Khó khăn nhận thức của học sinh trung học phổ thông khi kết nối không gian làm việc xác suất thực nghiệm và cổ điển qua mô phỏng bằng Excel

Tóm tắt

Although simulation and digital technologies are widely regarded as effective tools for teaching probability, many students still encounter difficulties in connecting experimental probability and theoretical probability. This study employs the Mathematical Working Spaces (MWS) framework to investigate students’ cognitive difficulties when establishing connections between the Frequentist Probability Working Space (FPWS) and the Classical Probability Working Space (CPWS) through Excel-based simulations. The study was conducted within a design research approach using a qualitative experimental methodology involving Grade 12 students in Hue and Da Nang, Vietnam. Data were collected from students’ worksheets, Excel simulation files, and semi-structured interviews. Two representative cases were selected and analyzed through the three dimensions of MWS: semiotic, instrumental, and discursive. The findings revealed three major types of cognitive difficulties: difficulties in coordinating probability representations, including frequency, relative frequency, and probability; an imbalance between instrumental genesis and discursive genesis; and the dominance of empirical references in students’ mathematical work when connecting FPWS and CPWS. The findings contribute to a deeper understanding of the nature of students’ difficulties in learning probability from an MWS perspective and suggest the need to design instructional activities that place greater emphasis on fostering connections among empirical data, technological tools, and probabilistic reasoning.