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Background: Past studies clarified the relationship between dimensions of teaching and achievement emotions. However, more information is needed about the underlying process behind this relationship among students with different mathematical abilities., Aims: This study examined the association between students' perceived teaching quality and achievement emotions in Chinese mathematics classrooms, focusing on students with different mathematics achievements., Samples: There are 1045 secondary school students (49.1% girls; M age  = 13.90, SD = .84) from Chinese mathematics classrooms in the present study., Methods: A multi-group structural equation model was adopted to test the relationship between teaching quality and achievement emotions between low- and high-achieving students., Results: Control-value appraisals mediated in teacher support and achievement emotions in both student groups. At the same time, control-value appraisals failed to mediate cognitive activation and achievement emotions in low-achieving students, while the mediating effect of control-value appraisals was identified in high-achieving students. Besides, classroom management was related to achievement emotions via academic value only in low-achieving students. In contrast, it was related to achievement emotions via control-value appraisals in high-achieving students., Conclusions: The results clarified the mediation roles of control-value appraisals in teaching quality and achievement emotions in students with low- and high-achieving achievements. Similarities and differences were also identified between the two student groups. Teacher support was beneficial to students' positive emotions while classroom management helped to lessen students' negative emotions. High-achieving students benefited more from activating teaching compared with low-achieving students., (© 2024 British Psychological Society.)

Background: To accurately measure students' science, technology, engineering and mathematics (STEM) career interest, researchers must get inside the 'black box' to understand students' conceptualizations of STEM careers., Aims: The aim of Study 1 was to explore whether students' conceptualizations of STEM included medical careers. The aim of Study 2 was to explore whether predictors of STEM career interest (e.g., gender and motivation) varied by STEM definition (inclusion/exclusion of medical careers)., Samples: In Study 1, the sample was US college students (N = 125) who were mostly White (80%). In Study 2, the sample was US 10th-grade high school students (N = 455) who were mostly Black (79%)., Methods: In Study 1, students completed an online questionnaire. In Study 2, students completed various measures of math achievement, motivation (science and math expectancies of success, interest and importance value) and career interest with an importance., Results: In Study 1, medical careers were less often classified as STEM careers than traditional STEM careers, but more often classified as STEM than non-STEM careers. In Study 2, science importance value was the only motivational predictor of students' STEM+Medicine career interest, and no motivation constructs predicted traditional STEM career interest. Boys expressed greater interest in traditional STEM careers, while girls expressed greater interest in STEM+Medicine careers., Conclusions: Students' conceptualizations of STEM are not binary. Thus, we recommend researchers are explicit about their definition of STEM with study participants, in their coding and in their publications., (© 2023 British Psychological Society.)

Tablet‐based technology has become a conduit for the administration of curriculum‐based measurement (CBM) tools. Using tablets to administer CBM probes has many advantages; however, little is known about how students perform on CBMs when administered via a tablet. The current investigation compared digits correct per minute obtained from 44 third‐grade students on CBM addition fluency probes administered via three different modalities. Students completed the probes using traditional paper and pencil, a tablet using their fingers to write the answer, or a tablet application using a keyboard to type the answer. A within‐subjects group design showed students performed significantly better on the tablet when using their finger to write the answer, even though most students (58%) indicated this was their least preferred modality. The discussion focuses on the implications for educators and the use of different CBM modalities for interindividual and intraindividual comparisons. Practitioner points: Third‐grade students responded to math facts faster when writing with their fingers on an iPad, even compared to paper and pencil.The results are inconsistent with other studies that found students were faster when using paper and pencil.Finally, most third‐grade students preferred answering addition facts with a pencil on paper. [ABSTRACT FROM AUTHOR]

Background: Recent research suggested fluent processing as an explanation on why number sense contributes to simple arithmetic tasks-'Fluency hypothesis'., Aims: The current study investigates whether number sense contributes to such arithmetic tasks when other cognitive factors are controlled for (including those that mediate the link); and whether this contribution varies as a function of participants' individual maths fluency levels., Sample: Four hundred and thirty-seven Chinese schoolchildren (186 females; Mage = 83.49 months) completed a range of cognitive measures in Grade 1 (no previous classroom training) and in Grade 2 (a year later)., Methods: Number sense, arithmetic (addition and subtraction), spatial ability, visuo-spatial working memory, perception, reaction time, character reading and general intelligence were measured., Results: Our data showed that the link between number sense and arithmetic was weaker in Grade 1 (Beta = .15 for addition and .06 (ns) for subtraction) compared to Grade 2 (.23-.28), but still persisted in children with no previous maths training. Further, math's performance in Grade 1 did not affect the link between number sense and maths performance in Grade 2., Conclusion: Our data extended previous findings by showing that number sense is linked with simple maths task performance even after controlling for multiple cognitive factors. Our results brought some evidence that number sense-arithmetic link is somewhat sensitive to previous formal maths education. Further research is needed, as the differences in effects between grades were quite small, and arithmetic in Grade 1 did not moderate the link at question in Grade 2., (© 2024 British Psychological Society.)

Understanding the magnitudes represented by numerals is a core component of early mathematical development and is often assessed by accuracy in situating numerals and fractions on a number line. Performance on these measures is consistently related to performance in other mathematics domains, but the strength of these relations may be overestimated because general cognitive ability has not been fully controlled in prior studies. The first of two meta-analyses (162 studies, 33,101 participants) confirmed a relation between performance on whole number (r = 0.33) and fractions number (r = 0.41) lines and overall mathematics performance. These relations were generally consistent across content domains (e.g., algebra and computation) and other moderators. The second (71 studies, 14,543 participants) used meta-analytic structural equation modeling to confirm these relations while controlling general cognitive ability (defined by IQ and working memory measures) and, in one analysis, general mathematics competence. The relation between number line performance and general mathematics competence remained significant but reduced (β = 0.13). Controlling general cognitive ability, whole number line performance consistently predicted competence with fractions but not performance on numeracy or computations measures. The results suggest an understanding of the magnitudes represented by whole numbers might be particularly important for students' fractions learning. RESEARCH HIGHLIGHTS: Two meta-analyses examined the link between the number line and mathematics performance. The first revealed significant relations across domains (e.g., algebra and computation). The second controlled for general cognitive ability and resulted in reduced but still significant relations. The relation between number line and fractions performance was stronger than relations to other domains., (© 2024 John Wiley & Sons Ltd.)

Background: Real-world problems are important in math instruction, but they do not necessarily trigger students' task motivation. Personalizing real-world problems by (1) matching problems to students' shared living environment (context personalization) and (2) asking students to pose their own problems (active personalization) might be two interventions to increase students' task motivation., Aim: In the current study, we investigated the effects of context personalization and active personalization on students' self-efficacy expectations, intrinsic value, attainment value, utility value, and cost., Sample: The participants were 28 fifth- and sixth-grade students who voluntarily took part in a six-month afterschool program in which they posed problems with the aim of creating a math walk in their hometown., Method: Using a within-subjects design, at the end of the afterschool program, the students rated their self-efficacy expectations and task values for four self-developed problems associated with their hometown, four peer-developed problems associated with their hometown, and four instructor-provided problems associated with unfamiliar locations., Results: Students reported higher self-efficacy expectations, intrinsic value, attainment value, and utility value for active-personalized than non-personalized problems. To a lesser extent, context personalization promoted intrinsic value and attainment value. No effect was found for cost., Conclusions: Active personalization (i.e. asking students to pose their own real-world problems) is suited to enhance students' task motivation, specifically their self-efficacy expectations, intrinsic value, attainment value, and utility value. Context personalization still boosts students' intrinsic value and attainment value. Implementation in classroom instruction is discussed., (© 2024 The Authors. British Journal of Educational Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.)

