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

Abstract

Statistics and probability constitute a key strand of Vietnam's 2018 General Education Curriculum in Mathematics. Probability can be challenging for upper secondary students because of the abstract nature of probabilistic language and the conceptual ambiguity associated with 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 activities involving random simulations using Excel. Four learning activities were designed and implemented in two Grade 12 classes in Hue and Da Nang. The findings indicate that students not only engaged meaningfully within each probability working space but also established clear connections and transitions among FPWS, SPWS, and CPWS. Excel-based simulations helped students generate reasonable subjective estimates and strengthen classical probabilistic reasoning, whereas theoretical calculations enabled them to revise their subjective estimates and recognize the convergence of relative frequency toward theoretical probability. The study demonstrates the pedagogical value of technology-enhanced simulation in school probability education.