The last few months have brought changes in the leadership of public education in Massachusetts. The new secretary of education and chair of the Board of Higher Education both have deep expertise in education reform and accountability, and broad experiences in business. This new leadership could bring momentum for a “systems approach” to reduce the achievement gap and increase rates of high school completion and college-going. A systems approach would improve the alignment of higher education curricula with workforce demand while integrating the liberal arts curriculum in professional and technical disciplines to provide college graduates better career mobility. Completing the leadership triumvirate, the Board of Higher Education recently selected a new commissioner of Higher Education. Their selection provides a level of continuity for advancing the Vision Project goals and sustaining efforts around increased access and success initiated by the outgoing commissioner.
As Massachusetts tackles the issues of college access and success and prepares for a reduction in its workforce by 2020 (predicted by the Federal Reserve Bank of Boston and others), the need to align our strategies in the public K-12 and higher education realms is greater than ever before. Community colleges present one of the best opportunities for economic advancement of low-income Americans, yet the average graduation rate at the Bay State’s public two-year colleges is below 20%. Math requirements continue to be a significant barrier to entry into college and graduation for a sizable portion of community college students. The challenge for Massachusetts is to correct the unfortunate evolution of math into a counterproductive role as a proxy for intelligence and academic ability and as an impediment to further education. All students, including those with little ability or interest in math, have a right to a higher education that will help them become self-sustaining citizens who contribute to society’s overall well-being.
Massachusetts has recently begun to grapple with this issue in two ways. In late 2013, the Board of Higher Education voted a new Policy On Developmental Math Education, which directed colleges to modify degree math requirements so that students would not have to take more math than their major’s requirements. More recently, the board tackled the problem of math-placement tests that have been directing many students into developmental non-credit courses; the board’s new policy allows students with four years of high school math and a grade point average across all high school courses of 2.7 or higher to enroll in credit-bearing college math courses. Whether one agrees with these measures or not, they indicate a useful concern with the role of math education in students’ persistence through completion of college.
We think it’s an opportune time for the state’s public education community to discuss more deeply the appropriate role of math in today’s education system, for which the issues of access and completion are central.
Math as sorter of students into paths … and barrier to higher ed
A continuing chorus has urged U.S. school systems to intensify efforts to improve math education. Many believe that stronger school math would increase individual and national success in an evermore high-skill, technological and global economy.
This makes sense for many students and for the country’s global competitiveness. For some high school students, however, the prescription of more math hurts their educational experience. For these students, the goal of intensified math education can play a counterproductive role. Lack of success leads to negative judgments about the student’s intelligence—by the student and by others—that adversely affect opportunities for further education. Some students would be better served by an educational program with reduced emphasis on math and more time spent on other studies that would better help them develop useful knowledge and skills. Such a program would help these students succeed in further education and move into family-sustaining jobs with a career ladder.
Math plays a role in sorting students into different paths. Strong high school students enter elite, near-elite and mid-range colleges that often require four years of high-school math and put considerable weight on the SAT math score for admissions and scholarship decisions. For many such schools, students with SAT math scores below certain cutoffs—600, 500 or 400 depending on the school—are unlikely to be admitted or to receive generous scholarship support. At the much less selective colleges, almost any student can find entry regardless of grades and SAT scores. But these schools often require three years of high school math and a high school diploma, so failure in high school math can still serve as a barrier to further education.
Meanwhile, many of the weakest students drop out of high school or graduate from high school directly to the low end of the job market or to unemployment. Discouragement or failure in math probably contributes significantly to these students stopping their education too soon.
For weaker students who do get to college, many fail math screening tests as freshmen and are required to take non-credit remedial courses before they proceed to college math requirements. The required remedial and regular math courses contribute to financial burden, discouragement and college dropout. At some colleges, requirements for a more demanding math course can also be used to limit students trying to enter certain majors. For example, prospective business majors may be required to pass calculus even though only some of those specializing in more technical sides of business will really need this math.
Many students whose progress is impeded by math could be turned on to education, to self-development, to useful skills and to the world of work, independence and self-sufficiency of an adult. A large range of careers requires little or no math. Yet in so many vocations and careers, higher education is required, so that math-based exclusion creates a wasteful barrier to human potential and opportunity with long-term and generational implications for society.
Better opportunities for students with weak math
Our argument to diversify math options for high school students is pragmatic. Anecdotal evidence from large urban high schools indicates that, among the students who say they will enroll in college the fall semester after their high school graduation, those with chronic math achievement problems are far less likely to attend. By addressing the adverse impact of math requirements on academically weaker students and offering alternatives, the commonwealth’s public education officials would help these students develop interests in rewarding careers that are less math-dependent. “Vocational” schools expand options for a small number of students, but broader choices should be available at all high schools.
