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With the advent of mobile technologies, well‐designed fraction apps can be used to help children gain fraction knowledge, a challenging topic for both teachers and students. The present pilot study adopted a quasi‐experimental design to investigate whether children can learn fraction concepts equally well if half of the lesson time (20 min) is replaced with game‐based learning. Keeping the total lesson time (40 min) identical, the control group (N = 33) received traditional instruction, and the experimental group (N = 32) was presented with a blended learning approach spending half of the class time (20 min) playing tablet‐based fraction games, where each of the learners had their own tablet. The results suggested that in the posttest, the experimental group achieved similar learning gains to the control group and appear to have achieved better performance in the transfer test than the control group. This paper also discusses the efficiency of game‐based learning, the mechanism of how fraction games might enhance learning, and the potential of integrating game‐based learning in educational settings. Lay Description: What is already known about this topicAs a significant mathematical concept in daily life, fractions are crucial for later success in math learning.As a promising new technology, educational games show a great potential for improving learning.Well‐designed fraction apps can be used to help children gain fraction knowledge.What this paper addsGame‐based fraction learning can be combined with formal learning in school education.Game‐based fraction learning might provide a more efficient approach to increasing students' conceptual knowledge of fractions.The result showed that the experimental group achieved a similar cognitive level as the control group although they spent half of the time playing a game, suggesting that children can gain knowledge from the experiences of playing games.What are the implications for practice and/or policyThe result suggests that the proper use of educational games in teaching fractions can make learning more efficient.Further research needs to be done to determine whether the fraction understanding gained through playing these games will have an impact on students' future learning of more complicated fraction concepts. [ABSTRACT FROM AUTHOR]

Let L=Δ−⟨∇ϕ,∇·⟩$L=\Delta -\langle \nabla \phi , \nabla \cdot \rangle$ be a symmetric diffusion operator with an invariant measure μ(dx)=e−ϕ(x)m(dx)$\mu (\mathrm{d}x)=e^{-\phi (x)}\mathfrak {m} (\mathrm{d}x)$ on a complete non‐compact smooth Riemannian manifold (M,g)$(M,g)$ with its volume element m=volg$\mathfrak {m} =\text{\rm vol}_g$, and ϕ∈C2(M)$\phi \in C^2(M)$ a potential function. In this paper, we prove a Laplacian comparison theorem on weighted complete Riemannian manifolds with CD(K,m)${\rm CD}(K, m)$‐condition for m⩽1$m\leqslant 1$ and a continuous function K$K$. As consequences, we give the optimal conditions on m$m$‐Bakry–Émery Ricci tensor for m⩽1$m\leqslant 1$ such that the (weighted) Myers' theorem, Bishop–Gromov volume comparison theorem, stochastic completeness and Feller property of L$L$‐diffusion processes hold on weighted complete Riemannian manifolds. Some of these results were well studied for m$m$‐Bakry–Émery Ricci curvature for m⩾n$m\geqslant n$ (Li, J. Math. Pures Appl. (9) 84 (2005), 1295–1361; Lott, Comment. Math. Helv. 78 (2003), 865–883; Qian, Q. J. Math. 48 (1987), 235–242; Wei and Wylie, J. Differential Geom. 83 (2009), 377–405) or m=1$m=1$ (Wylie, Trans. Amer. Math. Soc. 369 (2017), 6661–6681; Wylie and D. Yeroshkin, Preprint). When m<1$m<1$, our results are new in the literature. [ABSTRACT FROM AUTHOR]

Distance distributions are a key building block in many subfields in mathematics, science and engineering. In this paper, we propose a novel framework for analytically computing the closed form probability density function (PDF) of the distance between two random points each uniformly randomly distributed in respective arbitrary polygon regions. The proposed framework is based on measure theory and uses polar decomposition for simplifying and calculating the integrals to obtain closed form results. We validate our proposed framework by comparison with simulations and published closed form results in the literature for simple cases. We illustrate the versatility and advantage of the proposed framework by deriving closed form results for a case not yet reported in the literature. Finally, we also develop a Mathematica implementation of the proposed framework which allows a user to define any two arbitrary (concave or convex) polygons, with or without holes, which may be disjoint or overlap or coincide and determine the distance distribution numerically. [ABSTRACT FROM AUTHOR]

The problem of low attainment in mathematics has been an increasingly prominent feature of the policy discourse in England over the last 60 years; however, evidence from comparative studies indicates that little progress has been made in finding a solution. In this paper, we analyse the changing policy discourse of low attainment in mathematics through the main reports and speeches published in England, beginning with the Newsom Report, Half Our Future, in 1963, and continuing to the present day. We chart the evolving perspectives on the nature of ability, expectations, curriculum ideology and frame of reference through the changing language used in these documents, noting tensions and inconsistencies which arise through continuing lack of clarity about definitions and assumptions. [ABSTRACT FROM AUTHOR]

Math fluency (MF) is the ability to quickly and accurately solve simple math exercises. Proficiency in MF is one of the buildings of arithmetic achievement during school. However, so far only paper and pencil tests have been used to assess MF. In the current study, we present the BGU‐MF (Ben‐Gurion University Math Fluency) test, a new computerized tool for MF. MF was assessed by accuracy rates, response times, and the number of performed exercises. In order to examine its reliability, participants performed the test twice. In order to examine its validity, participants performed manual format of MF from the Woodcock–Johnson battery. Results indicated high reliability and validity of the BGU‐MF test. Performance in the BGU‐MF also predicted abilities in the math matriculation exam and psychometric exam. The advantages of the BGU‐MF computerized tool over the manual tool and further implications of the BGU‐MF are discussed. [ABSTRACT FROM AUTHOR]

It is commonly claimed that Kant's critical philosophy aims to limit reason's speculative use and its metaphysical pretensions. This paper argues that such claims should be amended in light of a technical distinction between negative limits and positive boundaries that Kant held throughout his career. Kant's only extended discussion of this distinction appears in §§57–60 of the Prolegomena, a division entitled "On pure reason's boundary‐determination". I examine these sections in detail in order to elucidate the account of the limits and boundaries of the activity of different cognitive faculties in the Critique of Pure Reason. I argue that once we understand a key ambition of the Critique to be the positive determination of the boundary between objects of experience and things in themselves, we gain insight into the essential contribution that Kant's theory of the positive utility of ideas of reason makes to the critical philosophy. [ABSTRACT FROM AUTHOR]

In this paper, we consider local smoothing estimates for the fractional Schrödinger operator eit(−Δ)α/2$e^{it(-\Delta)^{\alpha /2}}$ with α>1$\alpha >1$. Using the k$k$‐broad 'norm' estimates of Guth–Hickman–Iliopoulou (Acta Math. 223 (2019), 251–376), we improve the previously best‐known results of local smoothing estimates of Guo–Roos–Yung (arXiv:1710.10988 (2017)) and Rogers–Seeger (J. Für Die Reine und Ang. Math. (Crelles Journal), 640 (2010), 47–66). [ABSTRACT FROM AUTHOR]

