Mathematics has a strong presence in the school curriculum, often justified by its usefulness in social life, in the world of work and by its connections with other sciences. This interdisciplinary connection, in particular when it requires constructing and refining mathematical models and discussing their applications to solve problems of other sciences, can assist students to understand why mathematics is so important in school. In the development of interdisciplinary activities, the characteristics of the tasks emerge as an important aspect. The emphasis is on the use of technological materials and the way they can support the development of concepts, provide different representations and support deeper understandings, and offer a multifaceted support to collect data and simulate experiences. Based on these assumptions, the aim of this chapter is to present, analyse and discuss tasks that promote interdisciplinary technological approaches from a mathematical point of view. In this chapter we assume interdisciplinarity as a complex construct, and in order to clarify its meaning we will discuss several types of conceptions, from multidisciplinary, to interdisciplinary, and to transdisciplinary. We will then address related concepts, such as modelling and STEM, highlighting similarities and differences between them, to reach an understanding of interdisciplinarity. In the process of the interdiciplinary approach, digital technologies arise as a central element. Based on a set of tasks on mathematics and on different sciences, we discuss what can change on an interdisciplinary approach to the teaching and learning of mathematical content and on the articulation between subjects.

We present a new algorithm for solving large-scale unconstrained optimization problems that uses cubic models, matrix-free subspace minimization, and secant-type parameters for defining the cubic terms. We also propose and analyze a specialized trust-region strategy to minimize the cubic model on a properly chosen low-dimensional subspace, which is built at each iteration using the Lanczos process. For the convergence analysis we present, as a general framework, a model trust-region subspace algorithm with variable metric and we establish asymptotic as well as complexity convergence results. Preliminary numerical results, on some test functions and also on the well-known disk packing problem, are presented to illustrate the performance of the proposed scheme when solving large-scale problems.

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Polynomial interpolation or regression models are an important tool in Derivativefree Optimization, acting as surrogates of the real function. In this work, we propose the use of these models in the multiobjective framework of directional direct search, namely the one of Direct Multisearch. Previously evaluated points are used to build quadratic polynomial models, which are minimized in an attempt of generating nondominated points of the true function, defining a search step for the algorithm. Numerical results state the competitiveness of the proposed approach.

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In this paper we study the widely considered endomorphisms and weak endomorphisms of a finite undirected path from monoid generators perspective. Our main aim is to determine the ranks of the monoids $wEnd P_n$ and $End P_n$ of all weak endomorphisms and all endomorphisms of the undirected path $P_n$ with $n$ vertices. We also consider strong and strong weak endomorphisms of $P_n$.

High-strength concrete (HSC) slab-column connections with relatively low concrete strengths compared to today’s capabilities have been tested under seismic-type loading in the past. Herein, the hybrid use of HSC with compressive strength approximately 120 MPa and normal-strength concrete (NSC) is investigated through three reversed horizontal cyclic-loading tests with different geometries of the HSC region and a reference NSC specimen. The results show that HSC applied in the vicinity of the column can significantly enhance the seismic performance of slab-column connections. The best result in terms of drift capacity and economic use of HSC was achieved in the case of full-depth HSC extended from the column’s face up to 2.5 times the effective depth. Drift ratios up to 3.0% were achieved. A comparison with previous tests showed that the hybrid use of HSC and NSC can achieve similar results to the provision of punching shear reinforcement.

A suspensão das aulas presenciais na sequência da pandemia que estamos a atravessar trouxe para primeiro plano o ensino a distância. Neste artigo partilhamos algumas ideias e conceptualizações relativas a este tipo de ensino, abordamos aquilo que alguns autores que se têm dedicado à temática apontam como importantes desafios e oportunidades que se lhe encontram associados e, por fim, partilhamos algumas possíveis opções e recursos que pensamos poderem ser úteis para todos os professores que estão a viver a sua primeira experiência de ensino a distância.