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In this paper, we consider 2‐D nonlinear wave equations with small initial data of noncompact support when the quadratic terms of the nonlinearity satisfy the null conditions but the cubic ones do not. Due to the blow‐up result for the corresponding problem with the initial data of compact support, which was first obtained by S. Alinhac (The null condition for quasilinear wave equations in two space dimensions II. Amer. J. Math, 123 [2001], no. 6, 1071‐1101), this means that it is impossible to prove the global solvability in time in general. Therefore, in this case, what we can expect is to obtain the same lower bound of the lifespan as in Alinhac's work. That is, we also show the almost global existence, and the lower bound of the lifespan is ec/ε2 for sufficiently small ε>0 and some constant c>0. To achieve this goal, the methods we adopt are the "ghost weight" technique and the modified weighted L∞‐ L∞ estimates of the solutions to the linear wave equations. In addition, an alternative proof of the global existence is given for a similar case in three dimensions, using only the L∞‐ L2 estimates of the "good derivatives." [ABSTRACT FROM AUTHOR]

Any germ of a complex analytic space is equipped with two natural metrics: the outer metric induced by the hermitian metric of the ambient space and the inner metric, which is the associated riemannian metric on the germ. These two metrics are in general nonequivalent up to bilipschitz homeomorphism. We give a necessary and sufficient condition for a normal surface singularity to be Lipschitz normally embedded (LNE), that is, to have bilipschitz equivalent outer and inner metrics. In a partner paper (Neumann, Pedersen and Pichon, J. London Math. Soc. (2020), https://doi.org/10.1112/jlms.12280), we apply it to prove that rational surface singularities are LNE if and only if they are minimal. [ABSTRACT FROM AUTHOR]

DP‐coloring (also known as correspondence coloring) is a generalization of list coloring developed recently by Dvořák and Postle [J. Combin. Theory Ser. B 129 (2018), pp. 38–54]. In this paper we introduce and study the fractional DP‐chromatic number χDP*(G). We characterize all connected graphs G such that χDP*(G)⩽2: they are precisely the graphs with no odd cycles and at most one even cycle. By a theorem of Alon, Tuza, and Voigt [Discrete Math. 165–166 (1997), pp. 31–38], the fractional list‐chromatic number χℓ*(G) of any graph G equals its fractional chromatic number χ*(G). This equality does not extend to fractional DP‐colorings. Moreover, we show that the difference χDP*(G)−χ*(G) can be arbitrarily large, and, furthermore, χDP*(G)⩾d∕(2lnd) for every graph G of maximum average degree d⩾4. On the other hand, we show that this asymptotic lower bound is tight for a large class of graphs that includes all bipartite graphs as well as many graphs of high girth and high chromatic number. [ABSTRACT FROM AUTHOR]

As a core component of most cognitive diagnosis models, the Q‐matrix, or item and attribute association matrix, is typically developed by domain experts, and tends to be subjective. It is critical to validate the Q‐matrix empirically because a misspecified Q‐matrix could result in erroneous attribute estimation. Most existing Q‐matrix validation procedures are developed for dichotomous responses. However, in this paper, we propose a method to empirically detect and correct the misspecifications in the Q‐matrix for graded response data based on the sequential generalized deterministic inputs, noisy 'and' gate (G‐DINA) model. The proposed Q‐matrix validation procedure is implemented in a stepwise manner based on the Wald test and an effect size measure. The feasibility of the proposed method is examined using simulation studies. Also, a set of data from the Trends in International Mathematics and Science Study (TIMSS) 2011 mathematics assessment is analysed for illustration. [ABSTRACT FROM AUTHOR]

On Simone Weil's "Pythagorean" view, mathematics has a mystical significance. In this paper, the nature of this significance and the coherence of Weil's view are explored. To sharpen the discussion, consideration is given to both Rush Rhees' criticism of Weil and Vance Morgan's rebuttal of Rhees. It is argued here that while Morgan underestimates the force of Rhees' criticism, Rhees' take on Weil is, nevertheless, flawed for two reasons. First, Rhees fails to engage adequately with either the assumptions underlying Weil's religious conception of philosophy or its dialectical method. Second, Rhees' reading of Weil reflects an anti‐Platonist conception of mathematics his justification of which is unsound and whose influence impedes recognition of the coherence of Weil's position. [ABSTRACT FROM AUTHOR]

When solving a mathematical problem, students who do not have sufficient conceptual understanding may perform poorly and exhibit misconceptions. This study was aimed to examine students' conceptual understanding and significant misconceptions when solving number sense‐related problems. An online three‐tier diagnostic test was administered to 125 fifth‐grade students with varied socio‐economic backgrounds in Hong Kong. Only 14.40% of the students exhibited high performance with high confidence, indicating that these students had a profound conceptual understanding of number sense. In addition, the majority of the students (66.40%) did not demonstrate number sense; these students exhibited several significant misconceptions and could solve the questions only by using a rule‐based method or guessing. Accordingly, most students performed unsatisfactorily on number sense‐related problems. This study is imperative in identifying early predictors and provides information for further compatible interventions in the teaching and learning of number sense in Hong Kong in particular and worldwide in general. Lay Description: What is already known about this topic: Students must be instilled with conceptual understanding to achieve mastery of mathematical understanding and be able to properly solve complex or novel problems.Students would likely exhibit misconceptions if they do not have sufficient conceptual understanding.Students' conceptual understanding can be examined by evaluating their confidence levels in solving a problem. What this paper adds: A three‐tier diagnostic test (question and answer, reasoning, and confidence) can be used to examine students' conceptual understanding.Students performed unsatisfactorily on number sense because they lack conceptual understanding of topics related to number sense.Students held significant misconceptions on understanding the basic meaning of numbers and operations, recognizing the number size, using multiple representations of numbers and operation, recognizing the relative effect of operations on numbers, and judging the reasonableness of a computational result. Implications for practice and/or policy: Conceptual understanding of related topics reflecting number sense should be prioritized over procedural knowledge and mathematical rules.Lack of conceptual understanding of relevant topics and relying on mathematical rules and formulas are the main root causes of students' unsatisfactory performance.The deliberate use of estimation questions, multiple presentations, and judging the reasonableness of a result can help learners develop their conceptual understanding of number sense. [ABSTRACT FROM AUTHOR]

