- Open Access
Evaluating peer discussion in calculus-based mechanics using a cluster-randomized crossover design
Phys. Rev. Phys. Educ. Res. 22, 020104 – Published 14 July, 2026
DOI: https://doi.org/10.1103/wjhq-n354
Abstract
Peer discussion (PD) is widely used as an active-learning strategy in physics education, yet most prior research has focused on conceptual multiple-choice questions. Much less is known about how peer discussion functions when applied to mathematically structured problems typical of calculus-based mechanics courses. To address this gap, we compared the effects of PD and instructor explanation (IE) during short in-class exercise sessions in a calculus-based introductory mechanics course (). Using a cluster-randomized crossover design with two course sections, instruction alternated between PD and IE across weekly exercise topics. After each lesson, students completed a 16-item post-test; 12 of these items were also administered on the final exam. Across the 16 post-test items, we found no statistically significant evidence that PD outperformed IE on any single item. In unadjusted item-level analyses, four items that required greater abstraction and multistep mathematical reasoning showed a trend favoring IE, although none of these differences remained statistically significant after Holm correction for multiple comparisons. On the final exam, no statistically significant differences were observed between conditions. These results suggest that, within the instructional conditions of this study, PD did not produce consistent performance gains relative to IE, and any item-level differences may depend on task characteristics such as mathematical abstraction, novelty, and multistep reasoning demands.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (33)
- M. Prince, Does active learning work? A review of the research, J. Eng. Educ. 93, 223 (2004).
- J. Michael, Where’s the evidence that active learning works?, Adv. Physiol. Educ. 30, 159 (2006).
- S. Freeman, S. L. Eddy, M. McDonough, M. K. Smith, N. Okoroafor, H. Jordt, and M. P. Wenderoth, Active learning increases student performance in science, engineering, and mathematics, Proc. Natl. Acad. Sci. USA 111, 8410 (2014).
- Central Council for Education, Towards qualitative transformation of university education for building a new future: Universities fostering lifelong learning and independent thinking (report), 2012, in Japanese.
- R. R. Hake, Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses, Am. J. Phys. 66, 64 (1998).
- E. F. Redish and J. R. Burciaga, Teaching Physics: With the Physics Suite (John Wiley & Sons, Hoboken, NJ, 2003), Vol. 1.
- L. C. McDermott and E. F. Redish, Resource letter: PER-1: Physics education research, Am. J. Phys. 67, 755 (1999).
- L. Hsu, E. Brewe, T. M. Foster, and K. A. Harper, Resource letter RPS-1: Research in problem solving, Am. J. Phys. 72, 1147 (2004).
- D. E. Meltzer and R. K. Thornton, Resource letter ALIP–1: Active-learning instruction in physics, Am. J. Phys. 80, 478 (2012).
- C. Henderson and M. H. Dancy, Physics faculty and educational researchers: Divergent expectations as barriers to the diffusion of innovations, Am. J. Phys. 76, 79 (2008).
- C. Henderson and M. H. Dancy, Impact of physics education research on the teaching of introductory quantitative physics in the United States, Phys. Rev. ST Phys. Educ. Res. 5, 020107 (2009).
- M. Dancy and C. Henderson, Pedagogical practices and instructional change of physics faculty, Am. J. Phys. 78, 1056 (2010).
- M. Dancy, C. Henderson, and C. Turpen, How faculty learn about and implement research-based instructional strategies: The case of peer instruction, Phys. Rev. Phys. Educ. Res. 12, 010110 (2016).
- C. Henderson, M. Dancy, and M. Niewiadomska-Bugaj, Use of research-based instructional strategies in introductory physics: Where do faculty leave the innovation-decision process?, Phys. Rev. ST. Phys. Educ. Res. 8, 020104 (2012).
- E. Mazur, Peer Instruction: A User’s Manual (Prentice Hall, Upper Saddle River, NJ, 1997).
- C. H. Crouch and E. Mazur, Peer instruction: Ten years of experience and results, Am. J. Phys. 69, 970 (2001).
- I. D. Beatty, W. J. Gerace, W. J. Leonard, and R. J. Dufresne, Designing effective questions for classroom response system teaching, Am. J. Phys. 74, 31 (2006).
- M. K. Smith, W. B. Wood, W. K. Adams, C. Wieman, J. K. Knight, N. Guild, and T. T. Su, Why peer discussion improves student performance on in-class concept questions, Science 323, 122 (2009).
- B. L. Lan, P. M. Lim, and P. W. C. Ho, A modified peer instruction protocol: Peer vs teacher’s instruction, Phys. Teach. 61, 290 (2023).
- M. K. Smith, W. B. Wood, K. Krauter, J. K. Knight, and D. Ebert-May, Combining peer discussion with instructor explanation increases student learning from in-class concept questions, CBE Life Sci. Educ. 10, 55 (2011).
- T. Bauer, R. Biehler, and E. Lankeit, Conceptests in undergraduate real analysis: comparing peer discussion and instructional explanation settings, Int. J. Res. Undergrad. Math. Educ. 9, 426 (2023).
- K. L. Nielsen, G. Hansen-Nygård, and J. B. Stav, Investigating peer instruction: How the initial voting session affects students’ experiences of group discussion, Int. Scholarly Res. Not. 2012, 290157 (2012).
- Kyoto Sangyo University, Icebreakers you can use on campus!, https://www.kyoto-su.ac.jp/features/f/action/book.html, n.d., accessed: 24 September 2025.
- D. Hestenes, M. Wells, and G. Swackhamer, Force concept inventory, Phys. Teach. 30, 141 (1992).
- J. Epstein, Development and validation of the calculus concept inventory, in Proceedings of the Ninth International Conference on Mathematics Education in a Global Community (University of North Carolina Charlotte, Charlotte, NC, 2007), Vol. 9, pp. 165–170.
- W. K. Adams, K. K. Perkins, N. S. Podolefsky, M. Dubson, N. D. Finkelstein, and C. E. Wieman, New instrument for measuring student beliefs about physics and learning physics: The Colorado learning attitudes about science survey, Phys. Rev. ST. Phys. Educ. Res. 2, 010101 (2006).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/wjhq-n354 for the complete set of post-test items.
- S. Holm, A simple sequentially rejective multiple test procedure, Scand. J. Stat. 6, 65 (1979).
- J. Gleason, S. Bagley, M. Thomas, L. Rice, and D. White, The calculus concept inventory: A psychometric analysis and implications for use, Int. J. Math. Educ. Sci. Technol. 50, 825 (2019).
- M. Inui, N. Hatakenaka, and K. Hoshino, Kiso Kara Manabu Rikigaku (Fundamentals of Mechanics) (Baifukan, Tokyo, 2014). in Japanese.
Since the motion diagram is the same for both clockwise and counterclockwise cases, it was not possible to determine whether some students simply memorized the answer to the problem covered in class and used it to answer this question.
- P. R. Laughlin and A. L. Ellis, Demonstrability and social combination processes on mathematical intellective tasks, J. Exp. Soc. Psychol. 22, 177 (1986).
Physics Education Research Group at the University of Colorado Boulder, CU Boulder course materials: Classical mechanics/math methods 1, https://www.physport.org/curricula/CUBoulder/CM1, 2014, accessed:11 March 2026.
