This paper presents the results of an experimental teaching carried out on 12-year-old students. An open-ended task was given to them and they had not been taught the algorithmic process leading to the solution. The formal solution to the problem refers to a system of two linear equations with two unknown quantities. In this mathematical activity, students worked cooperatively. They discussed their discoveries in groups of four and then presented their answers to the whole class developing a rich communication. This study describes the characteristic arguments that represent certain different forms of reasoning that emerged during the process of justifying the solutions of the problem. The findings of this research show that within an environment conducive to creativity, which encourages collaboration, exploration and sharing ideas, students can be engaged in developing multiple mathematical strategies, posing new questions, creating informal proofs, showing beauty and elegance and bringing out that problem solving is a powerful way of learning mathematics.

Sustainable development has emerged as a critical priority for the global community, influencing all aspects of development worldwide. Within this context, the role of education and training in advancing sustainable development can contribute to this. This research aims to explore whether the integration of Information and Communication Technology educational tools into the curricula of engineering technicians helps trainees better understand the concepts of climate change and resource management, which are directly linked to the green transition and the green economy, compared to traditional educational methods. The study was conducted with trainees from Higher Vocational Training Schools (SAEKs) in the wider Athens area, Greece. According to the results, using educational technology to teach engineering courses aids students in developing the competencies needed to change production processes and business models in the direction of a greener future. This is especially crucial as future technicians will be able to use cutting-edge methods to lower emissions and boost resource use efficiency. The findings of the study could provide important information for all those involved in the design of educational curricula of engineering technicians. Concerns and thoughts on the effective use of educational technology in the educational process are also expressed.

What is the concept of the open-ended problem? Why is it necessary to pose open problems for research in the class? Which are the essential difficulties of treatment of the open problems in the class? How could we treat them? This text supplements a series of articles of the bibliography devoted to the resolution of the open problems. It presents short data of the practice and exposes many statements of the organized open problems of categories, favourable for research with groups of co-operation in the class with the level of the high school and senior high school. It brings new elements on the subject, and recalls for memory of the already treated questions.