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This paper serves as a corrigendum to the paper [Electron. J. Qual. Theor. Differ. Equ. 2018, No. 84, 1–14]. We present here a corrected version of Theorem 3.1 and Theorem 5.1.

With the rapid development of information technology, scientific social networks (SSNs) have become the fastest and most convenient way for researchers to communicate with each other. Many published papers are shared via SSNs every day, resulting in the problem of information overload. How to appropriately recommend personalized and highly valuable papers for researchers is becoming more urgent. However, when recommending papers in SSNs, only a small amount of positive instances are available, leaving a vast amount of unlabelled data, in which negative instances and potential unseen positive instances are mixed together, which naturally belongs to One-Class Collaborative Filtering (OCCF) problem. Therefore, considering the extreme data imbalance and data sparsity of this OCCF problem, a hybrid approach of Social and Content aware One-class Recommendation of Papers in SSNs, termed SCORP, is proposed in this study. Unlike previous approaches recommended to address the OCCF problem, social information, which has been proved playing a significant role in performing recommendations in many domains, is applied in both the profiling of content-based filtering and the collaborative filtering to achieve superior recommendations. To verify the effectiveness of the proposed SCORP approach, a real-life dataset from CiteULike was employed. The experimental results demonstrate that the proposed approach is superior to all of the compared approaches, thus providing a more effective method for recommending papers in SSNs. [ABSTRACT FROM AUTHOR]

Students' difficulty in working with fractions is attributed to their lack of understanding of the role of the numerator and denominator and their over-generalization of whole-number thinking. An activity designed to help third-grade students organize their conceptions about rational number notation by associating with well-established whole-number routines using paper plates is presented.

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Present Study as a "meta-analysis" research aims to determine the role and methods of communication, regarding verbal and nonverbal learning in mathematics is provided. Research conducted for this purpose (18 Researches) on mathematic teaching, in the form of research papers published in the Journal of Educational Innovations, as the main concept was considered. Out of the 8 research papers published in terms of attention to communication variables has more extension of the statistical society of this research. Then, according to the variables performance methods, questions and results showed in them was descriptive-qualitative and get “meta-analysis. The main question of this study is to research on mathematics teaching is based on the method of communication, what are the similarities and differences in the use of effective communication? During the investigation, it was determined that the communication patterns of multiple and sometimes conflicting have more attentions and proposed recommendations, which are as follows: emotional, participatory, supporting, visual, objective and balanced in a form of speech, physical, visual and audio that leads to any progress performance of learners and their learning mathematics and problem solving.

Problem solving in chemical kinetics poses substantial challenges for university students since it often involves significant use of mathematics as a tool and language, with challenging translations and transitions between chemical phenomena and mathematical representations. In this paper, we present key findings from a study investigating chemistry students solving tasks centred around the steady-state approximation. Building upon the mathematical modelling cycle (MMC), qualitative analysis of the data collected using a think-aloud protocol led to the development of the extended MMC. This empirically derived extended MMC offers a more detailed account of the processes involved in mathematical modelling of chemical phenomena, highlighting aspects such as the occurrence of deliberation and evaluation throughout the modelling cycle, as well as the varying characteristics, points of activation and roles of extra-mathematical resources during problem solving. We further introduce and use problem-solving trajectories as a tool for visualising and analysing the complex and diverse approaches used by students in their attempts at reaching a solution. Overall, the extended MMC provides a finer-grained model of the cognitive and metacognitive activities that students engage in, offering further insights for research and practice.

This paper provides evidence on the effect of local prescription opioid use on academic achievement of 3rd-8th graders between 2009 and 2018. Using county fixed effects models, I find that when counties have higher levels of prescription opioid use, students score lower on standardized assessments two to three years later, with variation by student subgroups and magnitudes comparable to effective interventions. I find the largest magnitudes in counties with higher poverty rates and states with below-median state education spending. As test score effects predict adult outcomes, these findings point to economic and public health challenges when affected children become adults.

In this paper, I analyze the impact of culture and metaphor on cryptology education. I will compare and contrast the historically grounded metaphors of cryptology-is-warfare and encryption-is-security to a set of counter-metaphors: cryptology-is-privacy and encryption-is-communication. Using this explicit understanding of conceptual metaphor, I present design recommendations and metaphorizing activities for educators building their undergraduate cryptology course.

