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Let S be a regular semigroup. A pair (e , f) of idempotents of S is said to be a skew pair of idempotents if f e is idempotent, but e f is not. T. S. Blyth and M. H. Almeida (T. S. Blyth and M. H. Almeida, skew pair of idempotents in transformation semigroups, Acta Math. Sin. (English Series), 22 (2006), 1705–1714) gave a characterization of four types of skew pairs—those that are strong, left regular, right regular, and discrete—existing in a full transformation semigroup T (X) . In this paper, we do in this line for partial transformation semigroups. [ABSTRACT FROM AUTHOR]

In this paper, we consider the experiences of mathematics lecturers in higher education and how they moved to emergency remote teaching during the initial university closures due to the COVID-19 pandemic. An online survey was conducted in May–June 2020 which received 257 replies from respondents based in 29 countries. We report on the particular challenges mathematics lecturers perceive there to be around teaching mathematics remotely, as well as any advantages or disadvantages of teaching mathematics online that they report. Over 90% of respondents had little or no prior experience teaching mathematics online, and, initially, 72% found it stressful and 88% thought it time-consuming. 88% felt there was a difference between teaching mathematics in this way compared with other disciplines. Four main types of challenges were associated with emergency remote teaching of mathematics: technical challenges; student challenges; teaching challenges; and the nature of mathematics. Respondents identified flexibility as the main advantage of online teaching, with lack of interaction featuring strongly as a disadvantage. We also consider respondents' personal circumstances during this time, in terms of working conditions and caring responsibilities and conclude by summarizing the impact they perceive this experience may have upon their future teaching. Forty-six percent% of respondents self-identified as having caring responsibilities, and 61% felt the experience would affect their future teaching. [ABSTRACT FROM AUTHOR]

The paper is a reflection on the author's work with students enrolled in undergraduate and graduate elementary mathematics content and methods courses. Two specific pedagogical issues make up the focus of the paper. The first issue deals with demonstrating to future teachers the diversity of mathematical ideas behind a contextual question asked by a second-grade pupil allowing for multiple solution strategies to be used in addressing the question. The second issue deals with the use of Wolfram Alpha in aiding different mathematical features of this demonstration. The paper is congruous with mathematics teaching standards used across six continents and illustrated by reflective comments of the author's students regarding their mathematics teacher education experiences. Teaching ideas shared in the paper may be of interest to instructors who want to explore elementary mathematics in depth with teacher candidates. [ABSTRACT FROM AUTHOR]

Discussions are presented by Morita and Sato in Mathematics 2017; 5, 62: 1–24, on the problem of obtaining the particular solution of an inhomogeneous ordinary differential equation with polynomial coefficients in terms of the Green's function, in the framework of distribution theory. In the present paper, a compact recipe in nonstandard analysis is presented, which is applicable to an inhomogeneous ordinary and also fractional differential equation with polynomial coefficients. The recipe consists of three theorems, each of which provides the particular solution of a differential equation for an inhomogeneous term, satisfying one of three conditions. The detailed derivation of the applications of these theorems is given for a simple fractional differential equation and an ordinary differential equation. [ABSTRACT FROM AUTHOR]

International research has pointed out the importance of integrating mathematical modeling and inquiry processes into the teaching and learning of mathematics. This paper aims to present an integrative model that enables analyzing the characteristics inquiry and modeling processes share in the same model with a view to using them when designing and implementing interdisciplinary teaching sequences. After presenting a synthesis of the literature review, our theoretical approach to inquiry and modeling for the analysis of an interdisciplinary teaching sequence will be introduced. We focus here on the case of an inquiry situation in an archaeological context where mathematics and history are interrelated. It was implemented at secondary school level with students aged 13–14. We use this particular case study to analyze the appearance of both processes, in order to look for coincidences, concatenations and synergies. The main result is an integrative model for the joint analysis of both processes. [ABSTRACT FROM AUTHOR]

This reply provides one-to-one responses to comments regarding the article entitled: "Investigation and Analysis of Acoustojets by Spectral Element Method" that has been published in Mathematics by MDPI. As a corresponding author, I am happy to receive constructive criticism about the aforementioned article, in particular, suggestions and/or comments that, when addressed, may further help the reader in understanding the published material. [ABSTRACT FROM AUTHOR]

