In this paper we report on an activity developed in the context of the Erasmus+ PUNTE Project, using the Poly-Universe material, which led to the learning of logic and mathematics among the 10th grade students of a school in the central region of Portugal. Three teachers, two of mathematics and one of philosophy, and 21 students of secondary education participated in the study. The data obtained, following the observation and application of questionnaires and pre- and post-tests, reveal the usefulness of Poly-Universe for the acquisition of notions about logical operations, for analysing arguments and their validity and solving mathematical problems, motivating the students for carrying out the activity.

Citizens and scientists can work together to improve the collective well-being, if citizens are inspired to help the advancement of science, and researchers motivated to listen to the voices of citizens. The benefits of such collaboration are increasingly recognized by both citizens and scientists, as reflected in the growing number of related publications and initiatives. This is especially relevant for emerging areas of research, where early involvement of citizens could help to envision, prioritize, and plan prospective studies. The Problematic Usage of the Internet (PUI) is one such area, which is fast becoming a public mental health concern. However, there remains a lack of clarity regarding the practical guidelines and ethical requirements for citizen involvement at the earliest stages of PUI. In our paper, we propose a conceptual framework and a template for initial involvement of citizens in PUI. They are derived from our community case studies, conducted in six European countries (Georgia, Greece, Malta, North Macedonia, Portugal, and Spain) and consisting of consultation with diverse groups of interested citizens (students, parents, teachers, and health professionals). Informed by our consultation exercises, we also highlight four ethical aspects for citizen involvement in the research on PUI or novel disciplines in general. They follow simple guiding principles to ensure that scientists will: enable a long-term commitment and inclusive opportunities for citizens, challenge established power hierarchies, and support collaboration, co-production and co-authorship with citizens. We believe that the proposed practical guidelines and ethical considerations, provide a valuable foundation on which to advance our understanding and generate international strategies for citizen involvement in PUI.

This study attempts to characterise what 7th- and 12th-grade students believe they do not know about artefacts and natural objects, as well as the dependence of what is unknown on a knowledge of these objects. The students were asked to make explicit through questioning what they did not know about a sample of objects. The unknowns generated were categorised according to a scheme based on lexical semantics theory. Two of the categories focused specifically on imprecise unknowns expressed through What is X? questions, and on unknowns concerning functions. The results showed, firstly, that a lower grade level and lower knowledge of a certain class of objects was associated with more imprecise unknowns. Secondly, unknowns about the functions of artefacts were significantly more frequent than unknowns about the functions of natural objects at any of the grade levels. Overall, the results were consistent with the hypothesis of a correspondence between knowledge and unknowns.

The aim of this study is to analyse the effect of tasks on the detection of explanation obstacles when secondary school students read scientific texts. Students were instructed to read short passages under different task conditions, and to ask questions if necessary. Obstacle detection was operationalised in terms of the type of questions asked by the students. The experiment examined the influence of goals associated with the task of reading to understand a text vs. reading to perform a procedure described by the text (a science experiment). Significantly, more explanation obstacles were found in the understanding condition than in the experiment condition. Scientific text also had an effect on the explanation obstacles detected.