Statistics education research, Comparing, Comparing probabilities, Proportional reasoning, Reasoning levels, Secondary students


We present an exploratory study of Costa Rican and Spanish students’ (11–16-year-olds) competence to compare probabilities in urns and compare ratios in mixture problems. A sample of 704 students in Grades 6 through to Grade 10, 292 from Costa Rica and 412 from Spain, were given one of two forms of a questionnaire with three probability comparison and three ratio comparison problems each. The full questionnaire consisting of both forms covers six different proportional reasoning levels for each type of problem. We analysed the percentages of correct responses to the items and the strategies used by students in each grade and in each country. The results suggest students had the highest difficulty in comparing probabilities for items at the same proportional reasoning level. The results also point to the probabilistic biases in students’ responses, although these biases were less frequent than in previous research.


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