to school or finding a job.

Perhaps the most important education of all for material success, and other kinds, is the exploration of the self as we interact with others, to identify the unique traits which we excel at, above all others (a limited supply) and which are also valued (a strong demand). In developing this intrapersonal intelligence, rigorous standards and measurements may be only moderately useful. Such traits often go unrecognized due to their uniqueness, since schools strive to promote activities in which everyone can participate. Yet, it is the rarity of these abilities which make them potentially the most valuable to other people.

There is also a school safety dimension to this issue which should be carefully considered. Creating an environment where students do not feel divided into rigid factions and can comfortably engage with administrative figures will contribute significantly to overall school safety. This approach, which emphasizes emotional and social security within the school community, may be more effective in ensuring safety than relying on physical security measures.

The Truth About Diversity

I have tried to show why looser math standards and emphasis on developing other skills may not be as detrimental to advanced students as some might fear. However, admittedly, there will always be a tension in serving the needs of different types of students with some inevitable compromises. Families with means have many options if their child’s education is not ideal. They can homeschool,  hire tutors, enroll their child in a private school, etc. But families without such means, or special needs, have fewer options. Public schools have a sacred duty to not sacrifice these students’ wellbeing for the sake of high-performing students, even as educators understandably measure themselves by the success of their top students.

The argument that high-performing students need an underclass to bolster their confidence is one that I cannot accept.

Most parents move into the Princeton community knowing full well it is a racially, ethnically, and socioeconomically diverse town. In these times, it is irrational to expect their child’s education in the town’s public school would not exhibit a corresponding amount of diversity. The argument that high-performing students need an underclass to bolster their confidence is one that I cannot accept. The dynamics between individuals and groups of different backgrounds can certainly be challenging, but also a great benefit, as kids learn about all kinds of people before heading off into their preferred social bubbles as adults.

Fortunately, for parents who are uncomfortable with Princeton’s particularly rich demographic makeup, the region is blessed with distinct communities of vastly different demographics mere minutes away, and nearly all of these amazing areas have significantly less expensive high-quality housing stock, in addition to a dazzling array of private schools, from which to choose an ideal educational setting for their children.

There is a persistent belief among many that differences in math ability are genetic and should therefore be managed through tracking or independent pathways. If placement tests and other criteria do indeed measure natural math ability, then school officials at PPS must conclude that Blacks and Hispanics have little natural ability to do advanced math, or that the tests measure something else, such as the ability of parents to mentor their children in math. This observer believes public schools must embrace a pedagogical philosophy and curriculum that emphasizes a child’s ability to learn through training and perseverance, rather than natural ability.

There is an even stronger belief that math inability results from cultural characteristics and oppositional psychology, particularly among African Americans. Karolyn Tyson’s book, “Integration Interrupted” explores this myth thoroughly. Like advanced math, one might ask why we rarely hear African American players in our acclaimed jazz and studio bands. Do African American families lack an appreciation of jazz? Are there no Black role models in jazz or popular music? Do they tend to lack rhythm? Forgive me for being facetious; the answer is obviously no. The reason for their paucity in these ensembles is not the audition choices of the directors, who are always striving for good players and routinely utilize African American singers. The cause is systemic, that is to say, there is something about the way in which student instrumentalists are developed that leaves many African Americans out, and we should seriously consider whether the lack of similar faces in advanced math is also systemic.

Possible Solutions

Most of what happens in a New Jersey school district is determined by state regulations, making fundamental change at the individual district and school board level difficult. If I were the NJ legislature, nearly every aspect of public school education would be overhauled, but alas, such change is not likely to happen, except in very gradual phases, if at all. Working within the current framework set by the state, there are still major improvements that can be achieved through local initiatives and community involvement, which might include the following general approaches:

1. First would be the guideline that teachers, parents, and students alike should not experience sudden unexpected changes to opportunities and expectations that were available when they came into the district. Rather, change should be gradual, opportunities “grandfathered” in, and future directions broadcast well in advance so that everyone in the community can plan ahead.
2. Dramatically improve the working environment for teachers, by reducing total student counts for core teachers (math, science, history, english) by 40% in middle school and high school, in return for specific changes in teaching styles and curriculum. This will necessitate more teachers, more classrooms, and/or fewer students. Leaving aside the cost of physical infrastructure, a back-of-the-envelope calculation suggests an additional $3.6 million would be needed on top of the existing $106 million annual district budget. Naturally, this initiative would do much more for students and teachers than simply alleviate the need for tracking, but small class sizes in themselves aren’t the improvement, it’s what small sizes allow educators to do that is important, and those improvements must be baked into teacher contracts in order for such plans to work.
3. Do not make a race out of mathematics study, with winners and losers. Do not weight student GPAs. Parents should be encouraged to direct and enrich their children’s education, but the district should not reward them for it through the use of accelerated placements and similar designations. This can be achieved by allowing (non-tutored) students to enroll in most courses under normal circumstances.
4. The district should not encourage skipping ahead. However, when a child is truly gifted (or ahead of their peers) at math, consult with parents about placing them in the following grade’s class instead of creating accelerated classes for them. Students gifted in other areas should have similar opportunities. Much of the challenge seems to revolve around trying to avoid mixing students from different grades in the same class (a result of crowded schools). Smaller classes would of course allow teachers to personalize materials and instruction for gifted students as well.
5. Avoid using math placement and math grades as a prerequisite for non-math courses. Courses such as Horticulture, Biology, Exercise Science, Chemistry, Astronomy, Java Programming, etc. do not need math prerequisites. Prerequisites should generally be suggestions rather than requirements.
6. Do away with the notion of “accelerated” or “advanced” or “honors” classes, and simply name them by the topics they cover. Montclair’s struggle with detracking is revealing. It resembles Princeton’s own debate with curriculum reform, except for them it was 9th grade English class that was tracked. In contrast, English Language studies at PHS are nearly ideal because of how the curriculum is structured and courses are labeled.
7. Course placements, when needed, should only be suggestions, based on diagnostic test scores. However, allow those decisions to be overridden and make sure parents know about any advanced pathways from the beginning. Allow kids to try challenging courses and switch to different classes if things do not work out. Struggle is a normal part of learning.
8. With respect to math sequences, we should anticipate that calculus will be offered in the 4th year of high school as one possible pathway (as it is now), but also offer statistics, data science, applied math, and above all, computing.

These proposed solutions are calibrated to Princeton’s unique strengths and weaknesses. They aim to squarely address current challenges while also paving the way for a K-12 educational environment that is adaptable, inclusive, and reflective of our fast-evolving societal and technological landscape. Comments, questions, and corrections are welcome below (moderated for spam).