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The pandemic emergency has almost forced the transition from face-to-face to remote evaluation. Starting from the results of the research in Mathematics Education, this exploratory work focuses on how to design effective closed-ended questions of different types, capable of reliably assessing mathematical learning outcomes, especially in terms of the involved competencies. We also investigate how to aggregate the questions into Moodle quizzes able to effectively replace the traditional open written exam. We propose a three-dimensional theoretical model, which takes into account the various types of questions, expected learning outcomes, and mathematical arguments, to shed light on the problems of validity, reliability, balance, and correctness of closed-ended quizzes. We discuss the results of the first implementation of the model within a Linear Algebra course for engineering freshmen.


Closed-ended Quiz Assessment University Mathematics Moodle

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How to Cite
Albano, G., & Telloni, A. I. (2021). From traditional exams to closed-ended quizzes: an exploration towards an effective assessment in mathematics at university level. Journal of E-Learning and Knowledge Society, 17(2), 45-55.


  1. Albano, G., and Ferrari, P.L. (2008), Integrating Technology and Research in Mathematics Education: The Case of E-Learning, In F.J. García-Peñalvo (Ed.), Advances in E-Learning: Experiences and Methodologies (pp.132-148). Hershey, NY: InformationScienceReference.
  2. Albano, G. and Ferrari, P.L. (2013), Mathematics education and e-learning: meaningful use of the quiz-modules, In E. Faggiano & A. Montone (Eds.). ICTMT 11 Conference Proceedings (pp.53-58).
  3. Albano G., Pi,erri, A. & Sabena, C. (2020), Enhancing formative assessment practices in undergraduate courses by means of online workshops, In: Proceedings of the 14th International Conference on Technology in Mathematics Teaching – ICTMT 14 DuEPublico, Duisburg-Essen Publications Online (pp. 155-162).
  4. Chakrabarrty, S.N. (2013) Best Split – half and Maximum Reliability, Journal of Research & Method in Education 3 (1), 1-8.
  5. Darlington, E. (2014), Contrasts in mathematical challenges in A-level Mathematics and Further Mathematics, and undergraduate mathematics examinations. Teaching Mathematics and its Applications, 3, 213–229.
  6. Dubinsky, E. (1997), On Learning Quantification, Journal of Computers in Mathematics and Science Teaching. 16 (213), 335-362.
  7. Duval, R. (2006), A cognitive analysis of problems of comprehension in a learning of mathematics, Educational Studies in Mathematics, 61, 103-131.
  8. Ferrari, P.L. (2019), Argomentare a scuola: intrecci fra matematica e lingua, L'insegnamento della matematica e delle scienze integrate, vol.42 A-B, n.5, 611-625.
  9. Ferrari, P.L. (2020). Educazione matematica, lingua, linguaggi. Costruire, condividere e comunicare matematica in classe. UTET Università.
  10. Garuti, R. & Martignone, F. (2019), Assessment and argumentation: an analysis of mathematics standardized items, In: U.T. Jankvist, M. Van den Heuvel-Panhuizen & M. Veldhuis (Eds.). Proceedings of CERME 11 (pp. 4075-4082) Utrecht: Freudenthal Group & Institute, Utrecht University and ERME.
  11. Iannone, P. (2020a), Assessing Mathematics at University: Covid-19 and beyond. London Mathematical Society, Newsletter, Issue 490, september 2020, 34-40.
  12. Iannone, P. (2020b), Assessment of mathematics in the digital age: the case of university mathematics. In: A. Donevska-Todorova, E. Faggiano, J. Trgalova, Z. Lavicza, R. Weinhandl, et al. (Eds.), Proceedings of the Tenth ERME Topic Conference (ETC 10) on Mathematics Education in the Digital Age (MEDA).
  13. Livingston, S. A. (2018). Test reliability—Basic concepts (Research Memorandum No. RM-18-01). Princeton, NJ: Educational Testing Service.
  14. Niss, M., and Højgaard, T. (2019), Mathematical competencies revisited, Educational Studies in Mathematics, 102, 9–28.
  15. Sangwing, C. (2013), Computer Aided Assessment of Mathematics, Oxford University Press.
  16. Scalise, K. and Gifford, B. (2006), Computer-Based Assessment in E-Learning: A Framework for Constructing “Intermediate Constraint” Questions and Tasks for Technology Platforms, Journal of Technology, Learning, and Assessment, 4.
  17. Skemp, R. (1976), Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
  18. Telloni, A.I. (2021), Design of individualized digital activities fostering strategic planning in linear algebra, In: G. Mele, P. Magnaghi-Delfino & T. Norando (Eds.) Faces of geometry II. Lectures Notes in Networks and Systems, 172, pp. 287-298. Springer International Publishing.
  19. Trinchero, R. (2006), Valutare l’apprendimento nell’e-learning, Erickson.
  20. Watson, K., Wawro, M., Zandieh, M & Kerrigan, S. (2017), Knowledge about student understanding of eigentheory: Information gained from multiple choice extended assessment, Proceedings of the 20th Annual Conference on Research in Undergraduate Mathematics Education, pp. 311-325.