Background: Math anxiety (MA) is a worldwide appearing academic anxiety that can affect student mental health and deter students from math and science-related career choices., Method: Using the Arabic version of the Modified-Abbreviated Math Anxiety Scale (m-AMAS), the prevalence of MA was investigated in a very large sample of students (N = 10093) from grades 7 to 12 in Qatar., Results: The results showed a better fit to the original two-factor model of the m-AMAS (learning MA and Evaluation MA) than to a single-factor solution. This two-factor model was also confirmed in each grade. Notably, the distribution of MA scores was right-skewed, especially for learning MA. Using the inter-quartiles ranges, norms for MA were provided: A score of ≤16 indicates low MA whereas a score of ≥30 identifies high MA. Previous studies conducted in Western countries defined high math-anxious students as those who score above the 90th percentile corresponding to a score of 30 on the m-AMAS. Using this cut-off criterion, the current study found that one-fifth of students in Qatar were highly math-anxious, with a higher proportion of females than males. We also calculated the percentage of participants selecting each response category for each questionnaire item. Results showed that attending a long math class was the context that elicited the highest levels of learning MA. In contrast, having an unexpected math test was the situation that triggered the highest levels of evaluation MA., Conclusion: The prevalence of MA might vary across different cultures., (© 2024 British Psychological Society.)

Convex in x domain, eigenfunction, level sets, local rearrangement Erratum to the paper "Convexity in x of the level sets of the first Dirichlet eigenfunction": (Published in Math. Nachr. Keywords: convex in x domain; eigenfunction; level sets; local rearrangement EN convex in x domain eigenfunction level sets local rearrangement 1025 1025 1 03/21/23 20230301 NES 230301 Lemma 3.2 is incorrect. [Extracted from the article]

This paper aims to trace the origins of dual entry beyond a Eurocentric boundary. The aim can be refined further by asking: did the Chinese use dual entry and how did dual entry appear in Europe. Double entry is more advanced as it includes the location of the account in which the contra entry is made. Dual entry approaches accounting, like mathematics, as a tautology, whereby an equation is constructed from a simple axiom. Defined as such, this paper argues that the concept of dual entry had its earliest origins in China. [ABSTRACT FROM AUTHOR]

In what way does a mathematical proof depend on the notation used in its presentation? This paper examines this question by analysing the computational differences, in the sense of Larkin and Simon's ‘Why a diagram is (sometimes) worth 10,000 words’, between diagrammatic and sentential notations as a means for presenting geometric proofs. Wittgenstein takes up the question of mathematical notation and proof in Section III of Remarks on the Foundations of Mathematics. After discussing his observations on a proof's ‘characteristic visual shape’ in Section III with respect to arithmetical proofs, the paper shows how the notion of a characteristic visual shape illuminates the special effectiveness of diagrammatic notation in geometry. [ABSTRACT FROM AUTHOR]

This paper concerns the bubbling phenomena for the L2$L^2$‐critical half‐wave equation in dimension one. Given arbitrarily finitely many distinct singularities, we construct blow‐up solutions concentrating exactly at these singularities. This provides the first examples of multi‐bubble solutions for the half‐wave equation. In particular, the solutions exhibit the mass quantization property. Our proof strategy draws upon the modulation method in Krieger, Lenzmann and Raphaël [Arch. Ration. Mech. Anal. 209 (2013), no. 1, 61–129] for the single‐bubble case, and explores the localization techniques in Cao, Su and Zhang [Arch. Ration. Mech. Anal. 247 (2023), no. 1, Paper No. 4] and Röckner, Su and Zhang [Trans. Amer. Math. Soc., 377 (2024), no. 1, 517–588] for bubbling solutions to non‐linear Schrödinger equations (NLS). However, unlike the single‐bubble or NLS cases, different bubbles exhibit the strongest interactions in dimension one. In order to get sharp estimates to control these interactions, as well as non‐local effects on localization functions, we utilize the Carlderón estimate and the integration representation formula of the half‐wave operator, and find that there exists a narrow room between the orders |t|2+$|t|^{2+}$ and |t|3−$|t|^{3-}$ for the remainder in the geometrical decomposition. Based on this, a novel bootstrap scheme is introduced to address the multi‐bubble non‐local structure. [ABSTRACT FROM AUTHOR]

Research on fostering learning about percentages within intelligent tutoring systems (ITSs) is limited. Additionally, there is a lack of data‐driven approaches for improving the design of ITS to facilitate learning about percentages. To address these gaps, we first investigated whether students' understanding of basic mathematical skills (eg, arithmetic, measurement units and geometry) and fractions within an ITS predicts their understanding of percentages. We then applied a psychological network analysis to evaluate interdependencies within the data on 44 subtopics of basic mathematical concepts, fractions and percentages. We leveraged a large‐scale dataset consisting of 2798 students using the ITS bettermarks and working on approximately 4.1 million mathematical problems. We found that advanced arithmetic, measurement units, geometry and fraction understanding significantly predicted percentage understanding. Closer inspection indicated that percentage understanding was best predicted by problems sharing similar features, such as fraction word problems and fraction/natural number multiplication/division problems. Our findings suggest that practitioners and software developers may consider revising specific subtopics which share features with percentage problems for students struggling with percentages. More broadly, our study demonstrates how evaluating interdependencies between subtopics covered within an ITS as a data‐driven approach can provide practical insights for improving the design of ITSs. Practitioner notes What is already known about this topic Longitudinal studies showed that basic mathematical skills predict fraction understanding. There is only limited evidence on whether similar predictions can be observed for percentage understanding—in general and within intelligent tutoring systems. Process data from such intelligent tutoring systems can be leveraged to pursue both educational research questions and optimizing digital learning software. Problems involving percentages typically are word problems requiring multiplications and/or divisions. What this paper adds Similar to the case of fractions, students' performance on advanced arithmetic, measurement units and geometry significantly predicted performance with percentages. Students' performance with fractions also predicted performance with percentages significantly. A psychological network analysis was applied to evaluate specific interdependencies between a range of subtopics (eg, Multiplying and dividing fractions, Adding and subtracting fractions and Calculating with percentages). Fraction word problems and fraction problems involving multiplication/division turned out to be the best predictors of understanding percentages. Implications for practice and/or policy When facing difficulties with percentages, revision of previous mathematical concepts sharing similar features (eg, fraction word problems, fraction/natural number multiplication/division problems) may be advised. Software developers may consider implementing such data‐driven revision recommendations for students facing difficulties within intelligent tutor systems. Psychological network analysis can be utilized as a learning analytics method for easy‐to‐access visualizations illustrating relationships between a large range of different subtopics. What is already known about this topic Longitudinal studies showed that basic mathematical skills predict fraction understanding. There is only limited evidence on whether similar predictions can be observed for percentage understanding—in general and within intelligent tutoring systems. Process data from such intelligent tutoring systems can be leveraged to pursue both educational research questions and optimizing digital learning software. Problems involving percentages typically are word problems requiring multiplications and/or divisions. What this paper adds Similar to the case of fractions, students' performance on advanced arithmetic, measurement units and geometry significantly predicted performance with percentages. Students' performance with fractions also predicted performance with percentages significantly. A psychological network analysis was applied to evaluate specific interdependencies between a range of subtopics (eg, Multiplying and dividing fractions, Adding and subtracting fractions and Calculating with percentages). Fraction word problems and fraction problems involving multiplication/division turned out to be the best predictors of understanding percentages. Implications for practice and/or policy When facing difficulties with percentages, revision of previous mathematical concepts sharing similar features (eg, fraction word problems, fraction/natural number multiplication/division problems) may be advised. Software developers may consider implementing such data‐driven revision recommendations for students facing difficulties within intelligent tutor systems. Psychological network analysis can be utilized as a learning analytics method for easy‐to‐access visualizations illustrating relationships between a large range of different subtopics. [ABSTRACT FROM AUTHOR]