The experience of weak math students indicates why continued math education may be unproductive. In the cumulative process of a math education, deficits build up over the years. Students who couldn’t solve more complicated equations in tenth grade involving roots, powers or fractions can’t then succeed in dealing with conic sections, or rational and exponential functions. Accumulated weaknesses in fundamental math concepts and in algebraic technique block the weakest students from understanding or working with the more advanced topics of eleventh- and twelfth-grade math.
As a result of these weaknesses, some students work hard for poor results, while others drop down to easier classes and easier grades. In some of the easier classes, students make little real progress—revisiting old topics and making only introductory forays into new topics. Among the weakest fifth of the students, most will never use algebra outside the classroom and will not be able to move on to more advanced math subjects. Learning so little of the more challenging topics and being blocked from future education in more advanced math, these students can hardly be gaining skills that will support our society’s need for greater skills in math, science and technology.
Redesigning for engagement, knowledge and skills
Students in their junior and senior years should be encouraged to follow their interests much more than they do now, and develop their skills to their greatest potentials. High schools should expand their offerings to provide better engagement and career options for students in the lowest percentiles in math performance. Such stronger programs will help schools retain students through their high school graduation, encourage them to attend college, and pursue fulfilling careers. These programs should appeal to and develop a variety of skills and intelligences, bringing more knowledge about the adult world and the different further educational paths possible in college. Consider:
- The social sciences, little taught in high school now, hold many opportunities to engage students on their interests and attract students toward college studies and professional development. Psychology, for example, offers students humanistic and scientific insight into the emotional and interpersonal world that so attracts them and can stimulate career directions into many of the helping professions such as social work, psychotherapy, special education and pastoral work. For another example, economics stimulates thinking: about one’s life as a consumer, worker, saver, entrepreneur or investor; about markets and public policy; about natural resources and the environment; about local and international life.
- The performing and graphic arts can bring intellectual rewards, enhanced confidence, and engagement with the school community. These can also bring career possibilities within the arts, and intellectual skills useful beyond.
- The high school science program holds a rich array of subjects worthy of study, tangible and relevant to student lives. Biology is bursting with attractive and useful subjects for high school students. Full looks at nutrition, health and disease, exercise, sexuality, the brain, sensory function, addiction and other topics could very usefully occupy an additional year and provide useful knowledge. Similarly, the study of the oceans, the evolving earth, the atmosphere and its weather, the planets and outer space all present more stimulating possibilities of engagement for most students.
Wasting high school, finding second chances
Some might fear that less high school math for some students would further “close doors” in their future education and work—just the opposite of what we want. Some students gain the capacity and motivation to study a subject like math early, others later on, and still others, never. All deserve equal chances at a college education. Whether students have good or poor math ability, strong or little math interest, they should be given the opportunity to develop their intellects and skills in higher education. Our best strategy is an integrated system of public education that provides real opportunities for students to advance themselves in citizenship, economic security, and equal membership in society.
Universal math education to the end of high school follows from our noble but mistaken vision of universal equal opportunity. Our goal should be to offer an education of equal value to all young people, not the same academic program for all, which actually means much opportunity for some and little for others. Our educational system should offer full opportunities for students of different ages to enter studies and careers of all types. In our current approach, students must typically choose some careers, such as engineering or nursing, as early as they apply for college; for other careers, for example medicine or law, students more typically select part way through college, at the end of college or later. These different approaches to career entry work well enough for students with adequate financial support or strong academic records. For less-advantaged students, these entry points need to be expanded, so that earlier or later entry is also possible.
Advancing access to higher education
The chorus recommending stronger math instruction has sung so long and loud that we need new thinking about how to build the more flexible system our students need. We see some signs that such new thinking can gain traction soon. To move further to build greater access and equality, many steps are needed. The key strategies will include:
- K-16 collaborations for systems-oriented discourse, approaches and implementation of solutions to the problem of math as a barrier to higher education;
- review of empirical data to measure the magnitude of the problem, especially for vulnerable populations;
- flexibility, choice and engagement across sectors and stakeholder groups, including students and families; and
- accountability to ensure that the agreed-upon goals are being reached with the desired level of quality and that additional actions are taken when they are not.
Public discussion today focuses greatly on the relationships among economic inequality, education and technological change—issues we hope to explore further in a follow-up to this article. Understanding in this area suffers from questionable assumptions about the value of math education for gaining useful skills when work opportunities and skill demands are so variable. Further research, debate and experimentation should create new understandings and models to build the flexible programs we need.
Tony Dreyfus taught math at Brookline High School outside Boston. He also worked with the public school systems in Chelsea, Revere and Everett in support of math improvement efforts in their elementary schools. 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 vice-president for strategic planning and partnership advancement at Massachusetts Bay Community College. She holds a master’s degree from the London School of Economics and a doctorate in education statistics from Boston College.