In this article special sequences involving the Butterfly theorem are defined. The Butterfly theorem states that if M is the midpoint of a chord PQ of a circle, then following some definite instructions, it is possible to get two other points X and Y on PQ, such that M is also the midpoint of the segment XY. The convergence investigation of those…

In this paper we introduce the reader to a foundational topic of differential geometry: the curvature of a curve. To make this topic engaging to a wide audience of readers, we develop this intuitive introduction employing only basic geometry without calculus and derivatives. It is hoped that this introduction will encourage many more to both…

The purpose of this case study was to examine prospective mathematics teachers' lessons in the context of choice and use of representations while teaching limit. The participants were four senior prospective mathematics teachers. The data were obtained from the participants' lessons plans, the video recordings of their lessons, and the…

The aim of this study was to identify the effects of GeoGebra software on students' conceptual and procedural knowledge and the achievement of Form Two students in Mathematics particularly on the topic Function. In addition, this study determined the role of procedural knowledge as a mediator between conceptual knowledge and students' achievement.…

This study focuses on mathematics teachers' professional development through elements of Japanese lesson study. The teachers designed a research lesson with regard to sense-making of the derivative using the integration of GeoGebra. In the second year of the four-year lesson study project, seven secondary school teachers--from different Dutch…

This article describes a professional development initiative for fifteen mathematics teachers in the use of dynamic geometry software GeoGebra. A four-day introductory workshop was given in Nepal to provide an overview of GeoGebra and its possible integration in the teaching/learning of secondary school mathematics there. Teachers' impressions and…

The papers in the monograph address different topics related to mathematics teaching and learning processes which are of great interest to both students and prospective teachers. Some papers open new research questions, some show examples of good practice and others provide more information about earlier findings. The monograph consists of six…

The Common Core State Standards for Mathematics (CCSSM) are founded on a long history of mathematics education research emphasizing the importance of teaching mathematics for understanding. The CCSSM along with the National Council of Teachers of Mathematics (NCTM) recommend the use of technology in the teaching of mathematics. New mobile…

Interactive Whiteboards (IWBs) are becoming commonplace throughout primary, secondary, and postsecondary classrooms. However, the focus of the associated lesson creation & management software tools delivered with IWBs has been the primary grades, while secondary and postsecondary mathematics lessons have requirements beyond what is delivered…

This study investigates 3 preservice secondary mathematics teachers' understandings of limits of sequences and their changing conceptions of limit during and after instruction involving interactive, dynamic sketches embodying the formal definition of the limit of a sequence. Manipulating a coherent visual representation of the formal definition in…

The concept of definite integral is almost always introduced as the Riemann integral, which is defined in terms of the Riemann sum, and its geometric interpretation. This definition is hard to understand for high school students. With the aid of mathematical software for visualisation and computation of approximate integrals, the notion of…

Today's classrooms are much different from those of yesterday. The increased diversity of learners, students' familiarity and attraction to technology, and the improved availability of technology in education have made it increasingly possible for teachers to use various forms of technology in instruction. The responsibility for addressing these…

Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new. It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and constants, and measurements are given as symbolic expressions. Mathematical…

This article demonstrates how within an educational context, supported by the notion of hidden mathematics curriculum and enhanced by the use of technology, new mathematical knowledge can be discovered. More specifically, proceeding from the well-known representation of Fibonacci numbers through a second-order difference equation, this article…

A problem that most high school calculus students can explore is presented. It can help students understand such mathematical topics as functional notation, composition of functions, the solving of systems of equations, and the derivative. A computer program is included. (MNS)