A Comparative Study of Proportional reasoning of Costa Rican and Spanish students in ratio comparison problems

[Objective] This study seeks to evaluate the level of proportional reasoning and strategies in ratio comparison problems of Costa Rican and Spanish students between 11 and 16 years old. [Methodology] Using an interpretative research approach, 704 students were given one of two questionnaires with three items on ratio comparison (a total of six different levels of proportional reasoning, according to Noelting). The percentage of correct answers and levels of proportional reasoning, and the result of a content analysis of correct and incorrect strategies are presented. [Results] The majority of students correctly answered the problems with the lowest Noelting proportional reasoning level (IA to IIA), with this proportion decreasing in grades 6 to 8 of General Basic Education as the proportional reasoning level of the problem increased. Similar results were obtained with respect to correct strategies. The most frequent incorrect strategies were the comparison of the first terms of ratios and additive comparisons. Virtually all students reached the first two proportional reasoning levels of Noelting, and as the course progressed, a higher proportion attained the following levels of reasoning, but few students achieved level IIIA, corresponding to formal operations, even in the highest grade (grade 10). [Conclusions] It was concluded that it is necessary to reinforce the teaching of reasoning about comparison of ratios, and to take it into account in the mathematical topics based on this reasoning.