Dendroidal sets have been introduced as a combinatorial model for homotopy coherent operads. We introduce the notion of fully Kan dendroidal sets and show that there is a model structure on the category of dendroidal sets with fibrant objects given by fully Kan dendroidal sets. Moreover we show that the resulting homotopy theory is equivalent to the homotopy theory of connective spectra.

The paper presents an overview of metal additive manufacturing technologies. The emphasis is on unconventional emerging technologies with firm background on welding technologies such as Ultrasonic Additive Manufacturing, Friction Additive Manufacturing, Thermal Spray Additive Manufacturing, Resistance Additive Manufacturing and Wire and Arc Additive Manufacturing. The particular processes are explained in detail and their advantages and drawbacks are presented. Attention is made on materials used, possibilities to produce multi-material products and functionally graded materials, and typical applications of currently developed technologies. The state-of-the-art on the Wire and Arc Additive Manufacturing is presented in more detail due to high research interests, it’s potential and widespread. The main differences between different arc additive manufacturing technologies are shown. An influence of processing parameters is discussed with respect to process stability and process control. The challenges related to path planning are shown together with the importance of post-processing. The main advantage of presented technologies is their ability of making larger and multi-material parts, with high deposition rate, which is difficult to achieve using conventional additive technologies.

Critical thinking is widely regarded as a key competency in STEM education, particularly in light of 21st-century challenges such as digitalisation, climate change, and technological transformation. Although critical thinking is included in educational policies, its implementation in classroom practice remains limited, partly resulting from a lack of a common understanding that is both theoretically grounded and usable for teachers. In this paper, we introduce a rubric that aims to support the integration of critical thinking into STEM education. The rubric is based on an epistemic understanding of critical thinking rooted in the scientific process of discovery. It was developed through an iterative design process grounded in the Synergy Model of Critical Thinking and piloted with pre- and in-service teachers in four European countries. Their feedback was collected using qualitative questionnaires and focus groups and was analysed using a comparative analysis of the pilot implementations. Results suggest that the rubric captures the central aspects of critical thinking from a scientific perspective and provides a useful reference point for STEM teaching and reflection. However, its use as an assessment tool for critical thinking in all its manifestations is limited, due to its reliance on subject-specific knowledge. Overall, the findings indicate that this rubric could be used to flexibly support instructional design and professional reflection, rather than as a standardised instrument for assessing student performance.

The design of inquiry-based tasks and problem situations for daily mathematics teaching is still a challenge. In this article, we study the implementation of two tasks as part of didactic scenarios for inquiry-based mathematics teaching, examining teachers’ classroom orchestra-tion supported by these scenarios. The context of the study is the Erasmus+ project MERIA – Mathematics Education: Relevant, Interesting and Applicable, which aims to encourage learning activities that are meaningful and inspiring for students by promoting the reinvention of target mathematical concepts. As innovative teaching materials for mathematics education in secondary schools, MERIA scenarios cover specific curriculum topics and were created based on two well-founded theories in mathematics education: realistic mathematics education and the theory of didactical situations. With the common name Conflict Lines (Conflict Lines – Introduction and Conflict Set – Parabola), the scenarios aim to support students’ inquiry about sets in the plane that are equidistant from given geometrical figures: a perpendicular bisector as a line equidistant from two points, and a parabola as a curve equidistant from a point and a line. We examine the results from field trials in the classroom regarding students’ formulation and validation of the new knowledge, and we describe the rich situations teachers may face that encourage them to proceed by building on students’ work. This is a crucial and creative moment for the teacher, creating opportunities and moving between students’ discoveries and the intended target knowledge.