In June 2015, we argued in a NEJHE article “Reducing Math Obstacles to Higher Education,” that intensified efforts to improve math education may make sense for many students, but for other students–those who lack ability or interest in math–the prescription of more math limits their ability to attain a college credential. As a result, heightened math requirements can limit some students’ employment options and play a counterproductive role in helping this segment of students achieve full participation in the economy.
Such students would benefit more from an educational program with reduced emphasis on traditional math. They could better spend more time on other studies that would help them develop themselves toward successes in further education and careers. All students, including those with little ability or interest in math, should have access to higher education and a college credential that will help them develop the abilities they will need as workers and citizens in a complex society.
In the current article, we focus more on economic issues. Public discussion today focuses greatly on the relationships among economic inequality, education and technological change. But understanding in this area suffers from assumptions about the value of math education for gaining useful skills when work opportunities and skill demands are so varied. With this article, we hope to stimulate research, debate and experimentation that could create new understandings and models to build the flexible programs we need to move closer to full economic participation and economic independence.
As our work has proceeded, a new book has greatly encouraged us: The Math Myth, And Other STEM Delusions by eminent political scientist Andrew Hacker (The New Press, March 2016). Hacker has written extensively about race, gender and income inequality, and with his wife Claudia Dreifus, authored the 2011 book Higher Education? How Colleges Are Wasting Our Money and Failing Our Kids—and What We Can Do About It. Many of Hacker’s points in The Math Myth dovetail closely with ours; he also provides much useful insight into how misleading arguments for more math education have exaggerated the benefits of current approaches to math and allied fields. We hope the publication of The Math Myth will contribute to the goal we hold of reducing math barriers to higher education and good jobs.
Technological progress and the need for math
Education beyond high school is becoming increasingly necessary for entry into the better-paid and more secure sectors of the job market. (Sandy Baum of the Urban Institute provides substantial evidence on the income benefits of college in “Higher Education Earnings Premium: Value, Variation, and Trends,” Feb. 24, 2014.) In so many vocations and careers, math plays little or no role, but higher education is required. As a result, math-based barriers to higher education block people from education toward careers in which they could prosper and contribute more to the nation. We all should have access to such education whether or not we are good at math.
The 20th-century experience showed how new technology could gain millions of users without demanding users’ expertise. If mechanized factories, the automobile, the telephone and the computer were to spread, some people had to master new knowledge and skills. But most people did not need to learn how to run an assembly line, repair a car engine or design the circuits inside a telephone or personal computer. The creation of technology requires scientists and engineers and its use demands technicians, operators and repair people. As a result, any member of our technology-dependent society inevitably relies on people with mathematical, scientific and engineering skills.
We need these technically and mathematically trained people—yes, many of them. But we do not all need higher math to contribute in the workplace; for a large number of jobs, higher math skills do not play any significant role.
One argument for sustained universal math education is that technological progress and global competition demand greater science and math skill. Such concerns can be seen in government reports such as “STEM Education: Preparing for the Jobs of the Future,” (from the U.S. Congress Joint Economic Committee, April 2012) or “Federal Science, Technology, Engineering, and Mathematics Education 5-Year Strategic Plan” (from the National Science and Technology Council, May 2013). While this argument partly springs from concerns that American companies face shortages in STEM skills that weaken their competitiveness, another concern is that workers without skills in science and math will suffer limited access to well-paid jobs. Those without science and math skills will, in this view, be denied access to the “new economy.” But this argument disregards key realities of the modern highly specialized economy. Technological and economic change increases math skill demands only for some workers, while leaving math skill demands unchanged or even reduced for others. In an economy with so much specialization of skill and inequality of opportunity, investment in math is a winning bet for some and a losing proposition for others.
In school, home and workplace, powerful math technology is included in handheld graphing calculators, in the most common spreadsheet software and in computer algebra and statistical systems. Such technology is also embedded in countless other programs and devices. What are the implications for math skill demands in the workplace and for what high school and college students should learn? As such technology spreads, who benefits from gaining greater math skills?
