From midterm to final: Using Rasch analysis to measure growth and fairness in university calculus assessments
Shirali Kadyrov 1 2 * , Rosemary Callingham 3 , Alfira Makhmutova 1 , Goncalo Pinto 1
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1 Department of General Education, New Uzbekistan University, Tashkent, UZBEKISTAN2 Department of Mathematics and Natural Sciences, SDU University, Kaskelen, KAZAKHSTAN3 School of Education, University of Tasmania, Hobart, AUSTRALIA* Corresponding Author

Abstract

This study investigates the reliability, validity, and fairness of university-level calculus assessments using Rasch analysis, focusing on the progression and alignment of key concepts across midterm and final exams. A cohort of 369 students from diverse academic disciplines was assessed using standardized exams designed to align with learning outcomes. The midterm and final exams, comprising conceptual and computational items, were analyzed separately and combined to evaluate their fit to the Rasch model. Summary statistics confirmed the reliability of item and person measures, while alignment analysis highlighted conceptual continuity across assessments. The results demonstrated the assessments’ efficacy in consistently measuring student ability across different subgroups and performance levels. Wright maps and item-level statistics provided a comprehensive view of student understanding, identifying areas requiring targeted pedagogical intervention. The study revealed significant growth in student performance from midterm to final exams, with Rasch analysis enabling the establishment of a consistent scale for tracking progress over time. Findings underscored the importance of aligning assessments with learning outcomes and ensuring fairness across diverse student groups. This research highlights the potential of Rasch analysis as a tool for improving the design, implementation, and evaluation of assessments in higher education, particularly in complex subjects like calculus. By integrating these insights, educators can refine assessment practices to better support student learning and achievement.

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 22, Issue 3, March 2026, Article No: em2790

https://doi.org/10.29333/ejmste/18065

Publication date: 11 Mar 2026

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