Fuzzy Analysis of Probability Framework Development in Eleventh-Grade Students at a Colombian School (Journal SCIENCEVOLUTION, 2025)
This research analyzes the levels of the probability notion in eleventh-grade students at an educational institution in Colombia, employing a fuzzy logic to evaluate their progress across the Intra, Inter, and Trans levels defined by APOE theory. A genetic decomposition of the probability concept was designed, structuring a sequence of didactic activities implemented in the classroom under the ACE Cycle (Activities, Class, Exercises) approach. The study was conducted using a mixed exploratory-descriptive approach, utilizing a structured questionnaire and interviews as data collection instruments. The results showed that 72.7% of the students reached Inter or Trans levels, while 27.3% remained at the Intra level, displaying limitations in understanding compound events, sample space, and the contextual application of probability. Common errors identified included the equiprobability bias and the mechanical use of formulas. The activities designed based on APOE theory facilitated the transition towards more complex cognitive structures, and the fuzzy metric enabled more.
Keywords: APOS; Metric Fuzzy; Fuzzy Logic; Probability; Genetic Decomposition