Those who head into industries focused on science and engineering may gain important advantages through math skill. The construction engineer may have skills and advantages over the road-building project manager who, in turn, probably has advantages over someone who lays asphalt or pours concrete. Managers and designers of all types—mechanical, electronic and financial—receive benefits from their greater skills.
But even in such technology-dependent industries, large numbers of jobs do not depend at all on math skill. The driver, the call-center worker, the bank teller or the salesperson relies on the math that they need being baked in to their equipment, so that machines operate safely, so that software gets the customer info to the right file, so that the deposit is added and the interest figured. To be sure, such tasks may still require human intelligence, for example, to evaluate the appropriateness of a transaction, to maintain good will with a customer, to recognize exceptional conditions that might cause danger and so forth. Powers of mathematical estimation and arithmetic could play a role.
Indeed, much of our efforts in design of equipment, software, jobs and larger systems are intended to protect operations from the human errors of the operators. Whether or not we like this development, the proportion of people who need to fully understand the mathematical principles or operations of their work is reduced. Perhaps a positive aspect is that more human energy can be devoted to human contact with customers and co-workers. (Andrew Hacker, in Chapter 4 of Math Myths, emphasizes that many people in scientific or technical jobs that require mathematical training, including physicians, engineers and actuaries, often do not draw on that training in any meaningful way.)
More detailed analysis of the experiences of students and of workers in STEM and other fields suggests that the supposed shortage of STEM skills has been exaggerated. Hal Salzman, Daniel Kuehn and B. Lindsay Lowell, in “Guestworkers in the high-skill U.S. labor market” (Economic Policy Institute, April 24, 2013), point out that only 5% of U.S. workforce jobs can be classified as STEM employment. And large proportions of graduates in STEM subjects, as much as half, do not end up working in their fields. (The low percentage of jobs in STEM fields does not include jobs in health.)
The “bad equilibrium” of weak high schools and economic inequality
Even as recent high school graduates wonder whether the cost of college is worth it, salary data continue to show that those with a college credential earn on average much more over a lifetime compared to those without. In fact, the job market in many areas of the country is less welcoming than it once was to people without any college experience. Many employers are increasingly using the college degree as they once used a high school diploma, as a screen to focus on potential employees for jobs at middle-skill levels that in the past were more often filled by people without college degrees. (A September 2014 report by Burning Glass Technologies, “Moving the Goalposts: How Demand for a Bachelor’s Degree Is Reshaping the Workforce,” includes detailed data on different job areas in which a bachelor’s degree is increasingly required.) Meanwhile, college-going rates across the country are at an all-time high, but income inequality continues to grow.
A full understanding of our rising economic inequality would help guide us to strategies toward greater equality. But this inequality is so multifaceted, affecting our society so deeply, that it remains hard to grasp. One key part of this “bad equilibrium” is the sorting of students by the educational system. Math plays a central role in this sorting by which different students are encouraged to pursue or are blocked from pursuing different amounts and levels of education. A second key part of the bad equilibrium is the reinforcing cycles of low wages and low skills.
For “first-generation” college students and students from low-income families, entry into college involves overcoming many obstacles, including a college environment that may be unfamiliar in many ways. As we pointed out in the prior article, math requirements serve as an effective barrier to entry into college and thus limit the potential for many to move to a higher income level with more marketable skills. Weakness in math should not exclude anyone from entry or success in the colleges that can develop these skills and to certify with diplomas that students have them. Yes, study of math can help develop some of these desired skills, especially tenacity in problem-solving, but many paths can help build this tenacity. All students deserve productive paths to develop the skills they need for employment, including mental discipline and problem-solving skills.
Adopting educational approaches that lead to full economic participation
Breaking this negative cycle of unequal opportunity will require many changes—in schools and across many of our social and economic institutions. Is wholesale change possible? We think so. But our country needs profound educational progress, so we can meet the many challenges emerging from rapid economic, technological and environmental change. We are proposing that the K-12 and higher education sectors take a long-term view in addressing existing exclusionary college-entry policies that discourage students who are weak in math from making long-term choices that will help them contribute to the economy at their full potential, generate personal wealth and earn income sufficient for financial independence.