Tingir et al. (2017) concluded from their meta‐analysis that the subject areas taught through mobile devices had significantly higher achievement scores (d = 0.48) than the ones taught with traditional teaching methods. Given the relatively high positive effect of mobile devices on student achievement, we carefully analysed the selected research in this meta‐analysis. We reviewed Tingir et al.'s (2017) meta‐analysis based on analysis of the methodology of the selected research, while drawing on the work of Slavin (2003), Cheung and Slavin (2016), and Sung et al. (2019). Twelve of the 14 (86%) studies included in the meta‐analysis done by Tingir and his team (2017) present such major methodological flaws that they should not have been included. Our analysis leads us to believe that the conclusion of Tingir et al. (2017) is not justified. It is recognized that duration of experiment is negatively correlated with effect size: the shorter the duration, the higher the effect (Burston, 2015; Slavin & Lake, 2009). Although demanding more effort, the field of education must raise the bar if it is to have knowledge of acceptable value. Lay Description: What is already known about this topic?: Tingir et al. (2017) concluded from their meta‐analysis that: "the subject areas taught through mobile devices had significantly higher achievement scores than the ones taught with traditional teaching methods" (p. 366). What this paper adds?: We therefore reviewed the meta‐analysis by Tingir et al. (2017) and the underlying research. Our analysis leads us to believe that the conclusion of Tingir et al. (2017) is not justified.The data on reading used in the meta‐analysis by Tingir et al. (2017) do not make it possible to calculate a legitimate effect size for reading or to make a judgment about the effectiveness of mobile devices in the classroom.With respect to mathematics, the weakness and biases of the studies selected in the meta‐analysis by Tingir et al. (2017) should not have allowed them to calculate an effect size and do not provide a clear answer on the effectiveness of mobiles devices in the classroom.The studies in science selected by Tingir et al. (2017) demonstrate a set of methodological flaws that cannot provide a sound basis for determining a convincing effect of mobile device in the classroom on student achievement. Implications for practice and/or policy: Tingir and associates (2017) calculated an overall mean effect of 0.48 for mobiles devices on student achievement by combining research in reading (effect = 0.666; N = 3), mathematics (effect = 0.16; N = 3) and science (effect = 0.528; N = 8). The authors did not do a school‐level analysis (elementary, high school) in their school subject groupings due to the small number of studies, particularly in reading and mathematics.Twelve of the 14 (86%) studies included in the meta‐analysis done by Tingir and his team (2017) present such major methodological flaws that they should not have been included. As mentioned in the introduction, Slavin and his colleagues found different results in a related field. Slavin et al. (2009) found an effect size of 0.11 for the use of technology in the classroom, in computer‐assisted and computer‐based instruction, and an effect size of 0.05 for the use of digital tools 10 years later (Slavin, 2019). Given all the above, it is our opinion that the meta‐analysis by Tingir et al. (2017) cannot be used to justify the use of mobile devices in the classroom. [ABSTRACT FROM AUTHOR]

Background: Motivation is an important factor in the learning process and supporting students' motivation in mathematics is a significant challenge for educators. Educational technologies, such as digital games, offer potential for engagement in mathematics learning activities. Objectives: To contrast the general decrement in student motivation in mathematics, a multilevel meta‐analysis was carried out to synthesize the results of studies concerning the impact of digital games on K‐12 student motivation in mathematics. Methods: Standardized measure of effect size (dppc2) for pre‐ post‐control group designs was used, and different sources of dependency among the effects were taken into account. Moreover, through meta‐regressions, we examined whether specific characteristics of the participants, interventions and outcomes were associated with effect size differences throughout the studies. Results and Conclusions: A total of 20 primary studies (43 effect sizes) meeting eligibility criteria was included. Results showed a significant overall effect (dppc2 = 0.27; 95%CI = [0.14; 0.41]) and a great heterogeneity between studies. Moderator analyses showed differences in effect size associated to the duration of intervention and motivational construct in terms of expectancy and value. Implications: Overall, the findings indicate that digital games are effective tools compared to conventional teaching practices. The results are promising and could be useful for the design of digital educational interventions aimed at promoting motivation in mathematics. Lay Description: What is already known about this topic: Motivation in term of expectancy and value is an important factor in the learning process.Digital games influence student motivation to learn in K‐12 education.Concerning mathematics, previous meta‐analyses studied the effects of digital games on math achievement but not on motivation. What this paper adds: This meta‐analysis synthesizes the impact of digital games on motivation in mathematics.The targeted learner audience is K‐12 students.Results show a significant overall effect of digital games on motivation and a great heterogeneity.The effect is greater if motivation is measured in terms of expectancy than of value.The duration of intervention moderates the effect: short interventions have the highest effects. Implications for practice and/or policy: Digital games promote motivation in mathematics for K‐12 students compared to conventional teaching practices.Engaging and innovative educational activities, such as digital games, might contrast the worldwide decline of enrolments in the STEM field. [ABSTRACT FROM AUTHOR]

Background: With the recent pivot to online instruction and/or to mixed online/face‐to‐face (i.e., hybrid) models of teaching necessitated by the novel coronavirus pandemic, the uses of technology to support instruction would seem to have great importance. Whereas effective integration of technology in mathematics classrooms requires recognition of students' needs and instructional goals that technology could fulfill, very few comprehensive meta‐analytical studies have focused on the roles of instructional technology in support of specific learning goals. Objectives: In this meta‐analysis, we investigated and reviewed the roles and affordances of technology in mathematics instruction and its effects on students' mathematics achievement. Methods: Cross‐searching multiple bibliographic databases generated a total of 3276 potentially relevant full‐text studies. After applying a series of inclusion/exclusion criteria, we kept 77 studies with 151 effect sizes. Two researchers then coded for seven sets of study features and student characteristics: technology roles, publication‐related features (years and resources), research design, sample size, grade levels, duration of interventions, and types of the testing instruments. The coding achieved acceptable levels of inter‐rater reliabilities. Since effect sizes varied across studies and student populations, random‐effects models were used for overall effect estimates and moderator analyses. Results and conclusions: Overall, this meta‐analysis revealed a small, positive, and statistically significant effect of technology on students' mathematics achievement with an average Hedges' s g (ḡ) of 0.23. The largest significant moderator effects were found when technology was used to design and support collaborative and communicative environments (ḡ = 0.49); the next‐largest moderator effects were found when using technology as supports for problem‐solving (ḡ = 0.39), followed by the roles of as supports for conceptual development (ḡ = 0.31) and as adaptive mathematics practices (ḡ = 0.28). This study also found that the effects of technology were differentiated as a function of publication resources, research design, duration of intervention, and the testing instrument. Major takeaways: Focusing on the roles and functions of technology, this study can contribute to guide potential synthetical studies as well as the future design of educational technology. In particular, technology is used effectively when it is used (a) to create and design a collaborative and communicative learning environment where students have chances to collaborate and interact with each other and (b) as supports for mathematics problem‐solving and for mathematics conceptual development. On the other hand, technology is less effective when it is used for monitoring and assessing students' learning processes without follow‐up instructions. The findings suggested that technology intervention lasting for a shorter time is the better choice. When technology is used for longer periods of instruction, maintaining its novelty and students' curiosity should be considered. This study also suggested that incorporating computer‐adaptive testing in technology‐based intervention programs is more likely to detect technology effects as adaptive testing could continuously adjust to the abilities of individual students. Lay Description: What is already known about this topic?: Technology is now widely used in mathematics classrooms for aiding teachers' instruction.The affordances and functions of technology and its alignment with instructional goals are the key to effectively integrate technology in mathematics classrooms. What this paper adds?: Our study contributes to a comprehensive and systematic taxonomical framework of technology roles, which integrated previous multiple theoretical perspectives, thus, this framework can reflect the complexity and the dynamic nature of technology integration in present‐day mathematics classroomsOur framework based on the roles and functions of technology has been shown to be useful to guide synthetical studies. Implications for practice and/or policy: Teachers might consider using technology to support collaborative learning in their mathematics classrooms in order to enhance their students' mathematics learning.Software developers and researchers also should place more efforts in designing interactive technology learning environments or systems where students can work together and learn from each other.Program implementors should consider incorporating adaptive testing in technology when testing students' learning outcomes from technology‐based intervention programs so that students' authentic learning performance and levels are measured. [ABSTRACT FROM AUTHOR]

