The particular problem solved in this paper is that of calculating the time required to overtake a distant object receding under cosmic expansion, and the speed at which that object is passed. This is a rarely investigated problem leading to some interesting apparent paradoxes. We employ the problem to promote a deeper understanding of the dynamic…

The purpose of this paper is to further the notion of defining as a mathematical activity by elaborating a framework that structures the role of defining in student progress from informal to more formal ways of reasoning. The framework is the result of a retrospective account of a significant learning experience that occurred in an undergraduate…

The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…

In this study, students' views were taken about history of Pythagoras theorem that contains improved activity which in the history people was thrilled at and there are a lot of their proofs. The study was conducted with 15 students 8th grade at a public elementary school in Trabzon during the spring term of 2009-2010 school year. Case study method…

The GeoGebra Workshop for the degree "Teacher in Primary Education" has been designed to work the main geometric competencies that primary pre-service teachers need to develop. In this paper, some case studies are included in which we analyse the development of geometric skills and the use of GeoGebra dynamic tools in three types of activities:…

This article describes a 21st century how-to model for successful career and technical education (CTE) programs. The Geometry in Construction program is the brainchild of two educators, a CTE and a math teacher, who wanted to design a rigorous geometry course taught through a project-based curriculum. This article discusses how they did it, and…

This paper reports from a case study with teachers at two schools in Norway participating in developmental projects aiming for inquiry communities in mathematics teaching and learning. In the reported case study, the teachers participated in one of the developmental projects focusing on implementation and use of computer software in mathematics…

In this study, 244 children (average age: 61 months) and their parents from the Dallas and Fort Worth metroplex area in Texas were surveyed to investigate children's proficiency in mathematics content on numbering, sizes, comparisons, and shapes. The researchers investigated children's proficiency in mathematics associated with children's gender,…

Piecewise linear functions and story graphs are concepts usually associated with algebra, but in the authors' classroom, they found success teaching this topic in a distinctly geometrical manner. The focus of the approach was less on learning geometric concepts and more on using spatial and kinetic reasoning. It not only supports the learning of…

Student activities focused on discovering mathematics play an important role in the teaching and learning process. WebMathematics Interactive (WMI2) was developed to offer a fast and user-friendly on-line web interface to enhance the quality of both theoretical and applied mathematics courses. For the teacher, in the classroom, it provides…

Teachers are increasingly integrating mobile digital technology into the classroom. The purpose of this study was to assess the effect of incorporating iPads in a secondary-level geometry course on academic achievement, student engagement, self-efficacy, and meta-cognitive self-regulation. Students in the iPad-using classroom experienced lower…

In introductory-level physics courses, the concept of surface tension is often illustrated using the example of capillary rise in thin tubes. In this paper the author describes experiments conducted using a planar geometry created with two small plates forming a thin wedge. The distribution of the fluid entering the wedge can be studied as a…

A square can be divided into two equal parts with any cut through the center. The first question that arises is, Would any cut through the center of a regular polygon divide it into two equal parts? If not, the second question is, What kind of lines through the center of the polygon would cut it into two halves? However, many objects are not…

We present a "base x height" approach to familiar results of Archimedes on the area of a parabolic sector. (Contains 1 figure.)

This is the third part of a study of plane transformations described in a complex setting. After the study of homotheties, translations, rotations and reflections, we proceed now to the study of plane similarities, either direct or inverse. Their group theoretical properties are described, and their action on classical geometrical objects is…