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This paper details a literature review of mathematics vocabulary intervention studies for students with mathematics difficulty. The primary aim was to identify instructional practices that support mathematics vocabulary development. We conducted a database search to identify mathematics intervention studies either focused exclusively on vocabulary or with an embedded vocabulary component. Ultimately, 13 studies with participants from kindergarten to Grade 8 were included in the review. The majority of included studies had dual foci on vocabulary and other mathematics content, including whole number computation, word problem solving, fractions, algebra, or geometry. All studies that measured mathematics vocabulary performance indicated positive student outcomes. In addition, multiple studies indicated positive effects on measures of other mathematics content beyond mathematics vocabulary knowledge. We noted six instructional practices across studies that bolstered the mathematics vocabulary performance of students with mathematics difficulty. From most to least common, these practices included formal vocabulary use, explicit instruction, use of representations, repeated exposures, pre‐teaching, and graphic organizers. Implications are addressed for both researchers and practitioners. [ABSTRACT FROM AUTHOR]

Elementary teachers are underprepared to teach mathematics, and there is a lack of field‐based support for mathematics‐specific pedagogies in the elementary grades. To address this theory to practice gap, we developed an innovative model of fieldwork that draws on the expertise of in‐service teachers (elementary mathematics specialists [EMSs]) who had recently completed a K–5 mathematics endorsement to work in the role of university supervisors supporting beginning teachers (BTs) in initial fieldwork. We argue that this model has three key aspects that will support BTs bridging the theory to practice gap: (1) as in‐service teachers the EMSs are keenly connected to the context of schools; (2) recent experience in university coursework in mathematics while serving as in‐service teachers required the EMSs to navigate the theory to practice gap themselves; (3) one‐on‐one mentorship supports strong and trusting relationships. Drawing on data from a 3‐year study we found that EMSs brought intimate knowledge of the school context and knowledge of the mathematics‐specific pedagogies taught at the university. These connections to the field and the university allowed EMSs to support BTs in implementing research‐based practices in their mathematics lessons that went against the norms of their school settings. [ABSTRACT FROM AUTHOR]

In this article, we examine how elementary classroom teachers who are pursuing their Elementary Mathematics Specialist certification—who we refer to as Elementary Mathematics Specialists in Training (EMSTs)—are positioned in their advice and information networks for mathematics. Analyzing the advice networks of six elementary schools in one district, we found that EMSTs were sought out by more individuals than other teachers, and when sought out by others, provided advice at a greater frequency than formal leaders. EMSTs' advice‐interactions were often with grade‐level peers, with interactions in the same grade occurring at a greater frequency than those spanning grade levels. We also found that, in the school with a formal mathematics‐specific leader, advice interactions were primarily directed at the formal leader, including the advice‐seeking of the EMSTs at that school. Based on our findings, we conclude with implications for how teacher education programs and school administrators can support mathematics teacher leaders in enacting leadership from their classrooms. [ABSTRACT FROM AUTHOR]

Many studies have reported poor school achievement in evening persons and general circadian fluctuations in cognition. The aim of this study was to analyze circadian fluctuations in a cross-sectional design and examine the effects of chronotype on situational emotions and intrinsic motivation. A cross-sectional survey study was conducted in three Turkish secondary schools with a total sample of 599 students (283 females and 316 males). Data were collected at the end of specific math lessons of the same grade level and content, using a form combining three scales. We found no gender-related differences in intrinsic motivation, while there were some differences in situational motivation. In math classes, female students exhibited higher level of interest, while boys scored higher on boredom. In addition, students who scored high on morning affect reported higher levels of interest, well-being, and less boredom. Students with higher stability (and lower fluctuations in mood and cognition during the day) reported a higher degree of enjoyment, perceived competence, perceived choice, and less pressure/tension in their math lessons. A positive association was observed between distinctness, interest, and well-being, while negative correlations existed between distinctness and boredom. This suggests that students with higher diurnal stability reported a higher level of interest, well-being, and a lower level of boredom. Additionally, the results of the analyses showed that morningness, distinctness, and eveningness were significant predictors of intrinsic motivation. Conversely, gender, time of application, morningness, and distinctness emerged as predictors for situational emotions in mathematics classes. [ABSTRACT FROM AUTHOR]

