Guideline Statement #4

Best Practices for Curriculum & Teaching

Departments in the mathematical sciences should determine the content and implementation of their program to ensure equity and consistent educational quality. This requires clear communication, consistent programming, flexible pedagogies, and a supportive environment for students. The program and related policies should enable student-faculty interaction, particularly with regards to class size and regular feedback. Further recommendations on diversity, equity, and inclusion as they pertain to curriculum and teaching will be addressed in a future guideline statement.

1. Course Planning and Review    2. Curriculum Access and Pedagogy       3. Technology and Pedagogy    
4. Program Recommendations of Professional Societies    

1. Course Planning and Review

a. Departments should have the primary responsibility in setting placement policies, prerequisites/corequisites, course content, and learning outcomes for departmental courses. (Related recommendations can be found in the MAA’s Guideline Statement #3, part I. -- “Best Practices for Student Support” -- placement and advising.).

b. Information about courses should be current and easily accessible in the course catalog and/or website. Course prerequisites and any policies on waiving prerequisites should be clearly stated. Current syllabi or extended course descriptions (i.e., documents that include course topics and objectives) for all courses should be available publicly for review by faculty colleagues and students. Courses that are not offered at least every two years should be clearly designated as such. If not offered within five years, a course should be removed from the course catalog.

c. Departments should plan course offerings to facilitate four-year graduation rates. Courses which are required in a student’s program of study should be scheduled and taught at least once every two years. If required courses cannot be offered at least once every two years, departments should reconsider the structure of their major or approve substitute requirements.

d. For all course transfer equivalencies from other institutions, departments should work with administrations to ensure that the appropriate equivalency is determined. Course equivalencies should be publicized to students and faculty. In cases where a department regularly teaches students who transfer from two-year colleges, the departmental faculty members at the institutions should work together to ensure compatibility of appropriate courses in content, technology and rigor.

e. Departments should have established procedures for periodic review of the curriculum. These reviews should include, but are not limited to, careful scrutiny of course content, prerequisites, texts, use of technology, and student learning outcomes. The curriculum should be examined within the context of departmental goals and institutional mission as well as with consideration of its relevance to and appropriateness for the students being served.

f. Courses that support other programs should be planned, implemented and reviewed in collaboration with client departments.

2. Curriculum Access and Pedagogy

a. The mathematical sciences curriculum should be responsive to the needs of the students enrolled in any departmental course. Course and program offerings should provide suitable academic challenges and should be based on the expectation that all students can learn mathematics. The spectrum of beginning courses should be broad enough to offer appropriate choices and placement in mathematics for all students entering the institution [6,7].

b. No one method of instruction is optimal for all students, for all faculty members, or for all subject matter. The department should encourage and support faculty members who investigate, implement, and evaluate pedagogical techniques that show promise based on results of research on teaching and learning.

c. To encourage student-faculty interaction and enable faculty to give students individual attention, the department should work with its administration to limit class sizes to at most 30 students whenever possible [1,2,3,4,5]. Restricted class sizes also give faculty members greater flexibility in meeting their students’ needs and adopting instructional methods that best fit the content being taught.

d. Assessment of student performance is crucial for both students and instructors. The instructional staff assigned to each course should be sufficient to allow for regular and frequent feedback in a variety of forms (e.g., peer review, evaluative) to inform students about their progress. Frequent evaluation of students also provides important information that the course instructor can use to make mid-course adjustments in teaching or course design.

e. It is important to provide opportunities for students to formally and informally voice praise and concerns based on their learning experiences, at the conclusion of a course. Such feedback can be useful formatively to develop excellence in teaching. However, the use of student course evaluations of faculty for tenure and other decisions is complicated because of their known biases. (A collection of articles on the subject of bias in student evaluations is available.) Use of these evaluations in evaluation decisions requires careful examination in light of these biases. In addition, students aren’t and can’t be expected to be experts in evaluating teaching in the same way professional colleagues are.