Background: Mindfulness practices enhance executive function skills and academic achievement, spurring interest in integrating mindfulness interventions into education. Embedding mindfulness practice into a digital math game may provide a low‐cost, scalable way to induce mindfulness and boost game‐based learning, yet this approach remains unexplored. Objectives: We investigated the learning benefits of integrating mindfulness exercises in a digital math learning game and examined how students' trait mindfulness might moderate the outcomes. Methods: Two classroom studies were conducted with 404 5th and 6th grade students from six public schools in the U.S. (nStudy 1 = 227, nStudy 2 = 177). The two randomized controlled experiments assigned students to one of the three conditions: passive control (playing the digital learning game Decimal Point), story‐enriched active control, or mindfulness‐enriched condition. Trait mindfulness, learning gains, and in‐game problem‐solving (including problem‐solving duration, error count and correctness after reminder) were assessed. Study 2 included a manipulation check to better understand the effects of the mindfulness intervention. Results: Findings showed no significant differences in learning gains, problem‐solving duration or error count among the conditions. Students' trait mindfulness did not moderate these outcomes. Mindfulness reminders in the mindfulness‐enriched game led to more correct answers after errors than jokes in the story‐enriched game. Study 2 revealed that we failed to induce higher state mindfulness through the mindfulness inductions. Conclusions: Mindfulness prompts could be especially beneficial for students experiencing frustration during gameplay, warranting more exploration for digital game‐based instruction. We highlight barriers and future directions for fostering mindfulness through computer‐based instruction in classrooms. Lay Description: What is currently known about this topic?: Researchers focus on digital games as productive learning environments for math, with potential for higher learning gains compared with traditional methods. However, results are mixed, and not all games lead to improved math outcomes.Executive function (EF) skills are crucial for math learning, and mindfulness‐based interventions show promise in enhancing EF skills in school‐aged students.Embedding mindfulness practice into a digital math game may provide a low‐cost, scalable way to induce mindfulness and, in turn, boost EF skills and game‐based learning, yet this approach remains unexplored What does this paper add?: This paper presents the results of two randomized control trials investigating the feasibility and benefits of incorporating mindfulness exercises into a digital math game designed for middle school students. Benefits are compared to those of a story‐enriched and regular version of the same digital math learning game.The paper also explores variations in the effects of the mindfulness‐enriched game based on students' initial trait mindfulness levels.We observe that listening to mindfulness inductions at the beginning of game sessions do not induce mindfulness, and therefore does not benefit math learning.We find that mindfulness prompts received after recurrent errors can be beneficial for students' problem solving. Implications of study findings for practitioners: Our study provides important information on how digital learning game designers should attempt to induce mindfulness in a digital game to promote learning.Digital learning game designers should consider incorporating mindfulness exercises into their games strategically. Presenting mindfulness inductions in audio format at the beginning of game sessions may not induce mindfulness or benefit math learning. Instead, designers should focus on integrating mindfulness prompts at moments when students encounter frustration within the learning game.Beyond embedding audio mindfulness exercises in the game, learning designers should also consider alternative technological and game features to induce mindfulness within a learning game. [ABSTRACT FROM AUTHOR]

Background: With the growing integration of technology in education, the adoption of blended learning (b‐learning) has gained attention. B‐learning combines traditional classroom teaching with online components, holding potential to enhance student outcomes and educational efficiency. Yet, current research predominantly concentrates on higher education institutions in urban areas, creating a void in understanding its impact on K‐12 education, particularly in rural settings. Objectives: This qualitative study aims to propose recommendations for successful implementation of blended learning in rural K‐12 areas by addressing the key stakeholders influencing its adoption and identifying the main factors affecting its success. Methods: We performed a content analysis of grey literature documents detailing the implementation of b‐learning in K‐12 education. Additionally, interviews with crucial stakeholders such as teachers, principals, and experts in rural schools in South America provide insights into the challenges and prospects of b‐learning adoption in these contexts. Results and Conclusions: The study identifies pivotal stakeholders for effective b‐learning implementation, outlining their roles and addressing challenges inherent in rural settings. Recommendations for enhancing b‐learning's implementation in developing countries are also proposed. The research underscores the significance of involving diverse stakeholders such as governmental bodies, school leaders, educators, students, and families to ensure a holistic and efficient approach to blended learning. Lay Description: What is currently known about this topic: Blended Learning Definition and Benefits: Blended learning combines face‐to‐face and online instruction, enhancing student engagement and personalization by providing diverse learning pathways.Growth in K‐12 Implementation: Blended learning gained traction in K‐12 education, boosting academic outcomes, driven by recognition of learner diversity and potential in meeting students' needs.Contextual Challenges: Implementation challenges arise in low‐income households and rural areas, including limited access to technology and internet connectivity, impacting student engagement and success. What does this paper add: Focusing on Rural Dynamics: This study helps to fill a gap by investigating blended learning in rural K‐12 settings, spotlighting key players and success drivers in these unique contexts.Recommendations from Various Sources: By combining interviews and grey literature, this research generates comprehensive, practical recommendations grounded in both empirical insights and real‐world perspectives.Insights into Rural Hurdles: This paper extends the discussion on blended learning by addressing specific rural barriers, proposing family involvement, private sector partnerships for training, and tailored pedagogical strategies. Implications for practice or policy: Leadership and Collaboration: Effective school leadership and collaboration with local governments are pivotal for fruitful blended learning implementation, ensuring defined roles, responsibility, and accountability.Adaptable Curriculum Design: An adaptable, centralized curriculum aligns with recommendations, fostering efficient tracking of student progress and enabling customized learning.Engagement‐Centric Pedagogies: Recommendations spotlight interactive, student‐centered teaching methods, tailored to diverse student needs, nurturing active participation and elevated learning outcomes. [ABSTRACT FROM AUTHOR]

Background: Evidence‐based practice is the principle governing a range of healthcare practices and beyond. However, it has suffered from a lack of philosophical rigour. This paper sets out to analyse the epistemological basis of evidence‐based practice. Method: The paper uses a conceptual analysis. First, it describes the implicit epistemology at work in evidence‐based practice. Second, it evaluates the implicit epistemological basis. Results: The analysis indicates that evidence‐based practice lacks an explicit epistemological basis. It shows, moreover, that the implicit epistemological basis is untenable. Conclusion: There is a need to re‐think the epistemological basis for evidence‐based practice. Evidence‐based practice is out of touch with developments within philosophy of science. [ABSTRACT FROM AUTHOR]

The author briefly reviews studies on the math teaching of secondary school students with mild intellectual disabilities. Then, the author demonstrates ways to teach secondary‐level mathematics to students with mild intellectual disabilities. In this article, readers will learn about how to use manipulatives, diagrams, and gestures to support students' thinking. Readers will also learn how to make connections between new and challenging math content to students' experiences inside and outside of school to support them as they think through mathematics. [ABSTRACT FROM AUTHOR]

We access most of our most cherished beliefs via testimony. Philosophy is no exception. We treat spoken and written philosophical testimony as evidence for philosophical claims. Nonetheless, this paper argues that philosophical testimony is unable to justify philosophical beliefs. If testimony is the only evidence we have to justify philosophical beliefs, this entails skepticism about philosophy. Call this the testimony challenge. First, the paper argues that philosophical testimony does not meet the conditions under which evidence can justify our beliefs. Second, it shows that philosophical testimony cannot provide preemptive epistemic reasons as science and mathematics do. Finally, it answers the self‐defeat objection and a set of objections aiming to block the thesis that philosophical testimony does not justify philosophical beliefs. The paper aims to rethink the role of philosophical testimony in philosophy and reinforce the skeptical worries raised by methodological and disagreement challenges. [ABSTRACT FROM AUTHOR]

