Relating students’ proportional reasoning level and their understanding of fair games

This paper analyzes the relationship between proportional reasoning and understanding fair games in Costa Rican students. We conducted a quantitative and qualitative analysis of the answers to six items on comparing ratios of increasing difficulty level and another item on prize estimation in a fair game. We describe the strategies employed and the semiotic conflicts detected in 292 Costa Rican students from Grades 6 to 10 (11-16-year-olds), comparing the findings with those established in previous research. The results show an increase in the level of proportional reasoning with the grade, although the age at which the higher levels are reached is lower than that assumed by Noelting. The percentage of students applying correct strategies in the fair game problem also increases with grade, and a relationship between the understanding of fair game and the level of proportional reasoning is observed.