Data on income inequality and wealth gaps point to interactions between race and ethnicity and individual and family wealth. In a 2015 report from Demos and the Institute on Assets and Social Policy called “The Racial Wealth Gap, Why Policy Matters,” Laura Sullivan and her co-authors show how changes in housing and educational policy could reduce the large racial and ethnic gaps in family wealth. We take the position that our educational policies and systems should reduce, certainly not worsen, the social conditions that limit economic mobility for marginalized populations, especially for students of color. In recent years, those populations have suffered significant setbacks. According to Rakesh Kochhar and Richard Fry writing for the Pew Research Center in December 2014, wealth inequality has grown along racial and ethnic lines since the Great Recession; the median wealth of non-Hispanic black households and of Hispanic households fell between 2010 and 2013 and neither group has experienced significant improvements since.
This link between race and income inequality is particularly concerning as demographers are predicting that minority groups will rise to over half of the total population by mid-century. As Sandra L. Colby and Jennifer M. Ortman described in their March 2015 Census report “Projections of the Size and Composition of the U.S. Population: 2014 to 2060, Population Estimates and Projections,” “no group will have a majority share of the total and the United States will become a ‘plurality’ of racial and ethnic groups.” We will all be depending on a more multi-colored workforce and need to develop schools, workplaces and policies that help us “pull together” in the context of a competitive global economy.
In an economy where education matters ever more, it becomes both a social and economic imperative that we provide education that works for students of all backgrounds. Our economic success depends upon learning how to make the path through school and the path from school to work successful for all types of students. Both the K-12 and higher education sectors can play active roles in disrupting the pattern of low skills and low wages. Reforming the roles of the K-12 and higher education systems will require many changes in our society as they are critical gate-keepers that determine who gets a shot at earning the credentials that can lead to individual economic prosperity.
Ideas for change
In “Reducing Math Obstacles to Higher Education,” we advocated new thinking about how to build a more flexible educational system of greater access and equality that students need. We called for K-16 collaboration toward solutions to the problem of math as a barrier to higher education and use of empirical data to measure the magnitude of the problem, especially for vulnerable populations. We now add some ideas for change that we think are needed.
- High schools should take a variety of steps to bring their programs more in line with the intellectual, personal and economic interests of their students. As we explained in the prior article, the third and fourth years of high school math are unproductive for many students who do poorly in math and have educational and career interests that do not benefit much from math. For some students, such steps might include less time studying math in the final two years of high school and more time on other subjects in which they can envision a career.
- At the same time, high schools should innovate in other ways to make their program more engaging and useful. As we noted in the earlier NEJHE piece, high schools should expand their mission to include strong programs in arts and social sciences that appeal to the expressive and social interests of adolescents, that develop a rich variety of skills and intelligences, and provide more knowledge about the adult world and the many fields of study available in college. High schools should also move the science program to a greater focus on biology and the applied disciplines of health, nutrition, environmental and earth sciences.
- To give high schools and high school students more flexibility in designing their curricula to meet student needs and interests, colleges should eliminate admission requirements of three or four years of high school math for those students not pursuing STEM degrees. Colleges should also eliminate general college graduation requirements that all students pass a math course at the same level regardless of their major and instead establish major requirements for math with renewed attention on what math is actually needed by the majority of the majors—much in many fields, less in others.
We advocate this reduction in math requirements, not because we want to “dumb down” education in the sense of making it easier and less useful. Instead, we think it is the fundamental duty of the educational community to make the invaluable benefits of skill and knowledge available to the widest possible proportion of students. We must challenge all our preconceptions about what is required to learn. Is calculus really needed for people to prepare for careers in medicine and other health professions? What math do accountants and coders really need to do their work? How much physics can one learn without calculus? How much chemistry can one learn without algebra? Progress on many questions such as these may open doors to many students who currently are excluded from knowledge and skills that can make their education more engaging, their citizenship more responsible, their work life more rewarding and their contribution to society more complete.
Some will object that reducing math requirements means “closing doors” or locking certain students into a disadvantaged class of people with a weak education. This concern appears well-intentioned, but we think misses the bigger picture and closes off opportunities for positive change.