Author Contributions Conceptualization, H.K., E.M., M.V. and A.Z. Writing - Review and Editing, H.K., E.M., M.V. and A.Z. All authors contribution in the article are equal. We have found that, in the right side of Equation (35) in our paper [[1]], the addend HT ht is missing. [Extracted from the article]

Autoencoder architecture updated from [[2]]." as follows and cited the figure's original source. References 1 Mushtaq Z.B., Nasti S.M., Verma C., Raboaca M.S., Kumar N., Nasti S.J. Super Resolution for Noisy Images using Convolutional Neural Networks. Super Resolution for Noisy Images Using Convolutional Neural Networks. [Extracted from the article]

Computational thinking is considered a set of skills necessary for living and working in today's society. It has recently become part of mathematics curricula in several European countries. In this study, we offer a glimpse into the informal classroom where statistical reasoning and computational thinking are developed simultaneously. The student–teacher discussion was analysed and categorised. The dialogue dealt with both statistical and computational thinking. Implying from the nature of the activity, sources of errors and variation in data were discussed and ways to overcome the errors were discussed. The discussions related to computational thinking mainly addressed the work with BBC micro:bit, whether with the manipulation and hardware of the coding. A variable was used from both perspectives, as a mathematical concept and as an entity used to store the information. We identified the notion of a variable as the intersection between statistics and computational thinking. [ABSTRACT FROM AUTHOR]

There is, in France, a long-term tradition of research in the didactics of mathematics. In this paper, we revisit this tradition using, as a specific lens, the research carried out on the educational use of digital tools and resources for teaching and learning mathematics. We first briefly introduce this tradition and the three main theories at the base of it: the theory of didactical situations, the theory of conceptual fields, and the anthropological theory of the didactic. Then, considering three different technological lenses, i.e., dynamic geometry environments, computer algebra systems, and digital resources, we show how these theories and the long-term connection established in this tradition with the fields of cognitive ergonomics and computer sciences have influenced technological research and its outcomes. We also show that, conversely, didactic technological research has led to original and influential theoretical constructions, such as the instrumental approach and the documentational approach to didactics, and that it has contributed in a substantial way to the opening of this didactic tradition to other didactic cultures and other communities, beyond the didactic one. [ABSTRACT FROM AUTHOR]

In this paper, we apply the pseudospectral method based on the Chebyshev cardinal function to solve the parabolic partial integro-differential equations (PIDEs). Since these equations play a key role in mathematics, physics, and engineering, finding an appropriate solution is important. We use an efficient method to solve PIDEs, especially for the integral part. Unlike when using Chebyshev functions, when using Chebyshev cardinal functions it is no longer necessary to integrate to find expansion coefficients of a given function. This reduces the computation. The convergence analysis is investigated and some numerical examples guarantee our theoretical results. We compare the presented method with others. The results confirm the efficiency and accuracy of the method. [ABSTRACT FROM AUTHOR]

The author wishes to make the following correction to this paper [[1]]: Everywhere it occurs, the phrase "for every convex set HT ht dense in HT ht " should be replaced with "for every convex set HT ht dense in HT ht ". Then, in the conclusion of Theorem 1, we can replace " HT ht " with " HT ht ". Finally, in the proof of Theorem 3, we take HT ht , so that condition HT ht is actually enough to prove equality (1). [Extracted from the article]

DP-coloring as a generalization of list coloring was introduced by Dvořák and Postle recently. In this paper, we prove that every planar graph in which the distance between 6 − -cycles is at least 2 is DP-3-colorable, which extends the result of Yin and Yu [Discret. Math. 2019, 342, 2333–2341]. [ABSTRACT FROM AUTHOR]

DP-coloring was introduced by Dvořák and Postle [J. Comb. Theory Ser. B 2018, 129, 38–54]. In this paper, we prove that every planar graph in which the 5 − -cycles are at distance of at least 3 from each other is DP-3-colorable, which improves the result of Montassier et al. [Inform. Process. Lett. 2008, 107, 3–4] and Yin and Yu [Discret. Math. 2019, 342, 2333–2341]. [ABSTRACT FROM AUTHOR]