Background: Mobile learning studies often focus on teachers' perspectives. This study instead considers students' experiences of learning with mobile devices (i.e., m‐learning) in secondary school mathematics and science. Objectives: The research aims to describe the m‐learning experiences of secondary mathematics and science students, and to determine the extent to which distinctive pedagogical dimensions impact students' perceived learning. Methods: A survey instrument using the iPAC mobile pedagogical framework as a theoretical lens is developed and validated. This framework highlights three pedagogical dimensions: personalization, authenticity, and collaboration. Structural equation modelling is used to investigate how each dimension predicts students' perceived improvement in learning, whilst accounting for usage context, among a sample of students in schools where mobile devices are used extensively. Results and Conclusions: Students were in agreement that personalization was a characteristic of their m‐learning experiences, but authentic and collaborative learning were not as strongly featured. M‐learning activities fostering personalization were most important for improving perceived learning; authenticity and collaboration were also significant, but no differences in perceived learning improvement due to location were found. Authentic m‐learning and perceived improvement in learning with mobile devices were significantly higher in science than mathematics subjects. Implications: When teachers design m‐learning tasks that enhance personalization, collaboration, and authenticity, students are predicted to perceive improvements in their learning. The findings suggest that teachers should consider designing technology‐enhanced tasks that improve students' experiences of collaborative and authentic learning, particularly in mathematics for greatest gains in students' perceived improvement in learning. Lay Description: What is already known about this topic:Mobile learning studies often focus on teachers' perspectives and practices or expert commentaries.Issues of usability, access, engagement, motivation, and potential risk are often highlighted rather than pedagogical factors.Mobile technologies provide students with opportunities for more personalized and autonomous seamless experiences across learning contexts.Science teachers frequently use authentic and project‐based m‐learning opportunities, whilst mathematics teachers prefer didactic, drill and practice approaches.What this paper adds:This study focuses on students' m‐learning in secondary mathematics and science.A multi‐item scale considering aspects of authenticity, personalization, collaboration and context is developed and validated.Personalization in m‐learning activities are most important for perceived learning, followed by authenticity and collaboration.Science students report greater authenticity and perceived learning in m‐learning than mathematics students.Implications for practice and/or policy:Highlighting the student perspective is a valued lens to evaluate m‐learning pedagogy and outcomes in student learning.Efforts should be made to develop mobile pedagogies, particularly with respect to authenticity and collaboration.Teachers in mathematics would benefit most from examining practices that improve authenticity. [ABSTRACT FROM AUTHOR]

This is an example of an original article in the layout expected by The Photogrammetric Record. The abstract is a concise summary of the essential elements of the paper and should not contain detailed results. It should be no longer than 150 words. This template indicates how a paper submitted to the journal should be structured and formatted, including figures, tables, mathematics and references. [ABSTRACT FROM AUTHOR]

One of the golden rules in instructional design methods is to optimize the use of working memory capacity and avoid cognitive overload. The study of cognitive load has historically relied on one's introspection. However, it is difficult to capture changes in cognitive load levels during learning sensitively. This paper suggests an approach to investigating dynamic changes in cognitive load by using a pupillometry. With the method, this study explores the effects of learners' prior knowledge and task complexity on cognitive load. An experiment was conducted on two groups of students (N = 19) with distinct levels of prior knowledge. In the experimental session, participants watched a video lecture on a mathematics proposition, while being eye‐tracked. The lecture consists of sections, which can be either a high task complexity or a low task complexity based on elements they have. Pupil dilations acquired in each section were used to explore the time course of cognitive load. To formulate cognitive load patterns, a time‐series clustering was used. The research conducted a chi‐square analysis to test differences in cognitive load patterns by prior knowledge and task complexity. Results show that pupil dilation patterns can be applied to monitor changes in cognitive load during learning. What is already known about this topic? Cognitive load is a dynamic construct so that it can be changed during learning.Pupil dilation is a valid indicator of showing changes in cognitive load during learning. What this paper adds? The study proposes a novel method to capture dynamic changes in cognitive load in video‐based learning by using a time‐series clustering.The proposed approach detected the changes in cognitive load as a function of learner's level of prior knowledge and task complexity in learning.The proposed approach found seven different types of cognitive load patterns during learning. Implications for practice and/or policy: The use of temporal approach can be a technique to capture dynamics of cognitive load learners are experiencing during learning. [ABSTRACT FROM AUTHOR]

In a short fragment published for the first time with his lost notebook in 1988 (Ramanujan, The lost notebook and other unpublished papers (Narosa, New Delhi, 1988)), Ramanujan offered two beautiful identities, associated, respectively, with the classical circle and divisor problems. In fact, they are analogues, with an additional variable, but not generalizations, of classical identities associated with these two famous problems. After Ramanujan's death in 1920, the lost notebook and fragments of papers of Ramanujan were sent to Hardy. We do not have any official record of what was included in this mailing, but it is likely that the aforementioned fragment was included in this parcel. If so, then it is possible that Ramanujan wrote it at the end of his life in either 1919 or 1920. On the other hand, from a paper that Hardy published in 1915 (Hardy, Quart. J. Math. (Oxford) 46 (1915) 263–283) on the circle problem, we are aware that by early in his stay in England, Ramanujan had a strong interest in these problems, and so the fragment may emanate from this period. Two of the present authors and Kim published a proof of the identity connected with the circle problem in 2013 (Berndt, Kim and Zaharescu, Adv. Math. 236 (2013) 24–59). In this paper, a proof of the second identity is given for the first time. [ABSTRACT FROM AUTHOR]

For the past forty years, United States school districts have increasingly hired mathematics specialists to support the teaching and learning of mathematics. Despite the prevalence of this professional development structure, this is a relatively new research topic for the mathematics education field. In this paper, we report findings from an exploration of literature between 1981 and 2018 to examine the role of mathematics specialists (MSs). In particular, we examine: (a) MS positioning across research; (b) historical trends of school‐based MS research; and (c) orientations of school‐based MSs within research. Using the McGatha and Rigelman framework as an analytic lens, we found that beyond the positions identified in their framework (coach, intervention specialist, teacher), there were four additional MS positionings within the research (learner, other p‐12 stakeholder, university stakeholder, unknown). Ultimately, we forward an expansion to the McGatha and Rigelman framework to include these new categories, as well as contextual descriptions and working definitions to support future research in more accurately and robustly capturing the ways in which MSs are investigated and reported on in research. [ABSTRACT FROM AUTHOR]

The product manifold S3×S3$\mathbb {S}^3\times \mathbb {S}^3$ is one of the only four homogeneous six‐dimensional nearly Kähler manifolds. It also admits a canonical almost product structure P, which is compatible with the almost complex structure (see Bolton et al., Tôhoku Math. J. 67 (2015), 1–17, and Moruz and Vrancken, Publ. Inst. Math. 103 (2018), no. 117, 147–158). In this paper, we investigate and describe the two‐dimensional surfaces of S3×S3$\mathbb {S}^3\times \mathbb {S}^3$ which are P‐invariant. [ABSTRACT FROM AUTHOR]

Grey wolf optimization (GWO) algorithm is a new emerging algorithm that is based on the social hierarchy of grey wolves as well as their hunting and cooperation strategies. Introduced in 2014, this algorithm has been used by a large number of researchers and designers, such that the number of citations to the original paper exceeded many other algorithms. In a recent study by Niu et al., one of the main drawbacks of this algorithm for optimizing real‐world problems was introduced. In summary, they showed that GWO's performance degrades as the optimal solution of the problem diverges from 0. In this paper, by introducing a straightforward modification to the original GWO algorithm, that is, neglecting its social hierarchy, the authors were able to largely eliminate this defect and open a new perspective for future use of this algorithm. The efficiency of the proposed method was validated by applying it to benchmark and real‐world engineering problems. [ABSTRACT FROM AUTHOR]

