We live our lives in three-dimensional space and encounter geometrical problems (equipment instructions, maps, etc.) every day. Yet there are not sufficient opportunities for high school students to learn geometry. New teaching methods can help remedy this. Specifically our experience indicates that there is great promise for use of geometry…

The purpose of this study is to identify the effect of using metacognitive strategies for problem solving in "geometry" on fifth grade students' achievement, metacognitive skills and attitude. Experimental method was used with a pretest/posttest control group design. Firstly, both groups were subject to a pretest that was comprised of…

Social development, the progress of technology, and changing economic forces certainly affect the development of the current educational system. One of the main problems of today's school system is how to maintain focus, concentration, and interest among students with regards to the learning that takes place during classes. An important feature of…

In many domains, problem solving involves the application of general domain principles to specific problem representations. In 3 classroom studies with an intelligent tutoring system, we examined the impact of (learner-generated) interactions and (tutor-provided) visual cues designed to facilitate rule-diagram mapping (where students connect…

The study aims to identify areas of difficulty in learning about volumes of solids of revolution (VSOR) at a Further Education and Training college in South Africa. Students' competency is evaluated along five skill factors which refer to knowledge skills required to succeed in performing tasks relating to applications of the definite integral, in…

This paper explores the use of blogs, a simple application of Web 2.0 technologies, in middle school geometry instruction. Specifically, it provides an overview of the interactive features of Web 2.0 technologies and the feasibility of using Web 2.0 technologies in geometry teaching and learning, as well as a proposed model for creating a…

This longitudinal study examined how language ability relates to mathematical development in a linguistically and ethnically diverse sample of children from 6 to 9 years of age. Study participants were 75 native English speakers and 92 language minority learners followed from first to fourth grades. Autoregression in a structural equation modeling…

This mixed-method, longitudinal study investigated the benefits of project-based learning (PBL) on secondary-mathematics students' academic skill development and motivated strategies for learning (i.e., cognitive, social, and motivational). The focus of this study was academic skill development (algebra- and geometry-assessment scores) and other…

In this thesis, we apply model theory to Lie theory and geometric group theory. These applications of model theory come via nonstandard analysis. In Lie theory, we use nonstandard methods to prove two results. First, we give a positive solution to the local form of Hilbert's Fifth Problem, which asks whether every locally euclidean local…

The concept of dimension, one of the most fundamental ideas in mathematics, is firmly rooted in the basis of the school geometry in such a way that mathematics teachers rarely feel the need to mention anything about it. However, the concept of dimension is far from being fully understood by students, even at the college level. In this paper, we…

This exploratory research project investigated graduate students' satisfaction levels with online learning associated with human (professor/instructor and instructional associate) and design factors (course structure and technical aspects) using a survey study. A total of 81 graduate students (master's students who majored in math and science…

This study examined the scaffolds that three high school mathematics teachers provided to their geometry students as they used technology to explore geometric ideas. Teachers often used structured activities using a dynamic geometry program and provided significant emotive feedback while students worked through the tasks. This provided…

Most people would agree that helping students learn new information is important; however, there are numerous methods for achieving this goal, and not all of them have been proven to be effective. One method with intuitive appeal and some empirical backing is prompting students to self-explain. A self-explanation can be defined as generating…

Although it can be visualized fairly easily and its symmetry group is easy to calculate, the permutahedron is a somewhat neglected combinatorial object. We propose it as a useful case study in abstract algebra. It supplies concrete examples of group actions, the difference between right and left actions, and how geometry and algebra can work…

Psychologists, philosophers, and educators have traditionally interpreted the phenomenon of insight learning as the result of the sudden comprehension of abstract/conceptual ideas. The present article shows that such phenomenon may also follow and emerge from the kinetic movements of the human body; that is, we conceptualize insight learning as a…