3. Technology and Pedagogy

a. Departments of mathematical sciences should employ technology in ways that foster teaching and learning, increase the students’ understanding of mathematical concepts, and prepare students for the use of technology in their careers or graduate study. Professional development needs to be offered to support the use of technology in teaching. Where appropriate, courses offered by the department should integrate current technology, such as computer algebra systems. (Related recommendations can be found in the MAA’s Guideline Statement #2, “Required Resources and Recommended Technology for College and University Mathematical Sciences Departments”.)

b. Special emphasis should be placed on giving prospective K-12 teachers the experience of learning mathematics aligned with methods practiced in schools. Prospective teachers should be educated to be leaders in the effective use of technology in the schools [6,7].

c. The department should develop and keep updated a general policy for assessment of student work that reflects the role of technology in the curriculum, and mathematics more generally, while taking into account those students that do not have access to computers or the Internet.

4. Program Recommendation of Professional Societies

a. The curricula of bachelor’s degree programs in the mathematical sciences should be consistent with the current recommendations of the MAA Committee on the Undergraduate Program in Mathematics (CUPM) [7].

b. A major, minor or concentration in statistics, the program should be consistent with the current American Statistical Association recommendations in its Guidelines for Assessment and Instruction in Statistics Education (GAISE) [8].

c. If the department offers a program for pre-service teachers, such as a major or concentration in mathematics education, the program should reflect the recommendations of the Conference Board on Mathematical Sciences [9] and the guidelines of the National Council of Teachers of Mathematics [10].

d. d. A valuable resource for guidelines in mathematical modeling is the Guidelines for Assessment and Instruction in Mathematical Modeling Education, as published by COMAP and SIAM [11].

References

1. “Class Size Matters”, Stephen L. Benton and William H. Pallett, Inside Higher Ed,  January 29, 2013.  Available at:  https://www.insidehighered.com/views/2013/01/29/essay-importance-class-size-higher-education
2. “Increasing Student Success: Smaller Classes, Innovative Pedagogy at UCF”, Association of American Colleges & Universities (AACU), 2010.  Available at:  https://www.aacu.org/campus-model/increasing-student-success-smaller-classes-innovative-pedagogy-ucf
3. “Class Size Matters: Heterogeneous Effects of Larger Classes on College Student Learning”, Timothy M Diette & Manu Raghav, Eastern Economic Journal, 2014.  Available at:  https://link.springer.com/article/10.1057/eej.2014.31
4. “The Effectiveness of Class Size Reduction”, William J. Mathis, National Education Policy Center, 2016.  Available at:  https://nepc.colorado.edu/sites/default/files/publications/Mathis%20RBOPM-9%20Class%20Size.pdf
5. “The Impact of Class Size on Outcomes in Higher Education”, James Monks and Robert M. Schmidt, The B.E. Journal of Economic Analysis & Policy, 2011.  Available at:  https://scholarship.richmond.edu/economics-faculty-publications/49/
6. Instructional Practices Guide, Mathematical Association of America, 2017.  Available at:  https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide
7. 2015 CUPM Curriculum Guide, Mathematical Association of America, 2015.  Available at:  https://www.maa.org/programs/faculty-and-departments/curriculum-department-guidelines-recommendations/cupm/2015-cupm-curriculum-guide
8. Guidelines for Assessment and Instruction in Statistics Education,  (GAISE), 2016.  Available at:  https://www.amstat.org/asa/education/Guidelines-for-Assessment-and-Instruction-in-Statistics-Education-Reports.aspx
9. The Mathematical Education of Teachers II, Conference Board of Mathematical Sciences (CBMS), 2012.  Available at:  https://www.cbmsweb.org/archive/MET2/met2.pdf
10. Principles to Actions: Ensuring Mathematical Success for All, National Council of Teachers of Mathematics (NCTM), 2014.  Available at https://www.nctm.org/PtA/
11. GAIMME: Guidelines for Assessment and Instruction in Mathematical Modeling Education, Second Edition, Sol Garfunkel and Michelle Montgomery, editors, COMAP and SIAM, 2019. Available at https://www.siam.org/Publications/Reports/Detail/guidelines-for-assessment-and-instruction-in-mathematical-modeling-education

Contributors

Ed Aboufadel, Grand Valley State University
Emily Puckette, University of the South
Audrey Malagon, Virginia Wesleyan University
Mary Pilgrim, Colorado State University
Jason Douma, University of Sioux Falls
Benedict Nmah, Morehouse College
Jill Dietz, St. Olaf College
Tim Flowers, Indiana University of Pennsylvania
Debra Lynn Hydorn, University of Mary Washington

October 2020