Illustrative Resources

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Mathematical sciences departments should encourage, support and reward faculty efforts to improve the efficacy of teaching and strengthen curricula.

Teaching and Learning

Project NExT (New Experiences in Teaching), with major funding by the ExxonMobil Corporation and additional funding from a variety of other sources, is a professional development program for new or recent Ph.D.s in the mathematical sciences. It addresses all aspects of an academic career: improving the teaching and learning of mathematics, engaging in research and scholarship, and participating in professional activities. It also provides the participants with a network of peers and mentors as they assume these responsibilities. Faculty who are just beginning or just completing their first year of full-time teaching at the college/university level can become Project NExT Fellows. In the Project’s first fourteen years, there have been almost 1000 Project NExT fellows. An article about the project was published in the February 2000 issue of the Notices of the AMS.  Most MAA sections now also offer local versions of Project NExT. Project Access is a similar program for faculty at two-year colleges.

The MAA Special Interest Group on Research in Undergraduate Mathematics Education (RUME) was formed to foster research on learning and teaching undergraduate mathematics and to provide a support network for those who participate in this area of research. This SIGMAA also welcomes members who teach post-secondary mathematics or are interested in the findings of RUME; such members often provide critical assistance in the grounding of research efforts in the realities of the classroom. The site above offers a literature database, publication links, and research resources.

In 1997 the International Commission on Mathematical Instruction (ICMI) drafted a discussion document addressing the teaching and learning of mathematics at the university level. Its purpose was to raise important issues related to the teaching and learning of mathematics at university level and to stimulate discussion and research on these topics as background for a conference in Singapore in December 1998. The 1998 conference focused on the following issues:
  -- Why a Study on the Teaching and Learning of Mathematics at University Level?
  -- Themes and Issues Pertaining to Research on the Teaching and Learning of Mathematics at University Level
  -- Themes and Issues Pertaining to Practice: Clientele, Curriculum, Student Activity, Pedagogy
  -- Themes and Issues Relating to Policy: Policy Issues relating to society at large, Policy Issues concerning a specific university or university department
  -- Call for Reactions
An article on the project by Michele Artigue was published in the Notices of the AMS in 1999, and the book The Teaching and Learning of Mathematics at University Level appeared in 2001. The book is divided into seven sections: Introduction, Practice, Research, Mathematics and Other Disciplines, Technology, Assessment, and Teacher Education. A review of the book was written by Lynn Arthur Steen, St. Olaf College, and additional information on the project is contained in an ICME progress report.

Faculty and Professional Development Programs

Professional Enhancement Programs (PREP) is a comprehensive, professional career enhancement project of the MAA funded by the National Science Foundation. The intended audience includes faculty at two-year colleges, liberal arts colleges, institutions primarily serving minority students, comprehensive universities, and research universities. PREP programs are open to all faculty, whether or not they are members of the MAA or any other professional organization. Although most of the programs in PREP are for faculty in the mathematical sciences, those from other disciplines are welcome, and some programs specifically encourage communication among mathematics faculty and those from other disciplines. PREP has offered and continues to offer a large number of workshops and short courses across the country. A sampling of recent programs includes: Assessment at the Department Level, Integration of Technology into Mathematics Instruction, Quantitative Literacy Across the Curriculum, Discrete Mathematics, Statistical Ratemaking, Computational and Mathematical Biology, Geometric Combinatorics, and Active Learning Approaches to Teaching Mathematics Content Courses for Elementary and Middle School Teachers.

Preparing Mathematicians to Educate Teachers (PMET), with major funding from the National Science Foundation, has four major components: workshops and minicourses to help mathematicians to be better prepared to provide high-quality mathematical education to teachers, information and resources  including talks, articles, and websites with course information, regional networks to help initiate, support and coordinate efforts at individual institutions, and mini-grants to improve teacher education programs and develop new instructional materials.

The Chautauqua Short Courses for College Teachers, funded by the National Science Foundation, provide faculty development workshops for college-level teachers of mathematics and science.  The workshops, typically three days in length, are held each summer throughout the country.  Some of the 2004 mathematics workshops were: How to Write a Mathematics Textbook and Course Materials, Data Analysis and Visualization Using Mathematica, Teaching Differential Equations from a Dynamical Systems Viewpoint, Combinatorics in Concert: For Teaching, Research, Outreach, and Recreation, and Cryptology, and The Breaking of the Axis Codes During WWII at Bletchley Park, England. 

Practices at Specific Institutions

The Excellence in Teaching Program at the University of Nevada at Reno provides support to faculty in an effort to promote strategic teaching, to facilitate strategic learning, to document teaching effectiveness, and to use technology to increase teaching and learning effectiveness. The website includes a description of the workshops that the Excellence in Teaching Program offers, as well as contact information.

North Carolina State University’s Faculty Center for Teaching and Learning (FCTL) was created to enhance student learning by promoting faculty growth and development. The FCTL website provides information, knowledge, and assistance for all faculty. In particular, there is encouragement for the use of Inquiry Guided Learning (IGL), an array of classroom practices that promote student learning through guided and, increasingly independent investigation of questions and problems that admit multiple answers. Also see Part 2, Section C.1.

In 1996, the Undergraduate Committee of the Department of Mathematics at The Ohio State University endorsed a proposal to change the teaching in the mathematics department. The plan of action outlined in the proposal was to: 1) return class sizes to manageable numbers and use the smaller classes to implement different teaching methods; 2) continue and augment special teaching initiatives currently  underway in the department (including assessment of the value of such efforts); 3) re-examine and articulate clearly the purpose and goals of each of the undergraduate math offerings, eliminate certain courses if appropriate, introduce new ones if needed, and clarify the foci, goals, and desired outcomes of all courses; 4) provide continuing exposure and training for all teachers, faculty, TA's, lecturers, casuals and teaching aides,  about teaching styles and methods (including fundamental ideas about how people learn); 5) augment the teaching staff (including hiring new faculty and enhancing TA recruitment), and employ new resources for teaching ( including the training of a cadre of undergraduate teaching aides). One result of the department’s efforts was the development of a Mathematics Teaching Support website.

