Proof, as a central and integral part of mathematics, is an essential component of mathematical education and is considered as the basic procedure for revealing the truth of mathematical propositions and for teaching productive reasoning as part of human civilization. Is there therefore room for conjectures in mathematics? In this paper after…

Geometry is a strand of mathematics that can benefit individuals in many areas of life. Test results, such as the TIMSS results, indicate that geometry is an area for growth among American students. With a need for students to better understand geometry, several academic standards have been created to direct geometry instruction in the United…

Conjecture formulation is crucial to mathematics education. Therefore, this study aimed to evaluate challenges prospective mathematics teachers (PMTs) encounter when using GeoGebra to formulate geometrical conjecture. A qualitative case study was conducted with an exploratory strategy to provide a complete comprehension of the occurrence. Six…

Unprecedented investments are being made in mathematics tutoring interventions for K-12 students, but results from these interventions are not always promising. Traditional online or distance math tutoring can treat learning as disembodied, and not give learners access to embodied resources like gestures, movements, and actions. Virtual Reality…

This study was conducted to optimize the designs of learning guides embedded in a computer-based simulation environment. The research was based on the Cognitive Theory of Multimedia Learning and Cognitive Load Theory. We investigated computer simulations under four conditions that combined representation and imagination learning strategies. This…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

Access to body-based resources has been shown to augment cognitive processes, but not all movements equally aid reasoning. Interactive technologies, like dynamic geometry systems (DGS), potentially amplify the link between movement and geometric representation, thereby deepening students' understanding of geometric properties. This study…

In this paper, we introduce a technology-enhanced pedagogical sequence for supporting lower secondary school students' sense-making of the concept of volume in a non-procedural and non-formula-driven way. Specifically, we illustrate a novel approach of using dynamic geometric environment (DGE) to introduce the meaning of volume and then deriving…

The study material on circle areas is contextually oriented and aids students in comprehending their surrounding environment. Higher-order thinking skills are imperative for the success of circular learning, as they help students grasp concepts holistically and solve concept problems. "What-if" questions can enhance students'…

This article presents a didactic situation focused on geometric reasoning using 3D GeoGebra, using the concepts Theory of Didactical Situations (TDS). The objective of this work is to bring a didactic proposal for the teaching of Spatial Geometry, working with the students' geometric perception, oriented and elaborated based on the dialectic of…

The paper describes two versions of an inquiry-based activity in geometry, designed as a game between two players. The game is inspired by Hintikka's semantic game, which is a familiar tool in the field of logic to define truth. The activity is designed in a dynamic geometry environment (DGE). The inquiry is initially guided by the game itself and…

Advancement of self-regulation during complex problem solving and the development of strategical reasoning are among the central educational goals linked to 21st century skills. In this paper we introduce the notion of "Stepped Tasks", which are specially designed in Top-Down structure to achieve these goals in mathematics instruction.…

Gifted students have potential to improve countries and this potential can be revealed and developed in schools where they spend most of their times with other regular students. However, these classrooms have some limitations for them; hence, they need some differentiated activities. Usage of dynamic geometry in mathematics lessons could be an…

This article aims to examine the impact of an online learning environment enriched with computer activities on geometry achievement and geometric habits of mind (GHoM). The study includes reflections from an online application of a one-term computer-aided mathematics teaching course in which the participants were preservice teachers (PTs) enrolled…

Understanding spatial reasoning is important to success in mathematics. This article shows how the proficiency strands in the "Australian Curriculum: Mathematics" provide the tools needed for effective teaching and learning of spatial thinking.