Changing Attitudes toward Student-Centered Approaches for Teaching Mathematics
By David Bressoud @dbressoud
Sandra Laursen
In 2019, AAAS published an important report, Levers for Change: An assessment of progress on changing STEM education. Edited by Sandra Laursen, senior research associate and co-director of Ethnography & Evaluation Research at the University of Colorado, Boulder, this is an extensive review of what we know about the state of undergraduate STEM education, with separate chapters on Chemistry and Biochemistry, Engineering and Computer Science, Geosciences, Mathematics, and Physics and Astronomy. The chapter on mathematics education is provocatively titled “Undergraduate Mathematics Instruction: Not as Bad as You’d Think?”.
The chapter on mathematics was written by Estrella Johnson, a member of the MAA team studying precalculus through calculus, and much of her data on mathematics instruction draws on the MAA studies of calculus instruction: Characteristics of Successful Programs in College Calculus (CSPCC) and Progress through Calculus (PtC) as well as the CBMS 2015 survey of departments in the mathematical sciences. She also draws on data from the Higher Education Research Institute (HERI), based at UCLA, and a number of more focused studies.
The evidence is mixed. Data from the 2014 HERI study (Eagan, 2016) found that two-thirds of mathematics instructors use extensive lecturing in most or all of their classes, with 35% of instructors using it in all of their classes. While perhaps disappointing, it is a considerable improvement since 2004 when 80% of instructors were using extensive lecturing in most or all classes.
On the positive side, the 2015 CBMS survey (Blair et al, 2018) revealed that 58% of mathematics departments have at least one person using inquiry-based learning, 58% have at least one person experimenting with flipped classes, and 66% have at least one person using activity based learning (Table 1). Carefully protocoled classroom observations by Marilyne Stains in 205 undergraduate mathematics classes found that 40% of classes spent at least 80% of the time in lectures, 40% were student-centered, and the remaining 20% involved lecture supplemented with student-centered strategies. However, when I asked her about these data, she clarified in a private email that she selected campuses where there was some evidence that they were interested in ways of improving their teaching. Thus, her data may not be nationally representative.
Table 1: Percentage of four-year mathematics and statistics departments reporting that various pedagogical strategies are used by some member of the department faculty. Table SP.26, page 78 in Blair et al, 2018.
The PtC data on instruction in Precalculus, Calculus I, and Calculus II in departments that offer a graduate degree in mathematics (Master’s or PhD) were less rosy (Table 2). Lecture, with allowance for student questions, was the dominant instructional technique for Precalculus in 59% of departments, for Calculus I in 74% of departments, and for Calculus II in 65%. If we add in those departments where the dominant method is still lecture, but with some active learning techniques such as think-pair-share or use of clickers, the percentages rise to 77% for Precalculus, 87% for Calculus I, and 82% for Calculus II. Around 10% of departments said that there was too much variation to identify a single dominant style of instruction (Apkarian & Kirin, 2017).
Table 2: Percentage of departments reporting primary style of instruction in Precalculus, Calculus I, or Calculus II. Source: Apkarian & Kirin 2017.
The conclusion is that lecture is still the dominant mode of instruction, especially in Precalculus and mainstream Calculus I and II. This is significant because just these three courses account for 63% of all undergraduate mathematics enrollments at the level of Precalculus or above (Blair et al, 2018). Most students experience lecture as the mode of instruction in mathematics. Nevertheless, there is interest in and experimentation with more student-centered approaches.
Both the CSPCC survey of Calculus I instructors (Bressoud et al, 2015) and a 2018 study of abstract algebra instructors (Johnson et al, 2018) found that about 60% of instructors agree with the statements “I think lecture is the best way to teach” and “I think students learn better if I first explain the material to them and then they work to make sense of the ideas themselves.” In apparent contradiction to this, 87% of instructors agreed that “I think students learn better when they do mathematics work (in addition to taking notes and attending to the lecture) in class” and 77% agreed that “I think students learn better when they struggle with the ideas prior to me explaining the material to them.” (Table 3) Johnson suggests that this set of beliefs is consistent with a desire for students to read the textbook before class (struggle with the ideas), have them explained by the instructor in class, do some practice problems in class, and then do homework. In other words, they could reflect a very traditional view of instructor-centered teaching.
Table 3: Belief items on Abstract Algebra Survey: Percentage of instructors reporting belief. Source: Johnson et al, 2018.
