Emanuela Botta, Stefania Pozio


Incorrect responses to an item requiring solving a geometry problem were analysed as part of a research project on an adaptive computer-based test assessing mathematical ability. The item bank was calibrated by using the Rasch model (1960) and the item revealed to be of a medium-high level of difficulty. Analyses of incorrect responses allowed to identify and hypothesize students’ problem-solving strategies. The responses were categorised using a two-level procedure, related to the basic steps of problem-solving processes. Errors were fairly distant from the correct answer and showed different levels of reasoning consistency. ANOVA was conducted on the mean ability of students to reveal the differences between the categories and relate the students’ abilities to the error. The results show that the ability is correlated to motivation to reach the solution and that there are significant differences in the mean ability between the different categories identified.

Parole chiave

Adaptive Test, MST Test, mathematical ability, problem solving

Full Text


Riferimenti bibliografici

Borasi, R. (1987). Exploring mathematics through the analysis of errors. For the learning of Mathematics, 7(3), 2-8.

Botta, E. (2021) a. Sperimentazione di un modello adattativo multilivello per la stima delle abilità in matematica nelle rilevazioni su larga scala, Roma: Nuova Cultura

Botta, E. (2021) b. Percorsi secondari di una prova adattativa multilivello e valutazione formativa. Excellence and Innovation in Learning and Teaching-Open Access, 6(2).

Chappell, M. F., & Thompson, D. R. (1999). Take Time for Action: Perimeter or Area? Which Measure Is It?. Mathematics Teaching in the Middle School, 5(1), 20-23.

Granberg, C. (2016). Discovering and addressing errors during mathematics problem-solving—A productive struggle? Journal of Mathematical Behavior, 42, 33-48.

Hambleton, R. K., Zaal, J. N., e Pieters, P. (1991). Computerized adaptive testing: Theory, applications, and standards. In R. K. Hambleton e J. N. Zaal (Eds.), Advances in educational and psychological testing, Norwell, MA: Kluwer, pp. 341–366

Jonsson, B., Norquist, M., Liljekvist, Y., & Lithner, J. (2014). Learning mathematics through algorithmic and creative reasoning. Journal of Mathematical Behavior, 36, 20-32

Kahneman, D. (2012). Pensieri lenti e veloci. Edizioni Mondadori, Milano, 2012

Luecht, R., Brumfield, T., e Breithaupt, K. (2006). A testlet assembly design for adaptive multistage tests. Applied Measurement in Education, 19(3), pp. 189-202.

Luecht, R. M., e Nungester, R. (1998). Some practical examples of computer-adaptive sequential testing. Journal of Educational Measurement, 35, 229-249

Moyer, S.P. (2001). Using representations to explore perimeter and area. Teaching Children Mathematics, vol 8(1), pag. 52 – 59

Ryan, J. & Williams, J. (2007). Children’s mathematics 4_15: Learning from errors and misconceptions. Maidenhead, England: Open University Press

Rasch G. (1960), Probabilistic Models for Some Intelligence and Attainment Tests. Danish Institute for Educational Research, Copenhagen

Sireci, S. G. (2004). Computerized-adaptive testing: An introduction. In J. Wall e G. Walz (Eds). Measuring up: Assessment issues for teachers, counselors, and administrators, Greensboro, NC: CAPS Press, pp. 685-694

Weiss, D. J. (1985). Adaptive testing by computer. Journal of consulting and clinical psychology, 53(6), p. 774



  • Non ci sono refbacks, per ora.

Copyright (c) 2022 Giornale Italiano di Educazione alla Salute, Sport e Didattica Inclusiva

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.