In this paper, we present a research project we conducted with 27 undergraduate students in a history of mathematics course in Greece during the academic year 2022-2023. In our study, we presented participants with an open-ended problem with historical background and evaluated their reactions and solving strategies. To reach findings we collected data via worksheets, questionnaires and interviews. We intended to focus on students’ techniques for open-ended issues while also investigating whether and how History of Mathematics may be included into its instruction. The results showed that such type of problems is able to catch the participants’ attention and support them in experimentation and development of multiple problem solving strategies. The students acquired a positive attitude towards the entire process, and they would like to repeat it in other university courses, too. This study might pave the way for a new curriculum that includes historically inspired open-ended assignments in school and university practice.

Proof, as a central and integral part of mathematics, is an essential component of mathematical education and is considered as the basic procedure for revealing the truth of mathematical propositions and for teaching productive reasoning as part of human civilization. Is there therefore room for conjectures in mathematics? In this paper after discussing at a theoretical level the concepts of proof and conjecture, both in a paper-and-pencil environment and in a dynamic geometry environment (DGE) as well as how school practice affects them, we fully explain a task involving various mathematical disciplines, which we tackle using elementary mathematics, in a mathematics education context. On the occasion of the Greek educational system we refer to some parameters of the teaching of geometry in school and we propose an activity, within a DGE, that could enable students to be guided in the formulation and exploration of conjectures. Finally, we discuss the teaching implications of this activity and make some suggestions.

This paper explores the relationship between primary school students’ pattern recognition and mathematical problem-solving. A mixed-method research approach combining worksheets and interviews is used to identify patterns in students’ responses, with a focus on spatial, repeating, and growing patterns. The results of preliminary experiments with four Greek students aged eight to 11 years old, suggest a preference for geometric concepts and real-world examples. The findings could contribute to the discussions on customized pedagogical strategies in mathematics education, highlighting the importance of individualized approaches for optimal learning outcomes. The study advocates for the inclusion of visual and applied elements to cultivate critical thinking and problem-solving skills in early education.

The well-known from the History of Mathematics “hundred fowls problem” is the topic of this paper. Our main aim is to analyze the historical background of the problem and to present some ways of solving it, which have different characteristics, and each one represents a particular strategy. The interaction of Eastern and Western mathematics and the combination of different fields like Algebra and Technology in order to solve the problem has been highlighted. The study of the specific topic revealed some teaching perspectives, which we note at the end together with some concluding remarks. This paper might have implications in future research in the field of indeterminate analysis but also in Mathematics Education.

In this paper we discuss, from a historical and philosophical point of view, a variation of the meaning of the five postulates in Euclidean Geometry and we make a short reference to D. Hilberts formalism. We examine, throughout the ages, the question what is Geometry by studying the segmentation and the unification of various geometries, been introduced by F. Kleins Erlangen Program. We concisely present three out of nine Cayley-Klein geometries and then we conclude with some didactic perspectives.