With facilitation of advanced technologies, design and application of smart become promising research issues in education. Although it is potential for students to learn geometric in authentic contexts, there were still lack of studies addressing smart learning issue in authentic context for geometry. This study aim to propose an app, called SmartUG, to support students smartly to consolidate geometry understanding and learning through enriching experience of exploring and applying related geometry surrounding. There were four smart mechanisms proposed in SmartUG (direction guidance, learning progress, object recognition and answer feedback) to guide students' measuring and applying geometry smartly and meaningfully in authentic contexts. A total of 83 fifth‐grade students participated in this experiment and were divided into three groups, an experimental group that learned with smart mechanisms, a control group that learned without smart mechanisms and a traditional control group that learning with traditional teaching approach. Basically, experimental group outperformed control group and traditional teaching group in term of geometry ability and estimation ability, which means students benefited from proposed SmartUG. Moreover, students showed positive attitude and high intention to use toward SmartUG. Students should be provided more chances to learn geometry smartly in authentic contexts with SmartUG. It is potential to future studies to implement more smart mechanisms to support students learning in authentic contexts. Moreover, the learning system can get smarter and smarter when the learning system gets more and more input data from students' use. Lay Description: What is already known about this topic: Geometry is important and strongly related to our surroundings.Students have few chances to learn Geometry through practicing in authentic contexts.Innovative technologies are potential to be utilized to facilitate smart learning. What this paper adds: Proposed a framework of smart mechanisms to support learning Geometry in authentic context.Utilized innovative technologies to facilitate smart learning in authentic context. Implications for practice and/or policy: Smart learning in authentic context helped improving students' motivation and achievements.The proposed smart mechanisms are effective to support smart learning.The smart mechanisms can be implemented not only for Geometry but also other subjects. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and asymptotic properties of solutions to the following fractional Schrödinger equation: (−Δ)σu=λu+|u|q−2u+μIα∗|u|p|u|p−2uinℝNunder the normalized constraint ∫ℝNu2=a2,where N ≥ 2, σ ∈ (0, 1), α ∈ (0, N), q ∈ (2 + 4σ/N, 2N/N − 2σ], p ∈ [2, 1 + 2σ + α/N), a > 0, μ > 0, Iα(x)=|x|α−N and λ∈ℝ appears as a Lagrange multiplier. In the Sobolev subcritical case q ∈ (2 + 4σ/N, 2N/N − 2σ), we show that the problem admits at least two solutions under suitable assumptions on α, a, and μ. In the Sobolev critical case q=2N/N−2σ, we prove that the problem possesses at least one ground state solution. Furthermore, we give some stability and asymptotic properties of the solutions. We mainly extend the results of S. Bhattarai published in 2017 on J. Differ. Equ. and B. H. Feng et al published in 2019 on J. Math. Phys. concerning the above problem from L2‐subcritical and L2‐critical setting to L2‐supercritical setting with respect to q, involving Sobolev critical case especially. [ABSTRACT FROM AUTHOR]

Background: Building on the Realistic Accuracy Model, this paper explores whether it is easier for teachers to assess the achievement of some students than others. Accordingly, we suggest that certain individual characteristics of students, such as extraversion, academic self‐efficacy, and conscientiousness, may guide teachers' evaluations of student achievement, resulting in more appropriate judgements and a stronger alignment of assigned grades with students' actual achievement level (as measured using standardized tests). Aims: We examine whether extraversion, academic self‐efficacy, and conscientiousness moderate the relations between teacher‐assigned grades and students' standardized test scores in mathematics. Sample: This study uses a representative sample of N = 5,919 seventh‐grade students in Germany (48.8% girls; mean age: M = 12.5, SD = 0.62) who participated in a national, large‐scale assessment focusing on students' academic development. Methods: We specified structural equation models to examine the inter‐relations of teacher‐assigned grades with students' standardized test scores in mathematics, Big Five personality traits, and academic self‐efficacy, while controlling for students' socioeconomic status, gender, and age. Results: The correlation between teacher‐assigned grades and standardized test scores in mathematics was r =.40. Teacher‐assigned grades more closely related to standardized test scores when students reported higher levels of conscientiousness (β =.05, p =.002). Students' extraversion and academic self‐efficacy did not moderate the relationship between teacher‐assigned grades and standardized test scores. Conclusions: Our findings indicate that students' conscientiousness is a personality trait that seems to be important when it comes to how closely mathematics teachers align their grades to standardized test scores. [ABSTRACT FROM AUTHOR]

Let σ=(σ1,σ2,⋯,σn)∈Sn−1 and dσ denote the normalized Lebesgue measure on Sn−1,n⩾2. For functions f1,f2,⋯,fn defined on R, consider the multilinear operator given by T(f1,f2,⋯,fn)(x)=∫Sn−1∏j=1nfj(x−σj)dσ,x∈R.In this paper, we obtain necessary and sufficient conditions on exponents p1,p2,⋯,pn and r for which the operator T is bounded from ∏j=1nLpj(R)→Lr(R), where 1⩽pj,r⩽∞,j=1,2,⋯,n. This generalizes the results obtained in (Bak and Shim, J. Funct. Anal. 157 (1998) 534–553; Oberlin, Trans. Amer. Math. Soc. 310 (1988) 821–835). [ABSTRACT FROM AUTHOR]

The aim of this study was to investigate the effect of using dynamic geometry software (GeoGebra) on the eighth‐grade students' conceptual understanding and the retention of learning regarding linear equations and slope. In this study, a quasi‐experimental design with pre‐test, post‐test and delayed post‐test was employed. This study was conducted with 52 eighth‐grade Turkish students (experimental group, n = 25; control group, n = 27). While GeoGebra software‐supported instruction was carried out in the experimental group, textbook‐based direct instruction was continued in the control group. Data were collected with the conceptual understanding test (CUT) which consists of 38 questions including open‐ended, multiple choice and fill in the blanks. CUT was applied to the experimental and control groups as a pre‐test and post‐test at both the beginning and the end of the instruction, respectively. Seven weeks after the instruction, CUT was applied to both groups as a retention test. Data were analysed through SPSS 17.0 statistical software by using a t‐test and ANCOVA test. It was indicated in the study results that GeoGebra software‐supported instruction for eighth‐grade students regarding linear equations and slope did significantly improve both their conceptual understanding and retention of learning in comparison to textbook‐based direct instruction. Lay Description: What is already known about this topic?: The subject of functions and their graphs are the basis of many mathematical concepts and subjects such as logarithm, limit, derivative and integral.It is indicated in many studies that middle‐grade students have some misconceptions and difficulties in learning the concept of a straight line and slope.It was determined in previous studies conducted at different grade level that using dynamic geometry software (DGS) increases students' mathematics achievement according to traditional instruction.There is a need for research investigating the effect of using GeoGebra software on eighth grade students' conceptual understanding and retention of learning regarding linear equations and slope. What this paper adds?: A quasi‐experimental design with pre‐test, post‐test and delayed post‐test was conducted.Using GeoGebra software had positive effects on eighth‐grade students' conceptual understanding regarding linear equations and slope.The learning environment with GeoGebra software increased the retention of learning. The implications of study findings for practitioners: This research provided evidence regarding the effects of using GeoGebra software on eighth‐grade students' conceptual understanding and retention of learning in mathematics.In future studies, the long‐term effects of GeoGebra on other mathematics topics and other learning outcomes within similar settings should be examined. [ABSTRACT FROM AUTHOR]

In this paper, I argue from a metasemantic principle to the existence of analytic sentences. According to the metasemantic principle, an external feature is relevant to determining which concept one expresses with an expression only if one is disposed to treat this feature as relevant. This entails that if one isn't disposed to treat external features as relevant to determining which concept one expresses, and one still expresses a given concept, then something other than external features must determine that one does. I argue that, in such cases, what determines that one expresses the concept also puts one in a position to know that certain sentences are true—these sentences are thus analytic relative to this determination basis. Finally, I argue that there are such cases: some sentences are analytic relative to what determines that we express certain key concepts, and these sentences include ones that have always been thought to be the best candidates for being analytic, namely, stipulative truths, and first principles of mathematics. [ABSTRACT FROM AUTHOR]

