Ariadne is a touch-based program for the learning of homotopies of paths, without the use of formalism, by building mental models. Using Ariadne, the user can construct points, paths by dragging points and homotopies by dragging paths as well as compute winding numbers of paths, all on a variety of surfaces, through touch gestures. Ariadne…

Computer-aided visualization provides meaningful insight into geography teaching, which helps improve comprehension. With dynamic geometry software (DGS), a teacher can easily create interactive mathematical learning materials. To fully benefit from DGS applied to subjects other than mathematics, their functionality must be extended with features…

Research reveals that many mathematics teachers find it difficult to stimulate learners' interest in learning geometry. One major reason suggested is that geometric concepts are not well conceptualised and comprehended by both learners and teachers. The study explored learners' views on how polygon pieces and dictionary mediate learning of…

The study and interest of figurate numbers can be observed even in ancient Greece. On the other hand, it becomes very important the historical understanding about an evolutionary process and the particular generalization of such 2D, 3D and m-D figurate numbers and they remain the interest of current scientific investigations. On the other hand, in…

In this research study, I investigated the relationships between preferences for solution methods, task difficulty, gender, and high school students' geometry performance. Data were collected from 161 geometry students at six high schools at a county located in the southeastern region of the USA at the time of the 2013-2014 school year. The result…

The concept of symmetry is vital for the study of science and developing spatial and geometric relationships. Yet few studies have been conducted to examine how students learn this concept. This study investigates 757 Year 4 to 10 students' ability to reason about symmetrical relationships. By analysing the semiotic processes through the lens of…

The present study is a part of design research in local instructional theory in a pre-algebraic lesson using the Realistic Mathematics Education (RME) approach. The article will focus on recommendations for the type of pre-algebra class that supports elementary school students' algebraic thinking. As design research study, it followed the three…

Extreme Learning Machine (ELM) is a training algorithm for Single-Layer Feed-forward Neural Network (SLFN). The difference in theory of ELM from other training algorithms is in the existence of explicitly-given solution due to the immutability of initialed weights. In practice, ELMs achieve performance similar to that of other state-of-the-art…

The purpose of this research study was to understand how linear algebra students in a university in the United States make sense of subspaces of vector spaces in a series of in-depth qualitative interviews in a technology-assisted learning environment. Fourteen mathematics majors came up with a diversity of innovative and creative ways in which…

One way to ease the solution of physics problems is to visualize the situation. However, by visualization we do not mean the pictorial representation of the problem. Instead, we mean a sketch for the solution of the problem. In this paper a new approach to solving physics problems, based on decomposing the problem into with and without gravity, is…

In this paper, we demonstrate how atypical visual representations of a triangle, square or a parallelogram may hinder students' understanding of a median and altitude. We analyze responses and reasoning given by 16 preservice middle school teachers in a Geometry Connection class. Particularly, the data were garnered from three specific questions…

Creativity is a dynamic process which generates ideas that are both novel and of value. However there is little understanding in what drives creativity in students and how to help teachers or education experts to detect creative thinking. This paper begins to address this gap by providing a platform and experiments for studying how creative…

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…

Virtual images are often introduced through a "geometric" perspective, with little conceptual or qualitative illustrations, hindering a deeper understanding of this physical concept. In this paper, we present two rather simple observations that force a critical reflection on the optical nature of a virtual image. This approach is…

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…