This Special Issue includes the most important studies of the Cryptocurrencies and Blockchain Technologies, such as the analysis of the Bitcoin price dynamics, the macroeconomic consequences of introducing Central Bank Digital Currencies (CBDC), and concerns about sustainable development or the Blockchain token economy. In this Special Issue, we focus on the pricing mathematics underlying mathematical and computational methods that can be useful tools for prediction or for estimating the reasonable value of something. This book contains the successful invited submissions [[1], [3], [5], [7], [9]] to a Special Issue of I Mathematics i on the subject area of "Mathematics, Cryptocurrencies and Blockchain Technology". [Extracted from the article]

A certain discrete probability distribution was considered in ["A discrete probability distribution and some applications", Mediterr. J. Math., 2023]. Its basic properties were investigated and some applications were presented. We now embed this distribution into a family of discrete distributions depending on two parameters and investigate the properties of the new distributions. [ABSTRACT FROM AUTHOR]

The effectiveness of technology-enhanced resources in mathematics in higher education is far from clear, nor is student engagement with such resources. In this review article, we investigate the existing literature in three interrelated areas: student engagement with technology in higher education and mathematics; what works and what does not in technology in education and in mathematics in higher education; evaluating the use of technology in higher education and mathematics; and the use of frameworks and models. Over 300 research articles were identified for this purpose and the results are reported in this review. We found a dearth of studies in undergraduate mathematics education that specifically focus on student engagement with technology. In addition, there is no overarching framework that describes both the pedagogical aspects and the educational context of technology integration in mathematics. [ABSTRACT FROM AUTHOR]

"Number" is an important learning dimension in primary mathematics education. It covers a large proportion of mathematical topics in the primary mathematics curriculum, and teachers use most of their class time to teach fundamental number concepts and basic arithmetic operations. This paper focuses on the nature of mathematics pedagogical content knowledge (MPCK) concerning arithmetic word problems. The aim of this qualitative research was to investigate how well the future primary school teachers in Hong Kong had been prepared to teach mathematical application problems for third and sixth graders. Nineteen pre-service teachers who majored in both mathematics and primary education were interviewed using two sets of scenario-based questions. The results revealed that innovative approaches were suggested for teaching third graders while the strategies suggested for teaching sixth graders were mostly based on a profound understanding of mathematical content knowledge. Many participants demonstrated sound knowledge about the sixth grader's mathematical misconception, but most of them were unable to precisely indicate the third grader's error in presenting a complete solution for a typical mathematics word problem. A deep understanding of elementary number theory seems to be a precondition for developing pre-service teachers' MPCK in teaching arithmetic word problems. [ABSTRACT FROM AUTHOR]

Hybrid numbers are generalizations of complex, hyperbolic and dual numbers. A hyperbolic complex structure is frequently used in both pure mathematics and numerous areas of physics. In this paper we introduce a special kind of spacelike hybrid number, namely the F (p , n) -Fibonacci hybrid numbers and we give some of their properties. [ABSTRACT FROM AUTHOR]

The popularity of deep reinforcement learning (DRL) applications in economics has increased exponentially. DRL, through a wide range of capabilities from reinforcement learning (RL) to deep learning (DL), offers vast opportunities for handling sophisticated dynamic economics systems. DRL is characterized by scalability with the potential to be applied to high-dimensional problems in conjunction with noisy and nonlinear patterns of economic data. In this paper, we initially consider a brief review of DL, RL, and deep RL methods in diverse applications in economics, providing an in-depth insight into the state-of-the-art. Furthermore, the architecture of DRL applied to economic applications is investigated in order to highlight the complexity, robustness, accuracy, performance, computational tasks, risk constraints, and profitability. The survey results indicate that DRL can provide better performance and higher efficiency as compared to the traditional algorithms while facing real economic problems in the presence of risk parameters and the ever-increasing uncertainties. [ABSTRACT FROM AUTHOR]

