This paper describes students' interactions with dynamic diagrams in the context of an American geometry class. Students used the dragging tool and the measuring tool in Cabri Geometry to make mathematical conjectures. The analysis, using the cK[cent sign] model of conceptions, suggests that incorporating technology in mathematics classrooms…

The first goal of this article to show the profound difference between how equality and similarity are understood in Greek geometry and how they are presented in modern mathematics classes. It highlights that the formula "equal-and-similar" reflects the distinct character of "equal" and "similar" as signs in Greek…

Students often find the difference in the electromagnetic and the acoustic Doppler formulae somewhat puzzling. As is shown below, geometrical diagrams and the concept of "event"--a point in spacetime having coordinates (x,y,z,t)--can be a useful and simple way to explain the physical background behind the fundamental differences between the two…

This paper proposes a taxonomy of the pedagogical opportunities that are offered by mathematics analysis software such as computer algebra systems, graphics calculators, dynamic geometry or statistical packages. Mathematics analysis software is software for purposes such as calculating, drawing graphs and making accurate diagrams. However, its…

Parabolic shapes are easy to find. Many homes outside the cable area have parabolic antennas to receive television transmissions from a satellite far out in space. Parabolic extrusions are used as reflectors behind fluorescent tubes and solar heated water pipes. Parabolic reflectors are used to build solar ovens, searchlights and radio telescopes.…

This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM…

This book examines the five key elements (meaningful use of symbols, mindful manipulation, reasoned solving, connection algebra with geometry, and linking expressions and functions) identified in "Focus in High School Mathematics: Reasoning and Sense Making" in more detail and elaborates on the associated reasoning habits. This volume is one of a…

This article reports the findings of an experimental study involving 36 primary school students (16 girls, 20 boys, Mean age = 9.5 years, age range: 8-10 years) in geometrical understanding of 2D and 3D objects. Students were assigned into two experimental groups and one control group based on a stratified random sampling procedure. The first…

The translation principle allows students to solve problems in different branches of mathematics and thus to develop connectedness in their mathematical knowledge. Successful application of the translation principle depends on the classroom mathematical norms for the development of discussions and the comparison of different solutions to one…

It is easy to fall into the trap of thinking that teaching mathematics should greatly differ from teaching language arts. Classroom teachers at Munich International School in Starnberg, Bavaria, Germany, did not pay much attention to what language means to learning and teaching mathematics--until their geometry students offered language surprises…

The main purpose of the work is to present a successful implementation of CLIL method in Mathematics lessons in elementary schools. Nowadays at all types of schools (elementary schools, high schools and universities) all over the world every school subject tends to be taught in a foreign language. In 2003, a document called Action plan for…

In 1999, Richard Lee Colvin published an article in "The School Administrator" titled "Math Wars: Tradition vs. Real-World Applications" that described the pendulum swing of mathematics education reform. On one side are those who advocate for computational fluency, with a step-by-step emphasis on numbers and skills and the…

As she sat in a high school geometry class and observed a beginning teacher, Matt (a pseudonym), teaching proof for the first time, the author was reminded of her own experiences in teaching formal proof to secondary school students. Matt seemed to struggle with some of the same challenges she encountered when she began teaching proof. For…

In this article, the author shares how she uses origami for her elementary students. Using origami in her classroom helps with classroom management. Students are enthralled to watch the paper as it is folded. Every student can feel a part of the experience. Origami can serve many functions in library classrooms: attention grabbers, geometry…

This article describes one classroom activity in which the author simulates the Newtonian gravity, and employs the Euclidean Geometry with the use of new technologies (NT). The prerequisites for this activity were some knowledge of the formulae for a particle free fall in Physics and most certainly, a good understanding of the notion of similarity…