As children progress through the elementary grades, they are expected to begin to use attributes of shapes to name and classify them. When listening to children talk about shapes, it becomes clear that the process of learning to reason geometrically is complex. Recognizing the complex nature of students' geometric reasoning, the authors present in…

We present a theoretical study that allows us to attempt framing in an embodied perspective the effectiveness of the drawing robot GGBot in the learning of geometry. The aim of the article is to set the intertwining of activity, semiotics, perception, and knowledge at the crossover of Radford's theory of objectification (TO) and Borba and…

This article uses a cultural-developmental framework to illuminate the interplay between collective and individual activity in the mathematical reasoning displayed in a university Masters level lesson on fractals. During whole class and small group discussions, eleven students, guided by an instructor, engage in inductive reasoning about the area…

The need to develop consistent theoretical frameworks for the teaching and learning of discrete mathematics, specifically of graph theory, has attracted the attention of the researchers in mathematics education. Responding to this demand, the scope of the Van Hiele model has been extended to the field of graphs through a proposal of four levels of…

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…

Limited literature addresses how elementary preservice teachers (PSTs) can advance their thinking about hierarchical geometric relationships. Informed by a commognitive perspective, we investigated this phenomenon as a matter of discursive change, focusing on word use, visual mediators, and narratives. We report on a teaching experiment involving…

This article is an advanced theoretical study as a result of a chapter from the first author's PhD study. The aim of the article is to discuss the relationship between commognition and the Van Hiele theory for studying discourse during Euclidean geometry problem-solving. Commognition is a theoretical framework that can be used in mathematics…

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…

In this paper, we examine the importance of building instructional units that incorporate metacognition intent processes that contribute to the development of geometric thinking. We show that the implementation of metacognition processes in the initial stages of constructing tailored instructional units will improve students' geometric ability.…

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'…

As a multifaceted concept, the learning of angle concepts takes years to achieve and is beset with challenges. This paper explores how the processes of constructing and validating a learning progression in geometric reasoning can be used to generate targeted teaching advice to support the learning of angle concept. Data from 1090 Year 4 to Year 10…

Despite significant research exploring students' quantitative reasoning, few studies have explored the semiotic processes that mediate its development. In this report, we present a case study to show how one student constructed a semiotic chain for a quantity as he worked with a mathematical task. Importantly, we connect frameworks for…

This paper aims to discuss the use of Brousseau's Theory of Didactical Situations in mathematics (TDS) for eighth-graders to explore the concept of triangle inequality in Euclidean geometry. Data sources included observation notes, video recordings of lessons, and students' written work. Data analysis was done through a deductive content analysis…

Spatial thinking has roles to facilitate learners to remember, understand, reason, and communicate objects and the connections among objects that are represented in space. This research aims to analyze the spatial thinking process of students in constructing new knowledge seen from the field-independent cognitive style learners based on…

Geometry is one of the basic skills to be mastered in Malaysian mathematics education. However, there is not much information on geometry attainment of the elementary school students based on van Hiele's levels. The purpose of this study was to determine the van Hiele's levels of geometric thinking among the elementary school learners. Three…