This paper considers a specific autonomous Schwarzian differential equation given by Sf=c(f−σ1)(f−σ2)/[(f−τ1)(f−τ2)]$$\begin{equation*} \hspace*{35pt} S_f=c(f-\sigma _1)(f-\sigma _2)/[(f-\tau _1)(f-\tau _2)] \end{equation*}$$and presents a complete characterization of its transcendental meromorphic solutions, thus confirming a conjecture posed by Liao and Wu recently. By combining our results with those obtained in a previous paper (Math. Z. 2 (2022), 1657–1672), we are able to explicitly construct all transcendental meromorphic solutions of the autonomous Schwarzian differential equations. Additionally, we identify all nonconstant rational solutions of the autonomous Schwarzian differential equations, with the exception of one special case. [ABSTRACT FROM AUTHOR]

The paper investigates semiotics as an integrative, foundational framework for operational research (OR). To this end, the semiotics of the pragmatist C.S. Peirce is explained and its application in OR research, and consulting practice is explored. It is the fourth in a series of papers each seeking to ground OR in a different logic: philosophic/mathematical logic, pragmatic logic, economic logic and now semiotic logic. For Peirce, semiotics is a logic, and as such it is argued in the paper that it can embrace philosophical/mathematical, pragmatic and economic logics. The comprehensive nature of semiotics is such that it brings to a close the research programme aimed at establishing foundations for OR. However, the closure of one programme opens up another—the application of semiotics in OR practice and academic research. Possible avenues for further research include learning from, and collaboration with, neighbouring disciplines such as information systems and computer science. [ABSTRACT FROM AUTHOR]

Background: A strong knowledge of mathematics, beginning at the elementary level, is critical for participation in today's complex world. The home may be one way to facilitate individualized mathematics instruction, given that children spend more time at home than in an academic institution. Therefore, researchers are interested to see whether the home numeracy environment (HNE) can provide a solid foundation for children's mathematics understanding. Further, children's digital mathematics exploration at home is increasingly common (e.g., using math apps). Objectives: The present study evaluates the digital home numeracy practice (DHNP) model and explores its effect on children's mathematics knowledge across five domains (numeration, number operation, pattern recognition, spatial sense, and applied problem‐solving). Methods: To conduct this study, 117 Canadian parents and their children from Grade 1 through 5 completed a DHNP survey and a range of in‐person mathematics measures. Results and Conclusions: The results identified significant relations between parents and children's implicit mathematics factors (e.g., math anxiety, motivation). Children's mathematics anxiety and parents' academic estimations and expectations for their children positively predicted children's mathematics knowledge. In terms of DHNP components, parental involvement in DHNP predicted children's numeration and applied problem‐solving knowledge. Implications: Taken together, the results detail the contribution of parental and child factors to children's mathematics knowledge and suggest that parents adjust their role in DHNP according to their children's mathematics ability. Lay Description: What is (not) known about the subject matter?: Research is less developed on the impact of home technology in the mathematics learning processExisting research did not use a multi‐measure approach to assess the relationships between a variety of home numeracy factors and fundamental mathematics concepts and processes What is the contribution of this paper?: The paper highlights the importance of considering different home related factors to understand the role of home numeracy practices in children's mathematics developmentIt provides a holistic view of digital home numeracy practice (DHNP) by examining several implicit and explicit components of home numeracy environmentChildren's mathematics anxiety predicts their mathematics knowledgeParental estimation and expectation about their children's mathematics performance predicts their mathematics knowledge across several domains whereas parental role on DHNP impacts children's numeration only What are the implications of the findings?: The findings provide an understanding of the significant value of including digital mathematics practices in the study of the home mathematics environmentThe outcome of the study provides guidance for educators and researchers to better understand and leverage DHNP, and its impact on children's mathematics educationFuture research should investigate to what extent digital features should be included in the DHNP model. This will provide insights into the impact of using well‐designed apps on children's mathematics learning [ABSTRACT FROM AUTHOR]

In this paper, we study the following fractional Choquard equation with weight (−Δ)su=1|x|N−α∗h(x)|u|ph(x)|u|p−2uinℝN,$$ {\left(-\Delta \right)}&#x0005E;su&#x0003D;\left(\frac{1}{{\left&#x0007C;x\right&#x0007C;}&#x0005E;{N-\alpha }}\ast h(x){\left&#x0007C;u\right&#x0007C;}&#x0005E;p\right)h(x){\left&#x0007C;u\right&#x0007C;}&#x0005E;{p-2}u\kern0.5em \mathrm{in}\kern0.5em {\mathrm{\mathbb{R}}}&#x0005E;N, $$where 02s,p>2,α>0$$ 02s,p>2,\alpha >0 $$ and h$$ h $$ is a positive weight function satisfying h(x)≥C|x|a$$ h(x)\ge C{\left&#x0007C;x\right&#x0007C;}&#x0005E;a $$ at infinity, for some a≥0$$ a\ge 0 $$. We establish, in this paper, a Liouville type theorem saying that if maxN−4s−2a,0<α

We show that if G$G$ is a finitely generated group such that its profinite completion Ĝ$\widehat{G}$ is "far from being projective" (i.e., the kernel of the universal Frattini cover of Ĝ$\widehat{G}$ is not a small profinite group), then the class of existentially closed G$G$‐actions on fields is not elementary. Since any infinite, finitely generated, virtually free, and not free group is "far from being projective," the main result of this paper corrects an error in our paper, Beyarslan and Kowalski (Proc. London Math. Soc., (2) 118 (2019), 221–256), by showing the negation of Theorem 3.26 in that paper. [ABSTRACT FROM AUTHOR]

Background: People with aphasia (PWA) can experience functional numeracy difficulties, that is, problems understanding or using numbers in everyday life, which can have numerous negative impacts on their daily lives. There is growing interest in designing functional numeracy interventions for PWA; however, there are limited suitable assessments available to monitor the impact of these interventions. Existing functional numeracy assessments lack breadth and are not designed to be accessible for PWA, potentially confounding their performance. Additionally, they do not include real‐life demands, such as time pressure, which may affect their ecological validity. Thus, there is a crucial need for a new assessment to facilitate further research of PWA's functional numeracy. Aims: To develop, validate and pilot a wide‐ranging, aphasia‐friendly functional numeracy assessment to investigate how functional numeracy is impacted by aphasia severity and time pressure demands, and to explore predictors of PWA's functional numeracy. Methods & Procedures: To develop the Functional Numeracy Assessment (FNA), 38 items inspired by the General Health Numeracy Test (GHNT) and Excellence Gateway were adapted for suitability for PWA and entered in a computerized psychometric‐style test. The final 23 items (FNA23) were selected based on 213 neurotypical controls' performance, and controlled for difficulty, response modality and required numeracy skills. Aphasia‐friendly adaptations of the GHNT and Subjective Numeracy Scale were used to examine the FNA23's concurrent validity. Internal consistency reliability and interrater reliability (for spoken responses) were also examined. A novel Time Pressure Task was created by slight adaptation of seven FNA23 questions to explore the effects of time pressure on functional numeracy performance. A total of 20 PWA and 102 controls completed all measures on an online testing platform. Outcomes & Results: The FNA23 demonstrated acceptable internal consistency reliability (KR‐20 = 0.81) and perfect interrater reliability (for spoken responses). FNA23 and GHNT scores were positively associated, suggesting satisfactory concurrent validity. PWA demonstrated poorer functional numeracy than controls and took longer to complete assessments, indicating that aphasia impacts functional numeracy. Time pressure did not significantly impact performance. PWA demonstrated a wide range of functional numeracy abilities, with some performing similarly to controls. Conclusions & Implications: The FNA23 is a wide‐ranging, valid and reliable assessment which, with further development, will be a useful tool to identify and monitor PWA's functional numeracy difficulties in research and clinical practice. Considering PWA's widespread functional numeracy difficulties evidenced by this study, all PWA would likely benefit from routine evaluation for functional numeracy difficulties as part of their neurorehabilitation journeys. WHAT THIS PAPER ADDS: What is already known on this subject: Few studies have investigated functional numeracy difficulties in PWA. No published functional numeracy assessments exist that have been specifically designed to be accessible for PWA. What this paper adds to existing knowledge: The newly developed FNA23 is a valid and reliable tool to extensively assess PWA's functional numeracy. This study confirmed previous findings of widespread functional numeracy difficulties in PWA that are related to their aphasia severity. What are the potential or actual clinical implications of this work?: The FNA23 can be used to assess PWA's functional numeracy to inform areas of strengths and difficulties to target in intervention, and to monitor progress towards achieving intervention objectives. All PWA should be routinely evaluated for functional numeracy difficulties. [ABSTRACT FROM AUTHOR]