With the technological improvements of innovative portable recording gadgets, augmented researchers' interest in exploring students' visual attention in their natural and normal occurring classrooms. The purpose of this study was to gauge students' visual attention in their Mathematics and English classrooms. This article reports on a study conducted in three schools in Santiago, Chile, where a sample of 113 randomly selected students wore a mini‐video camera mounted on eyeglass in their Mathematics and English lessons. Using Google images, we automatically and objectively examined 723,600 frames from the recordings where the classroom teacher appeared in the students' visual field. The results show that students' visual attention varies depending on four factors: (a) gender of the student, (b) age of the students, whether students are low/high attainers and (d) whether students are in English or Mathematics lessons. Surprisingly, students significantly paid more visual attention in their Mathematics than in English lessons. High attainers were more visually engaged than their low attainers counterparts. Students appeared to be visually engaged differently at different stages in their education. Furthermore, girls were more visually engaged than boys. The results of this study can have enormous practical implications for teachers and teacher education, in order to be better visually engaged with students during teaching. Lay Description: What is already known about this topic: The advantage of computers and technologies as tools in analysing teaching and learning.Measuring students' visual attention to teachers in different subject disciplines.Using first person's perspective (students' perspectives) in analysing classroom interaction. What this paper adds: Measuring students' visual attention to teachers in Mathematics and English classrooms using 723,600 frames.Students are more visually engaged to teachers in Mathematics versus English classrooms.Higher grade point average students are more visually engaged to teachers than their lower GPA counterparts.Female students significantly pay more visual attention to their teachers than their male peers.Students' visual attention to teachers is dependent on the year of study. Implications for practice and/or policy: Identifying students with lack of visual attention to the teacher objectively and automatically.Practical implications for teacher education courses, and also continuing Professional Development courses for in‐service teachers. [ABSTRACT FROM AUTHOR]

This study investigated changes in learners' motivation, engagement, performance, and spatial reasoning over time and across different levels of virtual reality (VR) immersion. Undergraduate participants explored a virtual solar system via a moderately immersive or highly immersive VR platform over three sessions. In a third condition, participants initially learned with moderate immersion and transitioned to higher immersion after the second session. Following research on novelty effects, we explored whether subjective experiences and performance would decline over time (e.g., decreasing motivation or performance) as participants became familiar with the virtual environment and tools. However, we hypothesized that transitional immersion (i.e., switching from moderate to higher immersion) might lead to a renewed sense of novelty. Results suggested that both moderate and higher levels of immersion were motivating, engaging, and supportive of learning. In contrast to predictions based on novelty effects, these outcomes did not decline overall as learners gained familiarity with the systems. However, transitional immersion emerged as a promising and testable pedagogical approach for future VR education. All participants also showed gains in spatial reasoning. Lay Description: What is already known about this topic?: Virtual reality can support motivation and learning in STEM education.Novelty may elicit motivation, engagement and learning.Virtual reality may benefit development of spatial reasoning skills. What this paper adds?: Motivation, engagement and performance persist across multiple sessions of VR learning.Switching from moderate to higher immersion increases motivation and engagement.Both moderate and higher immersion support improvements in spatial reasoning. Implications for practice and/or policy: Novelty effects are not a significant concern when implementing VR education over multiple sessions.More immersive VR tools may be progressively introduced during learning. [ABSTRACT FROM AUTHOR]

In this paper, we prove the upper semicontinuity of the strong global attractors 𝒜θ on the dissipative index θ in the topology of the stronger space for the Kirchhoff wave model with structural nonlinear damping: utt−ϕ(‖∇u‖2)△u+σ(‖∇u‖2)(−Δ)θut+f(u)=g(x), with θ ∈ [1/2, 1). It is continuation of the research in recent literatures1,2 where the upper semicontinuity of the strong attractor 𝒜θ on θ in the topology of natural energy space is obtained. This result improves and deepens those in recent literatures (Li and Yang in J Differ Equat. 2020; 268: 7741‐7743; Li, Yang and Ding in Appl. Math. Lett. 2020; 104:106258). [ABSTRACT FROM AUTHOR]

The purpose of this paper is to define a q‐analogue of a parametric generalization of Baskakov operators introduced by Aral and Erbay (Math. Commun. 24(1) (2019), 119‐131). We establish some local direct results for these operators by means of the modulus of continuity and the Peetre's K‐functional. Weighted approximation properties are also established. Next, we construct a bivariate case of the above q‐operators and determine the rate of convergence in terms of the moduli of continuity. A Voronovskaja‐type theorem is derived too. Further, we study the rate of approximation of Bögel continuous and Bögel differentiable functions by the associated generalized Boolean sum (GBS) operators with the aid of mixed modulus of smoothness. We illustrate the rate of approximation of the q‐operators, their bivariate, and the GBS cases by means of graphics and tables and show that the GBS operators provide better rate of convergence than the bivariate operators. [ABSTRACT FROM AUTHOR]

This paper discusses research on reading disorders during the period since their classification within the overarching category of neurodevelopmental disorders (Journal of Child Psychology and Psychiatry, 53, 2012, 593). Following a review of the predictors of learning to read across languages, and the role of language skills as critical foundations for literacy, profiles of reading disorders are discussed and putative causal risk factors at the cognitive, biological, and environmental levels of explanation considered. Reading disorders are highly heritable and highly comorbid with disorders of language, attention, and other learning disorders, notably mathematics disorders. The home literacy environment, reflecting gene‐environment correlation, is one of several factors that promote reading development and highlight an important target for intervention. The multiple deficit view of dyslexia (Cognition, 101, 2006, 385) suggests that risks accumulate to a diagnostic threshold although categorical diagnoses tend to be unstable. Implications for assessment and intervention are discussed. [ABSTRACT FROM AUTHOR]

We apply Carroll's model of school learning, which theorizes about the relationship between time and learning, to motivate the design of a large, first‐year, university mathematics course, where students have the choice to attend lectures and/or watch online videos. The theoretical model informs how the course and resources are designed in order to assist students to spend the time they need to master a task in an efficient manner. We examine the relationship between learning and time spent on lectures and/or videos, by analysing data collected on lecture attendance, videos accessed, and mathematical achievement, prior to, and at the end of, the course. Findings show that students use videos as either a complement to, or substitute for, the lecture, and time spent using either or both resources has a significant impact on learning. Lay Description: What is currently known about the subject matter: It is quite common for universities to make online lectures available as an additional resource to students enrolled to face‐to‐face courses.Students exhibit satisfaction with these online resources and use them to replace or review the live lecture and/or revise for examinations.Results on the impact of the availability of online lectures on performance are mixed.Most studies in the area consider online lecture resources that are in a one‐to‐one correspondence with the live lecture. What this paper adds: This paper uses a theoretical model of time and learning to present a rationale for the design of a university mathematics course where students can attend lectures and/or watch short videos.As design course intends, findings show that students use videos as either a complement to, or substitute for, lectures.Time needed to master course learning outcomes depends on student's prior mathematical achievement.Empirical findings show that time spent using either, or both, resources has a significant impact on learning. Implications of study findings for practitioners: This study provides a detailed description of a course designed explicitly to enable students to use videos and lectures in a complementary/substitutable manner.Students with low prior achievement, who require more time to mastery, should be advised on how to use videos as complements to lectures in order to scaffold how they spend this time. [ABSTRACT FROM AUTHOR]

This paper concerns a class of combinatorial objects called Skolem starters, and more specifically, strong Skolem starters, which are generated by Skolem sequences. In 1991, Shalaby conjectured that any additive group Zn, where n≡1 or 3(mod8),n≥11, admits a strong Skolem starter and constructed these starters of all admissible orders 11≤n≤57. Only finitely many strong Skolem starters have been known to date. In this paper, we offer a geometrical interpretation of strong Skolem starters and explicitly construct infinite families of them. [ABSTRACT FROM AUTHOR]

