A Common Vision for the Undergraduate Mathematics Program in 2025
In the 2012 report Engage to Excel: Producing One-Million Additional College Graduates with Degrees in Science, Technology, Engineering, and Mathematics, the Presidentﾒs Council of Advisors of Science and Technology (PCAST) acknowledged that fewer than 40% of students who enter college intending to major in a STEM field actually go on to complete such a degree (Presidentﾒs Council of Advisors on Science and Technology, 2012). The Council concluded that retaining more STEM majors is the best option for addressing the inadequate supply of STEM professionals in the U.S. workforce. An additional perplexing aspect of the retention challenge is retaining underrepresented groups (minorities and women) in mathematical sciences degree programs at all levels, undergraduate through doctoral.
Curricula and training programs require updates if they are to maintain relevance to current job opportunities for professional mathematicians as well as those for graduates with strong STEM competencies. The Mathematical Sciences in 2025 report (National Research Council, 2013) calls for mathematics departments to rethink the types of students they are attracting and wish to attract at all levels and to identify the top priorities for educating these students. The expansion of research opportunities in the mathematical sciences provides additional impetus to rethink the way students are prepared and how to attract more students into the discipline. Recent calls for reform (National Academy of Sciences, 2012; Presidentﾒs Council of Advisors on Science and Technology, 2012) have highlighted the need for us to ﾓengage with STEM discussions going on outside (our) own community and not be marginalized in efforts to improve STEM education... Change is unquestionably coming to lower-division undergraduate mathematics, and it is incumbent on the mathematical sciences community to ensure it is at the center of these changes and not at the peripheryﾔ (National Research Council, 2013).
At the graduate level, many students will not end up with traditional academic jobs but instead with jobs in which they are expected to deal with problems much less well formulated than those in the academic setting. This fact alone suggests that graduate education in the mathematical sciences needs to be reconsidered in light of the changing landscape, and consequently, undergraduate programs must be reconsidered as well. It is no longer enough to rearrange existing courses to create alternative curricula; rather, a redesigned offering of courses is needed. PCAST proposed specific mechanisms for improving programs, including the need to draw on empirical evidence of effectiveness. The Council highlighted the growing body of evidence for the effectiveness of class time spent actively engaging students in thinking about the concepts they are learning, and for the effectiveness and power of student research programs to attract and motivate students toward STEM careers.
A report on the evaluation of the NSFﾒs Vertical Integration of Research and Education in the Mathematical Sciences (VIGRE) program was released in 2009. The evaluation committee reported ﾓimpressive examplesﾔ (detailed in Cozzens, 2008) indicating the VIGRE program had indeed had a ﾓmeaningful impact on the educational programs of departments leading to the kind of systemic change called for when the program was conceivedﾔ (National Academy of Sciences, 2009). While it is impossible in a study such as this to establish a causal relationship between the VIGRE program and increases in numbers of mathematics and statistics majors and degrees conferred at participating institutions, the committee contended that the VIGRE program did produce notable qualitative changes (e.g., cultural) in these institutions. Several factors were identified as critical to the success of the VIGRE projects, factors that remain relevant today, as indicated in other recent reports addressing workforce development challenges (National Academy of Sciences, 2009; National Research Council, 2013; Presidentﾒs Council of Advisors on Science and Technology, 2012). The factors identified include: mentoring, transition experiences, dynamic curricula that include early research experiences, and internships, all of which can and should be incorporated into undergraduate mathematics programs across the country.
More broadly, there are many in the STEM community working to promote evidence-based approaches to teaching and learning within STEM disciplines, but they conduct much of their work within discipline-specific silos. Although sometimes appropriate, too much of the work is developed in isolation without adequate awareness of what is happening in other disciplines. As pointed out by Fairweather in his synthesis for the National Research Council (2008), ﾓThe pedagogical strategies most effective in enhancing student learning outcomes are not discipline dependentﾔ [his emphasis]. A large and growing body of evidence indicates that, across all STEM disciplines, active learning strategies that focus on engaging students in the learning process produce substantial gains in student learning (for reviews, see NRC, 2012; Springer, Stanne & Donovan, 1999; Ruiz-Primo et al., 2011). This is especially true of students who are often underserved by traditional, lecture-based methods, including women, students from minorities that are under-represented in the STEM disciplines, and other economically or educationally disadvantaged students (Fullilove & Treisman, 1990; Springer, Stanne & Donovan, 1999; Beichner et al., 2007; Gafney & Varma-Nelson, 2008; Preszler, 2009; Laursen et al. 2011; Haak et al., 2011). Overall, relatively few college students experience these so-called ﾓhigh-impactﾔ educational practices nationwide (Kuh, 2008). Engaging professionals from the broader STEM community in the collective action proposed in this project will provide us with valuable input from client disciplines and at the same time, provide us with the opportunity to leverage the knowledge and resources that exist in the STEM community at large to improve programs in the mathematical sciences.
