INTEGRATING COMPARATIVE JUDGMENT INTO AUTHENTIC ASSESSMENT IN MATHEMATICS EDUCATION
DOI:
https://doi.org/10.18173/2354-1075.2026-0047Keywords:
assessment in education, comparative judgment, authentic assessment, mathematics education, reliabilityAbstract
Alongside renewed teaching methodology required by the 2018 Vietnamese General Education Curriculum, the implementation of a corresponding assessment model is essential. In this context, authentic assessment is considered an appropriate approach, as it focuses on evaluating students’ ability to apply mathematical knowledge to real-world situations. However, the diversity of authentic tasks poses challenges to consistency when using fixed scoring rubrics. This study proposes a six-step procedure for applying comparative judgment as a feasible and integrative solution, and conducts a pedagogical trial with an authentic task in Grade 11 mathematics. The results indicate that comparative judgment not only ensures high reliability but also fosters students’ evaluative competencies through peer assessment. Accordingly, the study recommends integrating comparative judgment into authentic assessment to enhance the effectiveness of mathematics teaching and learning.
Downloads
References
- Alfieri, L., Nokes-Malach, T. J., & Schunn, C. D. (2013). Learning Through Case Comparisons: A Meta-Analytic Review. Educational Psychologist, 48(2), 87–113. https://doi.org/10.1080/00461520.2013.775712
- Bartholomew, S., & Yoshikawa, E. (2018). A Systematic Review of Research Around Adaptive Comparative Judgement (ACJ) in K-16 Education. CTETE - Research Monograph Series, 1. https://doi.org/10.21061/ctete-rms.v1.c.1
- Bisson, M.-J., Gilmore, C., Inglis, M., & Jones, I. (2016). Measuring Conceptual Understanding Using Comparative Judgement. International Journal of Research in Undergraduate Mathematics Education, 2(2), 141–164. https://doi.org/10.1007/s40753-016-0024-3
- Bloxham, S., & Price, M. (2015). External examining: Fit for purpose? Studies in Higher Education, 40(2), 195–211. https://doi.org/10.1080/03075079.2013.823931
- Bouwer, R., Lesterhuis, M., Bonne, P., & De Maeyer, S. (2018). Applying Criteria to Examples or Learning by Comparison: Effects on Students’ Evaluative Judgment and Performance in Writing. Frontiers in Education, 3. https://doi.org/10.3389/feduc.2018.00086
- Cantley, I. (2023). Philosophical perspectives on authentic assessment in mathematics: The 15th International Congress on Mathematical Education. 15th International Congress on Mathematics Education: Proceedings.
- Ellison, C. (2023). Effects of adaptive comparative judgement on student engagement with peer formative feedback. Practitioner Research in Higher Education, 15(1), 24–35.
- Flores, M. A., Veiga Simão, A. M., Barros, A., & Pereira, D. (2015). Perceptions of effectiveness, fairness and feedback of assessment methods: A study in higher education. Studies in Higher Education, 40(9), 1523–1534. https://doi.org/10.1080/03075079.2014.881348
- Jones, I., & Alcock, L. (2014). Peer assessment without assessment criteria. Studies in Higher Education, 39(10), 1774–1787. https://doi.org/10.1080/03075079.2013.821974
- Jones, I., & Inglis, M. (2015). The problem of assessing problem solving: Can comparative judgement help? Educational Studies in Mathematics, 89(3), 337–355. https://doi.org/10.1007/s10649-015-9607-1
- Jones, I., & Sirl, D. (2017). Peer assessment of mathematical understanding using comparative judgement. NOMAD Nordic Studies in Mathematics Education, 22(4), 147–164. https://doi.org/10.7146/nomad.v22i4.148924
- Jones, I., & Wheadon, C. (2015). Peer assessment using comparative and absolute judgment. Studies in Educational Evaluation, 47, 93–101. https://doi.org/10.1016/j.stueduc.2015.09.004
- Laming, D. (2003). Human judgment: The eye of the beholder. Cengage Learning EMEA.
- McConlogue, T. (2012). But is it fair? Developing students’ understanding of grading complex written work through peer assessment. Assessment & Evaluation in Higher Education, 37(1), 113–123. https://doi.org/10.1080/02602938.2010.515010
- Mueller, J. (2005). The Authentic Assessment Toolbox: Enhancing Student Learning through Online Faculty Development. https://www.semanticscholar.org/paper/The-Authentic-Assessment-Toolbox%3A-Enhancing-Student-Mueller/b4b5dfd76cb153ce12f303b66f8b4be1854c7f7b
- Nguyễn, C. K., & Đào, T. O. (2015). Giáo trình kiểm tra đánh giá trong giáo dục. NXB Đại học Sư phạm.
- Pachur, T., & Olsson, H. (2012). Type of learning task impacts performance and strategy selection in decision making. Cognitive Psychology, 65(2), 207–240. https://doi.org/10.1016/j.cogpsych.2012.03.003
- Pollitt, A. (2012). The method of Adaptive Comparative Judgement. Assessment in Education: Principles, Policy & Practice, 19(3), 281–300. https://doi.org/10.1080/0969594X.2012.665354
- Pollitt, A., & Whitehouse, C. (2012). Using adaptive comparative judgement to obtain a highly reliable rank order in summative assessment.
- Rezaei, A. R., & Lovorn, M. (2010). Reliability and Validity of Rubrics for Assessment through Writing. Assessing Writing, 15(1), 18–39. https://doi.org/10.1016/j.asw.2010.01.003
- Sadler, D. R. (2009). Indeterminacy in the Use of Preset Criteria for Assessment and Grading. Assessment & Evaluation in Higher Education, 34(2), 159–179. https://doi.org/10.1080/02602930801956059
- Seery, N., Canty, D., & Phelan, P. (2012). The validity and value of peer assessment using adaptive comparative judgement in design driven practical education. International Journal of Technology and Design Education, 22(2), 205–226. https://doi.org/10.1007/s10798-011-9194-0
- Svinicki, M. D. (2004). Authentic assessment: Testing in reality. New Directions for Teaching and Learning, 2004(100), 23–29. https://doi.org/10.1002/tl.167
- Đặng, T. T. T. (2022). Đánh giá như hoạt động học tập và học tập tự định hướng ở các cơ sở giáo dục đại học. Tạp chí Khoa học Giáo dục Việt Nam, 02(2), 7–12.
- van Daal, T., Lesterhuis, M., Coertjens, L., Donche, V., & De Maeyer, S. (2019). Validity of comparative judgement to assess academic writing: Examining implications of its holistic character and building on a shared consensus. Assessment in Education: Principles, Policy & Practice, 26(1), 59–74. https://doi.org/10.1080/0969594X.2016.1253542
- van Daal, T., Snajder, M., Nijs, K., & Van Dyck, H. (2023). Peer Assessment Using Criteria or Comparative Judgement? A Replication Study on the Learning Effect of Two Peer Assessment Methods. In O. Noroozi & B. De Wever (Eds.), The Power of Peer Learning: Fostering Students’ Learning Processes and Outcomes (pp. 73–101). Springer International Publishing. https://doi.org/10.1007/978-3-031-29411-2_4
- Wilson, J. W. (1973). Standardized Tests Very Often Measure the Wrong Things. The Mathematics Teacher, 66(4), 295–370.