Although the use of technology in the K12 classroom has been shown to have a positive impact, research on the use of open education resources (OER) is relatively limited, especially research focusing on low‐achieving students. The present study examines the relationship between usage of Algebra Nation, a self‐guided system that provided instructional videos and practice problems, and the performance of students who had failed the state‐administered Algebra I end‐of‐course (EOC) assessment the previous year. Indicators of usage of Algebra Nation consisted of logins, video views, and practice questions answered. Path analyses and logistic regressions were used to evaluate relationships between usage indicators and algebra scores, controlling for number of absences, free/reduced lunch eligibility, Hispanic/Latino origin, race, and gender. The results indicate that higher levels of logins, video views, and practice questions answered were related to higher scores when the students re‐took the assessment. Logins and practice questions were also related to increases in odds of passing the Algebra I EOC assessment, but not video views. The results suggest that there may be benefits to technology use in the form of an OER adopted by students and teachers on an informal basis and link self‐regulated learning strategies to student achievement. Lay Description: What is already known about this topic: Algebra courses typically have a high failure rate.Repeating algebra is costly for the education system and for the student.Open education resources could potentially be an effective and cost‐efficient approach to algebra instruction. What this paper adds: This study shows that logins, video views, and practice questions answered in an open education resource were positively related to scores on a state‐administered,high‐stakes algebra assessment.The study indicates that the relationship between a self‐regulated learning strategy (i.e., practice questions answered) and student algebra scores is stronger than that between video views and algebra scores.This study shows that student‐driven ad hoc use of online tutoring programme is associated with higher passing rates on the algebra exam. Implications for practice and/or policy: This study demonstrates that informal use of an open education resource with videos and a practice question system can be effective in increasing student scores on algebra assessments.Future research is needed to connect diverse types of student self‐regulated use of open education resources to academic achievement and on how to design resources that encourage effective self‐regulation. [ABSTRACT FROM AUTHOR]

Horváth and Kiss (Proc. Amer. Math. Soc., 2005) proved the upper bound estimate λnλm≤n2m2(n>m≥1) for Dirichlet eigenvalue ratios of the Schrödinger problem −y′′ + q(x)y  =  λy with nonnegative and single‐well potential q. In this paper, we prove that if q(x) is a nonpositive, continuous, and single‐barrier potential, then λnλm≥n2m2 for λn  >  λm≥ − 2q∗, where q∗=min{q(0),q(1)}. In particular, if q(x) satisfies the additional condition |q∗|≤π23, then λ1  >  0 and λnλm≥n2m2 for n  >  m  ≥  1. For this result, we develop a new approach to study the monotonicity of the modified Prüfer angle function. [ABSTRACT FROM AUTHOR]

Background: Key elements of instructional quality include the teacher's ability to immediately react in domain‐specific classroom situations. Such skills – defined as action‐related skills – can only be validly assessed using authentic representations of real‐life teaching practice. However, research has not yet explained how teachers apply domain‐specific knowledge for teaching and to what extent action‐related skills are transferable from one domain to another. Aims: Our study aims to examine (1) the relationship between action‐related skills, content knowledge, and pedagogical content knowledge, and (2) the domain specificity of action‐related skills of (prospective) teachers in the two domains of mathematics and economics. Sample(s): We examined German pre‐service and in‐service teachers of mathematics (N = 239) and economics (N = 321), including n = 96 (prospective) teachers who teach both subjects. Methods: Action‐related skills in mathematics and economics were measured using video‐based performance assessments. Content knowledge and pedagogical content knowledge were assessed using established paper–pencil tests. Correlation analyses, linear regressions, and a path model were applied. Results: In mathematics and economics, we find a similar pattern of moderate correlations between action‐related skills, content knowledge, and pedagogical content knowledge. Moreover, a significant correlation between action‐related skills in mathematics and economics can be explained almost entirely by underlying relations between content knowledge and pedagogical content knowledge in both domains. Conclusions: Our findings suggest that action‐related skills empirically differ from domain‐specific knowledge and should be considered as domain‐specific constructs. This indicates that teacher education should not only focus on domain‐specific teacher knowledge, but may also provide learning opportunities for action‐related skills in each domain. [ABSTRACT FROM AUTHOR]

A graph G is called (2,k)‐connected if G is 2k‐edge‐connected and G−v is k‐edge‐connected for every vertex v. The study of (2,2)‐connected graphs is motivated by a theorem of Thomassen [J. Combin. Theory Ser. A 110 (2015), pp. 67–78] (that was a conjecture of Frank [SIAM J. Discrete Math. 5 (1992), no. 1, pp. 25–53]), which states that a graph has a 2‐vertex‐connected orientation if and only if it is (2,2)‐connected. In this paper, we provide a construction of the family of (2,k)‐connected graphs for k even, which generalizes the construction given by Jordán [J. Graph Theory 52 (2006), pp. 217–229] for (2,2)‐connected graphs. We also solve the corresponding connectivity augmentation problem: given a graph G and an integer k≥2, what is the minimum number of edges to be added to make G(2,k)‐connected. Both these results are based on a new splitting‐off theorem for (2,k)‐connected graphs. [ABSTRACT FROM AUTHOR]

