In this paper we consider endomorphisms of an undirected cycle graph from Semigroup Theory perspective. Our main aim is to present a process to determine sets of generators with minimal cardinality for the monoids $wEnd(C_n)$ and $End(C_n)$ of all weak endomorphisms and all endomorphisms of an undirected cycle graph $C_n$ with $n$ vertices. We also describe Green's relations and regularity of these monoids and calculate their cardinalities.

In this paper we consider the monoids of all partial endomorphisms, of all partial weak endomorphisms, of all injective partial endomorphisms, of all partial strong endomorphisms and of all partial strong weak endomorphisms of a star graph with a finite number of vertices. Our main objective is to determine their ranks. We also describe their Green's relations, calculate their cardinalities and study their regularity.

In this paper we study the cyclic inverse monoid CI_n on a set Ω_n with n elements, i.e. the inverse submonoid of the symmetric inverse monoid on Ω_n consisting of all restrictions of the elements of a cyclic subgroup of order n acting cyclically on Ω_n. We show that CI_n has rank 2 (for n⩾2) and n⋅2^n−n+1 elements. Moreover, we give presentations of CI_n on n+1 generators and (n^2+3n+4)/2 relations and on 2 generators and (n^2−n+6)/2 relations. We also consider the remarkable inverse submonoid OCI_n of CI_n constituted by all its order-preserving transformations. We show that OCI_n has rank n and 3⋅2^n−2n−1 elements. Furthermore, we exhibit presentations of OCI_n on n+2 generators and (n^2+3n+8)/2 relations and on n generators and (n^2+3n)/2 relations.

In this note we give a presentation for the monoid IO_n of all order-preserving transformations of a n-chain whose ranges are intervals. We also consider the submonoid IO_n^- of IO_n consisting of order-decreasing transformations, for which we determine the cardinality, the rank and a presentation.

In this paper, we consider the monoid DPW_n of all partial isometries of a wheel graph W_n with n+1 vertices. Our main objective is to determine the rank of DPW_n. In the process, we also compute the ranks of three notable subsemigroups of DPW_n. We also describe Green's relations of DPW_n and of its three considered subsemigroups.

In this paper we consider three submonoids of the dihedral inverse monoid DI_n, namely its submonoids OPDI_n, MDI_n and ODI_n of all orientation-preserving, monotone and order-preserving transformations, respectively. For each of these three monoids, we compute the cardinal, give descriptions of Green's relations and determine the rank.

In this chapter, we examine the role of policies and other factors affecting digital technology (DT) integration in mathematics education. In particular, we develop a cross-national analysis of the impact on DT implementation in four countries: two countries in Europe (Italy and Portugal) and two countries in Latin America (Colombia and Mexico). We analyze the role that policies, political changes, reforms, curricula, educational organization and systems, sociocultural aspects, and teachers’ training, knowledge, and beliefs play toward possible DT implementations. We observe that there is a discourse in policies to promote digital technologies’ use, but in practice the availability and integration of such resources in mathematics classrooms is still scarce. We also note that the efforts done during the pandemic did not change this, promoting general ICT use, rather than DT resources that might enhance mathematics teaching and learning.

This study was conducted while 9th grade students learn to solve inequalities and seeks to understand their approach to solving problems with a real-life context. Specifically, the aim is to understand: (1) What are the main characteristics of the students’ approaches to the proposed problems? (2) What is the impact of the real context on the students’ resolutions? A qualitative and interpretative methodology is adopted, based on case studies, with data collected through documentary collection and audio recording of discussions between a pair of students while solving problems. The main conclusions suggest a trend to approach problems without establishing immediate connections with what was being done in the classroom, with students’ decisions being essentially guided by criteria of simplicity. The real context of the problems seems to have the potential to develop in students a more integrated mathematics, focused on understanding and not so much on the repetition of mechanical and meaning-independent procedures. The students’ familiarization with the context in question is one of the aspects highlighted by this study.

This study seeks reflection on the approaches of 11th grade students to Linear Programming problems, discussing the approaches taken at different moments of the teaching process. It aims to analyze:
How is the students’ mathematical competence characterized in relation to problemsolving;
What differences can be identified in the resolutions at different moments of the teaching and learning process.
We adopt a qualitative and interpretative methodology, analyzing the approaches of two pairs of students with different mathematical backgrounds. The analysis is guided by P´olya’s stages of solving a problem and aspects of the understanding of mathematical competence. The results show different approaches to the problems depending on the teaching moment and different competences. The mathematical background impacts the students’ success when they implement routine procedures, however it does not seem to determine the students’ competence to reason about a problem.

