Proportional Reasoning in Solving Sample Space Quantification and Probability Comparison Tasks by Primary School Students - Burgos, María (2025)
Proportional reasoning is considered a key element in probabilistic reasoning. Various studies have suggested that insufficient proportional reasoning may be the cause of many errors made by students when dealing with probability problems. [Objective] The aim of this study is to identify the proportional reasoning used by sixth grade students (11-12 years old) when solving sample space quantification and probability comparison tasks. [Methodology] Through an exploratory qualitative approach, the responses of 47 Spanish students from a public school were analyzed in relation to two problems: one focused on comparing probabilities (ratio comparison), and the other on determining the composition of a box to generate equal probabilities (proportional distribution). The analysis of the solutions using semiotic functions allows identification of relationships between objects involved in the tasks and the characteristic elements of proportional reasoning, facilitating interpretation of students’ errors. [Results] The results show that the students struggled to select the box with the highest probability of success, which indicates insufficient proportional reasoning. However, most students were able to correctly determine the composition of a box needed to maintain a given probability, whereas few could justify their reasoning based on probability or proportionality. [Conclusions] The results contrast with previous research findings and show previously unidentified difficulties in solving proportional distribution problems in a probabilistic or arithmetic context.