Background: Teachers often rely on the use of open‐ended questions to assess students' conceptual understanding of assigned content. Particularly in the context of mathematics; teachers use these types of questions to gain insight into the processes and strategies adopted by students in solving mathematical problems beyond what is possible through more close‐ended problem types. While these types of problems are valuable to teachers, the variation in student responses to these questions makes it difficult, and time‐consuming, to evaluate and provide directed feedback. It is a well‐studied concept that feedback, both in terms of a numeric score but more importantly in the form of teacher‐authored comments, can help guide students as to how to improve, leading to increased learning. It is for this reason that teachers need better support not only for assessing students' work but also in providing meaningful and directed feedback to students. Objectives: In this paper, we seek to develop, evaluate, and examine machine learning models that support automated open response assessment and feedback. Methods: We build upon the prior research in the automatic assessment of student responses to open‐ended problems and introduce a novel approach that leverages student log data combined with machine learning and natural language processing methods. Utilizing sentence‐level semantic representations of student responses to open‐ended questions, we propose a collaborative filtering‐based approach to both predict student scores as well as recommend appropriate feedback messages for teachers to send to their students. Results and Conclusion: We find that our method outperforms previously published benchmarks across three different metrics for the task of predicting student performance. Through an error analysis, we identify several areas where future works may be able to improve upon our approach. Lay Description: What is already known about this topic: Open‐ended questions are used by teachers in the domain of mathematics to assess their students understanding but automated support for these types of questions are limited in online learning platforms. Recent advancements in areas of machine learning and natural language processing have led to promising results in a range of domains and applications. What this paper adds: Emulating how teachers identify similar student answers can be used to build tools that support teachers in assessing and providing feedback to student open‐ended work. Implications for practice: Developing better automated supports can increase the amount of direct feedback students receive to guide their learning. [ABSTRACT FROM AUTHOR]

In this short paper, we analyse whether assuming that mathematical objects are "thin" in Linnebo's sense simplifies the epistemology of mathematics. Towards this end, we introduce the notion of transparency and show that not all thin objects are transparent. We end by arguing that, far from being a weakness of thin objects, the lack of transparency of some thin objects is a fruitful characteristic mark of abstract mathematics. [ABSTRACT FROM AUTHOR]

Background: As one of the mainstream forms of programming education, educational robotics (ER) have been a crucial way to develop K‐12 students' programming ability. Objectives: The purpose of this study is to clarify the content of programming ability, to verify the effectiveness of ER as a teaching method to improve students' programming abilities and the conditions for more effective instructional design. Methods: The method of meta‐analysis was adopted to conduct this study. 4180 K‐12 students from 36 studies with a total of 85 effect sizes were captured. Based on the contents of included literature, an ER programming ability model was put forward, which was composed of essential ability and generative ability. The meta‐analysis of essential ability (N = 22) and generative ability (N = 64) was carried out respectively. Results and conclusion: The results showed that ER activity has a positive effect on the essential ability (Hedges' g = 0.539 CI [0.327, 0.752], p < 0.001) and generative ability (Hedges' g = 0.535 CI [0.426, 0.643], p < 0.001). Additionally, the results of moderator analysis showed that utilizing ER to solve mathematics problems is able to more effectively develop students' essential ability, while the STEM interdisciplinary ER instruction had the largest effect on generative ability. Simultaneously, the individual programming form is conducive to students' essential ability, while the generative ability is significantly affected by the cooperative programming form. No matter for the evaluation of essential ability or generative ability, ER had the greatest effect on kindergarten children' programming ability. Moreover, the intervention duration ranging from 1 to 5 weeks, the samples size less than 50 and the choice of measurement scale can effectively improve students' programming ability. Implications: This research enriched the theoretical basis of programming ability, and provided reference and guidance for K‐12 programming teaching practitioners and researchers in ER teaching design and practise. Lay Description: What is (not) known about the subject matter?: Educational robotics (ER) is one of the mainstream form of K‐12 programming education.K‐12 students develop various abilities by coding ER.Different instruction conditions in ER education may affect the teaching effect. What is the contribution of this paper?: This study sorted out the specific content of programming ability in ER activities, and classified programming ability into essential ability and generative ability.This study respectively validated the effectiveness of ER activity on improving essential ability and generative ability of K‐12 students.This study considered discipline integration, cooperation degree, grade level, intervention duration, sample size and assessment tools as moderator variables, and analyzed their effects sizes on ER developing programming ability. What are the implications for practitioners?: This paper clarified the specific content of programming ability in K‐12 ER education, and enriched the theoretical basis of programming ability.It provided evidence for the effectiveness of K‐12 ER education.This study provided an reference and guidance for ER instructional design for K‐12 programming teachers and researchers. [ABSTRACT FROM AUTHOR]

Summary: Luis Raúl Pericchi Guerra was born in Caracas, Venezuela, on 11 March 1952. He completed a B.S. in Mathematics in 1975 at the Universidad Simón Bolívar in Caracas, an M.S. in Statistics at the University of California Berkeley in 1978 and a Ph.D. in Statistics at Imperial College London in 1981. After graduating from Imperial College, Luis Raúl went back to Universidad Simón Bolívar. There, he played a key role in the developing of graduate programmes in Statistics and single handedly built an internationally recognised group focused on Bayesian statistics. In 2001, he moved to the Universidad de Puerto Rico in Rio Piedras to become the Chair of the Mathematics Department. At Universidad de Puerto Rico, he was instrumental in the establishment of a Ph.D. track in Computational Mathematics and Statistics. Luis Raúl has published over 120 papers in statistical and domain‐specific journals, making significant contributions to several areas of Bayesian statistics (especially in the areas of model selection and Bayesian robustness) and their application (especially in hydrology). He is a Fellow of the American Statistical Association, the International Society for Bayesian Analysis, the John Simon Guggenheim Memorial Foundation and an Elected Member of the International Statistical Institute. This conversation took place over multiple sessions during the 2022 O'Bayes meeting in Santa Cruz, California, and the months that followed. [ABSTRACT FROM AUTHOR]

Despite extensive research on attainment grouping, the impact of attainment grouping on pupil attainment remains poorly understood and contested. This paper presents evidence from a study conducted with 2944 12–13 year olds, from 76 schools in England, who were allocated to between‐class attainment groups ('setting') in English and mathematics over the first 2 years of secondary schooling. After controlling for prior attainment, pupils in the top set performed significantly better than pupils in the middle and bottom sets in both English and mathematics. The findings indicate a widening gap in attainment, especially in the case of English. Findings, especially in the case of mathematics, provide more evidence of a relative benefit for pupils placed in top sets than a relative detriment for those in bottom sets. [ABSTRACT FROM AUTHOR]

