The Van Hiele model of geometric reasoning establishes five levels of development, from level 1 (visual) to level 5 (rigor). Despite the fact that this model has been deeply studied, there are few research works concerning the fifth level. However, there are some works that point out the interest of working with activities at this level to promote…

Although augmented reality has become one of the most commonly used materials that support learning, especially in learning geometric concepts, it is avoided to be used in the lessons due to its complex structure. At that point, artificial intelligence working as a personal assistant in many fields can help us learn to produce our own model with…

Creative thinking transforms existing information, either from long-term memory or external sources, into new representations and innovative ideas. Creative thinking is an activity that processes received information to produce new representations and innovative ideas. Developing this skill is essential for students; however, recent research has…

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.…

How to influence and assess whether students engage in conceptual thinking are longstanding methodological problems in mathematics education. Recently, eye-tracking technology has fueled a discussion on whether eye movement analysis can support valid inferences about mathematical thinking. This study investigates whether eye movement analysis can…

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 study identifies characteristics of polygon class learning opportunities for 8-9-year-old children during the whole-class instruction. We consider the interplay between the geometrical tasks demanding different ways of reasoning, features of children's geometrical thinking, and the teacher's moves to identify characteristics of learning…

Current research indicates the presence of highly skilled and motivated students with robust computational thinking backgrounds seeking opportunities to leverage their expertise in driving innovation and success in this era. These studies also reveal that students' computational thinking skills vary widely depending on educational resources,…

As an interdisciplinary and multicultural educational framework takes the centrality of the delivery of 21st-century education across all levels, this study attempts to address the competencies that prospective and neophyte teachers need to possess to effectively design contextualized education. Through stepwise multiple regression analysis,…

Background/Objective. This study aimed to assess the effectiveness of a multisensory approach based on the CRA framework in enhancing geometric thinking skills among fourth-grade students with learning difficulties in mathematics. It examined the relationship between sense preferences and performance and investigated how interactions among those…

In a previous article, "The Shape of Reasoning: Using Geometry to Promote the Reasoning Proficiency Strand" (EJ1286217), the author put forward the argument that no medium is more powerful than geometry as a vehicle for developing the mathematical proficiency strand of Reasoning. Because geometry is so visual and tactile, the…

The role of probability in curricula for children has fluctuated greatly over the past several decades. Recently, some countries have removed probability from their preschool and primary curricula, and others have retained it. One reason for such lack of agreement is that theory about early probability learning is still relatively new and under…

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…

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…

Angularity is a persistent quantity throughout K-12+ school mathematics, and many studies have shown that individuals often conflate angularity with linear attributes (e.g., the length of an angle model's sides). However, few studies have examined the productive ways in which students might reason about angularity while attending to linear…