In Portugal, digital transition was structured with national public policies since 2003. In 2017, initiatives for the adoption of Industry 4.0 concepts are implemented in Portugal. We analysed the diffusion and implementation of these technologies, in Portugal. Some questions were raised: has the interplay between public policies, state agencies and industrial relations players in the process been articulated, as in Germany? What have been the effects of these technologies on workers and organisations? Are the public initiatives in place enough or more is needed? Qualitative and quantitative approaches were used to collect evidence on the main features and constraints of a public policy for Industry 4.0, based on the case study of the automotive sector in Portugal. Findings suggest the need to balance regulatory policies on data related risks, and investment policies towards education, training and organisational innovation are needed to complement technology development and adoption support.

The adoption of I4.0’s technologies in the work cells accompanied by societal changes calls for new approaches to manage the current production systems. Nevertheless, the current models simulating the behavior of the work cells limit the representation of the operators to the average human, without regard for their individual characteristics, cognitive abilities or psychosocial state. The aim of this paper is to achieve two objectives: firstly, the authors propose a conceptual model for enhancing a human-centered production environment. Secondly, the paper summarizes how the literature characterizes the different dimensions of relations between cognitive and organizational factors. By integrating the collaborative, psychological, social, cognitive, organizational and system performance dimensions, the proposed model focuses on the relationships between these dimensions. Thus, operational models should be closer to the real production environment to improve the design choices of the manufacturing systems.

The potential of technology to enhance the learning of mathematics is widely acknowledged. However, realizing this potential requires teachers to possess the knowledge to effectively integrate it into their teaching practices. This study aims to characterize the mathematics teacher's knowledge when using different technologies in teaching and learning. It also aims to study the existence of relationships between the specific domains of the Knowledge for Teaching Mathematics with Technology – KTMT and the integration of graphing calculator and Excel. The methodology adopted is qualitative with an interpretative approach, using a case study of Mathematics teacher in the 11th grade (16-17 years old) with extensive experience in the use of technology. This study shows that different KTMT knowledge is mobilized, according to the technology chosen and the specific characteristics of each of the technologies used influenced the teacher's pedagogical choices.

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This study aims to discuss similarities and differences between knowledge models focusing on technology, developing the Global Model. This is not a new model, but rather a contribution to the articulation between different conceptual frameworks.

Este estudo visa discutir semelhanças e diferenças entre modelos de conhecimento com foco na tecnologia, desenvolvendo a partir destes o Modelo Global. Este não é um novo modelo, mas antes um contributo para a articulação entre diferentes quadros conceptuais.

Turiasauria is a clade of basal sauropod dinosaurs hitherto only known from the Middle Jurassic (Bathonian) to the Lower Cretaceous (Valanginian). A new find of a shed tooth crown from the Lower Jurassic (Pliensbachian), Halse Formation of Bornholm, Denmark, is spoon-like, asymmetrical, and heart-shaped, which identifies the tooth as turiasaurian, pushing the origin of the Turiasauria some 17 My back into the Lower Jurassic. This suggests a North Pangean/Laurasian origin of the turiasaurian clade, which then, during the Middle to Late Jurassic, dispersed through Europe, India, and Africa, with their latest representatives found in the Early Cretaceous of England and North America. Furthermore, this is the first record of a sauropod from the Pliensbachian in Europe.

Iguanodontia is a diverse clade of herbivorous ornithischian dinosaurs that were speciose and abundant during the Jurassic and Cretaceous. Although the monophyly of Iguanodontia is well supported, their internal relationships have sparked heated debate due to several phylogenetic paradigm shifts. Late Jurassic basally branching iguanodontians in particular are not well understood in terms of their systematic affinities and evolutionary relevance. Their fossil record in Europe is meager compared with North America, with only a few species currently recognized. Two taxa are currently known from the Upper Jurassic of England, the basally branching styracosternan Cumnoria prestwichii and the putative dryosaurid Callovosaurus leedsi. In the Upper Jurassic of Portugal, the styracosternan Draconyx loureiroi and the dryosaurid Eousdryosaurus nanohallucis are presently the only described basally branching iguanodontians. Here we report a new species of early diverging iguanodontian from the Upper Jurassic Lourinhã Formation of western-central Portugal. The new species is clearly distinguished from all other coeval taxa by an exclusive combination of characters that include a tibia with a cnemial crest that is directed craniolaterally and a fibular condyle that is angled at 90° with respect to the proximal epiphysis, a fibula with symmetrical proximal margins, and a reduced metatarsal I. The phylogenetic relationships of the Lourinhã iguanodontian were explored using maximum parsimony and Bayesian inference. The two analyses recover the Lourinhã iguanodontian as an indeterminate dryomorphan, with more precise affinities precluded due to the current available material. Body size is estimated between 3 and 4 meters for the holotype specimen, adding to the diversity of small ornithopods already recognized in the paleoichnological record of the Lourinhã Formation. http://zoobank.org/urn:lsid:zoobank.org:pub:5F4D52D0-0F0B-4809-8561-BE58C7C97D45