Italian domination can be described such that in an empire all cities/vertices should be stationed with at most two troops. Every city having no troops must be adjacent to at least two cities with one troop or at least one city with two troops. In such an assignment, the minimum number of troops is the Italian domination number of the empire/graph is denoted as γ I . Determining the Italian domination number of a graph is a very popular topic. Li et al. obtained γ I (C n □ C 3) and γ I (C n □ C 4) (weak {2}-domination number of Cartesian products of cycles, J. Comb. Optim. 35 (2018): 75–85). Stȩpień et al. obtained γ I (C n □ C 5) = 2 n (2-Rainbow domination number of C n □ C 5 , Discret. Appl. Math. 170 (2014): 113–116). In this paper, we study the Italian domination number of the Cartesian products of cycles C n □ C m for m ≥ 6 . For n ≡ 0 (mod 3) , m ≡ 0 (mod 3) , we obtain γ I (C n □ C m) = m n 3 . For other C n □ C m , we present a bound of γ I (C n □ C m) . Since for n = 6 k , m = 3 l or n = 3 k , m = 6 l (k , l ≥ 1) , γ r 2 (C n □ C m) = m n 3 , (the Cartesian product of cycles with small 2-rainbow domination number, J. Comb. Optim. 30 (2015): 668–674), it follows in this case that C n □ C m is an example of a graph class for which γ I = γ r 2 , which can partially answer the question presented by Brešar et al. on the 2-rainbow domination in graphs, Discret. Appl. Math. 155 (2007): 2394–2400. [ABSTRACT FROM AUTHOR]

The accelerated prox-level (APL) and uniform smoothing level (USL) methods recently proposed by Lan (Math Program, 149: 1–45, 2015) can achieve uniformly optimal complexity when solving black-box convex programming (CP) and structure non-smooth CP problems. In this paper, we propose two modified accelerated bundle-level type methods, namely, the modified APL (MAPL) and modified USL (MUSL) methods. Compared with the original APL and USL methods, the MAPL and MUSL methods reduce the number of subproblems by one in each iteration, thereby improving the efficiency of the algorithms. Conclusions of optimal iteration complexity of the proposed algorithms are established. Furthermore, the modified methods are applied to the two-stage stochastic programming, and numerical experiments are implemented to illustrate the advantages of our methods in terms of efficiency and accuracy. [ABSTRACT FROM AUTHOR]

This document is a correction notice for an article titled "The Effect of Preloaded Compressive Stress and Curvature of Defect on Blast-Induced Fracture Behavior by Caustic and Numerical Models." The correction includes the addition of a missing citation and the correction of a mistake in Figure 2b. The authors apologize for any inconvenience caused and state that the scientific conclusions are unaffected. The original publication has been updated to reflect these corrections. [Extracted from the article]

Our study commemorates this event by presenting a retrospective of the publications related to the use of mathematical tools for the analysis of economic, ecological, and environmental phenomena. We analyzed 1257 scientific publications using bibliometric techniques to examine the most productive and influential authors and their contributions in the economic, ecological, and environmental fields. Co-authorship among the top authors and countries, co-occurrence of the keywords, bibliographic coupling of the documents and authors, and author co-citation were analyzed by applying network analysis techniques using VOSviewer software, identifying the intellectual structure of the research and the collaborative networks in the fields. The results show that mathematics has grown impressively in terms of publication and citation. The contributions come from all over the world, but the majority are from the People's Republic of China and Spain. The results also show themes and trends in the economic, environmental, and ecological fields and a predominant use of mathematical tools in optimization processes in order to rigorously substantiate the decisions of investors and policymakers. Thus, our study offers support for any researcher to understand the current state of the art and develop a comprehensive understanding of journal publications. [ABSTRACT FROM AUTHOR]

In this work, we survey some research directions in which the ultraproduct construction and methods based on ultrafilters play significant roles. Rather different areas of mathematics have been considered: topics we are reviewing here include some aspects of the model theory of first-order and second-order existential logics, finite Ramsey theory and general topology. Special emphasis has been made for producing a uniform treatment and for highlighting interconnections between these different subjects. [ABSTRACT FROM AUTHOR]

The convexity is immediate for HT ht . I Let there be no trading constraints; the condition of no sure arbitrage i HT ht I be fulfilled. Let there be no trading constraints; the condition of no sure arbitrage i HT ht I is fulfilled. [Extracted from the article]

Our society is immersed in the Fourth Industrial Revolution due to the fast evolution of the new technologies that are modifying the labor market. In the near future, technologies related to Industry 4.0 will produce totally new goods and services. Therefore, the educational systems should adapt their programs to the future needs of an uncertain labor market. In particular, mathematics will play a key role in future jobs and there is a strong need to connect its teaching methodologies to the new technological scene. This work uses the STEAM approach (science, technology, engineering, arts and mathematics) along with active methodologies and educational robotics with the aim of developing a new strategy for the application of mathematics and physics in an engineering degree. In particular, a transportation challenge is posed to tackle the teaching–learning process of the Bézier curves and their applications in physics. A pilot project is developed using a LEGO EV3 robot and an active methodology, where students become the center of the learning process. The experimental results of the pilot study indicate an increase in the motivation due to the use of robots and the realistic context of the challenge. [ABSTRACT FROM AUTHOR]