This note is a corrigendum to the author's paper "On a Problem of Lang for Matrix Polynomials, Bull. London Math. Soc. 54 (2022), 1552–1567". [ABSTRACT FROM AUTHOR]

In data science, data are often represented by using an undirected graph where vertices represent objects and edges describe a relationship between two objects. In many applications, there can be many relations arising from different sources and/or different types of models. Clustering of multiple undirected graphs over the same set of vertices can be studied. Existing clustering methods of multiple graphs involve costly optimization and/or tensor computation. In this paper, we study block spectral clustering methods for these multiple graphs. The main contribution of this paper is to propose and construct block Laplacian matrices for clustering of multiple graphs. We present a novel variant of the Laplacian matrix called the block intra-normalized Laplacian and prove the conditions required for zero eigenvalues in this variant. We also show that eigenvectors of the constructed block Laplacian matrix can be shown to be solutions of the relaxation of multiple graphs cut problems, and the lower and upper bounds of the optimal solutions of multiple graphs cut problems can also be established. Experimental results are given to demonstrate that the clustering accuracy and the computational time of the proposed method are better than those of tested clustering methods for multiple graphs. [ABSTRACT FROM AUTHOR]

Objective This paper analyses how game theory can provide a framework for understanding the strategic decision-making that occurs in everyday scenarios in medical training and practice, and ultimately serves as a tool for improving the work environment and patient care. Game theory has been applied to a variety of fields outside of its native economics, but has not been thoroughly studied in the context of health care provision. Methods The paper discusses four of the most common 'games' and applies each to a scenario in medicine to provide new insight on the incentives and drivers for certain types of behaviour and a deeper understanding of why certain results are valued more strongly than others. Conclusions Using game theory as an integrative tool, in conjunction with good judgement and a sound knowledge base, trainees and physicians can work to better recognise where competing priorities exist, understand the motivations and interactions of the various players, and learn to adjust their approaches in order to 'change the game' when their preferred outcome is not the most likely one. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of full-order H2 linear parameter-varying filter design for continuous-time systems with bounded rate of variations under the condition that the scheduling parameters do not exactly fit the real ones. The scheduling parameters and their derivatives are supposed to belong to polytopes with known vertices. The synthesis conditions are formulated in terms of parameter-dependent bilinear matrix inequalities by means of parameter-dependent Lyapunov function and introducing some extra variables for the filter design. An iterative procedure is presented to cast the bilinear matrix inequalities problem into a linear matrix inequality optimization problem. The design of robust filters for both time-varying and time-invariant systems can be viewed as particular cases of the proposed method. The merit of the method presented in this paper lies in two fields. The first pertains to dealing with the measurement uncertainty in a less conservative manner than available approaches in the gain-scheduled filtering problem. The second is to provide more efficient methods than the existing ones in the literature for the robust filter design. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Background Estimates of energy requirements are needed in weight management and are usually determined using prediction equations. The objective of these two systematic reviews was to identify which equations based on simple anthropometric and demographic variables provide the most accurate and precise estimates of (1) resting energy expenditure (REE) and (2) total energy expenditure ( TEE) in healthy obese adults. Methods Systematic searches for relevant studies in healthy adults with body mass index ( BMI) ≥25 kg m−2 and published in English were undertaken using Cinahl, Cochrane Library, OpenGrey, PubMed and Web of Science (completed March 2014). Search terms included metabolism, calorimetry, obesity and prediction equations. Data extraction, study appraisal and synthesis followed guidelines from PRISMA (Preferred Reporting Items for Systematic reviews and Meta-Analyses). Results From 243 REE papers and 254 TEE papers identified, 21 and four studies, respectively, met the inclusion criteria. (1) The most accurate REE predictions varied with BMI subgroup: WHO (weight and height) ≥25 and ≥30 kg m−2; Mifflin 30-39.9 kg m−2; Henry ≥40 kg m−2. The most precise REE predictions were obtained using Mifflin in BMI 30-39.9 and ≥40 kg m−2, where approximately 75% of predictions were within 10% of measured REE. (2) No accurate or precise predictions of TEE were identified. Conclusions No single prediction equation provides accurate and precise REE estimates in all obese adults. Mifflin equations are recommended in this population, although errors exceed 10% in 25% of those assessed. There is no evidence to support the use of prediction equations in estimating TEE in obesity. [ABSTRACT FROM AUTHOR]

Recently, we came across the paper entitled “Quantification of network structural dissimilarities” published by Nature Communications. In this paper, Schieber et al claimed to propose a novel technique for measuring the structural similarity of networks. The authors of this commentary are familiar with this special area of network analysis. After reading the paper, we doubt that the graph similarity (distance) measure due to Schieber et al is entirely novel. Instead, parts thereof are very similar to contributions we have authored. Unfortunately, they have not been cited nor acknowledged in Schieber et al. [ABSTRACT FROM AUTHOR]