The bigger picture is that our system today–with its single high school path of uniform requirements for all students in a world of highly unequal resources–is effectively closing doors of opportunity for millions of students. Those attending strong high schools, good colleges and established graduate programs have diverse opportunities and salaries far higher than those who attend weak high schools and get little or no college education.
We need schools that come much closer to engaging the interests, desires and ambitions of students, to help people learn what they really can use in their intellectual development and in their work lives. Real economic opportunity demands a deep redesign of school programs. We hope to see some of this deep change in the next decades.
Sustained open doors
We focus on just two aspects of new directions that would complement reduced math requirements in order to improve access and effectiveness of higher education. The first aspect is “sustained open doors,” a strategy that responds directly to the concern about reduced math requirements limiting opportunities for students.
Inevitably, all students do not find motivation, ability and resources available together to support hard work at school. Hence we see early bloomers and late bloomers, school aces and strugglers, rich kids and poor kids. Many students lack the financial and family resources to continue their education into adulthood without interruption.
Yet long educational paths, as much as 20 years total, can pay off far better than short paths ending without any college. Our society must make special efforts to keep doors to education open over students’ lives so that hopes for equal economic opportunity remain real. The students who fail to take advantage of high school for diverse reasons deserve meaningful second chances. Many other students would also do well to leave school after high school or two years of college and to experience the world of work. All these students should later find welcoming opportunities to return to school, with full chances to learn whatever can further their intellectual and economic growth.
For example, someone wanting at age 25 or 30 to enter a field that requires more science or math should be able to study for a year or two and then rejoin a path of a more advanced education. As education for newly created careers becomes more necessary, such re-entries into math and other fields will become needed at various ages of life.
Intellectual focus, personal direction and connection to work
A second aspect of a more just and effective system of education would restructure the last two years of high school and first two years of college to better foster intellectual development, personal direction and engagement with the world of work.
We look at the education of students ages 16 to 21 as one continuum that is ripe for coordinated and systemic reform. Consider this span of education in three two-year periods: the last two years of high school (grades 11 and 12); the two years of community college or the first two years of four-year college (grades 13 and 14); and the last two years of four-year college (grades 15 and 16).
In each of these three two-year periods, students should be encouraged to make choices: to focus their studies for intellectual development and to learn about related careers and work skills. In grades 11 and 12, the degree of focus might be modest, e.g. having students choose one of several major areas for additional study such as science and math, the arts, history and society, or languages. Some focus such as this is common in European high schools for students of this age.
Students planning to finish or pause their education after high school or after only two years of college should have ample opportunities to gain work-related knowledge and skills through courses, internships and apprenticeships. But even those students planning on four-year college should be encouraged to choose a broad focus area and to include in their studies some work-related learning.
Similarly, a two-year college program or even the first two years of a four-year college could include a modest concentration in one subject area, like a minor in a subject such as science, language or history. Such a two-year concentration would help students gain more experience with choice about their academic and vocational lives. Students entering the last two years of college might choose a major related to or different from their focus from the first two years of college. But the earlier experiences of focus and connection to work could make the last half of the college career much more useful.
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Our preference for less focus on math is rooted in the fact that the prevailing math curriculum is blocking many students from completing high school, getting to college or completing college. Those who are least successful in math need more education, not less, that will help prepare them for better jobs and better lives. Our goal should be to offer an education of equal value to all young people—not the same goals for all, which wind up creating much opportunity for some and much less for others. These students less able or less interested in math have a fully equal right to a college education and to the wide opportunities for personal and economic growth that college can bring.
Tony Dreyfus taught math at Brookline High School outside Boston. He also worked with the public school systems in Chelsea, Revere and Everett, Mass., in support of elementary math improvement efforts through math coaches. His college studies in economics and master’s degree in city planning with a focus on regional economics included extended study of statistics and economic modeling.
Yves Salomon-Fernandez is interim president of Massachusetts Bay Community College. She is the incoming president of Cumberland County College in New Jersey. She holds a master’s degree from the London School of Economics and a doctorate in education statistics from Boston College.
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