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.

本文介绍了一项由一组 16 岁学生开发的定性研究，他们被要求估计有界曲面上的大量元素。以现实数学教育框架为参考，我们向学生展示了一个由四个不同任务组成的活动序列——每个任务都有不同的现实背景，它们是同一估计问题的变体。我们的数据包括学生在完成任务时提交的书面报告。学生为解决任务而部署的策略包括与测量和比例概念相关的程序的嵌入。对于每项任务，我们通过树状图形式的视觉资源呈现策略的特征。我们整合了四个任务的树状图，为一般问题生成了一个树状图。这使我们能够讨论上下文在学生报告使用的策略中的作用。