This meta‐analysis investigated the effects of learning video games on mathematics achievement of PreK‐12th‐grade students compared with traditional classroom instructional methods. Results from the 24 collected studies showed heterogeneity among effect sizes, both in magnitude and direction. Using a random effects model, a small but marginally significant overall effect (d¯RE=0.13,p=.02) suggested that mathematics video games contributed to higher learning gains as compared with traditional instructional methods. In addition, moderator analyses were mixed in terms of statistical significance and explored effect‐size heterogeneity across effects using grade level, instrument type, length of game‐based intervention, country, publication type, and study year characteristics. Overall findings indicate that video games are a slightly effective instructional strategy for teaching mathematics across PreK‐12th‐grade levels. Lay Description: What is already known about this topic: Math video games are gaining increased popularity in the classroom.Research on the effectiveness of math video games in PreK‐12 education is inconsistent.More empirical studies on math video games are needed. What this paper adds: This meta‐analysis focused on math video games versus traditional classroom instruction.The targeted learner audience was PreK‐12 students.The target learning outcome was mathematics achievement.Results indicate that video games contribute to higher learning gains compared with traditional instruction.Publication year and type influenced the strength of the video‐gaming intervention effect. Implications for practice and/or policy: Video games are an effective instructional strategy for teaching mathematics across PreK‐12th grades.Having more teaching instruction/intervention that includes video games might increase students' math achievement. [ABSTRACT FROM AUTHOR]

A promising method to support game‐based learning is to facilitate learners' externalization of cognitive and metacognitive processes. Externalizing Problem Representation (EPR) refers to a cognitive behaviour in which a learner constructs her own representations overtly. The purpose of this study is to investigate whether learning supports promoting EPR enhance qualitative understanding and quantitative proficiency in ratios and proportional relationships in a learning game (i.e., E‐Rebuild) context. Specifically, this study investigated the effects of representation format in problem representation on qualitative understanding and quantitative proficiency in a learning game context. The results of this study indicate that (a) symbolic learning supports better facilitate comprehension of math concepts and their relations than iconic learning supports in video game contexts, (b) symbolic learning supports better facilitate players' reflection for implicit understanding and promote their math problem‐solving skills, (c) participants in the symbolic learning support group increased significantly in qualitative understanding but not in quantitative proficiency after gameplay, and (d) participants in the iconic learning support group experienced significant growth in quantitative proficiency but not in qualitative understanding after gameplay. Lay Description: What is already known about this topic: Video games potentially facilitate implicit qualitative understanding more than quantitative knowledge test performance.Educational game designers lack a good understanding of the design and development of effective learning supports in educational games. What this paper adds: Symbolic learning supports for problem representation better facilitate comprehension of math concepts and their relations than iconic learning supports in video game contexts.Participants experienced significant growth in quantitative proficiency after they processed the iconic in‐game learning supports in game‐based math tasks.Participants' qualitative understanding in the symbolic learning support group increased significantly after playing E‐Rebuild‐based math game task. Implications for practice and/or policy: This study informs scholars and designers of game‐based learning about designing learning support and its properties in video game contexts: Learning support design to promote math problem representation across problem translation and problem integration.This study provides design principles for learning supports in math learning game; symbolic learning supports facilitate qualitative understanding whereas iconic learning supports facilitate quantitative proficiency in math learning game. [ABSTRACT FROM AUTHOR]

The paper deals with some existence results for an elliptic equation of Kirchhoff‐type with changing sign data and a logarithmic nonlinearity by direct variational method, Galerkin approach, and sub‐super solutions method. Our results are natural extension of Boulaaras' work in (Math Methods Appl Sci; 41(13):5203‐5210). [ABSTRACT FROM AUTHOR]

The main result of this paper is to extend from Q to each of the nine imaginary quadratic fields of class number 1 a result of [Serre, Duke Math. J. 54 (1987) 179–230] and [Mestre–Oesterlé, J. reine. angew. Math. 400 (1989) 173–184], namely that if E is an elliptic curve of prime conductor, then either E or a 2‐, 3‐ or 5‐isogenous curve has prime discriminant. For four of the nine fields, the theorem holds with no change, while for the remaining five fields the discriminant of a curve with prime conductor is (up to isogeny) either prime or the square of a prime. The proof is conditional in two ways: first that the curves are modular, so are associated to suitable Bianchi newforms; and second that a certain level‐lowering conjecture holds for Bianchi newforms. We also classify all elliptic curves of prime power conductor and non‐trivial torsion over each of the nine fields: in the case of 2‐torsion, we find that such curves either have CM or with a small finite number of exceptions arise from a family analogous to the Setzer–Neumann family over Q. [ABSTRACT FROM AUTHOR]

Considering the fact that authorship order plays such a significant role as a basis for scientific merit, this paper looks into the practices of authorship order from a research ethical perspective. We conclude that there is a wide variety of practices and no common understanding of what the different authorship positions signify. Authorship guidelines do not provide much help. We recognize that, regardless of what system for valuing authorship positions is used, it will be misleading and unfair in most applications because relative contributions vary in ways that are not captured by fixed value assignments to authorship positions. In theory, assigning percentage figures reflecting the relative contributions of the authors would solve that problem, but we argue that such a scheme is not likely to work in practice. It can also be questioned whether relative, rather than absolute, contributions should be the basis for scientific merit. Contributorship is discussed as an alternative, but is recognized to be insufficient both in communicating absolute and relative contributions, as standardly used. However, there may be a way forward with contributorship, but then, the level of detail needs to increase considerably and its application be standardized. [ABSTRACT FROM AUTHOR]