1. In the original paper, the value of the parameter HT ht is greater than 0. Throughout the article, the value of the parameter HT ht should be HT ht . 2. For the definition of function HT ht in (23), the original expression is. [Extracted from the article]

In this paper, we introduce a new graph operation called subdivision vertex-edge join (denoted by G 1 S ▹ (G 2 V ∪ G 3 E) for short), and then the adjacency spectrum, the Laplacian spectrum and the signless Laplacian spectrum of G 1 S ▹ (G 2 V ∪ G 3 E) are respectively determined in terms of the corresponding spectra for a regular graph G 1 and two arbitrary graphs G 2 and G 3 . All the above can be viewed as the generalizations of the main results in [X. Liu, Z. Zhang, Bull. Malays. Math. Sci. Soc., 2017:1–17]. Furthermore, we also determine the normalized Laplacian spectrum of G 1 S ▹ (G 2 V ∪ G 3 E) whenever G i are regular graphs for each index i = 1 , 2 , 3 . As applications, we construct infinitely many pairs of A-cospectral mates, L-cospectral mates, Q-cospectral mates and L -cospectral mates. Finally, we give the number of spanning trees, the (degree-)Kirchhoff index and the Kemeny's constant of G 1 S ▹ (G 2 V ∪ G 3 E) , respectively. [ABSTRACT FROM AUTHOR]

There are great economic benefits and qualities of life when a country invests in the development of professionals in STEM areas. Unfortunately, there is a gender gap, as women are lagging behind their peers, as well as minority groups such as Hispanics, who are grossly underrepresented in these careers. Therefore, it is a priority to generate assessing instruments that are adapted to the cultural context of Latino students in their language to attract a more diverse population to STEM areas. This study presents a thorough validation process of the adaptation of the Self-Efficacy Survey (MSES) to the Spanish language and Mexican engineering context. Exploratory and confirmatory factor analyses were conducted with data collected from 683 Mexican engineering students to analyze its validity. The results highlight that the original three dimensions of the MSES still show a sound structure to assess math self-efficacy, and the confirmatory factor analysis eliminated items that were outdated and out of the context of this specific population. As a result, this study presents a 12-item adaptation that could help Latino researchers to collect reliable math self-efficacy data to better understand how their students feel when they learn and practice mathematics. [ABSTRACT FROM AUTHOR]

In this study, we conduct a bibliometric review of the Mathematics journal to map its thematic structure, and to identify major research trends for future research to build on. Our review focuses primarily on the bibliometric clusters derived from an application of a bibliographic coupling algorithm and offers insights into how studies included in the review sample relate to one another to form coherent research streams. We combine this analysis with keyword frequency and topic modeling analyses to reveal the discourse that is taking place in the journal more recently. We believe that a systematic/computer-assisted review of the Mathematics journal can open a path for new developments and discoveries in research and help editors assess the performance and historic evolution of the journal and predict future developments. In so doing, the findings should advance our cumulative understanding in those areas consistent with the scope of the Mathematics journal, such as applied mathematics, analytics, and computational sciences. [ABSTRACT FROM AUTHOR]

Zipper-coupled tubes are a broadly applicable, deployable mechanism with an angular surface that can be smoothed by attaching an additional smooth sheet pattern. The existing design for the smooth sheet attachment, however, leaves small gaps that can only be covered by adding flaps that unfold separately, limiting applicability in situations requiring a seamless surface and simultaneous deployment. We provide a novel construction of the smooth sheet attachment that unfolds simultaneously with zipper-coupled tubes to cover the entire surface without requiring additional actuation and without inhibiting the tubes' motion up to an ideal, unfolded state of stability. Furthermore, we highlight the mathematics underlying the design and motion of the new smooth sheet pattern, thereby demonstrating its rigid-foldability and compatibility with asymmetric zipper-coupled tubes. [ABSTRACT FROM AUTHOR]

