Footprints of the Walking of Numbers: A Dynamic Visualization Task for Understanding Decimal Numbers in Secondary Education

TL;DR

This paper introduces a dynamic visualization task using geometric paths to enhance secondary students' understanding of decimal numbers and their infinite expansions, moving beyond traditional algorithmic approaches.

Contribution

It proposes a novel visualization task with GeoGebra that helps students interpret decimal structures through geometric representations, grounded in a theoretical-didactical framework.

Findings

Students can visually distinguish between terminating, repeating, and irrational decimals.

The task promotes deeper understanding of decimal structures through geometric exploration.

AI tools support computation without replacing mathematical reasoning.

Abstract

The study of decimal numbers in secondary education is often approached from algorithmic perspectives, which limits students' understanding of their structure. This paper presents the task Footprints of the Walking of Numbers, a dynamic visualization proposal aimed at supporting the understanding of decimal numbers through the exploration of their infinite decimal expansions. The task is based on assigning vectors to the decimal digits from 0 to 9, so that the sequence of digits of a number generates a dynamic geometric path in the plane. Through the use of GeoGebra as a visualization environment, students can observe, compare, and interpret traces associated with different types of numbers, such as terminating decimals, repeating decimals, and irrational numbers, identifying visual regularities linked to their decimal behavior. The analysis is developed from a theoretical-didactical perspective, using the Mathematical Working Space as an interpretative lens to characterize the potential of the task design. In addition, the paper discusses the punctual use of generative AI tools exclusively as instrumental support for computation, without shifting the focus away from mathematical reasoning.