The application of STEM (Science, Technology, Engineering, and Math) education in solving real-world problems is challenging. To tackle this challenge, a project-based learning approach that integrates robots with cost-effective self-made toys to problem-solving was adopted to assist rural primary school students to apply STEM skills. The purpose of this study was to evaluate the effects of the project-based learning approach which includes lecturing and hands-on activities on primary school students' STEM learning outcomes and attitudes. An experiment was conducted with 25 primary school students who voluntarily participated in a STEM summer-camp programme. Students were asked to assemble a paper house equipped with an IoT control module and LED light switches, and write and edit robot scripts to produce a robot-based storytelling narrative using the paper house they made as a context. The results show that the project-based learning approach was an effective approach for cultivating primary school students' STEM knowledge and skills as evidenced from the post-written test. The relationships between the students' STEM learning outcomes and attitudes were also confirmed by a clustering analysis. Students who had higher learning attitudes also achieved higher STEM learning outcomes; the findings are also supported by the feedback from the open-ended questionnaire items. This study suggests that integrating low-cost self-made toys and robots in project-based learning activities is an effective and practical approach to enhance primary school students' learning outcomes and learning attitudes in STEM education. [ABSTRACT FROM AUTHOR]

There is much excitement about the opportunity to harness the power of large language models (LLMs) when building problem-solving assistants. However, the standard methodology of evaluating LLMs relies on static pairs of inputs and outputs; this is insufficient for making an informed decision about which LLMs are best to use in an interactive setting, and how that varies by setting. Static assessment therefore limits how we understand language model capabilities. We introduce CheckMate, an adaptable prototype platform for humans to interact with and evaluate LLMs. We conduct a study with CheckMate to evaluate three language models (InstructGPT, ChatGPT, and GPT-4) as assistants in proving undergraduate-level mathematics, with a mixed cohort of participants from undergraduate students to professors of mathematics. We release the resulting interaction and rating dataset, MathConverse. By analyzing MathConverse, we derive a taxonomy of human query behaviors and uncover that despite a generally positive correlation, there are notable instances of divergence between correctness and perceived helpfulness inLLMgenerations, among other findings. Further, we garner a more granular understanding of GPT-4 mathematical problemsolving through a series of case studies, contributed by experienced mathematicians. We conclude with actionable takeaways for ML practitioners and mathematicians: models that communicate uncertainty, respond well to user corrections, and can provide a concise rationale for their recommendations, may constitute better assistants. Humans should inspect LLM output carefully given their current shortcomings and potential for surprising fallibility. [ABSTRACT FROM AUTHOR]

Effective mathematics education for Latinx students with learning disabilities (LD) necessitates teachers who uphold high academic expectations, facilitate access to rigorous math curricula, and champion inclusive and meaningful student participation. This study delves into teachers’ perspectives on instructing Latinx students with LD, including those identified as emergent bilinguals. Interviews were conducted with both general and special education math teachers who instruct Latinx students with LD from 3rd to 8th grades. Key findings from the study revealed a nuanced positioning of Latinx students with LD by teachers: (1) they are perceived as having potential for mathematical competence, (2) they are seen as reliant on external support, and (3) they often internalize a self-view of being less competent in math. Despite these mixed perceptions, teachers highlighted strategies to bolster the learning experience for these students, including promoting active class participation, demystifying complex math concepts, and, occasionally, modifying the curriculum. A recurring theme that was also noted was the occasional underestimation of the mathematical abilities of Latinx students with LD by educators, despite their expressed intention to support their learning journey. [ABSTRACT FROM AUTHOR]

