Problem solving and proofs have always played a major role in mathematics. They are, in fact, the heart and soul of the discipline. The using of a number of different proof techniques for one specific problem can display the beauty, and elegance of mathematics. In this paper, we present one specific, interesting geometry problem, and present four…

PWW style are presented. The difference of evidence is based on various additional auxiliary constructions, which in itself is a "mathematical art" that the student can master as a result of much practice. The PWW are accompanied by GeoGebra applets containing HINT buttons that allow the student to get step-by-step help in completing the…

The complexity of the art of teaching and learning, especially in the field of mathematics, calls for a broader approach than the traditional status quote. Proof without words in geometry coupled with the dynamic and interactive GeoGebra applet have the capacity to be used in all levels of mathematics education from grade schools to higher…

With the ever-evolving implementation of technology in the teaching and learning of geometry, the task of designing and/or finding suitable questions or problems that can facilitate and promote mathematical reasoning and accurately assess students' understanding of the subject matter can be a challenge. It is the aim of this article to share the…

The article presents some examples of plane geometric variance of an area with the use of computer technology. These tools can offer teachers opportunities for adaptation and preparation of pedagogical presentations which will help students along the process of fruitful conjectures formation and eventually construction of formal deductive proofs.…

Proof and argumentation are essential components of learning mathematics, and technology can mediate students' abilities to learn. This systematic literature review synthesizes empirical literature which examines technology as a support for proof and argumentation across all content domains. The themes of this review are revealed through analyzing…

An interesting Sangaku problem was chosen and a multidirectional study was performed, which included finding the locus of a circle's center moving while being tangent to two circles. It also included finding the radius of that circle given the datum that it is also tangent to the side of an isosceles triangle. Two different proofs are presented of…

Many mathematics educators are not aware of a strong connection that exists between the education of computer programming and mathematics. The reason may be that they have not been exposed to computer programming. This connection is worth exploring, given the current trends of automation and Industry 4.0. Therefore, in this paper we take a closer…

This document introduces, describes and exemplifies the technical features of some recently implemented automated reasoning tools in the dynamic mathematics software GeoGebra. The new tools are based on symbolic computation algorithms, allowing the automatic and rigorous proving and discovery of theorems on constructed geometric figures. Some…

Technology has changed school geometry in many aspects. Hand-made sketches can be substituted with precise dynamic constructions; computer software allows effective measuring of geometric quantities, persuasive visualisation, effective checking of properties, and even automated proving. Observation -- a process that is inherent in geometric…

The paper deals with searching for synthetic solution supported by the means of dynamic geometry. It consists of two parts. The first one describes how software influences searching for synthetic solutions of geometric problems. The second one describes a small pilot experiment in which students of Faculty of Education solved two more difficult…

In this paper, we focus our discussion on the strategy we follow to scaffold high school students to successfully build models of a real-life system. Our aim is for students to gradually achieve a higher level of autonomy and to use and further develop their mathematical knowledge. We present work students did when we asked them to build a model…

Dynamic geometry environment allows us to investigate geometric relationships and problems more efficiently than the pencil-and-paper method. Continuous variation of geometric configurations shows the relationship from different points of view. This paper aims to provide some indications of how a dynamic geometry environment, especially GeoGebra…

Stepwise program refinement techniques can be used to simplify program verification. Programs are better understood since their main properties are clearly stated, and verification of rather complex algorithms is reduced to proving simple statements connecting successive program specifications. Additionally, it is easy to analyse similar…

There is a recognised need in mathematics teaching for new kinds of tasks which exploit the affordances provided by new technology. This paper focuses on the design of prediction tasks to foster student reasoning about exponential functions in a mathematics software environment. It draws on the first iteration of a design based research study…