Mastery-Based Testing in Linear Algebra: An Entry Point to Alternative Grading
DOI:
https://doi.org/10.20343/teachlearninqu.13.10Keywords:
mastery learning, alternative grading, feedback loops, test anxiety, linear algebraAbstract
An increasing number of university faculty have become interested in alternative grading systems in recent years. While there is a growing body of research on such grading systems, implementation can be a challenge for instructors. Mastery-based testing is a grading system in which students learn from feedback and have multiple attempts to demonstrate proficiency in a written exam setting without penalty. Student exam scores are determined by the number of course learning outcomes successfully completed by the end of the course. Given that all other aspects of the course are left in place, this model can serve as a relatively simple entry point into alternative grading. We implemented mastery-based testing in three sections of a 16-week high-enrollment university linear algebra course and gathered data on student perceptions of and performance in this revised course. In this paper, we report on students’ descriptions of the benefits and drawbacks of this system, their beliefs about final grades in this course compared to other courses, and their self-reported study habits.
References
Anderman, Eric, and Tamera Murdock. 2007. “The Psychology of Academic Cheating.” In Psychology of Academic Cheating, edited by Eric Anderman and Tamera Murdock, 1–5. Elsevier Academic Press. https://doi.org/10.1016/B978-012372541-7/50002-4.
Bloom, Benjamin. 1968. “Learning for Mastery. Instruction and Curriculum.” Regional Education Laboratory for the Carolinas and Virginia, Topical Papers and Reprints 1 (2).
Blum, Susan, editor. 2020. Ungrading: Why Rating Students Undermines Learning (and What to Do Instead). Morganstown, WV: West Virginia University Press.
Braun, Virginia, and Victoria Clarke. 2006. “Using Thematic Analysis in Psychology.” Qualitative Research in Psychology 3 (2): 77–101. http://doi.org/10.1191/1478088706qp063oa.
Brookhart, Susan. 2008. How to Give Effective Feedback to Your Students. Alexandria, VA: Association for Supervision and Curriculum Development.
Carney, Deb, Nic Ormes, and Rebecca Swanson. 2015. “Partially Flipped Linear Algebra: A Team–Based Approach.” PRIMUS 25 (8): 641–54. https://doi.org/10.1080/10511970.2015.1047545.
Clark, David, and Robert Talbert. 2023. Grading for Growth. Routledge. https://doi.org/10.4324/9781003445043.
Collins, J.B., Amanda Harsy, Jarod Hart, Katie Anne Haymaker, Alyssa Marie Hoofnagle, and Mike Kuyper Janssen. 2019. “Mastery-Based Testing in Undergraduate Mathematics Courses.” PRIMUS 29 (5): 441–60. https://doi.org/10.1080/10511970.2018.1488317.
Feldman, Joe. 2018. Grading for Equity: What It Is, Why It Matters, and How It Can Transform Schools and Classrooms. Corwin.
Guskey, Thomas, and Sally Gates. 1985. “A Synthesis of Research on Group-Based Mastery Learning Programs.” Presentation at the 69th Annual Meeting of the American Educational Research Association (Chicago, IL).
Halperin, Alexander. 2020. “Mastery-Based Testing in Calculus with a Final Exam Component.” PRIMUS 30 (8–10): 1017–39. https://doi.org/10.1080/10511970.2019.1700575.
Harsy, Amanda. 2020. “Variations in Mastery-Based Testing.” PRIMUS 30 (8–10): 849–68. https://doi.org/10.1080/10511970.2019.1709588.
Harsy, Amanda, and Alyssa Hoofnagle. 2020. “Comparing Mastery-Based Testing with Traditional Testing in Calculus II.” International Journal for the Scholarship of Teaching and Learning 14 (2). https://doi.org/10.20429/ijsotl.2020.140210.
Harsy, Amanda, Christina Carlson, and Lauren Klamerus. 2021. “An Analysis of the Impact of Mastery-Based Testing in Mathematics Courses.” PRIMUS 31 (10): 1071–88. https://doi.org/10.1080/10511970.2020.1809041.
Howitz, William, Kate J. McKnelly, and Renée D. Link. 2021. “Developing and Implementing a Specifications Grading System in an Organic Chemistry Laboratory Course.” Journal of Chemical Education 98 (2021): 385–94. https://doi.org/10.1021/acs.jchemed.0c00450.
Kulik, Chen-Lin, James Kulik, and Robert L. Bangert-Drowns. 1990. “Effectiveness of Mastery Learning Programs: A Meta-Analysis.” Review of Educational Research 60 (2): 265–99. https://doi.org/10.3102/00346543060002265.
Linhart, Jean Marie, James A. Kulik, and Robert L. Bangert-Drowns. 2020. “Mastery-Based Testing to Promote Learning: Experiences with Discrete Mathematics.” PRIMUS 30 (8–10): 1087–09. https://doi.org/10.1080/10511970.2019.1695236.
Lovett, Marsha, Michael W. Bridges, Michele DiPietro, Susan A. Ambrose, and Marie K. Norman. 2023. How Learning Works: Eight Research-Based Principles for Smart Teaching. Indianapolis, IN: Jossey-Bass, An Imprint of Wiley.
Malouff, John, and Einar Thorsteinsson. 2016. “Bias in Grading: A Meta-Analysis of Experimental Research Findings.” Australian Journal of Education 60 (3): 245–56. https://doi.org/10.1177/0004944116664618.
Mangum, Amanda. 2020. “Implementation of Mastery-Based Testing in Calculus.” Primus 30 (8–10): 869–84. https://doi.org/10.1080/10511970.2019.1709587.
Moss-Racusin, Corinne, John Dovidio, Victoria Brescoll, Mark Graham, and Jo Handelsman. 2012. “Science Faculty’s Subtle Gender Biases Favor Male Students.” PNAS 109 (41): 16474–479. https://doi.org/10.1073/pnas.1211286109.
Nilson, Linda. 2014. Specifications Grading: Restoring Rigor, Motivating Students, and Saving Faculty Time. Routledge. https://doi.org/10.4324/9781003447061.
Pulfrey, Caroline, Céline Buchs, and Fabrizio Butera. 2011. “Why Grades Engender Performance-Avoidance Goals: The Mediating Role of Autonomous Motivation.” Journal of Educational Psychology 103 (3): 683–700. https://doi.org/10.1037/a0023911.
Schinske, Jeffrey, and Kimberly Tanner. 2014. “Teaching More by Grading Less (or Differently).” CBE–Life Sciences Education 13 (2): 159–66. https://doi.org/10.1187/cbe.cbe-14-03-0054.
Slavin, Robert. 1987. “Mastery Learning Reconsidered.” Review of Educational Research 57 (2): 175–213. https://doi.org/10.3102/00346543057002175.
Stommel, Jesse. 2023. Undoing the Grade: Why We Grade, and How to Stop. Denver, CO: Hybrid Pedagogy Inc.
Talbert, Robert. 2023. “A Growth-Focused Icebreaker.” Grading for Growth Blog. https://gradingforgrowth.com/p/a-growth-focused-icebreaker.
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Copyright (c) 2025 Rebecca Swanson, Aram Bingham, Megan Sanders, Carter Moulton
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