Background: Digital game‐based learning is gaining increased attention from both researchers and educators for improving mathematics instruction. However, the evidence for game‐based learning is mixed and research with rigorous research design and analyses are limited. Objective: Here, in a pre‐registered randomized controlled study, we investigated whether a fraction game designed collaboratively by educational experts and professional game developers may serve as a useful tool to enhance students' fraction knowledge. Methods: We assigned French fifth graders to either an experimental group who used the game (n = 110) or a control group (n = 78) who received traditional instruction on fractions. Fraction knowledge was assessed pre‐ and post‐intervention. Results: Results show that students in the active control group had superior overall fraction performance than students in the experimental group at the end of intervention. However, the game had a positive effect on decimal learning. We also found a positive relation between game performance and overall fraction knowledge scores at post‐test. Contribution: The study highlights the importance of game metrics as indicators of personalized assessment tools. Given the increased usage of games in learning mathematics and the equivocal results on the effectiveness of these games, our study also highlights the importance of pre‐registration and randomized controlled studies. Lay Description: What is already known about this topic: Digital game‐based learning (DGBL) is gaining popularity in mathematics teaching.DGBL shows potential for teaching difficult abstract concepts such as fractions.However, research evaluating DGBL for fractions is limited. What this paper adds: The study examines a fraction game designed by education experts and game designers.Students fraction knowledge is assessed using paper‐based test.Challenges associated with DGBL in the classroom are discussed in the paper. Implications for practice: The results will guide educators in designing effective fraction instruction in classroom.The study highlights the critical role of instructional support in DGBL for fractions.Game based metrics can be used to individualize instruction in the classroom. [ABSTRACT FROM AUTHOR]

Background: Despite its potentially significant functional and emotional impact, acalculia is still too rarely assessed and managed by speech and language therapists. Research on the rehabilitation of numerical transcoding remains scarce in the literature and, despite positive results, presents a low level of evidence. Aims: The present study aims to evaluate the effectiveness of a targeted rehabilitation of numerical transcoding in two patients suffering from a chronic secondary acalculia. Methods & Procedures: Two post‐brain injury females with secondary acalculia took part in a single‐case experimental design with multiple baseline across subjects according to a three‐phase experimental protocol: baseline involving global cognitive rehabilitation (5–7 measurements with randomized sequential introduction); targeted intervention (10 measurements); follow‐up (2 immediate measurements and 1 month after the end of the intervention). Repeated outcome measures consisted of six lists composed of numbers of equivalent difficulty that were used alternately to assess numerical transcoding. We used a reverse digit span as a control measure to assess the specificity of the intervention. Rehabilitation lasted 5 weeks and consisted of errorless learning with colour cues, tables and number–words cards. Outcomes & Results: During baseline period involving global cognitive rehabilitation, transcoding scores remained unchanged. In contrast, there was a significant improvement in scores for both patients during the intervention phase targeting transcoding and maintenance of benefits 1‐month post‐intervention. Conclusions & Implications: This study demonstrates that a specific rehabilitation targeting numerical transcoding following chronic secondary acalculia can be effective in improving transcoding skills. WHAT THIS PAPER ADDS: What is already known on the subject: Transcoding difficulties in patients with acalculia can cause a significant disability in everyday life activities. In secondary acalculia, rehabilitation of cognitive functions associated with number processing (attention, working memory, language) is not sufficient for improvement of transcoding. What this paper adds to existing knowledge: An intervention specifically targeting numerical transcoding significantly and durably improves the skills of patients with chronic secondary acalculia. What are the potential or actual clinical implications of this work?: Procedural error‐free intervention using colour cueing, tables, cards with number–words, copy and repetition seems effective to improve transcoding skills in chronic acalculia. [ABSTRACT FROM AUTHOR]

This paper explores how the twin processes of neoliberalism and neoconservatism work together on, and through, curricula and their associated pedagogies. It bridges the gap between policy and classroom practice, focusing on the particular example of the school subject of mathematics and the notion of mastery, operationalised in the English education system as Teaching for Mastery (TfM). From this context, it develops a theoretical argument using Dean's analytics of government as part of a broader Foucauldian frame, to analyse how TfM is constructed as a particular policy truth. It then shifts the analysis from a wide, social one to the individual classroom level using a psychological argument to critique TfM in its own terms, examining the onto‐epistemological nature of mathematics as a subject. In doing so, it explores ways in which mastery might be problematic in classrooms, even whilst appearing to offer a solution at policy level to long‐standing problems in English schooling. The aim is not to suggest that TfM has nothing to offer, but to point to ways in which it draws on the psychology of teaching and learning in a very particular manner, inscribing pupils with very specific mathematical subjectivities. By providing this insight into how neoliberal policy positions play out at practitioner level via curricula and pedagogies, the paper raises questions which are philosophical, political, and ethical, regarding the potential effect of TfM on teachers' and pupils' experiences of mathematics in schools, including implications for equity of this experience amongst the latter. [ABSTRACT FROM AUTHOR]

For any ring A$A$ and a small, pre‐additive, Hom‐finite, and locally bounded category Q$Q$ that has a Serre functor and satisfies the (strong) retraction property, we show that the category of additive functors Q→AMod$Q \rightarrow {}_{A} \operatorname{Mod}$ has a projective and an injective model structure. These model structures have the same trivial objects and weak equivalences, which in most cases can be naturally characterized in terms of certain (co)homology functors introduced in this paper. The associated homotopy category, which is triangulated, is called the Q$Q$‐shaped derived category of A$A$. The usual derived category of A$A$ is one example; more general examples arise by taking Q$Q$ to be the mesh category of a suitably nice stable translation quiver. This paper builds upon, and generalizes, works of Enochs, Estrada, and García‐Rozas (Math. Nachr. 281 (2008), no. 4, 525–540) and Dell'Ambrogio, Stevenson, and Šťovíček (Math. Z. 287 (2017), no. 3‐4, 1109–1155). [ABSTRACT FROM AUTHOR]

This survey introduces 101 new publications on applications of Clifford's geometric algebras (GAs) newly published during 2022 (until mid‐January 2023). The selection of papers is based on a comprehensive search with Dimensions.ai, followed by detailed screening and clustering. Readers will learn about the use of GA for mathematics, computation, surface representations, geometry, image, and signal processing, computing and software, quantum computing, data processing, neural networks, medical science, physics, electric engineering, control and robotics. [ABSTRACT FROM AUTHOR]

A celebrated theorem of Helmut Wielandt shows that the nilpotent residual of the subgroup generated by two subnormal subgroups of a finite group is the subgroup generated by the nilpotent residuals of the subgroups. This result has been extended to saturated formations in Ballester‐Bolinches, Ezquerro, and Pedreza‐Aguilera [Math. Nachr. 239–240 (2002), 5–10]. Although Wielandt's result is not true in arbitrary locally finite groups, we are able to extend it (even in a stronger form) to homomorphic images of periodic linear groups. Also, all results in Ballester‐Bolinches, Ezquerro, and Pedreza‐Aguilera [Math. Nachr. 239–240 (2002), 5–10] are extended to locally finite groups, so it is possible to characterize the class of locally finite groups with a locally nilpotent derived subgroup as the largest subgroup‐closed saturated formation X$\mathfrak {X}$ such that, for all SL$\mathbf {SL}$‐closed saturated formations F$\mathfrak {F}$, the F$\mathfrak {F}$‐residual of an X$\mathfrak {X}$‐group generated by F$\mathfrak {F}$‐subnormal subgroups is the subgroup generated by their F$\mathfrak {F}$‐residuals. Our proofs are based on a reduction theorem that is of an independent interest. Furthermore, we provide strengthened versions of Wielandt's result for other relevant classes of groups, among which we mention the class of paranilpotent groups. A brief discussion on the permutability of the residuals is given at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence of multiplicity of positive solutions to a new generalized Riemann–Liouville type fractional Fisher‐like equation on a semi‐infinite interval equipped with nonlocal multipoint boundary conditions involving Riemann–Liouville fractional derivative and integral operators. The existence of at least two positive solutions for the given problem is established by using the concept of complete continuity and iterative positive solutions. We show the existence of at least three positive solutions to the problem at hand by applying the generalized Leggett–Williams fixed‐point theorem due to Bai and Ge [Z. Bai, B. Ge, Existence of three positive solutions for some second‐order boundary value problems, Comput. Math. Appl. 48 (2014) 699‐70]. Illustrative examples are constructed to demonstrate the effectiveness of the main results. It has also been indicated in Section 5 that some new results appear as special cases by choosing the parameters involved in the given problem appropriately. [ABSTRACT FROM AUTHOR]