This paper describes how the notion of the strongly didactic contract can serve to characterize the teaching adopted to implement a task in probability. It is particularly focused on the reality of mathematical work performed by students and teachers. For this research, classroom sessions were developed in an in-service teacher training course designed (and adapted) according to the Japanese Lesson Study model. Through the combined use of the Theory of Didactical Situations (TDS) and the Theory of Mathematical Working Spaces (ThMWS), a coding of the sessions observed was developed. Based on this coding, different patterns emerged which gave each session a specific rhythm and identity from which it was possible to recognize and characterize different strongly didactic contracts. The study highlights the difference between the potential contracts intended by the teachers and those observed in practice. The tools, and especially the coding, developed for the study could be used for future research on instructional situations or in-service teacher training.

The present paper aims at investigating the relationship between students' attitudes toward online homework use and mathematics anxiety among secondary school students. In this study, a model has been proposed by integrating the technology acceptance model (TAM) with mathematics anxiety theory. Three hundred and forty-five secondary school students participated in the instrument of the study that included 20-item based on a 5-point Likert scale. The subsequent analysis using Partial Least Squares Structural Equation Modeling (PLS-SEM) supported the negative relationship between attitude toward an online homework (OHW) tool and mathematics anxiety. The results revealed that perceived usefulness and perceived ease of use are predictors of attitude toward the use of OHW. This study maximized the capability of acceptance of the OHW tool in mathematics learning. The findings provided by the study will encourage mathematics educators to implement mathematics OHW tools in the learning process.

This paper reports on students' conceptions of minima points. Written assignments and individual interviews uncovered salient, concept images, as well as erroneous "mis-out examples" that mistakenly regard examples as non-examples and "mis-in examples" that mistakenly grant non-examples the status of examples. We used Tall and Vinner's theoretical framework to analyze the students' errors that were rooted in mathematical and in real-life contexts.

In this paper we discuss the types of knowledge used by six middle school students as they engaged with a debugging task designed to integrate ideas from computer science, mathematics and science. Our findings show that the computational thinking practice of debugging is a rich source of opportunities to integrate these different disciplines. The analysis illustrates how the types of knowledge the students did and did not use at each step of the debugging process were related to their ability to succeed at each step. Our work contributes to theory and practice by uncovering implications for studying debugging through two refined frameworks and for designing debugging tasks to support transdisciplinary learning.

This article focuses on the enormous impact on the modern theory of partial differential equations by three articles of John Nash, all written before the age of 30, before the onset of his terrible disease. http://dx.doi.org/10.1090/bull/1560

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***** No abstract is available for this article. *****

If (S, ◦,≤) is an ordered hypersemigroup, an equivalence relation ρ on S is called congruence if (a, b) ∈ ρ implies (a ◦ x, b ◦ x) ∈ ρ and (x ◦ a, x ◦ b) ∈ ρ for every x ∈ S ; in the sense that for every u ∈ a ◦ x there exists v ∈ b ◦ x such that (u, v) ∈ ρ and for every u ∈ x◦a there exists v ∈ x◦b such that (u, v) ∈ ρ. It has been proved in Turk J Math 2021(5) [On the paper “A study on (strong) order-congruences in ordered semihypergroups”] that if S is an ordered hypersemigroup, then there exists a congruence ρ on S such that S/ρ is an ordered hypersemigroup. This result, is the main result for an involution ordered hypersemigroup by Xinyang Feng, Jian Tang and Yanfeng Luo in U.P.B. Sci. Bull, Series A, 2018, but its proof is wrong; the correct proof is given in the present paper. Examples illustrate the results. [ABSTRACT FROM AUTHOR]

Illustrated is the use of isometric graph paper in the discovery of nonstandard area formulas. The use of definitions, geometric construction, record keeping, and conjectures about triangles, rhombuses, hexagons, parallelograms, isosceles trapezoids, rectangles, and trapezoids are described. (YP)

An iterative procedure for adjusting examination marks from papers of varying standards is given. The convergence of the procedure is demonstrated and attention is drawn to an underlying linear model. (MP)

