We report on a group theory activity in which learners explored dihedral symmetries through a tangible geometric model. This approach has historical roots in the work of Felix Klein's Erlangen Program and his "Elementary Mathematics from an Advanced Standpoint." We situate our study with respect to this history as well as current…

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…

This study aims to examine the relation between spatial ability and creativity in Geometry. Data was collected from 94 ninth graders. Three spatial abilities were investigated: spatial visualization, spatial relations and closure flexibility. As for students' creativity, it was examined through a multiple solution problem in Geometry focusing on…

Although we move and live in three-dimensional space, many prefer "two-dimensional" thinking in mathematics lessons. As a result, the transition between physical objects and their graphical representations can be considered one of the most common difficulties in learning and teaching solid geometry. This paper describes results of our…

This article discusses the advanced characteristics of a mathematical and geometrical system explained and published in the course of several preceding journal articles (Teia, 2015, 2016, 2018a and 2018b). The reading of the preceding articles is encouraged for a clearer understanding of the discussion that follows.

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…

Visualisation is a necessary ability for students' mathematical education. The appearance of multiple Dynamic Geometry Software (DGS) has a stronger impact each day, and it raises many questions in the minds of researchers. In this paper, we present the findings of our exploratory case study in which a student preferring visual problem solving…

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…

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…

Aim/Purpose: This paper aims to evaluate the influence of an augmented reality mobile application on improving secondary students' visualization and comprehension of geometric concepts. Background: The study involved developing an AR app named Geometria to enhance geometry education. Methodology: In a specialized boarding school in Kokshetau,…

The aim of this study is to develop a valid and reliable measurement tool that measures mathematical visualization perceptions for mathematics teacher candidates. Therefore, the type of study is a survey research. Research was carried out with 462 (336 Female, 125 Male) mathematics teacher candidates from a university located in the Eastern…

Aiming to enhance understanding of visual obstacles inherent in two-dimensional (2-D) sketches used in high school spatial geometry instruction, we propose a measure of visual difficulty based on two attributes of the sketches: potentially misleading geometrical information (PMI) and potentially helpful geometrical information (PHI). The…

Technical Graphics is one of the technology subjects taught at Junior Certificate level in post- primary schools in Ireland. The Junior Certificate examination is held at the end of the Junior Cycle in post-primary schools, which caters for students aged from 12 to 15 years. As a teacher of Technical Graphics for the past seven years, I have…

There is growing acknowledgement of the importance of spatial abilities to student achievement across a broad range of domains and disciplines. Nets are one way to connect three-dimensional shapes and their two-dimensional representations and are a common focus of geometry curricula. Thirty-four students at year 6 (upper primary school) were…

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…