In this paper, I discuss a view proposed by Carl Hempel in his paper Reduction: Ontological and Linguistic Facets, published in 1969. Here, Hempel suggested that questions regarding the identification of mental states with physiological states, the relation between sociological phenomena and individual behavioral states, and between biological and physicochemical states should be given what he calls a 'linguistic' interpretation. His main point is that whether or not an object is physical or biological depends on how it is, or can be, described. In this paper, I wish to, firstly, explicate Hempel's suggestion, and, secondly, explore one argument in favor of Hempel's account. I will suggest that there is at least one use of the term 'physical' in philosophical discourse (and, for that matter, of related terms such as 'biological', 'mental', 'natural' etc.) that should be cashed out in linguistic or representational terms. [ABSTRACT FROM AUTHOR]

This paper investigates whether free access to scientific literature increases the participation of under‐represented groups in scientific discourse. To this end, we aggregate and match data tracing access to Sci‐Hub, a widely used black open access (OA) repository or shadow library, and publication data from the Web of Science (WoS). We treat the emergence of Sci‐Hub as an exogenous event granting relatively unrestricted access to publications, which are otherwise hidden behind a paywall. We analyze changes in the publication count of researchers from developing countries in a given journal as a proxy for general participation in scientific discourse. Our results indicate that in the exemplary field of mathematics, free access to academic knowledge is likely to improve the representation of authors from developing countries in international journals. Assuming the desirability of greater international diversity in science (e.g., to generate more original work, reproduce empirical findings in different settings, or shift the research focus toward topics that are overlooked by researchers from more developed countries), our findings lend evidence to the claim of the OA movement that scientific knowledge should be free and widely distributed. [ABSTRACT FROM AUTHOR]

In the process of autonomous vehicle motion planning and to create comfort for vehicle occupants, factors that must be considered are the vehicle's safety features and the road's slipperiness and smoothness. In this paper, we build a mathematical model based on the combination of a genetic algorithm and a neural network to offer lane‐change solutions of autonomous vehicles, focusing on human vehicle control skills. Traditional moving planning methods often use vehicle kinematic and dynamic constraints when creating lane‐change trajectories for autonomous vehicles. When comparing this generated trajectory with a man‐generated moving trajectory, however, there is in fact a significant difference. Therefore, to draw the optimal factors from the actual driver's lane‐change operations, the solution in this paper builds the training data set for the moving planning process with lane change operation by humans with optimal elements. The simulation results are performed in a MATLAB simulation environment to demonstrate that the proposed solution operates effectively with optimal points such as operator maneuvers and improved comfort for passengers as well as creating a smooth and slippery lane‐change trajectory. [ABSTRACT FROM AUTHOR]

This is a methodological critique of research by the Best Practice in Grouping Students (BPGS) project claiming teacher bias in allocating students to first‐year secondary school mathematics teaching sets (British Educational Research Journal, 45(4), 873–879). The research assumes that bias could be shown by non‐random relationships between 'misallocations' to sets and memberships of gender, ethnic and/or socio‐economic subgroups. This paper questions the authors' prescriptions for correct set placements and demonstrates two ways in which non‐random relationships between subgroup memberships and (alleged) misplacements could be generated despite all students with similar scores within a school being given the same chance of a set position deemed correct by the researchers. It suggests that the BPGS project results are largely artefacts of their evaluation approach. No claim is made herein that teacher bias plays no part in set allocation, merely that, if it does, the approach by Connolly et al. could not evidence it. A lesson from the critique is that, before drawing inferences from data aggregated from diverse clusters, it is wise for researchers to investigate the way the data are generated at source and patterned by aggregation. [ABSTRACT FROM AUTHOR]

Background: The substantial growth in gamification research has connected gamified learning to enhanced engagement, improved performance, and greater motivation. Similar to gamification, personalized learning analytics dashboards can enhance student engagement. Objectives: This study explores the student experiences and academic achievements using a gamified dashboard in a large, introductory STEM course. Methods: We examined two groups of students enrolled in different sections of a one‐semester‐long physical geology course with a total enrollment of 223 students. The only difference between the groups was that one had access to the dashboard. The data collection included students' assignments, overall performances, and exam scores. Students in both sections completed a Science Literacy Concept Inventory survey at the beginning and end of the term. Additionally, students completed an end‐of‐term survey containing open‐ended questions on their experience and interactions with specific elements. Results: Students shared mostly positive comments about their experience with the dashboard, and the final grade of students with access to the dashboard was 13% higher, on average, compared to their peers in the non‐dashboard section. Conclusion: With low costs and little time invested, gamified dashboards could have a significant impact on student performance in large STEM lecture courses. Lay Description: What is already known about this topic: Leaner dashboards that provide personalized feedback are linked to improved student performance in undergraduate STEM courses. However, students may be reticent to adopt dashboards, especially students in the middle range of the performance distribution, for whom the impact of the dashboard may be most significant.Prior research on gamification in STEM courses suggests that adding gameful elements like progress trackers, badges, and rewards can increase students' engagement in undergraduate coursework.The combination of personalized learning in dashboards and the motivational experience of gamification should boost student engagement, dashboard adoption, and ultimately foster academic achievement. What this paper adds: In this paper, we examine the differences in academic performance between students with and without access to a gamified learning dashboard in an undergraduate Geology course.We observe that students with access to the dashboard (the treatment group), outperform students without access (the control group). The greatest benefit is observed for students who use the dashboard more frequently.Students reported that the progress tracker, the badges, and the rewards all incentivized their use and provided useful feedback about their performance. Students who did not adopt the dashboard expressed a need for more detail about the tool and its purpose. Implications for practice and/or policy: Instructors and instructional designers for large enrollment undergraduate STEM courses should consider the affordances of gamified learner dashboards for increasing engagement and for providing synchronous feedback about learners' strategies in the course.Aligning the dashboard to the content of the curriculum—by ensuring that badges reflect key concepts‐ encouraged participation and helped students identify the utility of the tool. Dashboards should be personalized to individuals and to the course.Adding gameful elements in a low‐cost intervention for increasing adoption and engagement of dashboards in large enrollment introductory courses. [ABSTRACT FROM AUTHOR]

