## The Importance of Mathematical Sciences at Colleges and Universities in the 21st Century

This task force report by the Mathematical Association of America (MAA) articulates the role of mathematics, and by association, of academic mathematical sciences departments in colleges and universities, in the 21st century. It responds to challenges these departments face by describing the role of mathematics in preparing quantitatively literate citizens, in developing highly skilled STEM graduates, in preparing tomorrow’s K-12 teachers, and in generating new knowledge, both theoretical and applied, that will continue to provide our nation with economic advantages into the future.

Importance to Society Importance to Students

Importance to K-12 Education Importance to Departments

Mathematics is an indispensable component of business, design, innovation, basic research, and higher education. A critical mass of citizens trained in post-secondary mathematics is essential for economic growth and development. A recent report from the MAA on preparing the 21st century workforce emphasized the need to increase society’s awareness of the value of mathematics (Zorn et al., 2014):

Public awareness is scant -- even among employers, students, faculty and administrators -- about careers with links to STEM disciplines and about the importance of mathematics and statistics for both STEM and non-STEM careers. Such careers include a broad range of options, including finance, economics, and medicine, that require strong mathematical and statistical foundations. (p. 9)

However, mathematics plays a greater role in society than simply providing crucial workplace skills. Along with the Association of American Colleges and Universities (AAC&U) and the American Association of University Professors (AAUP), the MAA believes “institutions of higher education, if they are truly to serve as institutions of *higher* education, should provide more than narrow vocational training and should seek to enhance students’ capacities for lifelong learning.” As a core element of the traditional liberal arts, mathematics provides students opportunities to “foster intellectual curiosity about questions that will never be definitively settled - questions about justice, about community, about politics and culture, about difference in every sense of the word” (American Association of Colleges and Universities, 2018). Indeed, graduates with strong liberal arts foundations are more likely to embrace the necessity of lifelong learning and are better equipped to deal with ever increasing ambiguity within the societal context of social justice and cultural diversity issues and to serve in leadership roles in the workplace and at the local, state, and national levels of government.

In its report *A Common Vision for Undergraduate Mathematical Sciences Programs in 2025* (Saxe & Braddy, 2015), the MAA asserts:

Courses in the mathematical sciences have been taught as part of a classical education for thousands of years and continue to gain new meaning and relevance. There are now, perhaps more than ever, amazing career opportunities for people with training in mathematically-intensive fields. Rapid advances in technology and in connections between mathematics and other fields present tremendous opportunities, and the mathematical sciences community is at a pivotal point. Politicians across the country and mathematical scientists, not just mathematics educators, are more keenly focused on undergraduate mathematics and statistics education issues than in the past. (p. 5)

Mathematics provides both tangible and intangible benefits to society as a whole. The ideas, techniques, and methodologies of the field are essential to many other disciplines and a broad range of enterprises. Continued advancements in areas such as telecommunications, finance, medicine, basic science, economics, and political science require a solid foundation in mathematics acquired via courses taught at colleges and universities. Examples include the application of topology to neural codes (American Mathematical Society, 2016), the mathematical underpinnings of Google’s search engine (Wills, 2006), and the use of abstract algebra to construct UPC codes (Gallian, 2016). In addition, the intangible skills associated with problem solving, critical thinking, and abstraction are crucial to the development of versatile citizens prepared for rapid changes occurring in society. Students of mathematics learn how to weave together ideas from a variety of disciplines and are not intimidated by the diverse scope of data and information they encounter.

