In the article, we prove 18 inequalities involving inradius, a length of one side and one additional element of a given triangle. 14 of these inequalities are the necessary and sufficient conditions for the existence and uniqueness of such a triangle. All proofs are based on standard methods of calculus and can serve as a good demonstration of the…

Eye-tracking (ET) method provides a promising channel for educational researchers to connect learning outcomes to cognitive processes. The main principle of ET is that our gaze and our focus of attention are connected. Due to the advent of digital technologies, eye tracking studies are increasingly growing in different fields and in mathematics…

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these…

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…

Our article aims to show how illuminating mathematical work as a concept from didactics of mathematics is useful in understanding issues relating to proving and learning of proof, with or without technology. After posing our hypotheses on the relationship of proof with mathematical work, the pedagogical intent of historical elements of geometry…

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…

We shift the view of a special needs student away from the acknowledged view, that is as a student who requires interventions to restore a currently expected functioning behaviour, introducing a new paradigm to frame special needs students' learning of mathematics. We use the theory of objectification and the new paradigm to look at (and…

In this study, I examine the role of dynamic geometry software (DGS) in curricular proof tasks. I investigated seven US high school geometry textbooks that were categorised into three groups: technology-intensive, standards-based, and traditional curricula. I looked at the frequency and purpose of DGS use in these textbooks. In addition, I…

In this paper, I review both mathematics education and CSCL literature and discuss how we can better take advantage of CSCL tools for developing mathematical proof skills. I introduce a model of proof in school mathematics that incorporates both empirical and deductive ways of knowing. I argue that two major forces have given rise to this…

We explore how 13 year-olds construct meanings around the notion of curvature in their classroom while working with software that combines symbolic notation to construct geometrical figures with dynamic manipulation of variable. The ideas of curve as intrinsic dynamic construction, and curve as object with properties related to its positioning on…

Results of a study involving pre-constructed, web-based, dynamic geometry sketches in activities at the secondary school level revealed that the provision of accurate images is an issue. Many students do not automatically understand that an on-screen image is accurate. Others inadvertently create a special case by dragging, then generalise from…

This paper analyses a case study of a pair of students working together, who were asked to produce conjectures and to validate them within the dynamic geometry environment Cabri. Our aim is to scrutinize the students' reasoning, how the gap from perception to theory is filled, how Cabri influences the reasoning. We have singled out a sequence of…