This study proposes a computer‐assisted system with a design based on Polya's problem‐solving model. The system is designed to help average and low‐achieving second graders in mathematics with word‐based addition and subtraction questions. The emphasis of using the specific model was on dividing the problem‐solving procedure into stages and the concentration on the stages that are problematic for students. Specifically, we compared mathematical word problem‐solving performance and computational skills of students who utilized the computer‐assisted system with students who employed general strategy instruction. Participants consisted of 52 second‐grade students randomly assigned to treatment conditions. Students were pretested and posttested with mathematical problem‐solving and computation tests, and repeated measures of their progress with respect to word problem solving were registered. The results showed there was a significant difference between the experimental and control groups in terms of the word problem‐solving progress measure, favouring the experimental group. This confirms that providing students with a computer‐assisted system offered the opportunity to explore all stages of the problem‐solving procedure as one possible way to enhance their problem‐solving skills. Lay Description: What is currently known about the subject matter Problem‐based learning is recognized as an instruction method that positively influence learning outcomes along with higher order thinking skills.The use of computers to implement findings from qualitative research related to problem‐solving teaching strategies can develop reasoning skills in mathematics and problem solving of elementary students with learning difficulties in mathematics.Polya's model helps students to solve mathematical word‐based problems. What the paper adds to this subject This paper suggests that efforts to improve word problem solving should focus on episodes students neglect when solving problems.This study proposes a computer‐assisted system with a design based on Polya's problem‐solving model.This empirical study investigates whether providing students with computer‐based assistance at each stage of the problem‐solving process helps students to overcome their difficulties.This study explores whether students fail to solve the problem because they do not understand the specific relations among the three problem quantities, or in choosing a correct solution strategy, or in carrying out the solution strategy correctly. The implications of study findings for practitioners Combining Polya's model with computer assistance at each solving procedure stage enhances student's capabilities to solve mathematical word‐based problems.Students encountered problems when reviewing their solutions; this signifying that students did not recognize the variants of the problem. [ABSTRACT FROM AUTHOR]

Learning and teaching algebra concepts are frequent problems for both students and teachers alike. Students struggle to learn algebra, and teachers struggle to identify the best way to teach algebra. It is recurrent that teachers use instructional methods that promote memorization, and, consequently, the learning process may prove unsatisfactory. This paper introduces Virtual Algebra Tiles, an open educational resource whose purpose is to enable students to use algebra tiles from a computer to enhance their knowledge of algebra concepts. To evaluate the effectiveness of the system, we designed a case study. The participants were 40 students of engineering degrees who were randomly assigned to experimental or control groups. Results indicate that the system has a large effect size (ES = 0.83, p < 0.001) on learning effectiveness and a promising long‐term knowledge retention (ES = 0.79, p < 0.001). Students concluded that this version of algebra tiles is more motivating than other versions, because it is presented in a format that stands natural to them. Students feel more comfortable in virtual environments, and therefore, the learning process becomes a more pleasant task. Lay Description: What is already known about this topic: Inadequate teaching methodologies can lead to student failure.It is necessary to decrease the emphasis on memorization and to favour active learning techniques.The use of mathematical manipulatives increases students' learning gains.Algebra tiles are an educational resource that helps students understand algebra concepts by using geometric figures. What this paper adds: Virtual Algebra Tiles is a multimedia version of the educational resource algebra tiles.Virtual Algebra Tiles has a large effect size on students' learning achievements.Virtual Algebra Tiles improves students' long‐term knowledge retention. Implications for practices and/or policy: Teachers should participate in the development of digital pedagogical material to enrich their lectures.It is necessary to develop more open educational resources, which can be accessed by students and teachers.Digital educational resources must take into account the special needs of particular users. [ABSTRACT FROM AUTHOR]

This paper concerns two paradoxes involving propositions. The first is Russell's paradox from Appendix B of The Principles of Mathematics, a version of which was later given by Myhill. The second is a paradox in the framework of possible worlds, given by Kaplan. This paper shows a number of things about these paradoxes. First, we will see that, though the Russell/Myhill paradox and the Kaplan paradox might appear somewhat different, they are really just variants of the same phenomenon. Though they do this in different ways, the core of each paradox is to use the notion of a proposition to construct a function, f, from the power set of some set into the set itself. Next we will see how this paradox fits into the Inclosure Schema. Finally, I will provide a model of the paradox in question, showing its results to be non‐trivial, though inconsistent. [ABSTRACT FROM AUTHOR]

Abstract: The long‐standing debate into the potential benefit of developing mathematical thinking skills through learning to program has been reignited with the widespread introduction of programming in schools across many countries, including England where it is a statutory requirement for all pupils to be taught programming from 5 years old. Algorithm is introduced early in the English computing curriculum, yet there is limited knowledge of how young pupils view this concept. This paper explores pupils' (aged 10–11) understandings of algorithm following their engagement with 1 year of ScratchMaths, a curriculum designed to develop computational and mathematical thinking skills through learning to program. A total of 181 pupils from 6 schools undertook a set of written tasks to assess their interpretations and evaluations of different algorithms that solve the same problem, with a subset of these pupils subsequently interviewed to probe their understandings in greater depth. We discuss the different approaches identified, the evaluation criteria they used, and the aspects of the concept that pupils found intuitive or challenging, such as simplification and abstraction. The paper ends with some reflections on the implications of the research, concluding with a set of recommendations for pedagogy in developing primary pupils' algorithmic thinking. [ABSTRACT FROM AUTHOR]

The increasing availability of extensive and accurate clinical data is rapidly shaping cardiovascular care by improving the understanding of physiological and pathological mechanisms of the cardiovascular system and opening new frontiers in designing therapies and interventions. In this direction, mathematical and numerical models provide a complementary relevant tool, able not only to reproduce patient‐specific clinical indicators but also to predict and explore unseen scenarios. With this goal, clinical data are processed and provided as inputs to the mathematical model, which quantitatively describes the physical processes that occur in the cardiac tissue. In this paper, the process of integration of clinical data and mathematical models is discussed. Some challenges and contributions in the field of cardiac electrophysiology are reported. [ABSTRACT FROM AUTHOR]

This study focused on an examination of how type, quality and children's awareness of design features in digital math games, along with an awareness of the mathematics goals of the game, were related to learning outcomes. We conducted a parallel conversion mixed methods study with 45 students in Grades 3 and 4 (ages 9–10). Students participated in clinical interviews using three digital math games. The results suggest a moderated mediation relationship in which the quality of the design features moderated the mediating impact of children's awareness of the game's design features, specifically when the child was aware of the mathematics content learning goal (MCLG) of the game. These findings show how important it is that design features are of high quality in a digital math game, and how this is intertwined with children's awareness of the features and the MCLG. When these variables intertwined in just the right way, the interactions between the children and the digital math game afforded mathematical learning growth. Lay Description: What is currently known about the subject matter: Some game features, and the types of representations designed into the games, may have a greater impact than others.Some design features provide general learning support, and some provide specific mathematics support.There is a relationship between the subject (i.e., a child), the artefact (i.e., a digital math game) and the object (i.e., the mathematics).Understanding that relationship is complex because there are no clear‐cut variables that can be isolated; rather, these variables need to be considered together. What our paper adds to this subject matter: Seven classifications of design feature types were coded in digital math games.Children's awareness of the mathematics content learning goal (MCLG) matters in conjunction with their awareness of the design features.High‐quality features, that are directly related to the MCLG, matter.The complex variable interactions help explain children's learning outcomes. Implications of study findings for practitioners: Even if a child had an awareness of the MCLG and high feature awareness, if the movements (either physically or mentally) associated with those features were of low‐quality with respect to the MCLG, this did not afford growth.Understanding these relationships can help practitioners select high‐quality digital math games for children's use in both classroom settings and at home.Understanding these relationships can also help game designers create more high‐quality digital math games. [ABSTRACT FROM AUTHOR]

