Understanding Ratio Through the Pirie-Kieren Model

Resumo

Background: Research in educational mathematics has shown that elementary school students poorly understand the concept of ratio due to the difficulties that emerge from its interpretation as a fraction. Objective: Therefore, based on the Pirie-Kieren theoretical model, we intend to analyse the comprehension process that appears when students solve tasks on ratio. Design: The approach is qualitative, and the research design was a case study. We used the field observation technique. Context and participants: The study was done in a primary school in the state of Guerrero, Mexico. The cases involved four students (11-12 years old) enrolled in the 6^th grade. Data collection and analysis: The data was collected through a questionnaire (task) and an interview. For data analysis, the eight levels of understanding of the theoretical model were used. Results: The results indicate that the students do not manage to formalise their comprehension of the concept of ratio because of difficulties in applying mathematical strategies correctly when solving the proposed tasks. Conclusion: The results indicate that for students to reach higher levels of comprehension, it is necessary to carry out the dynamic process of repeating between levels as it makes one reflect on what is required to advance comprehension.