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…

In this paper the authors described the influence of the computer-based environment on students' learning achievement of the multidimensional calculus, in particular double integrals. The research was conducted with the second year students at the University of Kragujevac, Serbia, with two groups of students: the experimental and the control one.…

Geometry is one of the topics that students must comprehend in mathematics. However, in reality, the students' ability concerning geometry is relatively low due to their low spatial reasoning ability. The ELPSA framework is one of the solutions to develop students' spatial reasoning abilities. This study aimed to describe students' spatial…

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…

This unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This…

Children practice their spatial skills when playing with spatial toys, such as construction materials, board games, and puzzles. Sex and SES differences are observed in the engagement in such spatial play activities at home, which relate to individual differences in spatial performance. The current study investigated the effects of explicitly…

Learning to think spatially in mathematics involves developing proficiency with graphics. This paper reports on 2 investigations of spatial thinking and graphics. The first investigation explored the importance of graphics as 1 of 3 communication systems (i.e. text, symbols, graphics) used to provide information in numeracy test items. The results…

The aim of this study is to investigate the effectiveness of Google SketchUp, which is a computer aided design (CAD) software, on the Mental Rotation Skills of eighth grade students. For this purpose, in the spring semester of the 2011-2012 academic year, a treatment was conducted with 62 students comprised of 8A and 8B classes in the GSD…

Generations have been inspired by Edwin A. Abbott's profound tour of the dimensions in his novella "Flatland: A Romance of Many Dimensions" (1884). This well-known satire is the story of a flat land inhabited by geometric shapes trying to navigate the subtleties of their geometric, social, and political positions. In this article, the authors…

In this article, the author features "Flatland," by Edwin Abbott, a fantastic story about a square who lives in a two-dimensional world and who receives a visitor from the third dimension. Written in 1884 by a teacher-theologian who dabbled in mathematics, the novel is full of rich themes, including social class structure, the treatment of people…

Most students love to play games. Ernest (1986) believed that games could be used to teach mathematics effectively in four areas: motivation, concept development, reinforcement of skills, and practice of problem-solving strategies. Fifteen is an interesting and thought-provoking game that helps students learn mathematics at the same time. Playing…

Whereas origami is said to have pedagogical benefits in geometry education, research is inclusive about its effect on spatial ability and geometric knowledge among preservice teachers. The study investigated the effect of origami instruction on these aspects using pretest posttest quasi-experiment design. The experimental group consisted of 52…

This study investigated the effectiveness of a unit plan designed to enhance students' three-dimensional geometry and spatial ability skills. Research participants consisted of 50 students, 19 males and 31 females, and two teachers from a public high school in a suburban middle-class community. The students in this study were 9th and 10th graders…

Twelve pentagons are sufficient and necessary to form a fullerene cage. According to this structural feature of fullerenes, we propose a simple and efficient method for the construction of I[subscript h] symmetrical fullerenes from pentagons. This method does not require complicated mathematical knowledge; yet it provides an excellent paradigm for…

Many epistemic activities, such as spatial reasoning, sense-making, problem solving, and learning, are information-based. In the context of epistemic activities involving mathematical information, learners often use interactive 3D mathematical visualizations (MVs). However, performing such activities is not always easy. Although it is generally…