Secondary School Students’ Performances on Ratio Comparison Problems

Resumo

Background: Proportional reasoning is a fundamental part of the Primary and Secondary Education curriculum. However, research has shown that both primary and secondary students find it difficult to reason proportionally. Most of these studies have used missing-value proportional problems, so studies focused on how primary and secondary school students use the concepts of ratio and proportion when solving ratio comparison problems are scarce. Objectives: This study characterises how secondary school students (12-16 years old) solve ratio comparison problems. Design: The instrument used to collect data was two ratio comparison problems with intensive quantities that could be solved as a couple of expositions or compositions. Settings and participants: 248 secondary education students from 7^th to 10^th grade (12-16 years) solved these problems. Data collection and analysis: An inductive analysis was carried out in order to identify categories of students’ performances. Results: Three types of students’ performances were identified depending on whether the students showed an understanding of the relative quantities: relative comparison, relative trend, and non-relative comparison. The subcategories identified in the relative trend performance showed difficulties with the critical components of the problems: difficulties with the referent and with the norming techniques. Conclusions: Results showed that, at the end of secondary education, students’ difficulties in understanding the ratio concept and the intensive quantities persisted.