A well-designed mathematics program provides students with core knowledge in the mathematical sciences that is in high demand in the job market. Graduates are able to use calculus, statistics, linear algebra, data analytics, and programming tools to solve problems and are able to apply these tools in multiple settings. They have the ability to apply a rigorous standard of proof when constructing or critiquing others’ arguments. They have developed both verbal and written communication skills to clearly and effectively collaborate with coworkers. They have learned to move from the specific to the general by identifying underlying assumptions and focusing on the key issues. (MAA, 2015)

Strong undergraduate programs provide multiple pathways into and through mathematical sciences majors with early exposure to statistics, modeling, and computation (Saxe & Braddy, 2015). They also include experiential learning opportunities and capstone experiences that enable students to identify workplace applications of their academic experiences. A curriculum that is sufficiently robust, so that ubiquitous concepts can be understood in their universality and not as standalone items, highlights the versatility of mathematics and provides the maximum value to students of mathematics. A high level of mathematical expertise is required for maintaining a relevant curriculum and consequently must remain the purview of faculty in the mathematical sciences.

The study of mathematics also provides great value to students who pursue majors other than mathematics. Relatively few entry-level, post-baccalaureate jobs specifically require a mathematics degree. Rather, many positions require analytical, data management, problem solving, and technical communication skills, along with the ability to both generalize and integrate ideas. Such skills are naturally embedded in undergraduate mathematics courses and programs which prepare graduates for a rapidly changing, technology-focused, data-driven workplace. In fact, Valparaiso University marketed its mathematics major using the slogan “Mathematics + Anything = Everything” to highlight this versatility.

Focusing on science, technology, engineering, and mathematics (STEM) fields, the Georgetown Center on Education and the Workforce reported that job opportunities in STEM “pay more than most jobs at each level of education, and at the graduate level (are) exceeded only by a small slice of managerial and healthcare occupations” (Carnevale, Smith, and Melton, 2011, p. 7). In fact, 47% of bachelor’s degree recipients in STEM fields earn more money than Ph.D. recipients in non-STEM fields (Carnevale, Smith, and Melton, 2011). In 2014, the United States Bureau of Labor Statistics predicted that “the STEM group that is projected to grow fastest from 2014 to 2024 is the mathematical science occupations group at 28.2 percent, compared with the average projected growth for all occupations of 6.5 percent” (Fayer, Lacey, and Watson, 2017, p. 10).

Regarding workforce preparation, Saxe and Braddy (2015) note, “The mathematical sciences are in the national spotlight in part because mathematical competencies can lead to higher paying jobs, and thus can play a profound role in students’ economic mobility.” Mathematics majors consistently appear in “Top 10” lists for starting salaries, with recent graduates earning an average of about $69,000. (Somers, 2017)

Higher salaries are in part the result of an insufficient number of STEM-trained employees in the workforce, as the demand for workers in STEM occupations is increasing at every level of education. Much of this demand is interdisciplinary, with mathematical skills an increasing necessity in fields such as healthcare, manufacturing, architecture, and computing. Consequently, “the dispersion of cognitive competencies outside of STEM has resulted in an artificial shortage - not of workers, but of workers with STEM competencies” (Carnevale, Smith, and Melton, 2011, p. 8). There is a wealth of occupational opportunities for students who pursue degrees in mathematics.

The National Science Board (2014) reported that in 2012, only 20% of bachelors, 18% of masters, and 8% of doctoral degrees in mathematics were awarded to Black, Latinx, Native American, Native Alaskan, and Hawaiian students combined, despite the fact that these racial groups compose approximately 30% of the U.S. population. To support the success of underrepresented students, mathematical sciences departments “must utilize effective methods for supporting students … as [they] work to change departmental and institutional processes, policies, and cultures that act as barriers to student success” (MAA, 2018, p. 161). Departments are the key to ensuring “all students have the opportunity to experience the rigor, practicality, elegance, and beauty of mathematics” and ensuring all students benefit from the economic and societal benefits this knowledge provides (MAA, 2018, p. 161).

