Typology and complexity assessment of calculation problems based on fuzzy logic

UDC 37-0444.3:005.6
DOI 10.20339/AM.02-26.055

Artem A. Zaripov, Postgraduate student, Major in 6.8.7. “Methodology and Technology of Professional Education”, Faculty of Pedagogical Education, Lomonosov Moscow State University, https://orcid.org/0009-0008-6794-5048, e-mail: a_zaripov9622@mail.ru

Olga V. Andryushkova, Cand. Sci. (Chemistry), Docent, Associate Professor, Head of the Laboratory of Methods of Teaching Chemistry, Department of General Chemistry, Faculty of Chemistry, Lomonosov Moscow State University, Russia; https://orcid.org/0000-0002-1566-3427; e-mail: andryushkovaov@my.msu.ru

This article examines an approach to constructing Fond of Appraisal Monitoring (FAM) based on a typology of learning tasks and a fuzzy assessment of their complexity. It substantiates the need to move from disparate sets of tasks to structured pools in which each task is described not only by content but also by difficulty level. A model is proposed in which task complexity is represented by a three-component structure (subject, mathematical, and heuristic components), and integral complexity is determined using fuzzy logic methods.

A description of the practical implementation of the model is provided: selecting and classifying tasks, engaging instructors to assess complexity components, constructing membership functions and a fuzzy inference rule base, calculating the integral complexity index, and incorporating it into the AST structure. It demonstrates how the obtained results enable task ranking and the design of assessment materials. The possibility of transferring the approach to other academic disciplines is discussed.

Keywords: Fond of Appraisal Monitoring; educational tasks; task typology; fuzzy set theory; fuzzy logic

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