AbstractThe study examined how mathematics self-concept, mathematics anxiety and endorsement of mathematics gender stereotypes may impact female students’ response pattern in multiple-choice examinations in courses with mathematical content. Questionnaires measuring these three variables were completed by 435 undergraduates (327 enrolled in a non-mathematical course and 108 in a course with mathematical content). Achievement was measured via multiple-choice examinations, thus allowing us to analyse students’ response patterns (i.e. not only their mark but also the number of hits, errors and unanswered questions). In females, a poorer mathematics self-concept and higher levels of mathematics anxiety (compared with male classmates) did not impact negatively on their final mark in the course with mathematical content. However, the response pattern in this course differed according to gender and mathematics self-concept: a poorer mathematics self-concept was associated with a higher number of unanswered questions in women and a tendency toward a greater number of errors in men. This suggests that a poorer mathematics self-concept leads women to be more cautious during multiple-choice examinations so as to minimise mistakes, whereas in males it tends to be associated with a risk-taking response strategy. These results raise further concerns about the use of multiple-choice examinations, particularly for assessing mathematical knowledge in students with low mathematics self-concept. [ABSTRACT FROM AUTHOR]

In this paper, we explore Norwegian teachers’ perspectives on inclusive teaching practices in the mathematics classroom, defined as practices which maximise every pupil’s potential regardless of prior attainment. As previous research suggests, both mathematics teachers’ perspectives in general and the conceptualisation of inclusion, inclusive education, and inclusive practices are culturally situated, varying significantly across countries and educational systems. We draw on data from a large project in Norway focusing on the use of grouping by attainment and its relation to policy and pedagogical practices around inclusion in mathematics. Participants were 13 primary and lower-secondary mathematics teachers from six schools in the Oslo area. Analysis of semi-structured interviews focusing on strategies for inclusion of all pupils in mathematics classrooms reveals the cultural particularities of mathematics teachers’ perspectives on inclusive practices, highlighting the value of similar investigations in other cultural contexts. [ABSTRACT FROM AUTHOR]

Based on the expectancy-value perspective on identity and identity formation, this paper explores the relationship between math identity (MI) and the dimensions of motivation (i.e. intrinsic value, attainment value, utility value and perceived competence) and math achievement in primary school. An additional aim of our research was to explore these relationships in different cultural contexts and investigate potential gender and grade differences concerning MI. The participants were 11,782 primary school students from Norway, Sweden, Estonia, Finland, Portugal and Serbia. All predictors from the motivation spectrum were significant for students' MI across the examined countries and had a stronger association with MI than math achievement. Among the motivational dimensions, intrinsic value had the strongest association with students' MI. Boys had significantly more positive math identities than girls in Estonia, Finland, Norway and Portugal. The results showed that the grade 4 students perceived themselves less as "math persons" than their grade 3 peers in all countries. [ABSTRACT FROM AUTHOR]

Research has shown that some students who underperform in mathematics overestimate their performance, while others who excel in mathematics underestimate it. Looking at this mismatch of performance and confidence judgement—the Dunning–Kruger effect (DKE)—the current study investigates how well students' confidence judgement and item-specific mathematics competence relate with each other and whether such a relationship differs across six European countries (i.e., Norway, Sweden, Finland, Estonia, Serbia and Portugal). We also examine whether perceived competence, mathematics identity, gender, socioeconomic status and immigration background predict this mismatch and whether these demographic factors function differently between the examined countries. The results show that the DKE could be found across grades three and four in all six countries. However, there are country-specific patterns regarding the relationship between performance, mathematics identity and perceived competence; the DKE; and how different demographic variables predict its occurrences in particular subpopulations. [ABSTRACT FROM AUTHOR]

