Building on Shulman's (1986, 1987) construct of Pedagogical Content Knowledge (PCK), Ball and colleagues (Ball, Thames & Phelps, 2008) created a model of mathematical knowledge for teaching that differentiates between subject matter knowledge and PCK. The model categorises different types of knowledge within these two domains. In this research…

The aim of this research was to examine the effect of GeoGebra-aided REACT strategy on the understanding of geometry concepts and to investigate the interaction between learning strategy and spatial ability on the understanding of geometry concepts. This research involved 60 students of Grade 8 at a private Junior High School in Borong, province…

This study contrasted the standardized test scores of impoverished students who took secondary courses in a virtual setting with those of impoverished students who took secondary courses in a traditional brick-and-mortar setting in a selected school district in Florida. The selected school district is located on Florida's central eastern coast,…

This article describes a project using Design Based Research methodology to ascertain whether a pedagogical task based on a dynamic figure designed in a Dynamic Geometry Software (DGS) program could be instrumental in developing students' geometrical reasoning. A dragging strategy which I have named "Dragging Maintaining Symmetry" (DMS)…

This paper deals with a brief history of the most remarkable Euler numbers "e,"?"i"?and?"?" in mathematical sciences. Included are many properties of the constants "e,"?"i"?and?"?" and their applications in algebra, geometry, physics, chemistry, ecology, business and industry. Special…

In the second paper of this series, the effect of transverse femoral stresses due to locomotion in theropod dinosaurs of different sizes was examined for the case of an unchanging leg geometry. Students are invariably thrilled to learn about theropod dinosaurs, and this activity applies the concepts of torque and stress to the issue of theropod…

Many problems related to synthesis with intelligent tutoring may be phrased as program synthesis problems using AI-style search and formal reasoning techniques. The _x000C_first two results in this dissertation focus on problem synthesis as an aspect of intelligent tutoring systems applied to STEM-based education frameworks, specifically high…

Considering the performances of the students in the Timss and Pisa examinations, it is seen that they can not solve the problems, do not animate the objects they can not ask geometry questions in three dimensions and can not understand them. For this reason, origami lessons should be put into teacher training programs. Secondary teacher trainees…

In that current study, pattern conversion ability of 25 pre-service mathematics teachers (producing figural patterns following number patterns) was investigated. During the study participants were asked to generate figural patterns based on those number patterns. The results of the study indicate that many participants could generate different…

The Programme of International Student Assessment (PISA) has been administered to 15-year- olds every three years since 2000. Since then, the U.S. has performed below average in mathematics, with no significant changes in performance. The objective of this study was to examine the alignment of the content students in the U.S. are assessed on in…

We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner. First, using geometrical software, we investigate four theorems that represent interesting geometrical properties,…

Information competency is one of the essential qualities of a person living in the information age. It includes skills in information handling in both educational domains and the outside world, as well as readiness and capability to use modern information and communication technologies when involved in various types of information activities.…

This ethnographical study aims to interpret how an intelligent tutorial system, geogebraTUTOR, mediates to the student's argumentative processes. Data consisted of four geometrical problems proposed to a group of four students aged 16-17. Qualitative analysis of two selected cases led to the identification of the development of argumentative…

Over 50% of secondary students failed the geometry end-of-course test in a Florida school district, indicating a need to improve academic performance. Secondary school students' learning characteristics and the effectiveness of teachers' instructional strategies are imperative to educational success. In this qualitative case study, geometry…

This study investigates teacher responses to a common set of high potential instances of student mathematical thinking to better understand the role of the teacher in shaping meaningful mathematical discourse in their classrooms. Teacher responses were coded using a scheme that disentangles the teacher move from other aspects of the teacher…