A Common Vision

Five major mathematical societies—AMATYC, AMS, ASA, MAA, and SIAM—have just released a joint report, A Common Vision for Undergraduate Mathematical Sciences Programs in 2025, authored by Karen Saxe and Linda Braddy and distributed by the MAA. This is a coordinated call for “modernizing undergraduate programs in the mathematical sciences.” For many years, all five of the societies have been proclaiming the need to improve the teaching and learning of undergraduate mathematics and statistics. For the first time, they have come together to identify their common concerns and to support shared recommendations. What follows is my own précis of the contents of this report. I strongly encourage you to read it for yourself. A full reference, with the address of the PDF file of the report, is at the end of this column.

The central message, repeated throughout this document, is that “The status quo is unacceptable.” Specifically, A Common Vision issues a joint appeal to

1. Update curricula, 
2. Articulate curricula across the critical divide between high school and college mathematics,
3. Scale-up the use of evidence-based pedagogical methods, 
4. Remove barriers at critical transition points, and 
5. Establish stronger connections to other disciplines.

These are accompanied by a call to support those faculty engaged in these efforts. After explaining the need for these changes and summarizing the reports that have been issued by the five societies, A Common Vision describes in further detail the common themes that have emerged:

Curricula. The greatest concentration of themes reported in A Common Vision circles around curricular issues. These include calls for presenting key ideas from a variety of perspectives and motivating them through the use of applications to contemporary topics. The cited reports recognize the importance of providing multiple pathways into and through undergraduate mathematics, with particular concern that departments attend to the barriers that students often confront. Solutions should include entry points that emphasize modeling, statistics, and applications as well as programs that focus on the development of computational and statistical skills.

There is a recognized need for more statistics, computation, and modeling for all students within the first two years of undergraduate mathematics. And there is recognition of the need for closer cooperation with and awareness of the needs of other disciplines. The report includes a call for more attention to the development of the skills needed for effective mathematical communication, both orally and in writing. And, finally, this report highlights the common awareness among the five societies of the need to address issues of transition: from high school to college, in transfer between institutions, in issues of placement, and at critical juncture points such as the start of proof-based courses.

Course Structure. There is a consensus among all of the societies that instruction needs to move beyond simple lecture and embrace a variety of active learning approaches that engage students in grappling with the difficulties of mathematics. These include providing opportunities for collaboration and communication. In addition, all five societies advocate the use of technology in those situations where it can enhance student learning.

Workforce Preparation. Mathematics departments need to work with those in client departments within their own institutions as well as with the consumers of our graduates in business, industry, and government to understand the workforce skills that graduates will need. This must be done not as narrow technical training but in the recognition that our task is to equip students with a broad base of skills that will serve them in our rapidly evolving economy.

Faculty Development and Support. All of the five societies recognize the need to provide training opportunities for faculty to broaden their expertise in areas of the mathematical sciences where great needs have not been met. These include data analytics and computational science. We also must foster an institutional culture that encourages and values work on the issues raised in these reports.

Other Issues. In addition, other issues have arisen in one or more of the society reports. These include the need

1. To attend to issues of student diversity, particularly the retention of students in at- risk groups,  
2. To ease difficulties as students move between institutions, 
3. To recognize the special needs of contingent faculty, 
4. To devote energy toward the preparation of K-12 teachers, 
5. To properly prepare graduate students for their contributions to the teaching mission of the department, 
6. To recognize and address the issues that lead to high failure rates, 
7. To look for ways of improving courses in developmental mathematics so that they retain and adequately prepare students, 
8. To shape calculus instruction so that it responds to the reality that most students studying calculus in college have already experienced it in high school,  
9. To be aware of technology-enabled models of delivery of course content and to critically consider when and where they might be beneficial, 
10. To gather and use empirical data to refine programs and improve student learning, 
11. To scale successful efforts by involving more faculty within each department, by increasing communication about these efforts within the mathematical sciences community, and by understanding the obstacles to effective transfer of successful programs.

This report, which is only intended to be a summary of the common themes of these five societies, is nevertheless an important first step in recognizing the commonalities in the messages they are all sending and in working toward coordinated efforts to improve undergraduate education in the mathematical sciences.

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Karen Saxe & Linda Braddy. 2016. A Common Vision for Mathematical Sciences Programs in 2025. Forward by William “Brit” Kirwan. Washington, DC: Mathematical Association of America. www.maa.org/sites/default/files/pdf/CommonVisionFinal.pdf