This article is an excerpt from a master's thesis developed in Brazil, in which we approach recurrent and linear sequences, given some intriguing particularities in their definitions and the scarcity of discussion of this topic in the literature of the History of Mathematics, especially with regard to its geometric representation. Thus, we aim to…

The German national educational standards state explicitly that students should be enabled to successfully interact with dynamic geometry software. In a feasibility study on providing a standardized assessment instrument by digital means, in order to assess students' mathematical competencies, the implementation of a task with such a dynamic…

GeoGebra is a dynamic software that is frequently used and of increasing importance in mathematics teaching processes in our digital age. Accordingly, in this study a new perspective has been brought to the proofs of the "two square difference identity" expressed for the square, which is a flat polygon, made with different approaches.…

PWW style are presented. The difference of evidence is based on various additional auxiliary constructions, which in itself is a "mathematical art" that the student can master as a result of much practice. The PWW are accompanied by GeoGebra applets containing HINT buttons that allow the student to get step-by-step help in completing the…

Problem solving is one of the high-level thinking skills and essential in teaching mathematical concepts and procedures. The eye-tracking method allows educators to see and interpret different problem-solving behaviours of students. The purpose of this study was to investigate the problem-solving behaviours of university students based on eye…

This article investigates the knowledge arising in mathematics teachers' planning of how to manage transitions within and beyond dynamic geometry environments in the topic of circle theorems. The notion of situated abstraction is used to elaborate the central TPACK construct within mathematics education and address previous criticisms of the…

This article reports on the design and implementation of a didactic sequence in the frame of a design-based research study. The research aim is to test the hypothesis that affordances of dynamic geometry may support students' awareness of logical relationships between geometrical properties of constructed figures. We elaborate on the task design…

Background: Teachers must have the skills to find, select, design and use technology-based mathematical activities that focus on high-level cognitive demands--supporting student reasoning. However, they experience various difficulties in creating, planning and making decisions about how and when to utilize technological affordances. Objectives:…

This article focuses on the possible relationship between predictions, developed during the resolution of geometrical tasks within a Paper-and-Pencil Environment (PPE), and subsequent explorations within a Dynamic Geometry Environment (DGE). Building on Fischbein's Theory of Figural Concepts, and to gain insight into the transition of predictions…

Previously defined profiles for using a computer algebra system (CAS) describe prototypical uses of such a tool. When students use a dynamic geometry environment (DGE), however, new opportunities arise for transitions within and beyond the DGE. In this article, CAS profiles are used to explore students' uses of a DGE. Four cases of students, all…

The aim of this study is to show how the GeoGebra software-supported collaborative learning environment contributes to a group of students using multiple representations and reaching generalisations while solving problems collectively. Blending individual and collaborative learning activities were carried out with a learning method called ACODESA…

The aim of the study informing this paper was to investigate pre-service teachers' (PSTs') approaches to task design, posing the research question: How do pre-service teachers respond when they are asked to design an exploratory task using GeoGebra for 8th grade students? The research study and this paper focus on the PSTs' design stories rather…

Aim/Purpose: This study presents some activities that integrate computational thinking (CT) into mathematics lessons utilizing GeoGebra to promote constructionist learning. Background: CT activities in the Indonesian curriculum are dominated by worked examples with less plugged-mode activities that might hinder students from acquiring CT skills.…

This study examines a Technology, Pedagogy, Content Knowledge (TPACK) training framework for pre- and in-service mathematics teachers that enables them to experience inquiry-based learning as learners in a dynamic geometry environment that serves as a mathematics laboratory. We investigate the effect of this experience on the teachers' TPACK,…

This study investigates whether Vietnamese students face specific challenges when visualizing skew versus intersecting lines and whether using the anaglyph feature of GeoGebra can help overcome these difficulties. Employing a design-based research approach over four phases with 12th-grade students, the study involved tasks in traditional…