Meeting society’s need for a quantitatively literate citizenry and meeting workforce demands for mathematically prepared professionals require highly skilled mathematics teachers at both the K-12 and post-secondary levels (Conference Board of the Mathematical Sciences, 2012). Thames and Ball (2010, as cited in Saxe and Braddy, 2015, p. 26) argued that attending to the preparation of K-12 teachers is critical to the future of our profession, and mathematical sciences departments should work with schools of education to ensure pre-service teachers are well-prepared for the classroom. Colleges and universities must attend to the preparation of teachers, a task that falls naturally to mathematical sciences departments for both content and pedagogy since “(t)he specialized knowledge required for teaching mathematics is distinct from the mathematical knowledge needed for other mathematically-intensive occupations and professions” (Saxe & Braddy, 2015, p. 26, referencing Thames & Ball, 2010).

While it is absolutely critical to provide future K-12 teachers with a broad mathematical perspective and deep content knowledge, it is also critical to provide the same to graduate students who will eventually serve as faculty instructing these K-12 teachers. Mathematicians are the only faculty equipped to instill the value of this perspective in students in both STEM and non-STEM disciplines.

Colleges and universities must support their mathematical sciences departments in providing comprehensive preparation for K-12 mathematics teachers. Learning mathematics from a mathematician provides understanding from a mathematical perspective on the world rather than from an engineering perspective or a humanities perspective. Specifically, key goals of mathematics are to unify ideas, to generalize concepts (e.g., business calculus, engineering calculus, and calculus for biology are fundamentally the same), and to provide sound arguments for theory. It is imperative that mathematics instruction be provided by those who are knowledgeable about the deeper meaning of mathematical principles. This includes a mathematical approach to understanding that emphasizes precision of language, persistence, addressing problems with multiple approaches, “checking one’s work” (Korchinski, 2018), and even key historical context.

The size and constitution of the faculty in a mathematical sciences department can vary greatly with the size and mission of the institution. The foremost consideration is the presence of sufficient permanent (i.e., tenure-track or long-term contract) full-time faculty to enable the development, implementation, assessment, and ongoing modernization of a curriculum in alignment with the educational needs of a diverse student body in both STEM and non-STEM disciplines within the context of the institution’s mission. Thus, an ideal department contains researchers, mathematics educators, and faculty with ties to other disciplines. Contingent (e.g., short-term full-time or part-time) faculty should be used judiciously to expand the reach of a department, fill temporary instructional gaps, or provide specialized knowledge and expertise. In all cases, contingent faculty should be integrated into the life of the department as much as possible. (MAA, 2017)

Mathematical sciences departments are essential for serving the educational needs of other disciplines as well. “The partner disciplines need students who can apply mathematics to questions in their fields, reformulate such questions using the appropriate mathematical tools, and use appropriate technology to carry out actual computations. Students can perform these tasks accurately and confidently only if they understand the related mathematical structure” (Ganter & Barker, 2004, p. 34) Collaboration with partner disciplines is particularly important for instruction in the first two years (Ganter & Barker, 2004) and requires mathematics faculty to take the lead in curriculum planning from an interdisciplinary perspective, acknowledging the needs and interests of other disciplines while contributing a uniquely mathematical perspective. Ultimately, “a central task for mathematics faculty at institutions of higher education, and more broadly, the mathematical sciences community as a whole, is to create a coherent, intriguing introduction to collegiate mathematics for **all** students.” (Saxe & Braddy, 2015, p.2)

It is incumbent upon faculty in mathematical sciences departments to maintain strong engagement with students, other faculty, the institution, and the community, and to initiate conversations about curriculum, shared resources, employment prospects, and economic development. There are many ways for faculty in mathematical sciences departments to ensure these conversations occur. Faculty can offer mathematics majors an orientation to careers in mathematics (Zorn et al, 2014), initiate discussions of curricula with faculty in partner departments, ensure mathematics is represented at highly-visible campus events such as student scholarship days, and be present at or create new alumni events and outreach programs. Mathematical science departments can track the job placement of graduates, follow the stories of alumni, and understand the role of mathematics in both STEM and non-STEM disciplines. Sharing this information with the public, with college or university administrators, with faculty in partner disciplines, and with prospective majors helps demonstrate the value and versatility of mathematics.