This paper outlines the development of a comparative research framework in subject didactics and applies this in the process of analysing the transformations from academic disciplines across different school subjects. The theoretical framework builds on the concepts of 'powerful knowledge' and 'transformation' and 'epistemic quality' within which transformation processes from the classroom to the societal level are considered as 'trajectories of powerful knowledge and epistemic quality'. The framework is used to analyse the findings from recent empirical studies across school subjects that have been reported on in publications arising from the Knowledge and Quality across School Subjects and Teacher Education (KOSS) network. The paper then focuses on analysing the transformations from disciplines across school subjects, given that the first boundary in defining powerful knowledge concerns knowledge that is specialized in both how it is produced and transmitted. To analyse this boundary, the findings from the empirical studies are grouped into broad subject categories. These are then compared with the corresponding disciplines by using the widely cited Biglan classification scheme of academic disciplines in higher education. Finally, we consider the implications for curriculum planning and teacher education policy and reflect on the concept of subject-specific educational content knowledge (SSECK).

This special issue introduces recent research on mathematics in interdisciplinary STEM education. STEM education is widely promoted by governments around the world as a way of boosting students' interest and achievement in science, technology, engineering, and mathematics and preparing STEM-qualified workers for twenty-first century careers. However, the role of mathematics in STEM education often appears to be marginal, and we do not understand well enough how mathematics contributes to STEM-based problem-solving or how STEM education experiences enhance students' learning of mathematics. In this survey paper, we present a narrative review of empirical and conceptual research literature, published between 2017 and 2022. These literature sources are organised by a framework comprising five thematic clusters: (1) interdisciplinary curriculum models and approaches; (2) student outcomes and experiences; (3) teacher preparation and professional development; (4) classroom implementation and task design; and (5) policy, structures, and leadership. We use the framework to provide an overview of the papers in this issue and to propose directions for future research. These include: investigating methods and rationales for connecting the constituent STEM disciplines so as to preserve the disciplinary integrity of mathematics; clarifying what is meant by student "success" in interdisciplinary STEM programs, projects, and other educational approaches; moving beyond classroom practices that position mathematics as just a tool for solving problems in other disciplines; understanding what makes a STEM task mathematically rich; and asking how STEM education research can productively shape STEM education policy.

Dyslexia is a type of Specific Learning Disability (SLD) that affects the educational development of a student, as it is the reason of difficulties not only in writing or reading but also in other disciplines like Mathematics. Research has proven that Information and Communication Technologies (ICT) can have a positive effect to the educational development of a dyslexic student. In this paper, twenty 6 th -grade primary-school students were observed while using computers during exams - ten with Dyslexia and ten with no SLDs. All students were called to solve a digital test and a paper test that were including some basic mathematic operations. The researcher recorded and examined the differences between the results from the two tests. Descriptive and deductive statistical analysis showed that students had better results when examined via a computer compared to a traditional written examination. [ABSTRACT FROM AUTHOR]

We attempt to identify the 25 most-cited statistical papers, providing some brief commentary on each paper on our list. This list consists, to a great extent, of papers that are on non-parametric methods, have applications in the life sciences, or deal with the multiple comparisons problem. We also list the most-cited papers published in 1993 or later. In contrast to the overall most-cited papers, these are predominately papers on Bayesian methods and wavelets. We briefly discuss some of the issues involved in the use of citation counts. [ABSTRACT FROM AUTHOR]

In order to recognize outstanding papers that have been published in Symmetry, the Editorial Board established an annual “Symmetry Best Paper Award”. We are pleased to announce the first “Symmetry Best Paper Award” for 2015. Nominations were selected by the Editorial Board Office, with all research articles published in 2013 and 2014 eligible for consideration. Following review and voting by the Symmetry Best Paper Award Committee, the following three papers have won Symmetry Best Paper Awards for 2015:

Comparative judgement methods are commonly used to explore standards in examination papers over time. However, studies are limited by a paucity of graded candidate scripts from previous years, as well as the expense and time required to standardise scripts. We present three studies that attempted, without the use of graded candidate scripts, to replicate and extend previous results about standards in mathematics examination papers. We found that re-typesetting examination papers into a consistent format was necessary, but that comparative judgement of examination papers without an archive of graded candidate scripts offered a reliable and efficient method for revealing relative demand over time. Our approach enables standards comparison where previously this was not possible. We found a reasonable correlation between judgments of actual student scripts and judgments of the items only, meaning that conclusions may be drawn about the demand of examination papers even when graded candidate scripts are not available. [ABSTRACT FROM AUTHOR]