This paper extends the application of the Local Geary c statistic to a multivariate context. The statistic is conceptualized as a weighted distance in multivariate attribute space between an observation and its geographical neighbors. Inference is based on a conditional permutation approach. The interpretation of significant univariate Local Geary statistics is clarified and the differences with a multivariate case outlined. An empirical illustration uses Guerry's classic data on moral statistics in 1830s France. [ABSTRACT FROM AUTHOR]

Given an iterated function system (IFS) of contractive similitudes, the theory of Gromov hyperbolic graph on the IFS has been established recently. In the paper, we introduce a notion of simple augmented tree which is a Gromov hyperbolic graph. By generalizing a combinatorial device of rearrangeable matrix, we show that there exists a near‐isometry between the simple augmented tree and the symbolic space of the IFS, so that their hyperbolic boundaries are Lipschitz equivalent. We then apply this to consider the Lipschitz equivalence of self‐similar sets with or without assuming the open set condition. Moreover, we also provide a criterion for a self‐similar set to be a Cantor‐type set which completely answers an open question raised in [Luo and Lau, Adv. Math. 235 (2013) 555–579]. Our study extends the previous works. [ABSTRACT FROM AUTHOR]

What is the best approach to educating students is, evidently, the pivotal question in educational research. In the general debate on this question, clear positions are often taken―for example, whether teacher‐led instruction or more student‐directed approaches should be followed. In the current narrative review, this central question and the different stances taken are explored for a specific field of learning, STEM (science, technology, engineering, and mathematics) domains. The current article starts with an argument as to why the traditional, more directive teacher‐led educational approach to STEM learning may not always lead to deep conceptual knowledge and proposes exploring more engaged forms of learning. More specifically, a particular arrangement for engaged learning, inquiry learning, is taken as an example in this exploration. It is argued that the effects of educational methods are influenced by a multitude of (interacting) factors related to student and teacher characteristics, context, domain, frequency of use, timing, and probably more. Therefore, this article tries to outline a more nuanced and balanced stance towards choosing educational approaches. A picture is presented to show that adopting and combining different approaches, at both the lesson and the curricular levels, may be necessary to reach optimal levels of learning. Existing and upcoming technologies may play a decisive role in realizing this more complex, but also more realistic view of learning in STEM. [ABSTRACT FROM AUTHOR]

Affinity propagation is a message‐passing‐based clustering procedure that has received widespread attention in domains such as biological science, physics, and computer science. However, its implementation in psychology and related areas of social science is comparatively scant. In this paper, we describe the basic principles of affinity propagation, its relationship to other clustering problems, and the types of data for which it can be used for cluster analysis. More importantly, we identify the strengths and weaknesses of affinity propagation as a clustering tool in general and highlight potential opportunities for its use in psychological research. Numerical examples are provided to illustrate the method. [ABSTRACT FROM AUTHOR]

Motivated by the recent replication and reproducibility crisis, Gelman and Carlin (2014, Perspect. Psychol. Sci., 9, 641) advocated focusing on controlling for Type S/M errors, instead of the classic Type I/II errors, when conducting hypothesis testing. In this paper, we aim to fill several theoretical gaps in the methodology proposed by Gelman and Carlin (2014, Perspect. Psychol. Sci., 9, 641). In particular, we derive the closed‐form expression for the expected Type M error, and study the mathematical properties of the probability of Type S error as well as the expected Type M error, such as monotonicity. We demonstrate the advantages of our results through numerical and empirical examples. [ABSTRACT FROM AUTHOR]

Task solving processes and changes in these processes have long been expected to provide valuable information about children's performance in school. This article used electronic tangibles (concrete materials that can be physically manipulated) and a dynamic testing format (pretest, training, and posttest) to investigate children's task solving processes and changes in these processes as a result of training. We also evaluated the value of process information for the prediction of school results. Participants were N = 253 children with a mean age of 7.8 years. Half of them received a graduated prompts training; the other half received repeated practice only. Three process measures were used: grouping behaviour, verbalized strategies, and completion time. Different measures showed different effects of training, with verbalized strategies showing the largest difference on the posttest between trained and untrained children. Although process measures were related to performance on our dynamic task and to math and reading performance in school, the amount of help provided during training provided the most predictive value to school results. We concluded that children's task solving processes provide valuable information, but the interpretation requires more research. Lay Description: What is already known about this topic: Dynamic testing provides information on a child's ability to learn.Solving process information provides indications for intervention.Computerized testing can be of great help in recording process information. What this paper adds: Process‐oriented dynamic testing provides explanatory information beyond traditional tests.The use of a tangible user interface (TUI) console uncovers valuable information on solving processes.Process measures are related to series completion performance, math, and reading.Need for instruction is the best predictor of math and reading ability.Implications for practice and/or policy: A framework for interpreting process information is necessary in dynamic testing.Process‐oriented dynamic testing may be more suitable to inform education.TUIs provide a more natural testing environment. [ABSTRACT FROM AUTHOR]

How computers in schools impact on children's learning has been studied through research that explores student achievement at one point in time or by comparing different classroom contexts with differing results. The introduction of an optional netbook purchasing scheme for children in a low socio‐economic community provided an opportunity to compare the academic improvement for those who joined the scheme with those who did not with both groups learning within the same context with the same teachers. Using nationally calibrated assessment tools that test reading, writing, and mathematical skill progression, the student achievement data from six schools across a 2‐year period were analysed using chi‐square testing, regression analysis, propensity score matching, and cumulative logit modelling. The results identified few significant differences between the students in most aspects of achievement and no significant difference in academic improvement between the two groups. Lay Description: What is currently known about the subject matter: Whole class use of netbooks can improve achievement in reading, writing and mathematics.Children in low socio‐economic contexts have limited access to the Internet or netbooks for learning. What this paper adds to this: The use of netbooks alone has an insignificant effect on achievement in standardized assessments.Academic progress of children in the same context is similar whether using netbooks or not. Implication of study findings for practitioners: Introduction of netbook schemes should enable all students to have dedicated access. [ABSTRACT FROM AUTHOR]