By engaging productively with students, partner disciplines, administrators, and the public at large, mathematical sciences departments can clarify and heighten their perceived value. Departments must actively communicate their activities and successes to constituents through both formal and informal and formal channels to help ensure institutions and society as a whole continue to value the critical work of faculty in mathematical sciences departments.

#### References

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American Mathematical Society. (2016). *Current Events Bulletin.* Retrieved from https://www.ams.org/meetings/currentevents2016final.pdf

Carnevale, A. P., Smith, N., & Melton, M. (2011). *STEM: Science, Technology, Engineering, Mathematics.* Washington, DC: Georgetown University Center on Education and the Workforce.

Conference Board of the Mathematical Sciences (2012). *The Mathematical Education of Teachers II. *Providence, RI and Washington, DC: American Mathematical Society and Mathematical Association of America

Fayer, S., Lacey, A., and Watson, A. (2017, January).* STEM Occupations: Past, Present, And Future. *Retrieved October 1, 2018 from https://www.bls.gov/spotlight/2017/science-technology-engineering-and-mathematics-stem-occupations-past-present-and-future/pdf/science-technology-engineering-and-mathematics-stem-occupations-past-present-and-future.pdf

Gallian, J. A. (2016). *Contemporary abstract algebra* (9th ed.). Belmont, CA: Brooks/Cole, Cengage Learning.

Ganter, S. & Barker, W. (Eds, 2004). *The Curriculum Foundations Project: Voices of the Partner Disciplines.* Washington, DC: Mathematical Association of America.

Korchinski, A. (2018, March 14). *Lessons from My Math Degree That Have Nothing to Do with Math. *Retrieved from https://medium.com/s/story/6-life-lessons-from-my-math-degree-that-have-nothing-to-do-with-math-d38aba90edfe

Mathematical Association of America. (2018). *MAA Instructional Practices Guide. *Retrieved from https://www.dropbox.com/s/42oiptp46i0g2w2/MAA_IP_Guide_V1-2.pdf?dl=0

Mathematical Association of America. (2017). *Best Practices in Recruitment, Retention, Development, and Evaluation of Faculty in College and University Mathematical Sciences Departments.* Retrieved from https://www.maa.org/programs-and-communities/professional-development/committee-on-faculty-and-departments/guideline-statement-1

Mathematical Association of America. (2015). *2015 CUPM Guide to Majors in the Mathematical Sciences. *Washington, DC: Mathematical Association of America.

National Science Board. (2014). *Science and Engineering Indicators 2014. *Arlington, VA: National Science Foundation.

Saxe, K. and Braddy, L. (2015).* A Common Vision for Undergraduate Mathematical Sciences Programs in 2025. *Washington, DC: Mathematical Association of America.

Somers, D. (2017, September 25). *10 College Majors With the Best Starting Salaries. *Retrieved from https://www.usnews.com/education/best-colleges/slideshows/10-college-majors-with-the-highest-starting-salaries?slide=8

Thames, M. H. & Ball, D. L. (2010). What mathematical knowledge does teaching require? Knowing mathematics in and for teaching. *Teaching Children Mathematics*, 17(4), 220–225.

Wills, R.S. (2006, May 1).* Google’s PageRank: The Math Behind the Search Engine. *Retrieved from https://pdfs.semanticscholar.org/3356/6b740d3cd0c0dde57e13b5da148bef37376f.pdf

Zorn, P., Bailer, J., Braddy, L., Carpenter, J., Jaco, W., & Turner, P. (2014).* The INGenIOuS Project: Mathematics, Statistics, and Preparing the 21st Century Workforce. *Washington, DC: Mathematical Association of America.

#### Task Force Members

Ed Aboufadel

Linda Braddy

Jenna Carpenter

Lloyd Douglas

Rick Gillman

Document received with gratitude by the MAA Board of Directors, October 2018