Morton Brown wrote a report “Planning and Change: The Michigan Calculus Project” in which he described the process of changing the mode of instruction for Calculus at the University of Michigan. According to the report, when the University of Michigan Mathematics Department began to reform their calculus program in 1991, no one involved realized the impact these changes would have on mathematics education at the university level. Key components of the program are an emphasis on student activities rather than lectures, extensive instructor training, smaller classes, and the team approach to completing assignments. Brown and lecturer Pat Shure, working with staff from the University’s Center for Research on Learning and Teaching (CRLT), developed an instructor’s handbook for use in the training programs of faculty in the new calculus courses. CRLT staff members were involved in various aspects of the evaluation of the effectiveness of the new program. A related article is Implementation and Assessment of Online Testing by Gavin P. LaRose and Robert Megginson.

At the United States Military Academy (USMA), all new instructors participate in a five-week Faculty Development Workshop the summer prior to their first semester of teaching. This workshop is intended to familiarize new faculty members with the Military Academy and with the Department of Mathematical Sciences, and to prepare new faculty for classroom teaching. Participants in the program become familiarized with the current technology systems and tools; discuss educational philosophies about teaching, learning and assessment; visit and learn about the other math, science and engineering departments; teach practice classes; observe and provide feedback to others teaching practice classes; and prepare lesson plans for the upcoming semester. The department conducts shorter Faculty Development Workshops prior to each semester aimed at the particular core courses being taught. The department also hosts a faculty development workshop in the spring for faculty members who will be acting as course leaders the following fall.  While most workshops focus on classroom and course activities, the leader workshop focuses on how the courses fit into the department vision.  Information on the faculty development program at the USMA is on the website for the Center for Faculty Development and the recruiting homepage for the mathematics department.

Regional and national meetings of the Mathematical Association of America offer a large number of hour talks, contributed paper sessions, minicourses, and panels to allow faculty to share experiences with courses, curricula, technology, and instructional techniques. For example, the following listing is just a fraction of the sessions at the Atlanta meeting in 2005: Getting Students to Discuss and To Write About Mathematics, My Favorite Demo: Innovative Strategies for Mathematics Instructors, Courses Below Calculus: A New Focus, Mathematics and Sports, Getting Students Involved in Undergraduate Research, Visual Linear Algebra, Developing Your Department’s Assessment Plan, A Problem-based Core Program, and Mathematical Finance.

Additional Resources

The MAA Guidelines for Programs and Departments in Undergraduate Mathematical Sciences includes a number of specific suggestions as well as a listing of MAA publications that support efforts to improve the teaching of mathematics. Under the section Program Faculty and Staffing, subsection Promoting Excellence in Teaching, the guidelines provide the following advice to departments. 1) Teaching ability and commitment to teaching should be key factors in all appointments to the teaching staff. 2) Orientation and training programs should be provided to familiarize new staff members with departmental expectations and the needs of students. New faculty should receive a description of the teaching and teaching-related duties expected of them and the means by which those duties will be evaluated. 3) Faculty should be supervised, monitored, and evaluated in order to help them improve their teaching. 4) The courses assigned to faculty, especially those newly hired, should be chosen to aid in their development as teachers. 5) A regular program for maintaining and improving teaching expertise is essential for all academic mathematical scientists (this is further elaborated in the document). 6) In certain circumstances, part-time faculty can make unique contributions to a mathematical sciences department. Departments that employ part-time instructors should provide them with all of the resources necessary for teaching that are provided to full-time instructors, including office space as well as computer, internet, and library resources. Full-time faculty should mentor part-time faculty in resolving problems, in meeting responsibilities, and in familiarizing them with the procedures and expectations of the department. 7) Departments should ensure that senior faculty assume a leadership role in the undergraduate program by participating fully in teaching, curriculum development, and student advising. In addition, they have key responsibility for reviewing and nurturing junior faculty and teaching assistants. 8) Both senior and junior faculty should, at least on occasion, teach courses at all levels of the undergraduate program.

The Mathematical Sciences Digital Library is an online resource managed by the Mathematical Association of America with funding by the National Science Foundation. The site provides online resources for both teachers and students of collegiate mathematics, including: the Journal of Online Mathematics and its Applications (JOMA); Convergence, an online magazine devoted to enhancing the teaching of mathematics by using its history; Digital Classroom Resources, a collection of free online learning materials that have been classroom tested and peer reviewed; and Osslets, which are open source, sharable mathlets. 

The Carnegie Foundation set up the Carnegie Academy for the Scholarship of Teaching and Learning (CASTL) as a follow-up to the two influential books Scholarship Reconsidered, by E. Boyer, published in 1990, and Scholarship Assessed, by C. Glassick, M.T. Huber, and G. Maeroff, in 1997.  The website contains a listing of online publications. It also has information about the CASTL Affiliates Program for “education organizations prepared to make a commitment to the scholarship of teaching and learning by exploring the place of such work in their settings, and undertaking activities that provide support and recognition for ongoing inquiry into evidence-based improvement of student learning.”

Math Archives and Math Forum are two other online sources for the teaching of mathematics.  Both sites include teaching materials and links to mathematics related websites.  The Math Archives site also lists available software while the Math Forum site includes discussion groups and resources for mathematics education.