Background: Previous studies indicated that working memory (WM) updating and WM capacity play essential roles in mathematical ability. However, it is unclear whether WM capacity mediates the effect of WM updating on mathematics, and whether the cascading effects vary with different mathematical domains. Aims: The current study aims to explore the longitudinal mediating role of WM capacity between WM updating and mathematical performance, and how the relations change with the age and domains. Sample: A total of 131 Chinese first‐graders participated the study. Methods: Participants were required to complete tasks on WM updating and WM capacity in Grade 1 and Grade 2, as well as paper‐and‐pencil tests on mathematics achievement in Grade 3. The role of WM updating and capacity in the development of pupil's mathematical achievement was examined. Results: Results revealed that verbal WM updating in Grade 1 predicted basic arithmetic and logical‐visuospatial ability in Grade 3 via its cascading effect on verbal WM capacity in Grade 2. Moreover, visuospatial WM updating in Grade 1 predicted visuospatial WM capacity in Grade 2. Visuospatial WM capacity in Grade 1 predicted logical‐visuospatial ability in Grade 3 instead of basic arithmetic ability in Grade 3. Conclusions: The findings suggested that WM updating exerts effect on pupil's mathematical performance via WM capacity, meanwhile, this effect depends on children's mathematics domain. [ABSTRACT FROM AUTHOR]

Educational applications (apps) are ubiquitous within children's learning environments and emerging evidence has demonstrated their efficacy. However, it remains unclear what the active ingredients (ie, mechanisms), or combination of ingredients, of successful maths apps are. The current study developed a new, open‐access, three‐step framework for assessing the educational value of maths apps, comprised of type of app, mathematical content and app design features. When applied to a selection of available maths apps previously evaluated with children in the first 3 years of school (the final sample included 23 apps), results showed that practice‐based apps were the most common app type tested (n = 15). Basic number skills, such as number representation and relationships, were the most common area of mathematics targeted by apps (n = 21). A follow‐up qualitative comparative analysis showed observed learning outcomes with maths apps were enhanced when apps combined the following: a scaffolded and personalised learning journey (programmatic levelling) and explanations of why answers were right or wrong (explanatory feedback), as well as praise, such as 'Great job!' (motivational feedback). This novel evidence stresses the significance of feedback and levelling design features that teaching practitioners and other stakeholders should consider when deciding which apps to use with young children. Directions for future research are discussed. Practitioner notesWhat is already known about this topic Educational apps have been shown to support maths attainment in the first 3 years of school.Several existing frameworks have attempted to assess the educational value of some of these maths apps.Emerging experimental evidence also demonstrates the benefits of specific app design features, including feedback and levelling.What this paper adds Practice‐based maths apps are the most common type of app previously evaluated with young children.These evaluated maths apps have mostly focused on basic number skills.The combination of explanatory and motivational feedback, with programmatic levelling (either dynamic or static), was a necessary condition for enhancing learning outcomes with maths apps.Implications for practice and policy The inclusion of feedback and levelling in maths apps should be considered by app developers when designing apps, and by educational practitioners and parents when deciding which apps to use with their children.Further consideration is also needed for the development of educational apps that include a broad range of maths skills. [ABSTRACT FROM AUTHOR]

Background: Prior work has shown that middle school students struggle with algebra and that game‐based educational technologies, such as DragonBox and From Here to There!, are effective at improving students' algebraic performance. However, it remains unclear which aspects of algebraic knowledge shift as a result of playing these games and what game design features support algebraic learning. Objective: Using the data from a randomized controlled trial conducted in the 2020–2021 academic year, we (a) examined students' relative performance on assessment items measuring conceptual knowledge, procedural knowledge and procedural flexibility in algebraic equation solving, and (b) identified changes in these aspects of algebraic knowledge after playing DragonBox or From Here to There!. Methods: Eight hundred eighty‐seven seventh‐graders were randomly assigned to playing DragonBox or From Here to There! for nine 30‐min sessions throughout the school year. Students also completed a pretest, midtest and posttest measuring their algebraic knowledge. Results and Conclusion: First, prior to the intervention, students scored the highest on procedural knowledge and lowest on conceptual knowledge. Second, students significantly improved and maintained learning gains on conceptual knowledge throughout the intervention. Their performance on procedural knowledge and procedural flexibility items increased at midtest but decreased at posttest. Third, the pattern of results was consistent for students in the DragonBox and From Here to There! conditions, suggesting that both games may support students' conceptual understanding of algebra. The findings have implications for research and practice on supporting algebraic learning through game‐based technologies during and beyond educational disruptions. Lay Description: What is already known about this topic: Middle school students struggle with aspects of algebra.DragonBox and From Here to There! are two game‐based technologies designed to support students' algebraic learning.Both games implement point rewards and dynamic interactions; they differ in the uses of algebraic notation and problem structures. What this paper adds: Both games improved seventh‐graders' conceptual knowledge of algebraic equivalence.Students also improved on procedural knowledge and procedural flexibility, but the gains did not last to the end of the intervention. Implications for practice and/or policy: The games and their shared features may provide an engaging way to support students' conceptual understanding of algebra. [ABSTRACT FROM AUTHOR]

This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based on the author's memoir L. Positselski, Memoirs of the American Math. Society 212 (2011), no. 996, vi+133. The paper is intended to serve as a pedagogical introduction and a summary of the covariant duality between DG‐algebras and curved DG‐coalgebras, as well as the triality between DG‐modules, CDG‐comodules, and CDG‐contramodules. Some personal reminiscences are included as a part of historical discussion. [ABSTRACT FROM AUTHOR]

Mathematics and its applications try to make available a simple and accurate approach to handle nonlinear equations. The present paper investigates for the first time the application of the linearizing method to determine both the approximate frequency and displacement amplitude for the third‐order differential equations. The main merit of the linearized method is a collection of simplicity and accuracy for the solution of high‐order nonlinear conservative or non‐conservative oscillators. The current work sheds light on the approximate proposition to the damped third‐order nonlinear differential equations. The fast estimated solution is simulated to the accurate solution gained through the numerical methods. It is significant to conclude that the non‐perturbative method considered here is simpler and easier to apply than the other perturbation methods. This paper enriches some existing literature. [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]

Context Although many medical schools seek to improve diversity, they grapple with the challenge of how to weight the scores of different admission methods to achieve a balance between obtaining high predictiveness and ensuring diversity in the selected student pool. Yet, in large‐scale employment settings, substantial progress has been made on this front: Pareto‐optimization has been introduced as an elegant statistical tool to assist decision makers in determining the weights assigned to selection methods in advance (before the selection has taken place) so that a selection system is designed to achieve an optimal balance as reflected by the trade‐off that one outcome (e.g., predictiveness) cannot be improved without harm to the other outcome (e.g., diversity). Aims: This paper reviews the theory and research evidence about Pareto‐optimization and explains how Pareto‐optimization permits medical schools to better balance predictiveness and diversity in medical admission systems. Methods: After reviewing common weighting schemes (unit, regression‐based and ad hoc weighting) and their drawbacks, we introduce the theory and logic of Pareto‐optimization for better balancing predictiveness and diversity. To this end, we also offer an illustrative example. Next, we review the mathematical basis and available research evidence regarding Pareto‐optimization. Finally, we discuss potential criticisms (i.e., complexity and legal concerns). Conclusions: Compared to traditional unit weighting, regression‐based weighting and ad hoc weighting, Pareto‐optimization leads to substantial increases in diversity intake (up to three times more), while keeping the predictiveness of the selection methods at the same level. Moreover, the Pareto‐optimization is robust to sampling variability and variability of the input selection parameters. This paper explains how Pareto‐optimization permits medical schools to better balance predictiveness and diversity in medical admissions. [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]

In this paper, we study the uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball in ℝ3$$ {\mathrm{\mathbb{R}}}&#x0005E;3 $$. Under suitable conditions, we prove that, for any given positive integer k$$ k $$, the problem we considered has at most one solution possessing exactly k−1$$ k-1 $$ nodes. Together with the results presented by Nagasaki [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 36 (2): 211–232, 1989] and Tanaka [Proc. Roy. Soc. Edinburgh Sect. A. 138 (6): 1331–1343, 2008], we can prove that more types of nonlinear elliptic equations have the uniqueness of nodal radial solutions. [ABSTRACT FROM AUTHOR]