Number theory is an area of mathematics not unknown to students majoring in mathematics teaching. As early as in junior high, they may encounter basic number theory concepts such as prime numbers, multiples, divisors, or even the fundamental theorem of arithmetic—the proof of which, however, will only be included in the university curriculum of mathematics teacher students. When teaching number theory, in addition to inspiring and motivating students, it is important to have them ask the right questions. Proofs are important, but so is the proper formulation of mathematical conjectures, not to mention intuitions regarding mathematical properties and relationships. These processes are facilitated by the software used, developed to visualize functions related to number theory. Our study aims to assess the relevance of visualization in the teaching and understanding of certain arithmetic functions among mathematics teacher students. Furthermore, we aim to investigate the practical usability of our visualization software, relying on student feedback. According to our results, students found the software useful, as it helped them to discover previously unknown relationships in the examined arithmetic functions. We may conclude our software fills a niche, with student feedback indicating its usefulness. [ABSTRACT FROM AUTHOR]

This work aims to examine how the learning of mathematics in early childhood is developed in different policies, particularly within the processes of formal education and care in early years institutions. A comparative analysis of early mathematics education policies across countries must consider cultural differences, teaching practice, structural differences and institutional framework conditions, as well as the initial training and professional knowledge of teachers and educators. Extracted from the official country regulations, the following pages include some of the main characteristics of the national systems of early childhood education and care (ECEC) in Portugal, Slovenia and Spain, as well as a comparison of the ECEC guidelines concerning mathematics education between these three countries. There is an international consensus on an approach to early mathematics education inspired by realistic mathematics education (RME), i.e., on the importance of working mathematically in context, as well as on the idea of doing so through play, developing the language to communicate mathematical ideas. However, we found that these three aspects are reflected very differently in the official regulations of the three countries: while in Spain the development is very detailed and emphasizes the holistic approach and the role of mathematics in exploring the environment, the Portuguese curriculum emphasizes the role of mathematics as a form of language. The Slovenian curriculum, at last, focuses on the concepts and procedures associated with each mathematical sense. Furthermore, there are structural features concerning the regulation and type of ECEC system that have an influence in the implementation of the curriculum. [ABSTRACT FROM AUTHOR]

Attitudes are central to the affective domain in mathematics. However, we still have a long way to go to reach a clear consensus on the characterization of such construct and its operationalization, as there are a wide variety of intertwined approaches depending on the theoretical framework that accompanies each of them. In this article, we explore the idea of incorporating ethics as part of a new characterization of attitude in problem solving contexts by means of an instrumental case study consisting of a key informant 10th grade student. Data were collected via classroom observations, questionnaires, semi-structured interviews and written productions. Results were analyzed using the lens of Aristotelian Ethics and the Theory of Creative Intelligence and show how happiness, responsibility and strength are key concepts that help to describe and understand the way the student behaves when solving mathematical problems. We conclude that besides the traditional attention paid to attitudes towards math, it is worth directing our attention towards attitudes influenced by ethics and personal affect as a whole. [ABSTRACT FROM AUTHOR]

Peer tutoring in combination with math digital tools was employed with middle school students learning mathematics. A total of 112 students in 9th grade (14 to 15 years old) participated in the study. A pretest–posttest with control group design was used. Students worked with systems of linear equations during the experience. The effects of the intervention of peer tutoring in combination with math digital tools on students' mathematics achievement were examined using quantitative methods. The way students in the experimental group learned and their motivation towards using digital tools compared with students in the control group were analysed qualitatively. Statistically significant improvements and a large effect size were reported for students' mathematics achievement in the experimental group. No statistically significant differences were reported between the pretest and the posttest for the control group. The qualitative analyses revealed that students in the experimental group achieved a higher level of autonomous learning, showed a greater association of mathematical concepts, helped their peers more, did more exercises and problems than students in the control group, and enjoyed the experience. [ABSTRACT FROM AUTHOR]

History of mathematics and mathematics education research allows us to know, among other issues: the influence that certain textbooks have had on the teaching of school mathematics, in academic or professional training, during a certain historical period; as well as the scientific advances achieved in each historical period and their incorporation into the teaching of the subject matter. In this work, we focus our attention on the applications of the method of finding maxima and minima included in the textbooks published during the 18th century in Spain. Specifically, we identify the approach of the algorithm used, the shortcomings or deficiencies that the posing of the proposed problems may have, the verification of the nature of the optimal points obtained and the consideration—or not—of the negative solutions in the process of resolution. [ABSTRACT FROM AUTHOR]

