We previously observed students gesturing during a symmetry and group theory activity. This prompted additional interviews, wherein we attempted to understand the semiotic function of these gestures. We report here on the gestures that students used in this context to represent symmetry elements, symmetry operations, and other related ideas. In…

This study provides a framework for explaining the way individuals might construct the final result of infinite iterative processes in a geometrical context. To this end, 30 undergraduate students were interviewed. The analysis of the data collected yielded two different views: first, there were those who believed that the presented infinite…

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…

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…

Symmetry studies in autism are inconclusive possibly due to different types of stimuli used which depend on either local or global cues. Therefore, this study compared symmetry detection between 20 autistic and 18 non-autistic adults matched on age, IQ, gender and handedness, using contour integration tasks containing open and closed contours that…

While some researchers place negative numbers on a so-called extended mental number line to the left of positive numbers, others claim that negative numbers do not have mental representations but are processed through positive numbers combined with transformation rules. We measured spatial associations of negative numbers with a modified implicit…

We examined how high school students use their cognitive and metacognitive skills in the geometry problem-solving process. This research employed a mixed-methods descriptive sequential design. Data were collected in the 2019-2020 academic year at secondary education institutions in the central districts of Adana, Türkiye. Using stratified…

Task-relevant actions can facilitate mathematical thinking, even for complex topics, such as mathematical proof. We investigated whether such cognitive benefits also occur for action predictions. The action-cognition transduction (ACT) model posits a reciprocal relationship between movements and reasoning. Movements--imagined as well as real ones…

Geometric habits of mind (GHoM) are the approaches that individuals use to solve geometry problems. This study aimed to determine the effect of dynamic geometry software (DGS) in activating the GHoM of pre-service mathematics teachers. The study was conducted with six teacher candidates who were enrolled in a semester-long course titled…

The present study aims to examine mathematical creativity in students' work in geometry. Research conducted was based on two aspects: (a) examining the influence of geometrical figure apprehension on the production of multiple solutions and (b) how the necessity to construct auxiliary lines in the given shape promotes the production of multiple…

This study was conducted to reveal potential sources of students' difficulty and misconceptions about geometrical concepts with the help of eye tracking. In this study, the students' geometrical misconceptions were explored by answering the questions on the geometry test prepared based on the literature and test-taking processes and represented…

In mathematics, problem-solving can be considered to be one of the most important skills students need to develop, because it allows them to deal with increasingly intricate mathematical and real-life issues. Often, teachers attempt to try to link a problem with a drawn diagram or picture. Despite these diagrams, whether given or constructed, the…

Many test items use both an image and text, but present them in a spatially separate manner. This format could potentially cause a split-attention effect in which the test taker's cognitive load is increased by having to split attention between the image and text, while mentally integrating the two sources of information. We investigated the…

Euclidean geometry has formed the foundation of architecture, science, and technology for millennia, yet the development of human's intuitive reasoning about Euclidean geometry is not well understood. The present study explores the cognitive processes and representations that support the development of humans' intuitive reasoning about Euclidean…

In this exploratory work, the discourse of first-year computer engineering undergraduate students of graph theory was analyzed with the aim of improving the teaching of this branch of mathematics. The theoretical framework used is the theory of commognition, specifically, we focus on commognitive conflicts because they are learning opportunities…