Costa Rican students’ proportional reasoning and comparing probabilities in spinners

This research aimed to relate Costa Rican students (11-16-year-olds) competence to compare probabilities in spinners and proportional reasoning in the comparison of ratios. We gave one of two questionnaires to a sample of 292 students (grade 6 to grade 10) with three probability comparison and three ratio comparison problems each. Globally both questionnaires cover six different proportional reasoning levels for each type of problem. Additionally, each questionnaire contains two comparison probabilities items intended to discover a specific bias. We analyze the percentages of correct responses to the items, strategies used to compare probabilities per school grade, and students’ probabilistic reasoning level. The results confirm more difficulty in comparing ratio than in comparing probability and suggest that the reasoning level achieved is lower than established in previous research. The main bias in the students’ responses was to consider the physical distribution of colored sectors in the spinners. Equiprobability and outcome approach were very scarce.