Different Ways of Using GeoGebra in Mathematical Problem-Solving Beyond the Classroom: evidences of techno-mathematical fluency

Abstract

This paper addresses a mathematical problem-solving activity with technology in the context of an online beyond school competition. The study aims to describe the underlying aspects of simultaneously resorting to mathematical and technological knowledge in such an activity, focusing on the development of conceptual models for the solutions of problems. The research, following a qualitative approach, is based on the analysis of a set of digital solutions produced with GeoGebra. Main results show that the software is used freely and willingly to structure and amplify the mathematical thinking, influencing the solving and expressing processes. Besides supporting the materialization of the problematic situations and promoting the transformation of static ideas into dynamic ideas, it drives mathematization processes that support quite different conceptual models. The fundamental features that lead to different ways of solving-and-expressing a given problem with GeoGebra are explained in terms of the techno-mathematical fluency of each participant.

Key-Words:
Techno-Mathematical Fluency; GeoGebra; Conceptual Models; Problem Solving