The final chapter looks at the over-arching lessons from a comparison of what is happening in the various STEM disciplines. What I found most interesting was the characterization of the levers for change in each field. For mathematics, the three highest were professional development of instructors, graduate TAs, and future faculty (here I think especially of Project NExT), local leaders and internal change agents with a vision (the CBMS survey revealed that this was the most common impetus for the introduction of active learning approaches), and federal and private funders’ investments in STEM education (certainly NSF’s Division of Undergraduate Education plays a huge role here). Close behind these were guiding documents from professional societies (here I think especially of A Common Vision and the MAA’s Instructional Practices Guide) and communities of practice such as the community that has built up around inquiry based learning (IBL), facilitated by the Academy of IBL.
Among the levers that are not very effective are resource collections (unless they are tied to a narrow community of practice such as IBL) and results from educational research. For the former, Laursen points to the NSF’s frustrated attempt to create digital libraries of classroom resources. The problem is that there is too much to curate effectively, they are too diverse and often too prescriptive, and they are unwieldy to browse. The problem with educational research is that most of it is written to satisfy the needs of scholarship in what is, in fact, a social science. Laursen suggests a need for the development of a field of scholarship analogous to translational research in medicine.
Given the pivotal role of local change leaders, I would like to conclude with nine tactics and functions of local change leaders that Laursen extracts from the literature (Kezar et al 2011; Laursen 2016):
1. Connect people who are teaching particular courses to communities of practice, and to new ideas;
2. Model attitudes and conversations for their colleagues;
3. Call for conversations in the department about pedagogy and strategy;
4. Connect the department to campus expertise on teaching, learning, and assessment;
5. Communicate with senior administrators to understand how to align department goals with institutional interests and what evidence will be persuasive to leaders;
6. Mobilize local resources for pilot projects (“Mini-grants of $5000 or less seem to get a lot of effort out of people.”);
7. Raise awareness and elevate the status of RBIS (Research Based Instructional Strategies) studies and practices through local communication mechanisms, such as department meetings, newsletters, on- and off-campus publicity, serving as a “rudder for messaging”;
8. Identify opportunities to shift local policies and reward and recognition structures; and
9. Curate information about external pressures and opportunities, including workforce issues.
References
Apkarian, N., & Kirin, D. (2017). Progress through Calculus: Census Survey Technical Report. Available at https://www.maa.org/sites/default/files/PtC%20Technical%20Report_Final.pdf
Blair, R. M., Kirkman, E. E., Maxwell, J. W., & American Mathematical Society. (2018). Statistical abstract of undergraduate programs in the mathematical sciences in the United States: Fall 2015 CBMS survey. Washington, DC: American Mathematical Society.
Bressoud, D. M., Mesa, V., & Rasmussen, C. L. (Eds.) (2015). Insights and recommendations from the MAA National Study of College Calculus. Washington, DC: Mathematical Association of America.
Eagan, K. (2016). Becoming more student-centered? An examination of faculty teaching practices across STEM and non-STEM disciplines between 2004 and 2014. A report prepared for the Alfred P. Sloan Foundation. Higher Education Research Institute, UCLA: Los Angeles.
Johnson, E., Keller, R., & Fukawa-Connelly, T. (2018). Results from a survey of abstract algebra instructors across the United States: Understanding the choice to (not) lecture. International Journal of Research in Undergraduate Mathematics Education, 4(2), 254–285.
Kezar, A., Bertram Gallant, T., & Lester, J. (2011). Everyday people making a difference on college campuses: The tempered grassroots leadership tactics of faculty and staff. Studies in Higher Education, 36(2), 129-151.
Laursen, S. L. (2016). Organizational features that influence departments’ uptake of student-centered instruction: Case studies from inquiry-based learning in college mathematics. In T. Fukawa-Connelly, N. Engelke Infante, M. Wawro, S. Brown, eds., Proceedings of the 19th Annual Conference on Research in Undergraduate Mathematics Education, pp. 1022-1030. http://sigmaa.maa.org/rume/RUME19v3.pdf
Laursen, S. L. (2019). Levers for Change: An assessment of progress on changing STEM instruction. Washington, DC: American Association of the Advancement of Science. Available at https://www.aaas.org/sites/default/files/2019-07/levers-for-change-WEB100_2019.pdf
Stains, M., Harshman, J., Barker, M. K., Chasteen, S. V., Cole, R., DeChenne-Peters, S. E., Eagan, M. K., Esson, J. M., Knight, J. K., Laski, F. A., Levis-Fitzgerald, M., and others (2018). Anatomy of STEM teaching in North American universities. Science, 359, 1468-1470
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