In this paper, we study a system of the form −Δλu=v−Δλv=upinℝN,where p∈ℝ, and Δλ is a sub‐elliptic operator defined by Δλ=∑i=1N∂xiλi2∂xi.Under some general hypotheses of the functions λi, i=1,2,...,N, we first prove that the system has no positive super‐solution when p ≤ 1. In the case p > 1, we establish a Liouville type theorem for the class of stable positive solutions. This result is an extension of some result in Hajlaoui et al. (Pacific J Math. 2014;270(1):79–93) for the case of Laplace operator. [ABSTRACT FROM AUTHOR]

While response time and accuracy indicate overall performance, their value in uncovering cognitive processes, underlying learning, is limited. A promising online measure, designed to track decision‐making, is computer mouse tracking, where mouse attraction towards different locations may reflect the consideration of alternative response options. Using a speedy arithmetic multiple‐choice game in an online adaptive learning environment, we examined whether mouse movements could reflect arithmetic difficulties when error rates are low. Results showed that mouse movements towards alternative responses in correctly answered questions mapped onto the frequency of errors made in this online learning system. This mapping was stronger for the younger children, as well as for easy arithmetic problems. On an individual level, users showed more mouse movement towards their previously made response errors than towards other alternative options. This opens the possibility of adapting feedback and instruction on an individual basis through mouse tracking. Lay Description: What is currently known about this topic: In online learning environments, detecting systematic difficulties for students during learning is challenging due to the required high success rate.Previous studies have found that computer mouse tracking offers a window into the cognitive process of considering multiple alternatives before deciding.What is lacking is a validation outside the lab, whether mouse tracking can be a source for detecting systematic difficulties students might have. What the paper adds to this: Mouse tracking was implemented outside the lab in a large‐scale online learning environment for primary school children practicing maths.Novel mouse metrics were developed to measure attraction towards multiple distractors instead of one.Findings show that mouse movements reveal cues to arithmetic difficulties without the need for errors. Implications of the study findings: Mouse tracking is a useful tool to investigate difficulties in the learning process in a motivating practice system.Diagnosing these arithmetic misconceptions for individuals can help to adapt feedback and instruction.The developed mouse method can be used for more daily‐life complex designs with multiple attractors. [ABSTRACT FROM AUTHOR]

The overarching goal of this research project is to develop a set of theoretical and empirical based design principles to support student engagement in flipped mathematics learning. We used a design‐based research approach in which a series of studies was conducted in a secondary school. First, an analysis of practical problems was performed via exploratory studies (Studies 1A and 1B), randomized experiments (Studies 2A and 2B), and a literature review (Study 3). Second, a basic flipped lesson prototype was developed based on our empirical findings and relevant theoretical work of student engagement and self‐determination theory. Third, we refined and evaluated our practice with two empirical studies (Studies 4 and 5). Finally, we reflected on each stage of our research project to produce a set of design principles for future practice. This study thus contributes to our knowledge of methods to support student engagement in flipped mathematics learning. Lay Description: What is already known about this topic: Flipped learning can increase student achievement in mathematics education.After flipping, studies reported non‐significant or even negative results in terms of student engagement.Little work has been done to support student engagement in flipped learning. What this paper adds: This study investigated methods to support student engagement in flipped mathematics learning.A 2‐year design‐based research was conducted consisting of a series of five studies.Theoretical work of student engagement and self‐determination theory were drawn. Implications for practice and/or policy: The use of group competitions increased student engagement in flipped mathematics learning.Peer interaction inside the classroom fostered students' cognitive engagement.Design principles are proposed to support student engagement in future practice.The principles cover five major instructional activities of flipped learning. [ABSTRACT FROM AUTHOR]

Aims: GFR estimated with the creatinine‐based Chronic Kidney Disease Epidemiology Collaboration (CKD‐EPICr) equation is used to screen for diabetic kidney disease and assess its severity. We systematically reviewed the process and outcome of evaluating CKD‐EPICr in estimating point GFR or GFR decline over time in adults with type 1 or type 2 diabetes. Methods: In this systematic review, MEDLINE, Embase and Cochrane Central Register of Controlled Trials were searched up to August 2019. Observational studies comparing CKD‐EPICr with measured GFR (mGFR) in adults with diabetes were included. Studies on people with kidney transplant, non‐diabetes related kidney disease, pregnancy, potential kidney donors, and those with critical or other systematic illnesses were excluded. Two independent reviewers extracted data from published papers and disagreements were resolved by consensus. Risk‐of‐bias was assessed using the Quality Assessment of Diagnostic Accuracy Studies‐2 tool. (PROSPERO registration number: CRD42018108776). Results: From the 2820 records identified, 29 studies (14 704 participants) were included. All studies were at risk of bias. Bias (eight different forms) ranged from −26 to 35 ml min−1 1.73 m−2; precision (five different forms) ranged between 9 and 63 ml min−1 1.73 m−2; accuracy (five different forms) ranged between 16% and 96%; the correlation coefficient between CKD‐EPICr and mGFR (four different forms) ranged between 0.38 and 0.86; and the reduced major axis regression slope ranged between 0.8 and 1.8. Conclusions: Qualitative synthesis of data suggested CKD‐EPICr was inaccurate in estimating point GFR or GFR decline over time. Furthermore, a lack of consistency in the methods and processes of evaluating the diagnostic performance of CKD‐EPICr limits reliable quantitative assessment. The equation needs to be improved in adults with diabetes. [ABSTRACT FROM AUTHOR]

Item nonresponses are prevalent in standardized testing. They happen either when students fail to reach the end of a test due to a time limit or quitting, or when students choose to omit some items strategically. Oftentimes, item nonresponses are nonrandom, and hence, the missing data mechanism needs to be properly modeled. In this paper, we proposed to use an innovative item response time model as a cohesive missing data model to account for the two most common item nonresponses: not‐reached items and omitted items. In particular, the new model builds on a behavior process interpretation: a person chooses to skip an item if the required effort exceeds the implicit time the person allocates to the item (Lee & Ying, 2015; Wolf, Smith, & Birnbaum, 1995), whereas a person fails to reach the end of the test due to lack of time. This assumption was verified by analyzing the 2015 PISA computer‐based mathematics data. Simulation studies were conducted to further evaluate the performance of the proposed Bayesian estimation algorithm for the new model and to compare the new model with a recently proposed "speed‐accuracy + omission" model (Ulitzsch, von Davier, & Pohl, 2019). Results revealed that all model parameters could recover properly, and inadequately accounting for missing data caused biased item and person parameter estimates. [ABSTRACT FROM AUTHOR]

Abstract: This is the second paper of an essay in two parts. The first paper (Part I) is a critical discussion of Mark Risjord's conception of nursing knowledge where I argued against the conception of nursing knowledge as a kind of nursing science. The aim of the present paper (Part II) is to explicate and substantiate the thesis of nursing as a kind of concrete philosophy. My strategy is to elaborate upon certain themes from Wittgenstein's Tractatus in order to canvass a general scheme of philosophy based on a distinction between reality and the world. This distinction will be employed in the appropriation of certain significant features of nursing and nursing knowledge. By elaborating on the contrast between the abstract and the concrete, I will suggest that nursing may be seen as a kind of concrete philosophy, being primarily concerned with reality (and secondarily with the world). This thesis, I will argue, implies that philosophy is the kind of theory that is essential to nursing (which is not so much a theory than a certain kind of activity). [ABSTRACT FROM AUTHOR]