There is a great deal of follow-up work to be done investigating the efficacy of previous recommendations related to undergraduate mathematics curricula and instructional methodologies. For example, which, if any, recommendations have been instituted and which, if any, have resulted in improved student outcomes? This project will build on past and current work in an effort to avoid repeated mistakes, misdirection, and re-inventing successful initiatives. It will contribute in a significant way to the goal of modernizing programs in the mathematical sciences and creating a vibrant, sustainable pipeline of graduates with strong mathematical competencies for the U.S. workforce. It will strategically examine past work to identify promising practices in curriculum revision and will work toward catalyzing widespread implementation of modernized undergraduate mathematics courses by making exemplary curricular and pedagogical initiatives visible to the broader mathematical sciences community. It can also guide funding agencies regarding best bets for targeted federal investments likely to have catalytic impact within the community.
This project will bring together bring together stakeholders in the mathematics education enterprise to reconsider long-standing traditions, both curricular and pedagogical. The primary goal of this initiative is to develop a shared vision in the mathematical sciences community of the need to modernize the undergraduate mathematics program, especially the first two years. This vision is one that a core group of professional societies can endorse and promulgate, and about which the societies have some degree of confidence a broad cross-section of the community will embrace. It is critical to the success of this project that we have participation from a broad range of professional societies; as such, project leaders have been drawn from the leadership of the MAA and also from the American Mathematical Association of Two-Year Colleges (AMATYC), the American Mathematical Society (AMS), the American Statistical Association (ASA), and the Society of Industrial and Applied Mathematics (SIAM).
Research on ﾓcollective impactﾔ (Kania & Kramer, 2011) suggests that, in achieving significant and lasting change in any area, a coordinated effort supported by major players from all existing sectors is more effective than an array of new initiatives and organizations. A key strategy is to invest in developing common agendas and language, work toward agreed upon metrics of success, facilitate communication, and support evidence-based modifications of existing efforts. Such collective action, characterized by coordinated efforts of disparate entities within a community in order to achieve desired outcomes, is more powerful in affecting change than the sum of the individual efforts made by those same entities working in isolation. Such collective action is not about getting everyone to do the same single thing, but to get the existing and future efforts coordinated in such a way that everyone is pulling in the same general direction to leverage the collective power of the whole. This project proposes such action to highlight existing efforts and draw on the collective wisdom of a diverse group of stakeholders to articulate a shared vision for modernizing the undergraduate mathematics program.
Mathematics courses in the first two years of college function as pathways to many different majors and also as a key component in the preparation of mathematically literate citizens. Four societies (MAA, ASA, AMS, and SIAM) recently released a report on the INGenIOuS Project (Zorn et al., 2014) calling for the mathematical sciences community to focus on strategies for increasing the flow of students with strong science, technology, engineering, and mathematics (STEM) competencies into the workforce pipeline to meet the rising demand for mathematically and scientifically proficient employees. The MAA now proposes partnering again with these and other societies to consider how we might modernize our programs (i.e., our curricula and instructional strategies) to better prepare students for the demands of the 21st century workplace. While we acknowledge there is no ﾓone-size-fits-allﾔ solution, we aim to catalyze widespread adoption of curricula and pedagogies that are (1) geared toward developing a broad base of intellectual skills and competencies to better prepare students for the workforce and (2) simultaneously endorsed by a broad cross-section of the mathematical sciences community. This will require curricula centered on compelling content communicated in ways that fully engage students and encourage them to be agents of their own learning. Good curricula alone will not necessarily lead to increased student success in coursework, degree completion, and job placement, however; instructional approaches and methods of delivery also play a key role in student learning and cannot be dismissed as trivial factors. Thus, this proposed project encompasses the parallel emphases of the need to revise the mathematical content taught in undergraduate programs coupled with effective implementation of evidence-based instructional strategies.
Courses taught at colleges and universities during the first two years range from remedial courses to advanced calculus and differential equations, and we aim to include any mathematics course a student at a higher education institution might take in their first two years of college in the primary focus of this project. We will examine the undergraduate program using a wide-angle lens, inclusive of modeling, statistics and computation along with applications in the broader mathematically-based sciences. We will include actuarial studies and operations research, engineering and the physical sciences, the life and social sciences, and quantitative business topics like accounting. The mathematical sciences community must begin to think in terms of a broader range of entry courses and pathways through our curriculum for all students, including mathematics and STEM majors as well as non-STEM majors. For example, according to Beyond Crossroads (AMATYC, 2006), approximately 56% of students at two-year colleges and 15% of those at four-year colleges and universities take at least one remedial mathematics course. A major objective of the proposed project is to highlight alternative pathways through the general education mathematics requirement, including alternatives to traditional remedial mathematics courses, for entering students not adequately prepared for college mathematics that more effectively prepare them for their future careers.