Necessary conditions for the existence of a super‐simple, decomposable, near‐resolvable (v,4,6)‐balanced incomplete block design (BIBD) whose 2‐component subdesigns are both near‐resolvable (v,4,3)‐BIBDs are v≡1 (mod 4) and v≥17. In this paper, we show that these necessary conditions are sufficient. Using these designs, we also establish that the necessary conditions for the existence of a super‐simple near‐resolvable (v,4,3)‐RBIBD, namely v≡1 (mod 4) and v≥9, are sufficient. A few new pairwise balanced designs are also given. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of some infinite families of 2‐designs from n‐dimensional projective geometry PG(n,q), which admit (n+1)‐dimensional projective special linear group as their flag‐transitive automorphism group. [ABSTRACT FROM AUTHOR]

Scientific literacy implies an adequate understanding of central notions which characterize scientific reasoning. Nature of Science studies have lead to a general consensus of what experiments, models, theories and laws imply at school. They do not take into account how these terms are handled in recent domain‐specific theory and research. In order to come to a closer understanding we analyzed domain‐specific literature and conducted a survey into the notions of these terms by interviewing experts of the science subjects and mathematics. The results of literature analysis reveal differences in the meaning of the terms between subjects. Moreover, experts show serious inconsistencies in using the terms. The results will be presented in this paper and can be used as a starting point to draw conclusions for science teacher education. [ABSTRACT FROM AUTHOR]

Time‐dependent reliability analysis of structures by the use of an outcrossing approach normally requires the so‐called outcrossing rate to be estimated. A variety of methods has been recorded in the literature to evaluate this rate both for continues and discrete processes. Despite the availability of these methods, still more general and at the same time less sophisticated approaches are desired. In this paper, attempt is made to use the basic idea of "parallel system reliability formulation" to calculate the outcrossing rate for circumstances where the processes are continuous. These calculations are carried out by directional simulation. It is shown that this approach is simple to implement and may be used for the cases where the problem involves nonstationary processes and also for the cases where several limit state functions may have to be considered. [ABSTRACT FROM AUTHOR]

Studies have shown that educational robotics (ER) may impact student learning, especially in relation to STEM (science, technology, engineering, and mathematics) areas. In the STEM framework, particularly for younger children, the "E" and the "T" are considered to be missing letters, because few studies have concentrated on teaching and evaluating technology and engineering through ER activities. This study aimed to develop and test the efficacy of an ER protocol to teach robotics in a sample of 389 students, hypothesizing that girls would be as successful as boys. A Robotics Questionnaire assessing the basics of robotics was developed for this study. A Wilcoxon nonparametric test was performed in order to evaluate improvements (p < 0.05). A Mann–Whitney nonparametric test was performed in order to test the presence of gender differences (p < 0.05). Data indicated significant improvements for all the age ranges considered. No gender differences were found. In order to evaluate the efficacy of a didactic intervention utilizing ER, it is important to assess the impact on children's technological and engineering (robotics, in particular) knowledge. Lay Description: What is already known about this topic: Studies have shown that educational robotics (ER) has a potential impact on student learning.In the STEM framework, the "E" and the "T" are considered the STEM missing letters.What this paper adds: This study aims at developing and testing the efficacy of an ER protocol to teach robotics.The hypothesis that girls will be equally successful than boys is explored too, and no gender differences were found.Implications for practice and/or policy: Our results suggest that ER can be utilized to learn robotics, bringing technology in the schools.ER could be considered as a tool able to contribute to girl's involvement in STEM. [ABSTRACT FROM AUTHOR]

Suggested by the max‐product sampling operators based on sinc‐Fejér kernels, in this paper, we introduce truncated max‐product Kantorovich operators based on generalized type kernels depending on two functions ϕ and ψ satisfying a set of suitable conditions. Pointwise convergence, quantitative uniform convergence in terms of the moduli of continuity, and quantitative Lp‐approximation results in terms of a K‐functional are obtained. Previous results in sampling and neural network approximation are recaptured, and new results for many concrete examples are obtained. [ABSTRACT FROM AUTHOR]

This paper establishes a regularity criterion for the strong solution to the Leray‐α‐MHD in Campanato‐Morrey space. We show that if the magnetic field b satisfies the following condition: ∫0T‖∇b(τ,·)‖M˙qp2p2p−3+‖D2b(τ,·)‖M˙qp2p2p−3dτ<∞, the strong solution (v,b) to the 3‐D Leray‐α MHD equation can be extended beyond T > 0. We also prove that if the magnetic field b satisfies ∫0T‖∇b(τ,·)‖M˙qppp−1dτ<∞, the strong solution (v,b) to the 2‐D Leray‐α MHD equation can be extended beyond T > 0, which extends the results in previous studies. [ABSTRACT FROM AUTHOR]

