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…

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…

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 purpose of this study was to describe students' thinking processes in relating quantities to the problem of covariation in the process of solving mathematical problems. This study used a descriptive exploratory approach within the scope of qualitative research involving 87 students as prospective subjects from three different high schools. The…

Visuo-semiotic models, such as Lewis structures and ball & stick models, are widely used to enhance students' learning. However, there is limited research about the impact of these models on specific visuo-semiotic reasoning skills. In the current research, we aimed to determine the extent to which physical molecular models could enhance…

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…

In this study it was aimed to determine the effect of geometrical-mechanical intelligence games activities that are conducted with concrete materials and in computer environment on the spatial visualization and mental rotation skills of prospective teachers and to examine the opinions of prospective teachers about the activities. The research was…

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…

This study is focused on identifying and describing the reasoning patterns of middle grade students when examining potentially similar figures. Described here is a framework that includes 11 strategies that students used during clinical interview to differentiate similar and non-similar figures. Two factors were found to influence the strategies…

Misconceptions in geometry are an essential problem in the understanding of geometric terms by primary and pre-primary aged children. Present research shows some misconceptions in geometry demonstrated in the understanding of circles, squares, triangles and oblongs for children in the last year of kindergarten and pupils in the last year of…

This commentary adopts a broad perspective in considering the contributions of papers from cross- and interdisciplinary fields of mathematics education, psychology, child development and neuroscience. The discussion aims to complement the commentary by Dindyal, focused on background research on geometry and implications for pedagogy and curricula.…

In this work, certain task designs to enhance middle school students' spatial visualisation ability, in the context of an instrumental approach, have been developed. 3D modelling software, SketchUp®, was used. In the design process, software tools were focused on and, thereafter, the aim was to interpret the instrumental genesis and spatial…

There is an emerging consensus that spatial thinking is fundamental to later success in math and science. The goals of this study were to design and evaluate a novel test of three-dimensional (3D) mental rotation for 4- to 8-year-old children (N?=?165) that uses tangible 3D objects. Results revealed that the measure was both valid and reliable and…

Karina Wilkie discusses functional thinking in the primary classroom. She provides a useful learning progression with sample responses to a growing pattern task.