By Benjamin Braun, Editor-in-Chief, University of Kentucky
While one important component of successful teaching and learning is what happens inside the classroom, an equally important component involves decisions made at the administrative level that impact our classroom environments. A challenge that mathematics departments face is to make successful arguments for resources that support high-quality programs and courses for our students. Such arguments are often bolstered when the activities of a department are placed within the context of recommendations from professional societies.
In this article we survey a selection of recent reports and recommendations related to courses in the first two years of college study, with the goal of providing an overview of these reports for faculty and department leaders. It is worth noting that most of these were created with grant support from the National Science Foundation (NSF). There are at least seventeen professional societies involved in mathematics education efforts, of which six are represented in these reports: American Mathematical Society (AMS), Mathematical Association of America (MAA), American Statistical Association (ASA), Society for Industrial and Applied Mathematics (SIAM), American Mathematical Association of Two-Year Colleges (AMATYC), and National Council of Teachers of Mathematics (NCTM).
A Common Vision for Undergraduate Mathematical Science Programs in 2025 (AMS, MAA, ASA, SIAM, AMATYC)
The MAA Common Vision project brought together leaders from the AMS, MAA, ASA, SIAM, and AMATYC to collectively reconsider undergraduate curricula and ways to improve education in the mathematical sciences. This was the first time that these five professional societies had engaged in a joint project regarding postsecondary mathematics education, reflecting the current emphasis in the mathematical community on developing coherent responses to the challenges we face across all types of institutions. Project participants represented not only these mathematical sciences associations, but also partner STEM disciplines, higher education advocacy organizations, and industry. The resulting report includes an in-depth examination of seven curricular guides published by these five associations, with the primary goal of identifying common themes in the guides. The report reflects a synthesis of these themes with other research and input from project participants and other thought leaders in the mathematical sciences community.
Some of the prominent common themes from these seven curricular guides identified by the report are:
- the role of careful curricular development, including both content issues and consideration of pathways into and through coursework needed for majors in STEM fields and other partner disciplines;
- the crucial role played by modeling and computation in mathematics education;
- the need for students to develop communication skills in mathematical contexts;
- the need to diversify pedagogical methods in mathematics courses, e.g. incorporating a blend of traditional lecture and active learning techniques;
- using technology appropriately to enhance the student learning experience;
- developing meaningful partnerships with faculty in other disciplines; and
- the strong institutional support for resources and faculty development necessary to establish and maintain these qualities of effective mathematics education.
From two-year colleges to research-focused universities, from the context of teaching STEM-focused students to engaging students struggling with basic quantitative literacy, it is important to have in mind the common challenges of teaching and learning mathematics. While there are certainly unique challenges for different teaching environments and student populations, the Common Vision report helps identify the ways in which we can provide a coherent response to all these challenges, given a solid level of support and adequate resources. The full 2015 Common Vision report is available at http://www.maa.org/programs/faculty-and-departments/common-vision.
Partner Discipline Recommendations for Introductory College Mathematics and the Implications for College Algebra (MAA)
College Algebra is one of the courses that plays a role across the mathematical sciences. Between 1999 and 2011, the MAA Committee for the Undergraduate Program in Mathematics conducted a series of NSF-funded activities as part of their CRAFTY project, i.e., Curriculum Renewal across the First Two Years. In the first phase of this project, a series of workshops involving mathematicians and faculty from partner disciplines were organized to identify desirable student learning outcomes for mathematics courses. In the second phase of this project, the focus narrowed to developing guidelines for College Algebra based on these workshops. Of particular note is the coherence between these guidelines and the main themes from the Common Vision report, especially with regard to:
- the importance of modeling;
- the emphasis on development of student communication skills; and
- the importance of careful curricular development including both conceptual understanding and mastery of procedural algebraic techniques.
The reports from CRAFTY are of interest to faculty involved in revising their college algebra courses, as well as to faculty who are searching for a starting point for discussions with faculty in partner disciplines. Further, the CRAFTY reports contain chapters detailing the experiences of various institutions through modeling-based revisions to their college algebra courses, including successes and failures. These reports, including guidelines for College Algebra courses, can be found at the CRAFTY website.
Characteristics of Successful Programs in College Calculus (MAA) and the MAA/NCTM Joint Position Statement on Calculus
While College Algebra is important across all partner disciplines, in STEM disciplines it is Calculus courses that play a central role. Beginning in 2009, with support from the NSF, the MAA has undertaken studies regarding the state of college Calculus. The first phase of this project consisted of a national survey of Calculus students and instructors followed by site visits to programs identified as effective based on the survey results. The second phase of this project began in 2015 and will broaden its scope to include Precalculus through Calculus II. The primary result of the first phase of the Calculus study was the identification of the following seven characteristics of successful calculus programs:
- Regular use of local data to guide curricular and structural modifications;
- Attention to the effectiveness of placement procedures;
- Coordination of instruction, including the building of communities of practice;
- Construction of challenging and engaging courses;
- Use of student-centered pedagogies and active-learning strategies;
- Effective training of graduate teaching assistants; and
- Proactive student support services, including the fostering of student academic and social integration.
The motivation for an ongoing study of Calculus in the United States is that despite its centrality in the postsecondary mathematics curriculum, Calculus instruction is in a state of crisis. In 2012 the MAA and NCTM released a joint position statement on Calculus, including a background document motivating the position statement in which the authors conclude:
The United States has fallen into a seriously dysfunctional system for preparing students for careers in science and engineering, guaranteeing that all but the very best [students] rush through essential parts of the mathematics curriculum [in high school] and then are forced to sit and spin their wheels while they try to compensate for what was missed.
University Calculus courses are taught in a complicated broader context involving high school Calculus courses, the AP exam system, the rapid increase of dual and concurrent enrollment programs, and other factors, significantly complicating postsecondary Calculus instruction. For departments that are interested in rethinking their Calculus courses, these resources can help clarify our conversations and provide refined focal points for improvement.
Articles and reports from the MAA Calculus Study can be found at http://www.maa.org/programs/faculty-and-departments/curriculum-development-resources/national-studies-college-calculus. The MAA/NCTM joint position statement on Calculus, including a background document with more information, can be found at http://www.nctm.org/Standards-and-Positions/Position-Statements/Calculus/.
There are several other reports that are worthy of attention from faculty and department leadership, a few of which are briefly discussed here. The NRC Mathematical Sciences in 2025 report is a comprehensive review of the mathematical sciences, including a vision for the future over the next decade. The NRC report was completed at the request of the NSF, and includes information about a wide range of topics in the mathematical sciences, including education and diversity. The MAA CUPM Curriculum Guides from 2004 and 2015 are discussed in the Common Vision report, and together form a substantial set of recommendations for courses, departments, and programs. The other curricular guidelines discussed in the Common Vision report are each worth serious consideration beyond the summaries given in Common Vision. For mathematics departments that teach large numbers of preservice K-12 teachers, the CBMS Mathematical Education of Teachers II from 2012 and the NCTM Principles to Actions report are important and informative.
Regardless of the specific focus of an individual department or institution, framing our activities in a broader context and making use of resources produced by the professional societies can significantly strengthen our arguments in favor of increased support and resources for our mission of teaching and learning. These resources also serve to inform and inspire us as we revise our courses and programs.