This paper shows that the following nonlinear boundary value problem: ( 1 + δ y ) y ′ ′ + 2 x y ′ = 0 , 0 < x < ∞ , y ( 0 ) = 0 , y ( ∞ ) = 1 , where δ≥ − 1 and y is defined as a modified error function, can be reduced to the boundary value problems for the generalized Emden‐Fowler equation and Abel differential equation of the second kind in the canonical form, which do not usually have closed‐form solutions. The existence and uniqueness of the solution are established by considering another contraction mapping. Highly accurate approximate solutions of this problem are also provided. [ABSTRACT FROM AUTHOR]

Abstract: Tablets have much to offer children with learning difficulties, but evidence of their effectiveness to teach academic skills is limited and cannot be easily separated from the quality of the software. This paper analyses data from 3 iterative cycles of designing an app for children with Down syndrome to support their awareness of quantity through an inclusive game. Research with neurotypical children suggests that representation of quantity (or magnitude) is an area with considerable potential in supporting the foundations for children's mathematical learning. It has received little attention as an aspect for intervention for children with Down syndrome. Data collected in this study illustrate the need to carefully align the game mechanic to the target skills, strengthen levels of access, and introduce gradations of attentional demand. They also signal the interrelationship between children's cognitive and affective responses to the game, making it essential to find the optimal level of challenge. Children's strategies in response to mistakes indicate the importance of creating an agile responsive system. The data also suggest that developers routinely extend the number of features that are optional, enabling a greater level of personalization and a more inclusive game. [ABSTRACT FROM AUTHOR]

This paper focuses on the newly developed notion of minimum gain and the corresponding Large Gain Theorem. The Large Gain Theorem is an input-output stability result particularly well suited to unstable plants connected in feedback with stable or unstable controllers. This paper aims to facilitate the practical application of these results. An altered definition of minimum gain broadens the applicability of the Large Gain Theorem, and the novel Minimum Gain Lemma provides LMI conditions that imply and are often equivalent to a minimum gain for LTI systems. Numerical examples are provided to clarify the differences between the existing and proposed definitions of minimum gain, highlight the utility of the newly established Minimum Gain Lemma, and demonstrate how the paper's contributions may be employed in practice. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The purpose of this study was to investigate the effect of a computer-based story, which was designed in anchored instruction framework, on sixth-grade students' mathematics word problem-solving achievement. Problems were embedded in a story presented on a computer as computer story, and then compared with the paper-based version of the same story and to a condition that presented the problems as typical, isolated word problems (i.e., a non-story condition including only problems). One hundred twenty-eight sixth-grade students from two public middle schools in Turkey participated in this study. In a pretest-posttest experimental design, students were randomly assigned to one of the treatment groups mentioned earlier in which they solved the same mathematics word problems. A one-way analysis of covariance was used to analyse students' achievement in the treatment groups. The results indicated that students who solved the problems in the computer story treatment had significantly higher achievement scores than students who solved the problems in the paper story and isolated word problems treatments. In addition, the story was found to be significantly more effective than the non-story treatment when it was presented on computer. [ABSTRACT FROM AUTHOR]

Capillary dynamics has been and is yet an important field of research, because of its very relevant role played as the core mechanism at the base of many applications. In this context, we are particularly interested in the liquid penetration inspection technique. Because of the obviously needed level of reliability involved with such a non-destructive test, this paper is devoted to study how the presence of an entrapped gas in a close-end capillary may affect the inspection outcome. This study is carried out through a one-dimensional ordinary differential model that despite its simplicity is able to point out quite well the capillary dynamics under the effect of an entrapped gas. The paper is divided into two main parts; the first starts from an introductory historical review of capillary flows modelling, goes on presenting the one-dimensional second order ordinary differential model, taking into account the presence of an entrapped gas and therefore ends by showing some numerical simulation results. The second part is devoted to the analytical study of the model by separating the initial transitory behaviour from the stationary one. Besides, these solutions are compared with the numerical ones, and finally, an expression is deduced for the threshold radius switching from a fully damped transitory to an oscillatory one. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper the influence of heat input and preheat temperature on the critical implant stress was analyzed for the weld metal of API 5L X80. High strength steel marked as API 5L X80 is produced with a thermo - mechanical controlled process (TMCP), its chemical composition shows low carbon content due to which the steel has good weldability, but in the weld metal zone cold cracking can occure. The goal of this paper is to define optimal work conditions in form of flux cored arc welding (FCAW) welding parameters at which no cold cracks can be found. The experiment was conducted using central composite design (CCD) and design of experiments (DoE) with two independent variables (preheat temperature and heat input). Mathematical models were developed for all three different wire types that were used (two rutile, one basic flux cored wire). The samples in this paper which had cold cracks were further analyzed on the scanning electron microscope (SEM). [ABSTRACT FROM AUTHOR]

Biomedical imaging is an important and exponentially growing field in life sciences and clinical practice, which strongly depends on the advances in mathematical image processing. Biomedical data presents a number of particularities such as non-standard acquisition techniques. Thus, biomedical imaging may be considered as an own field of research. Typical biomedical imaging tasks, as outlined in this paper, demand for innovative data models and efficient and robust approaches to produce solutions to challenging problems both in basic research as well as daily clinical routine. This paper discusses typical specifications and challenges of reconstruction and denoising, segmentation, and image registration of biomedical data. Furthermore, it provides an overview of current concepts to tackle the typically ill-posed problems and presents a unified framework that captures the different tasks mathematically. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. [ABSTRACT FROM AUTHOR]