This study examines the effects of COVID-19-related measures on the mathematics achievement of university students in social sciences in Slovenia. Our particular concern was to compare two student populations (pre-pandemic and pandemic) in terms of factors affecting student performance in mathematics courses. Data were collected over nine consecutive academic years (from 2013–2014 to 2020–2021) and analyzed using two-stage structural equation modelling (SEM). The analyses confirmed that the conceptual model developed before the pandemic was applicable during the pandemic period. For both populations (pre-pandemic and pandemic), mathematics confidence, perceived level of math anxiety, background knowledge from secondary school, and self-engagement in mathematics courses at university were confirmed as factors influencing mathematics achievement. Moreover, both populations perceived the effects of the factors in the same way, and the magnitude of the effects is comparable. The rather high values of determination coefficient for mathematics achievement (greater than 0.66 for both student populations) indicate that the variables "Perceived Level of Math Anxiety" and "Self-Engagement in Mathematics Course at University" together explain a significant proportion of the total variance before and during the pandemic. Consequently, the results of our case study indicated that pandemic measures did not have a significant impact on our students' mathematics achievement. Although a more in-depth study of a broader sample of academic courses would be needed to confirm our findings, our experience indicates that mathematics courses at the tertiary level of education can be successfully delivered online. [ABSTRACT FROM AUTHOR]

Old mathematics books and textbooks have focused different researchers onto the history of mathematics and mathematics education. However, books are not the only information source for this field; for example, researchers can also study periodical-type publications from the past (such as diaries, weeklies, newspapers, etc.). Considering this, this study developed an instrument to analyze publications about mathematics and mathematics education included in newspapers, weeklies, journals, etc., which were not exclusively devoted to science, from the perspective of the history of mathematics and mathematics education. In order to do so, a descriptive research focused on the analysis of historical texts was carried out using the content analysis technique. The different labels and categories of this instrument are here exemplified by the categorization of some entries included in several periodical publications published in the 18th century in Spain. [ABSTRACT FROM AUTHOR]

Several universities are witnessing an increase in students' enrolment in mathematics-intensive programmes over the last decades. This increase has come with the price of high failure rates in foundational mathematics courses, which poses challenges to mathematics teaching and learning in higher education. It is therefore inevitable, for some universities, to transform the teaching and learning of mathematics to more student-centred approaches that engage the students mathematically and enhance their success rates. We approach this transformative effort by investigating students' perception of teaching, feedback, and assessment as a first step in reforming the teaching of a first-year mathematics course at a Norwegian university. The results of both quantitative and qualitative analyses of the data generated using a questionnaire from 107 (80 men) engineering students show that the status quo of teachings offers little support for learning. The teaching is dominated by teacher-led instruction, note-taking, and large pieces of proof which make learning difficult for students during class activities. The results also show that the current structure of the course offers limited formative feedback to students and that the assessment tasks require restructuring to capture students' time and effort. We discuss the implications of these findings and make some recommendations for improvement. [ABSTRACT FROM AUTHOR]

This article is an independently written continuation of an earlier study with the same title [Mathematics, 2022, 10, 1225] on the Newton Process (NP). This process is applied to solve nonlinear equations. The complementing features are: the smallness of the initial approximation is expressed explicitly in turns of the Lipschitz or Hölder constants and the convergence order 1 + p is shown for p ∈ (0 , 1 ]. The first feature becomes attainable by further simplifying proofs of convergence criteria. The second feature is possible by choosing a bit larger upper bound on the smallness of the initial approximation. This way, the completed convergence analysis is finer and can replace the classical one by Kantorovich and others. A two-point boundary value problem (TPBVP) is solved to complement this article. [ABSTRACT FROM AUTHOR]

In industrial engineering degrees in Spain, mathematics subjects are usually taught during the first two academic years. Consequently, it is often the case that students sometimes do not feel motivated to learn subjects such as Mathematics II (calculus). Nevertheless, this subject is fundamental for understanding other subjects in the degree study plan, as well as for the graduate's future professional career as an engineer. To address this, a problem-based teaching methodology was carried out with the help of a fourth-year student who explained an activity to first-year students in a manner which was both friendly and approachable. In this experiment, the student went through a series of practical problems taken from different engineering subjects, which required multivariable integrals to be calculated and which he had learned in mathematics as a first-year student. In addition, a method based on pre-test and post-test assessments was applied. From this work, various benefits were observed in terms of learning, as well as an increase in the level of motivation of first-year students. There was a greater appreciation of the usefulness of calculus and computer programs to solve real-life problems, and the students generally responded positively to this type of activity. [ABSTRACT FROM AUTHOR]