We envision this project as Phase I of a two-part initiative. Phase I will focus on introspection: we will seek internal coherence within the mathematical sciences community. Phase II of the project will be an outward looking period focused on wide-spread dissemination and full-scale implementation of modernized curricula and delivery methods. Phase I will begin with a focus on the first two years of post-secondary education, and Phase II will expand to a focus on the entire undergraduate mathematics program. An important objective of this initiative is ensuring smooth entry and exit experiences for students in the first two years of college mathematics. This will necessitate:
ﾕ Identifying curricular pathways through mathematics that are appropriate and beneficial for all students pursuing post-secondary education, whether in STEM or non-STEM fields.
ﾕ Collaborating with K-12 educators to better prepare students for these pathways and to identify ways to help students avoid remediation after high school.
ﾕ Building on recent collaborations of the MAA with other STEM professional societies to leverage existing knowledge across the disciplines and to garner input from client disciplines on issues related to undergraduate mathematics courses.
A number of challenges exist that warrant particular attention.
1. The issue of scale. Scaling up successful initiatives is difficult because most initiatives are not designed with scale in mind. Rather, they are designed as small-scale pilots, many of which stall at the limited scope, limited impact ﾓboutique programsﾔ scale.
2. Disparate views of the undergraduate program. There is a broad range of views within the mathematics community about what the curriculum in the first two years of college should comprise, who it should serve, whether or not it should be explicitly connected to other disciplines, and whether or not it should include an introduction to data science and computational science.
3. Ongoing professional development for contingent faculty and graduate teaching assistants. These instructors are more likely to be assigned to introductory courses, and in fact, carry the majority of the national teaching load for mathematics courses in the first two years. They are also more likely to lack the resources and opportunities for extended professional development activities.
4. Rapidly increasing connections between the mathematical sciences and other fields (both STEM and non-STEM). We are challenged to provide alternative pathways into and through the mathematics curriculum for students with varied career interests, pathways that increase student engagement in learning.
5. New and emerging technologies. Modern technologies are literally changing the face of education, but there is a broad range of views within the mathematics community about the benefits vs. disadvantages of using instructional methods that employ electronic options currently available. Current technologies affect how we interact with our students, how they interact with peers, and how content is developed and delivered.
The project will involve a two-and-a-half-day, face-to-face, by-invitation workshop held the spring of 2015 at the headquarters of the ASA in the Washington, D.C. area. Total attendance at the workshop will be approximately 50 people, including the leadership team and Thought Leaders Council. Following the workshop, the leadership team will draft a written report on the workshop outcomes. Three potentially transformative aspects of this project are:
1. Employing the collective impact principle to assemble the joint statement and articulate the shared vision for the undergraduate mathematics program.
2. Using a different approach from the traditional workshop/conference model to produce a survey of the current landscape of undergraduate mathematics curriculum and instructional strategies from the perspective of evidence of effectiveness in increasing student success in mathematics courses, particularly in the first two years.
3. Leveraging expertise outside the mathematical sciences within the broader STEM community by engaging interdisciplinary perspectives to increase the impact of the vision.
? Conference calls with leadership team
? Project planning
? Create document of executive summaries from existing curriculum guidelines and recommendations from professional societies; ask leadership team to read prior to face-to- face meeting Denver (see next bullet).
? IBL conference (Denver, Jun 18-19)
? First face-to-face meeting of leadership team
? Generate list of at least 70 potential invitees to May workshop; set workshop dates
? Draft and hone curriculum guidelines and recommendations summary document
? Panel to create project awareness in broader community
Summer 2014 ? Write a journal article about the Denver meeting, disseminate as widely as possible (e.g., via the news magazines of each of the five professional societies involved, the Chronicle of Higher Education)
? Finalize list of invitees to May workshop (50 total)
? MathFest (Portland, Aug 6-9)
? Meeting of leadership team
? Focus groups from to solicit input from broader community
? Curriculum guides summary document finished by early October
Fall 2014 ? Conference calls with leadership team
? Solicit draft statements from professional societies embracing common themes and goals for undergraduate mathematics education
? Create project webpage (at www.maa.org)
? Face to face meeting at MAA headquarters with leadership group and advisory board
? Leadership team presents workshop plans, advisory board provides input
? Conclude workshop planning
? Focus groups at AMATYC annual meeting in November
JMM 2015 ? Meeting of leadership team
? Panels and workshops to increase project awareness in and solicit input from broader community (e.g., existing projects people know about, data on effectiveness)
Spring 2015 ? Conference calls with leadership team to organize information on existing projects and data, finish prep for May workshop
May 2015 ? Workshop at ASA headquarters with 50 attendees, including leadership team, Though Leaders Council, and other key stakeholders
Summer 2015 ? Write and publish workshop report to summarize what occurred at the workshop and provide a roadmap for ongoing work.
