BA KHÔNG GIAN LÀM VIỆC XÁC SUẤT VÀ SỰ KẾT NỐI TRONG CÔNG VIỆC TOÁN HỌC CỦA HỌC SINH TRUNG HỌC PHỔ THÔNG

Abstract

Probability constitutes a key knowledge strand in the 2018 Vietnamese upper secondary mathematics curriculum. However, current textbooks predominantly adopt the classical approach, while the frequentist and subjective perspectives receive limited attention. This imbalance restricts students’ opportunities to develop a comprehensive understanding of probability. Drawing on the Theory of Mathematical Working Spaces (MWS), this study distinguishes three probability working spaces - the Classical Probability Working Space (CPWS), the Frequentist Probability Working Space (FPWS), and the Subjective Probability Working Space (SPWS) - as an analytical framework for examining students’ mathematical work in probability learning situations involving random simulation with Excel spreadsheets. Four learning situations were designed and implemented in two grade 12 classes in Hue and Da Nang. In these activities, students used Excel to simulate random events, compute probabilities, formulate subjective probability estimates, and compare outcomes across different probability models. Data collected from group work and semi-structured interviews were analyzed using the three dimensions of MWS: instrumental genesis, semiotic genesis, and discursive genesis. Findings indicate that students not only engaged meaningfully within each individual probability working space but also exhibited clear connections and transitions among FPWS, SPWS, and CPWS. Experiences with Excel-based simulation supported students in generating reasonable subjective estimates and strengthening classical probabilistic reasoning, while theoretical probability calculations enabled students to adjust their subjective probability estimates and recognize the convergence between relative frequency and theoretical probability. The study clarifies the role of the three probability working spaces in fostering a deeper understanding of probability among secondary students and highlights the pedagogical value of technology-enhanced simulation in the teaching and learning of school probability.