Abstract: Salomon Maimon argued forcefully for the indispensability of what he called “the method of fictions” in mathematics and physics, but also in philosophy. This last claim provoked critical responses from G. E. Brastberger, G. E. Schultze, and K. L. Reinhold. This paper offers a brief exposition of Maimon's “method of fictions” and an analysis of his response to critics of his claims concerning the employment of this method within philosophy. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, I argue that in spite of suggestions to the contrary, Merleau‐Ponty defends a positive account of the kind of abstract thought involved in mathematics and natural science. More specifically, drawing on both the Phenomenology of Perception and his later writings, I show that, for Merleau‐Ponty, abstract thought and perception stand in the two‐way relation of “foundation,” according to which abstract thought makes what we perceive explicit and determinate, and what we perceive is made to appear by abstract thought. I claim that, on Merleau‐Ponty's view, although this process can sometimes lead to falsification, it can also be carried out in such a manner that allows mathematics and natural science to articulate what we perceive in a way that is non‐distortive and in keeping with the demands of perception itself. [ABSTRACT FROM AUTHOR]

Putnam and Searle famously argue against computational theories of mind on the skeptical ground that there is no fact of the matter as to what mathematical function a physical system is computing: both conclude (albeit for somewhat different reasons) that virtually any physical object computes every computable function, implements every program or automaton. There has been considerable discussion of Putnam's and Searle's arguments, though as yet there is little consensus as to what, if anything, is wrong with these arguments. In the present paper we show that an analogous line of reasoning can be raised against the numerical measurement (i.e., numerical representation) of physical magnitudes, and we argue that this result is a reductio ad absurdum of the challenge to computational skepticism. We then use this reductio to get clearer about both (i) what's wrong with Putnam's and Searle's arguments against computationalism, and (ii) what can be learned about both computational implementation and numerical measurement from the shortcomings of both sorts of skeptical argument. [ABSTRACT FROM AUTHOR]

Using data from the Early Childhood Longitudinal Study Kindergarten Class of 2010-2011 ( n = 11,000), this study examined the developmental outcomes of 5-year-old children in multigrade classrooms (combined prekindergarten and kindergarten classrooms serving 3-, 4-, and 5-year-olds) compared with those of 5-year-olds attending kindergarten-only classrooms serving primarily 5-year-olds. Results from regression and propensity score analyses revealed that 5-year-old children who attended multigrade classrooms with prekindergarteners made smaller gains in math and literacy skills and demonstrated less optimal executive function at the end of the school year than children who attended kindergarten-only classrooms. Classroom-level factors largely explained the differences in children's academic achievement but did not consistently explain differences in their executive functioning. No consistent differences emerged for children's social-behavioral development. Highlights This paper examines the implications of multigrade kindergarten classrooms for 5-year-olds' school success and the mechanisms through which these classrooms affect children., Five-year-olds who attended multigrade classrooms demonstrate smaller gains in academics and exhibit less optimal executive function, which was partially explained by classroom-level factors., When possible, the implementation of multigrade kindergarten classrooms may need to be re-evaluated. [ABSTRACT FROM AUTHOR]

Despite the growing body of research on parents' beliefs and practices, relatively little is known about the relations between parents' knowledge of children's development, home-based activities, and children's early reading and math skills. This study used data from the Early Childhood Longitudinal Study-Birth Cohort to examine the differences in Asian, Black, Latino, and White children's early reading and math skills at kindergarten entry and whether parents' knowledge of children's development and home-based activities mediate the relation. Parents' knowledge of children's development was assessed when children were 9 months. Home-based activities, including home literacy and enrichment, were assessed when children were preschool age. Asian and White children started kindergarten with significantly higher reading and math scores than Black or Latino children. There also were significant differences across groups in the frequency of engagement in home literacy and enrichment activities. Associations between race/ethnicity and reading/math scores were mediated by parents' knowledge of children's development and home literacy activities. Discussion addresses the importance of parents' knowledge of educationally relevant activities and how to engage in such activities to foster children's reading and math skills and to close racial/ethnic gaps. Highlights This paper examined racial/ethnic difference in children's reading and math skills in kindergarten and explores whether parents' knowledge of children's development and home-based activities mediate the relation between race/ethnicity and children's reading and math skills., By using data from the Early Childhood Longitudinal Study Birth Cohort, this study found that there were systematic racial/ethnic differences in parents' knowledge of children's development, home-based activities, and children's reading and math skills at the start of kindergarten., Parents' knowledge of children's development and home-based activities were found to mediate the association between race/ethnicity and children's reading and math skills for all groups. [ABSTRACT FROM AUTHOR]

The growth of the higher education population and different school paths to access an academic degree has increased the heterogeneity of students inside the classroom. Consequently, the effectiveness of traditional teaching methods has reduced. This paper describes the design, development, implementation and evaluation of a tutoring system (TS) to improve student's engagement in higher mathematics. The TS design was based on the Personalized System of Instruction of the Mastery Learning pedagogical approach and can be implemented in any higher education course with mathematics needs. The TS consists on small self-paced modularized units of educational contents, including tutorial videos, notes and formative e-assessment with personalized feedback. The TS ensures that the student is only allowed to proceed to the next unit after he or she achieves the required mastery criterion of the current unit. The TS was implemented in the Quantitative Methods course of an undergraduate degree and received good acceptance from students. It was also recognized that TS contributed to learning and engagement with the discipline. Through an experimental research experience, it has been shown that the imposition of restrictions on the advance to the next level by a mastery criterion leads to a significant improvement in student's engagement and performance. [ABSTRACT FROM AUTHOR]

This paper deals with the following chemotaxis system: [ABSTRACT FROM AUTHOR]