Konštrukcia a pilotné psychometrické overenie testu porozumenia výrokovej logiky
Construction and Pilot Psychometric Validation of a Propositional Logic Understanding Test
Abstract
This article presents the development and pilot psychometric evaluation of a test assessing secondary school students’ understanding of propositional logic. The test was constructed in two parallel forms, A and B, and focused on basic concepts of propositional logic, logical connectives, negation, implication, propositional formulas, truth tables, and word problems. The pilot study included 368 students, of whom 190 completed form A and 178 completed form B. The equivalence of the forms was examined by comparing total scores. Because the score distributions deviated from normality and a slight ceiling effect was observed, the Mann–Whitney U test was used. No statistically significant difference between the forms was found, and the effect size was negligible, indicating that the forms can be considered comparable in terms of overall performance. Item difficulty analysis showed that students were more successful in straightforward tasks involving terminology and simple symbolic representation. More demanding items involved quantified statements, truth tables, and implication in word problems. Reliability analysis indicated acceptable internal consistency for a short pilot test and identified items requiring revision. The results suggest that the test may serve as a useful diagnostic tool and provide a basis for further refinement and validation.
- Keywords
- propositional logic, test, version, difficulty, reliability
- Classification
- 97E30
References
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Black, P., Wiliam, D. 1998. Assessment and classroom learning. In Assessment in Education: Principles, Policy & Practice. ISSN 0969-594X, roč. 5, č. 1, s. 7–74. https://doi.org/10.1080/0969595980050102
Durand-Guerrier, V. 2008. Truth versus validity in mathematical proof. In ZDM Mathematics Education. ISSN 1863-9690, roč. 40, č. 3, s. 373–384. https://doi.org/10.1007/s11858-008-0098-8 Epp, S. S. 2003. The role of logic in teaching proof. In: The American Mathematical Monthly, ISSN 0002-9890, rok 2003, roč. 110, č. 10, s. 886-899. https://doi.org/10.1080/00029890.2003.11920029
Fehér, Z., Jaruska, L., Szarka, K., Tóthová Tarová, E. 2023. Students’ propositional logic thinking in higher education from the perspective of disciplines. In Frontiers in Education. ISSN 2504-284X, rok 2023, roč. 8, s. 1 – 10. https://doi.org/10.3389/feduc.2023.1247653 Hattie, J., Timperley, H. 2007. The power of feedback. In Review of Educational Research. ISSN 0034-6543, roč. 77, č. 1, s. 81–112. https://doi.org/10.3102/00346543029848 Hawthorne, C., Rasmussen, C. 2015. A framework for characterizing students’ thinking about logical statements and truth tables. In International Journal of Mathematical Education in Science and Technology. ISSN 0020-739X, rok 2015, roč. 46, č. 3, s. 337-353. https://doi.org/10.1080/0020739X.2014.979895 Hoyles, C., Küchemann, D. 2002. Students' understandings of logical implication. In Educational Studies in Mathematics. ISSN 0013-1954, rok 2002, roč. 51, č. 3, s. 193-223. https://doi.org/10.1023/A:1023629608614 Jonsson, B., Granberg, C., Lithner, J. 2020. Gaining mathematical understanding: The effects of creative mathematical reasoning and cognitive proficiency. In Frontiers in Psychology. ISSN 1664-1078, rok 2020, roč. 11, s. 1-16. https://doi.org/10.3389/fpsyg.2020.574366 Kerby, D. S. 2014. The Simple Difference Formula: An Approach to Teaching Nonparametric Correlation. In Comprehensive Psychology. ISSN 2165-2228, rok 2014, roč. 3. https://doi.org/10.2466/11.IT.3 Ketterlin-Geller, L. R., Yovanoff, P. 2009. Diagnostic assessments in mathematics to support instructional decision making. In Practical Assessment, Research, and Evaluation. ISSN 1531-7714, rok 2009, roč. 14, č.16, s. 1-11. https://doi.org/10.7275/vxrk-3190 Kuder, G. F., Richardson, M. W. 1937. The Theory of the Estimation of Test Reliability. In: Psychometrika. ISSN 0033-3123, rok 1937, roč. 2, č. 3, s. 151 – 160. https://doi.org/10.1007/BF02288391
Lithner, J. 2008. A research framework for creative and imitative reasoning. In Educational Studies in Mathematics. ISSN 1573-0816, rok 2008, roč. 67, s. 255-276. DOI 10.1007/s10649-007-9104-2 Markechová, D., Stehlíková, B., Tirpáková, A. 2011. Štatistické metódy a ich aplikácie. Nitra: UKF v Nitre, 2011. 534 s. ISBN 978-80-8094-807-8 Sadler, D. R. 1989. Formative assessment and the design of instructional systems. In Instructional Science. ISSN 0020-4277, roč. 18, č. 2, s. 119–144. https://doi.org/10.1007/BF00117714 Sellers, M. E., Roh, K. H., Parr, E. D. 2021. Student quantifications as meanings for quantified variables in complex mathematical statements. In The Journal of Mathematical Behavior. ISSN 0732-3123, roč. 61, s. 1 – 16. https://doi.org/10.1016/j.jmathb.2020.100802
Schildkamp, K., van der Kleij, F. M., Heitink, M. C., Kippers, W. B., Veldkamp, B. P. 2020. Formative assessment: A systematic review of critical teacher prerequisites for classroom practice. In International Journal of Educational Research. ISSN 0883-0355 , rok 2020, roč. 103, s. 1-16. https://doi.org/10.1016/j.ijer.2020.101602 Thompson, N. 2023 Classical Test Theory: Item Statisticsonline. [Cit. 4. 5. 2026]. Dostupné na https://assess.com/item-statistics-classical-test-theory/
Štátny pedagogický ústav. 2015. Vzdelávací štandard pre učebný predmet Matematika – gymnázium so štvorročným a päťročným vzdelávacím programom. [cit. 13. 1. 2026] Dostupný online: https://www.statpedu.sk/files/articles/dokumenty/inovovany-statny-vzdelavaci-program/matematika_g_4_5_r.pdf