Communicating on the mathematical language, problem solving, and reasoning are competencies tested on international test. The aim of this research is to study how secondary school pupils do geometrical constructions, how they give mathematical argumentation and use geometrical notions in their explanations.

Being a mathematician, the author started to wonder if there are any theorems in mathematics that seem very ordinary on the outside, but when applied, have surprisingly far reaching consequences. The author thought about this and came up with the following unlikely candidate which follows immediately from the definition of the area of a rectangle…

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…

Many high-school mathematics teachers have likely been asked by a student, "Why does the cross-multiplication algorithm work?" It is a commonly used algorithm when dealing with proportion problems, conversion of units, or fractional linear equations. For most teachers, the explanation usually involves the idea of finding a common denominator--one…

With the increased use of computer manipulatives in teaching there is need for theoretical discussions on the role of manipulatives. This paper reviews theoretical rationales for using manipulatives and illustrates how earlier distinctions of manipulative materials are broadened to include new forms of materials such as virtual manipulatives.…

This article highlights a project that encourages students to connect reading and mathematics instruction by using a data analysis approach. Students analyze sonnets from statistical, literary, and historical points of view in an effort to uncover the true identity of William Shakespeare. (Contains 10 figures.)

A conceptual knowledge of numbers, especially fractions, is an important link to a conceptual understanding of variables. This article suggests activities that explicitly show the connections between numbers and variables using the number line as the connecting device. (Contains 7 figures and a bibliography.)

North Korea is one of the most closed nations in the world. It is difficult to access information about their education system. North Korea's economic system was reorganized on July 1, 2002, as well as the education system. This change has impacted North Korea's mathematics education. With limited information on North Korean mathematics textbooks,…

This paper highlights a teacher's perspective when changing her accustomed and traditional way of teaching into a pedagogic approach philosophically inspired by critical mathematics education. The focus here is on the practitioner's identities during the teaching process, in a context of change. The research is socio-culturally grounded and…

The purpose of this study was to examine the extent and manner in which teachers use mathematics textbooks in their daily teaching. Specific attention was given to textbook implementation differences related to two types of mathematics textbooks where the mathematical content is organized differently. Only schools where a dual curricular option…

It is important to use rich problem-solving tasks to develop students' understanding of important mathematical ideas (NCTM 2000). Rich tasks are complex, nonalgorithmic, and nonroutine, requiring reasoning, problem solving, and communication of thinking. Evidence has shown that using rich tasks in student-centered classrooms is especially…

Looping, a school structure where students remain with one group of teachers for two or more school years, is used by middle schools to meet the diverse needs of young adolescents. However, little research exists on how looping effects the academic performance of students. This study was designed to determine if looping influenced middle school…

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…

Casyopee is an evolving project focusing on the development of both software and classroom situations to teach algebra and analysis at upper secondary level. In this article, we sketch the rationales for the Casyopee project in relationship with the focus on functions in upper secondary curricula. To evaluate Casyopee's contribution, we present…

In this article, we demonstrate that prospective teachers' content knowledge related to defining mathematical concepts is dependent on content area. We use the example of generation (a research tool we developed in a previous study) to investigate prospective teachers' knowledge. We asked prospective secondary mathematics teachers to provide…