Benford's law is an empirical observation, first reported by Simon Newcomb in 1881 and then independently by Frank Benford in 1938: the first significant digits of numbers in large data are often distributed according to a logarithmically decreasing function. Being contrary to intuition, the law was forgotten as a mere curious observation. However, in the last two decades relevant literature has grown exponentially—an evolution typical of “Sleeping Beauties” (SBs) publications that go unnoticed (sleep) for a long time and then suddenly become the center of attention (are awakened). Thus, in the present study, we show that the two papers, Newcomb ( ) and Benford ( ), Newcomb ( , American Journal of Mathematics, 4, 39–40) and Benford (1938, Proc. Am. Phil. Soc., 78, 551–572) papers are clearly SBs. The former was in a deep sleep for 110 years, whereas the latter was in a deep sleep for a comparatively lesser period of 31 years up to 1968, and in a state of less deep sleep for another 27 years, up to 1995. Both SBs were awakened in the year 1995 by Hill ( , Statistical Science, 10, 354–363). In so doing, we show that the waking prince (Hill, ) is more often quoted than the SB whom he kissed—in this Benford's law case, wondering whether this is a general effect—to be usefully studied. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a new multi‐wing chaotic attractor is constructed. Based on the proposed multi‐wing system, the paper presents a novel method to generate hyperchaotic multi‐wing attractors. By introducing a flux‐controlled memristor into the proposed multi‐wing system, hyperchaotic multi‐wing attractor is observed in new memristive system. At the same time, the new memristive system has no equilibrium. The phase portraits and Lyapunov exponents are used to analyze the dynamic behaviors of the no‐equilibrium memristive system. Moreover, we analyze the influence on multi‐wing system when adding the memristor in different position. The electronic circuit is realized by using off‐the‐shelf components. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper examines the relationships among the quality and quantity of parent-child shared book reading (SBR) engagements and children's reading and mathematics outcomes in preschool. Additionally, we explore how child and family characteristics predict the quality and quantity of SBR. Quantity was measured using parental reports of the frequency of SBR. Quality was measured by observational protocols evaluating for questioning, vocabulary, and discussion depth. A structural equation model was estimated using data from a nationally representative sample of 700 children living in the United States from the Early Childhood Longitudinal Study-Birth cohort. Results indicated that the quality of book reading was associated with children's mathematics outcomes, and the quantity was associated with reading outcomes controlling for contextual variables. Socioeconomic status, race or ethnicity, and children's age predicted the quality and quantity of book reading experiences. These findings indicate that frequent exposure to high-quality book reading may positively impact children's mathematics and reading development, but that variation in SBR exists. SBR is a common practice among many parents; helping parents understand the multiple benefits of the practice may further increase the frequency and quality of the engagement. Implications for research and practice are addressed. Highlights This paper describes the relationship between parental book reading practices, mathematics, and reading outcomes., Structural equation models reveal relationships between the quantity of book reading and children's reading outcomes, as well as the quality of book reading and children's mathematics outcomes., High-quality book reading may positively impact academic achievement in multiple domains, but results may vary based on contextual factors. [ABSTRACT FROM AUTHOR]

This study investigates the effect of E‐learning (EL), blended learning (BL) and flipped learning (FL) approaches on the mathematics achievement, self‐regulation and mathematics self‐efficacy. Participants consist of 163 first‐year students attending an associate degree program (a 2‐year program) of a state university. The EL, BL and FL settings in the research were designed based on Merrill's 'First Principles of Instruction Design Theory'. In the research in which a quasi‐experimental pre‐test–post‐test research design was used, the data were obtained by means of mathematics achievement test, self‐regulation and self‐efficacy questionnaires. The experimental results showed that the mathematics achievement post‐test scores of FL students were significantly higher than those of the students of EL and BL. No significant difference was found between BL and EL settings. In addition, FL students showed significantly higher self‐regulation and mathematics self‐efficacy than the other groups' students. According to these results, it can be said that the usage of FL approach in mathematics courses has a positive effect on the learning process of students. It is expected that the findings will be helpful in the future design and implementation of mathematics courses at vocational colleges. Lay Description: What is already known about this topic?: The flipped learning approach has the potential to develop mathematics teachingThe ability of student's own learning regulation becomes one of the key concepts of flipped learning setting.Little is known about the design and implementation of flipped learning settings in mathematics courses. What this paper adds: This study investigates the effect of E‐Learning (EL), Blended Learning (BL) and Flipped Learning (FL) approaches on the mathematics achievement, self‐regulation and mathematics self‐efficacy.The EL, BL and FL settings in the research were designed based on Merrill's 'First Principles of Instruction Design Theory'.The usage of FL approach, developed in line with Merrill's First Principles of Instruction design theory, improves the mathematics achievement, self‐regulation and mathematics self‐efficacy levels of students. Implications for practice and/or policy: This research provided evidences for effects of Merrill's "First Principles of Instruction Design Theory" on online learners.The FL approach, developed in line with Merrill's First Principles of Instruction design theory, may serve as a reference for improving students' learning performance.It is expected that the findings will be helpful in the future design and implementation of mathematics courses at vocational colleges. [ABSTRACT FROM AUTHOR]

This paper reports on a research project undertaken with a group (n = 19) of Irish preservice student teachers (PSTs) during the third year of a five‐year undergraduate education course. A series of workshops were carried out on the classification and design of mathematics tasks. The research is presented as a case study using mixed methods to gather data at three points, before the workshops, after the workshops, and two years later, when PSTs were in their final year. We argue that task classification and design are curriculum‐making activities for mathematics teachers. Through critically classifying and designing mathematics tasks, PSTs developed skills of evaluating the cognitive demand of tasks and showed evidence of using these skills in curriculum making. Through using frameworks to classify tasks, the PSTs demonstrated a capacity to take a more critical role in curriculum making. Our data show that the development of skills in these areas has lasting effects on PSTs' practices and willingness to engage meaningfully with the curriculum in mathematics. The research highlights the need for PSTs to work on evaluating and designing tasks. How frameworks can support and enhance PSTs' capacity to make curricular decisions is evidenced. [ABSTRACT FROM AUTHOR]

The principles of Conditional Excluded Middle (CEM) and Simplification of Disjunctive Antecedents (SDA) have received substantial attention in isolation. Both principles are plausible generalizations about natural language conditionals. There is however little discussion of their interaction. This paper aims to remedy this gap and explore the significance of having both principles constrain the logic of the conditional. Our negative finding is that, together with elementary logical assumptions, CEM and SDA yield a variety of implausible consequences. Despite these incompatibility results, we open up a narrow space to satisfy both. We show that, by simultaneously appealing to the alternative‐introducing analysis of disjunction and to the theory of homogeneity presuppositions, we can satisfy both. Furthermore, the theory that validates both principles resembles a recent semantics that is defended by Santorio on independent grounds. The cost of this approach is that it must give up the transitivity of entailment: we suggest that this is a feature, not a bug, and connect it with recent developments of intransitive notions of entailment. [ABSTRACT FROM AUTHOR]

In this paper, we establish a weak Serrin‐type blowup criterion for the Cauchy problem of the three‐dimensional (3D) compressible barotropic Navier–Stokes equations in the whole space. It shows that the strong or smooth solution exists globally if the velocity satisfies the weak Serrin's condition and the L∞(0,T;Lα0)‐norm of the density is bounded, where α0 is positive constant. Therefore, if the weak Serrin norm of the velocity remains bounded, it is not possible for other kinds of singularities (such as vacuum states vanish or vacuum appears in the non‐vacuum region or even milder singularities) to form before the density becomes unbounded. Furthermore, the initial data can be arbitrarily large and contain vacuum states. The proof is based on the new a priori estimates for 3D compressible Navier–Stokes equations. In particular, this extends the corresponding Huang et al.'s results (SIAM J. Math. Anal. 43 (2011) 1872–1886). [ABSTRACT FROM AUTHOR]