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.…

Geometry learning has a long history with the connection to human cognitive development. The ability to mentally or physically orient 2D shapes or 3D objects in space is believed to support achievement in science, technology, engineering, and mathematics (STEM) disciplines. Thus, geometry by its description is characterised by space; hence its…

In this article, researchers conducted a study that integrates Augmented Reality application with Computational Thinking into Geometry Topics. Three variables were measured, Computational Thinking, Visualisation Skills and Geometry Topic achievement. The study was implemented with 124 students in two different schools using quasi-experimental…

Globally, the use of visuo-semiotic models (VSMs) in the mathematics classroom is called for across levels and topics. Literature confirms that visual cognition/literacy in teachers is limited and that their capabilities in visual representation is low. The aim of this study was therefore to explore pre-service teachers' (PSTs) conception of VSMs…

Understanding fraction as a quantity has been identified as a key developmental understanding. In this study, students in Grades 5, 8, and 11 were asked to compare the areas of two halves of the same square--a rectangle and a right triangle. Findings from this study suggest that students who understand fraction as a quantity use reasoning related…

Reasoning is handled as a basic process skill in mathematics teaching. When the literature was examined, it was seen that many types of reasoning related to mathematics education were mentioned. In the present study, it was focused on visual reasoning, which is one of the types of reasoning and also used in different research areas. The purpose of…

In this paper, I share an activity that reinforces students' understanding of translations, reflections, and rotations via body movement. As a result of this activity, students gain a different perspective compared to previous explorations on paper, communicate mathematics, and visualize transformations as rigid motions on the plane. Furthermore,…

The 21st-century mathematics classrooms should equip learners with well-grounded knowledge and thinking skills pertaining to geometry. However, Euclidean geometry remains one of the challenging, if not the most difficult topic for many learners. As a result, the purpose of this article is to interpret Grade 12 learners' learning difficulties in…

The definition of creativity among professional mathematicians and the definition of mathematical creativity in the classroom context are significantly different. The purpose of this study was to investigate the relationship between students' mathematical creativity (i.e., cognitive flexibility) and figure apprehension when solving geometric…

There is increasing evidence for the impact of spatial training on mathematics performance in early years of education, however little research has focused on secondary school environments, which are traditionally more discipline driven. In the present study, a large-scale classroom-based intervention saw the introduction of twelve hours of…

Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with…

The relationships between visuo-spatial abilities and geometry performances in school-aged children were examined. A battery of tests assessing non-verbal reasoning, visuo-spatial mental imagery, and academic achievement in geometry (i.e., geometric knowledge and geometric problem-solving competencies) was presented to 162 8-9.5-year-old pupils…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

Students often have the misconception that mathematics involves reading the problem, staring at the page, and then writing down an answer. With more than twenty years of experience working with students in eighth-grade math through college calculus, the author has been increasingly interested in how she can foster problem-solving skills in her…

The purpose of this study was to investigate kindergartners' geometric (shape, area and symmetry) and spatial (spatial orientation and spatial visualization) thinking skills, in the context of gender and age. Whether kindergartners' geometric and spatial thinking skills vary by their age or gender was questioned. A total of 73 kindergartners (40…