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…

This research aims to investigate the construction of the area of rectangle with GeoGebra and how students can formulate it. It focuses on describing the cognitive process involved in constructing this concept and how technology mediates such a process. The research was conducted in a classroom with 5th grade students in a secondary school and was…

While patterning was commonly seen as evidence of mathematical thinking, interdisciplinary interest has recently increased due to pattern-recognition applications in artificial intelligence. Within two empirical studies, we analyze the analogical-transfer capability of primary school students when completing three types of bi-dimensional patterns,…

As an important branch of mathematics, geometry plays a very significant role in developing students' thinking, but many students need to improve their geometric thinking abilities, especially in understanding graphics and forms. Therefore, it is worthwhile to explore techniques and methods for developing students' geometric thinking, and…

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…

In this report, we present how one prospective elementary teacher (PT) engaged in the Ant Farm Task, which we designed to investigate PTs' reasoning about coordinate systems. We highlight the cognitive resources the PT drew upon in solving the task via the establishment of a Cartesian coordination and consider educational implications. [For the…

Spatial reasoning is critical across the STEM disciplines. Examining deaf and hard of hearing (DHH) children's spatial reasoning in mathematics, particularly geometry, as an embodied phenomenon opens new possibilities for deaf education. The authors inquire into the embodied processes and forms of DHH learners' spatial reasoning, considering how…

The concept of angles is important for future geometric knowledge (Arslan et al., 2016; Moore, 2013; Yigit, 2014). However, although Piaget (1948) suggests angles lead to the discovery of lines, angles are typically taught later in schools, after points, lines, and planes (Charles, 2011). Therefore, the way in which angles are taught can affect…

This study examined pre-service teachers' views and experiences of building geometric constructions on paper and with the interactive whiteboard. The study group consisted of 26 pre-service elementary teachers in a state university in the Black Sea region of Turkey who took the Geometry Teaching course. The data were obtained from an opinion form…

In this study, we investigated the potential of a hypothesized geometrical measurement learning progression (LP) to examine students' thinking and understanding in this domain.We interviewed 30 third to fifth graders using 3 LP-based cognitive tasks that asked the students to find the length, perimeter, area, surface area, and volume measurement…

In this study, the relationship between the usability of a mobile Augmented Reality (AR) tutorial system and cognitive load was examined. In this context, the relationship between perceived usefulness, the perceived ease of use, and the perceived natural interaction factors and intrinsic, extraneous, germane cognitive load were investigated. In…

Over three decades of research has shown that spatial reasoning and mathematics performance are highly correlated. Spatial visualization, in particular, has been found to predict mathematics performance in primary and middle school children. This research sought to determine the effectiveness of a spatial visualization intervention program on…

Inferences about student knowledge, skills, and attributes based on digital activity still largely come from whether students ultimately get a correct result or not. However, the ability to collect activity stream data as individuals interact with digital environments provides information about students' processes as they progress through learning…

Awareness of one's own strengths and weaknesses during visualisation is often initiated by the imagination -- the faculty for intuitively visualising and modelling an object. Towards exploring the role of metacognitive awareness and imagination in facilitating visualisation in solving a mathematics task, four secondary schools in the North West…

This case study contrasts the strategies used by two students in solving bilateral symmetry and reflection tasks, based on the differential properties they attended to. The ninth grader focussed on congruence of sides as the main property of reflection whereas the eighth grader focussed on perpendicularity and equi-distance, as is the normative…