We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…

As calls are made for reasoning-and-proving to permeate school mathematics, several textbook analyses have been conducted to identify reasoning-and-proving opportunities outside of high school geometry. This study looked within geometry, examining six geometry textbooks and characterizing not only the justifications given and the…

Take a strip of paper and fold a crease intersecting the long edges, creating two angles. Choose one edge and consider the angle with the crease. Fold the opposite edge along the crease, creating a new crease that bisects the angle. Fold again, this time using the newly created crease and the initial edge, creating a new angle along the chosen…

Mathematics is full of surprises and beauty. In this article, the author discusses three favourite topics that he finds both amazing and amusing: (1) the problem of the possibility of subdividing a rectangle into a number of different squares; (2) the arrangement formed when several soap bubbles meet; and (3) circles and spheres.

Kinesthetic intelligence is one of the seven kinds of intelligence identified by Gardner's multiple intelligence theory (1983). The kinesthetic approach to teaching has numerous pedagogical advantages and can be adapted to the teaching of mathematics. This article describes a series of kinesthetic activities designed to explore the properties of…

We provide several constructions, both algebraic and geometric, for determining the ratio of the radii of two circles in an Apollonius-like packing problem. This problem was inspired by the art deco design in the transom window above the Shadek Fackenthal Library door on the Franklin & Marshall College campus.

Many illustrations and problems on the vector nature of forces have weights and forces in a vertical plane. One of the common devices for studying the vector nature of forces is a horizontal "force table," in which forces are produced by weights hanging vertically and transmitted to cords in a horizontal plane. Because some students have…

Educators often speak of teaching as "listening," yet they seldom encounter it in practice. What converts pedagogical space into authentic educational experience is a climate of respect that is born of serious, just, humble, and generous relationships in which both the authority of the teacher and the freedom of the students are ethically…

The authors wanted their students to consider mathematical notions of space and dimension, which are typically not part of the middle school curriculum. They developed a two-week lesson that was drawn from the curriculum unit "Exploring the Shape of Space" (Weeks 2001). They began by considering implications of living in a two-dimensional…

The purpose of this study was to investigate the effect of technology on one student's solution methods when solving mathematical tasks that included algebra word problems. The student was presented with context tasks in both paper-pencil and computer environments. The results of this study revealed that the student's solution methods differed in…

Students with special needs often require additional assistance in order to learn at the university level. This article documents a professor's efforts in teaching a visually impaired prospective elementary school teacher geometry content knowledge. The goal of this article is to shed light upon the iterative process of accommodating for…

In this paper we aim to contribute to the process of networking between theoretical frames in mathematics education by means of forging connections between Constructionism and Instrumental Theory to discuss a design for instrumentalisation. We specifically focus on instrumentalisation, i.e. the ways in which students make changes to digital…

The Timepix hybrid silicon pixel detector has been used to investigate the inverse square law of radiation from a point source as a demonstration of the CERN [at] school detector kit capabilities. The experiment described uses a Timepix detector to detect the gamma rays emitted by an [superscript 241]Am radioactive source at a number of different…

The aim of this study is to investigate the effect of dynamic geometry software GeoGebra on Van Hiele geometry understanding level of students at 11th grade geometry course. The study was conducted with pre and posttest control group quasi-experimental method. The sample of the study was 42 eleventh grade students studying in the spring term of…

In the study, it was researched the effect of internet-based application on student success. Internet-based application was used at the teaching of triangles subject which is included in 8th grade units of triangles and algebra. The study was carried out over the internet with a computer software program: Vitamin Program. The study was carried out…