The Economic Society of Friends of the Country of Asturias, Spain, was an instrument of enlightened reformism which operated in a region with serious economic backwardness. It was born in 1780 at the initiative of Campomanes and responds to the Matritense model, meaning that it focused on economic development and popular education. It is known that Jovellanos directly participated in the establishment of the Royal Institute of Nautical Studies and Mineralogy of Gijón. In this work, the historical method of research in education was used with the objective of determining the sociogenesis of the kind of technical mathematics that was taught in this Institute. The results show the role of the Asturian Economic Society in the creation of the Institute and we also analysed the teaching and curriculum of mathematics that was taught there, and if it was in line with the internal debates of the discipline in that historical moment. The limitations of the Jovellanista model of the Technical Training School for Sailors and Miners created in Gijón are made clear, although the attempt to start it up in such a peripheral place is no less remarkable. [ABSTRACT FROM AUTHOR]

With an empirical study, we explore the process of designing modeling tasks for teaching mathematics in a Dynamic Geometry environment. We address the research questions: What are the characteristics of the tasks that pre-service teachers design to teach mathematics in digital and modeling environments? What are the activities like that these tasks encourage in students? By means of a qualitative methodology, we characterize the tasks designed by secondary pre-service mathematics teachers and identify the activities that these tasks encourage in students. By analyzing the process of designing and planning a class, we can determine how the characteristics of the modeling tasks are modified based on the software used. In this context, the software also acts as a medium that reflects aspects of the models involved, the objectives of the tasks, and the activities intended for the students. The results contribute to the discussion regarding task design, where technology is a means of supporting the exploration, understanding, and study of different phenomena. [ABSTRACT FROM AUTHOR]

In an earlier contribution to Mathematics, we presented a new teaching concept for abstract algebra in secondary school mathematics, and we discussed findings from mathematics education research indicating that our concept could be used as a promising resource to foster students' algebraic thinking. In accordance with the Design-Based Research framework, the developed teaching concept is now being revised in several iteration steps and optimised towards student learning. This article reports on the results of the formative assessment of our new teaching concept in the laboratory setting with N = 9 individual learners leveraging a research method from science education: The acceptance survey. The results of our study indicate that the instructional elements within our new teaching concept were well accepted by the students, but potential learning difficulties were also revealed. On the one hand, we discuss how the insights gained in learners' cognitive processes when learning about abstract algebra with our new teaching concept can help to refine our teaching–learning sequence in the sense of Design-Based Research. On the other hand, our results may serve as a fruitful starting point for more in-depth theoretical characterization of secondary school students' learning progression in abstract algebra. [ABSTRACT FROM AUTHOR]

In this study, a mobile learning system (MLS) was developed and adopted to facilitate elementary second-grade students to learn mathematics. A quasi-experimental design was adopted. There were two learning models, including the typical instruction group (TI group) and MLS group. The learning content is the topic of multiplication. A total of 93 s-grade students from four classes in a public elementary school in Northern Taiwan participated in this research. Participants were randomly divided into the MLS group (47 participants: 22 boys and 25 girls) and the TI group (46 participants: 26 boys and 20 girls). Participants in the MLS group received mathematics instruction in the MLS, whereas those in the TI group received direct instruction in typical classrooms. All students took the pretest and posttest of mathematics learning achievement test and mathematics learning interest scale assess their improvement of learning achievement and learning interest after the learning activities. The findings revealed that students in the MLS group had significantly better improvement in their mathematics learning interest and mathematics learning achievement than those in the TI group. In addition, students in the MLS group had significantly better performance in answering items of comprehension and application levels in the mathematics learning achievement test. [ABSTRACT FROM AUTHOR]

Moreover, if A is a real evolution algebra, then every natural basis of A is a natural basis of i HT ht . References 1 Bustamante M.D., Mellon P., Velasco M.V. Determining When an Algebra Is an Evolution Algebra. Determining When an Algebra Is an Evolution Algebra. [Extracted from the article]