The Role of Context for Characterising Students’ Strategies when Estimating Large Numbers of Elements on a Surface

This paper presents a qualitative study developed with a group of 16-year-old students who were asked to estimate large numbers of elements on a bounded surface. Taking the realistic mathematics education framework as a reference, we presented the students with an activity sequence comprised of four different tasks—each one with a different realistic context, which were variations of the same estimation problem. Our data comprises the written reports that the students submitted on completing the tasks. The strategies deployed by the students to solve the tasks consisted in the incardination of procedures related to the concepts of measurement and proportionality. For each task, we present the characterization of the strategies through a visual resource in the form of a tree-like diagram. We integrated the treelike diagrams of the four tasks to generate a tree-like diagram for the general problem. This allowed us to discuss the role of context in the strategies the students reported having used.