A four-member leadership team will work with the PI and co-PI on all aspects of this project. A larger ﾓThought Leader Councilﾔ will play a key role in the project as well. The larger group will include both mathematics and mathematics education researchers; academic administrators; professional society education officers; representatives from the entire spectrum of higher education institutions, including community colleges as well as comprehensive, private, minority-serving, research, and land-grant institutions. The members of this council will also represent diverse geographic regions of the country.
1. Karen Saxe (PI; MAA, Macalester College)
2. Linda Braddy (co-PI; MAA)
3. Rob Faranelli (AMATYC)
4. Vilma Mesa (MAA, University of Michigan)
5. Uri Treisman (AMS, Charles A. Dana Center at the University of Texas)
6. Peter Turner (SIAM, Clarkson University)
ﾕ Summary of existing curriculum and instruction guidelines and recommendations from professional mathematics and statistics societies, including:
o MAAﾒs CUPM (https://www.maa.org/programs/faculty-and-departments/curriculum-department-guidelines-recommendations/cupm/cupm-guide-2004)and CRAFTY (https://www.maa.org/programs/faculty-and-departments/curriculum-department-guidelines-recommendations/crafty) recommendations.
o AMATYCﾒs Crossroads (https://www.amatyc.org/?page=GuidelineCrossroads) and Beyond Crossroads (https://beyondcrossroads.matyc.org/doc/PDFs/BCAll.pdf) documents
o ASAﾒs GAISE reports (https://www.amstat.org/education/gaise/).
o SIAMﾒs Modeling Across the Curriculum projects (https://www.siam.org/reports/modeling_12.pdf).
o NRCﾒs Mathematical Sciences in 2025 report (https://www.nap.edu/openbook.php?record_id=15269).
ﾕ Written report on the spring 2015 workshop that includes:
o A summary of the workshop activities.
o An annotated bibliography listing initiatives with existing evidence supporting their effectiveness in improving student learning outcomes.
o A list of potential initiatives and further directions to explore in Phase II.
o A proposal for sustainability of this initiative into Phase II.
ﾕ A joint statement comprising a collection of statements from the professional societies embracing common themes and goals, encouraging broad community engagement and effort, building on existing successful or promising efforts, and avoiding reinvention and acting without adequate understanding of prior work across the community.
ﾕ An article in each societyﾒs news magazine and on each website putting the joint statements in context of that specific society.
The mathematical sciences community recognizes that there are significant leaks in the pipeline of graduates with adequate mathematical competencies entering the U.S. workforce. The recent report The Mathematical Sciences in 2025 (National Research Council, 2013) suggests that we reassess the training of future generations of mathematical scientists in light of the increasingly cross-disciplinary nature of the mathematical sciences. Substantial efforts have been undertaken to help us understand the challenges; indeed, promising curricular updates and pedagogical practices have been recommended. However, many such practices arenﾒt being implemented at a scale necessary to make a significant impact on the number of mathematics graduates entering the workforce, the number of students pursuing a degree in mathematics, and the number of graduates in all fields who have adequate mathematics skills and competences to meet current workforce demands. Plugging the leaks in the pipeline requires the well-coordinated effort, or collective action, of multiple stakeholders, including funding agencies, professional societies, employers, higher education administrators, and faculty. By bringing together thought leaders from these various sectors, this project will ultimately serve to catalyze widespread adoption of modernized curricula and pedagogies that are (1) geared toward developing a broad base of intellectual skills and competencies to better prepare students for the workforce and (2) simultaneously endorsed by a broad cross-section of the mathematical sciences community.
The MAA has, for more than half a century, provided leadership in the mathematical sciences related to the undergraduate mathematics program. Leading this proposed initiative uniquely positions the organization to leverage existing connections with key stakeholders in the mathematics education enterprise. MAA's robust history of providing curricular guidelines and resources designed to support effective, innovative instructional strategies adds to the strength of this proposal. A primary focus of the MAA continues to be supporting mathematics faculty and providing them with tools to facilitate preparation of students for current demands of the workplace.
The MAA actively focuses on supporting underrepresented groups in the mathematical sciences via programs such as the National Research Experiences for Undergraduates Program (NREUP), the Strengthening Underrepresented Minority Mathematics Achievement (SUMMA) program, and the Tensor Women and Mathematics Grants program (see www.maa.org for details). The MAA supports other initiatives to enhance opportunities for women and underrepresented minorities in the mathematical sciences as well. Three national MAA committees are charged with increasing the involvement of these groups in the affairs of the MAA and to develop MAA activities to encourage women and minorities in careers in the mathematical sciences. The committees suggest panels and speakers for national conferences and prepare materials to inform all members of the MAA about critical issues related to the participation of underrepresented groups in the MAA and the mathematical sciences in general.