Although learned helplessness has a long research tradition, neither its contextual predictors nor the ways that they take effect are fully understood. This study inquired into the role of selected aspects of the home learning environment for academic helplessness. We tested whether three dimensions of parent-child school-related interactions—school-related assistance, structure, and responsiveness—predicted helplessness in maths. The study also verified whether student self-efficacy in maths partially mediated the relationships. The analyses were run on a sample of 6726 German secondary school students and used structural equation modelling. They confirmed that higher school-related assistance, structure, and responsiveness in Grade 7 were associated with lower helplessness in maths in Grade 7. Moreover, self-efficacy in maths was a partial mediator of these relationships. Additional analyses with helplessness in maths measured in Grade 9 revealed the same pattern of results for school-related assistance and responsiveness, but only an indirect link was present in the case of structure. The results highlight the protective role that parent-child interactions around school may play against academic helplessness. [ABSTRACT FROM AUTHOR]

Number line estimation has been found to be strongly related to mathematical reasoning concurrently and longitudinally. However, the relationship between number line estimation and mathematical reasoning might differ according to children's level of performance. This study investigates whether findings from previous studies that show number line estimation significantly predicting mathematical reasoning replicate, and whether this relationship holds across several points of the mathematical reasoning distribution. Participants include 324 Singaporean children (162 girls, Mage = 74.1 months, SDage = 4.0) in their second year of kindergarten who were assessed on the number line estimation task (0–10 and 0–100) and mathematical reasoning skills. The results replicate previous findings showing that higher accuracy on the number line estimation task is predictive of higher mathematical reasoning, for both the 0–10 and 0–100 number line. Quantile regressions show that performance on the number line task similarly predict mathematical reasoning across the performance distribution. Possible differences between the 0–10 and 0–100 number line's predictive capacity are discussed. [ABSTRACT FROM AUTHOR]

This exploratory study evaluated the effects of self-regulated strategy development (SRSD) on students' written expression when asked to solve a word problem and explain reasoning. A secondary question evaluated potential for differential effects based on determination of having mathematics difficulty (MD). We implemented a quasi-experimental design with 163 students with and without MD in grade 4. Results indicated that students in the treatment group (n = 83) significantly outperformed students in the comparison group (n = 80) on measures of mathematical writing involving subtraction and division word problems. For the subtraction problems, students in the treatment group improved their overall written expression of mathematics scores (g = 0.688), yielding a medium effect. The intervention differentially benefited students without MD. Our findings call for greater integration of systematic writing opportunities in mathematics and highlight the importance of explicitly teaching students how to approach the written expression of their mathematical reasoning. [ABSTRACT FROM AUTHOR]

This note remedies an error in our paper tilted Conormal Spaces and Whitney Stratifications (Found. Comput. Math., 2022). [ABSTRACT FROM AUTHOR]

Background: Fetal alcohol spectrum disorders (FASD) include a range of neurocognitive and behavioral impairments resulting from prenatal alcohol exposure (PAE). Among the PAE‐related cognitive deficits, number processing is particularly affected. This study examines alterations in number processing networks and whether changes in functional connectivity mediate the adverse effects of PAE on arithmetic performance. Methods: Magnetic resonance imaging (MRI) was acquired in 57 children (mean (SD) age = 11.3 (+0.9) yr), 38 with FASD (19 fetal alcohol syndrome (FAS) or partial FAS (PFAS), 19 heavily exposed (HE)) and 19 controls. Whole‐brain correlation analyses were performed from five seeds located in regions involved in number processing. Results: Children with FAS/PFAS showed dose‐dependent reductions in resting state functional connectivity between the seed in the right (R) posterior superior parietal lobule and a cluster in the left (L) inferior frontal gyrus, and between a seed in the R horizontal intraparietal sulcus and clusters in the R precentral gyrus and L cerebellar lobule VI. HE children showed lower resting state functional connectivity in a subset of these regions. Lower functional connectivity in the two fronto‐parietal connections partially mediated the adverse effects of PAE on arithmetic performance. Conclusion: This study demonstrates PAE‐related functional connectivity impairments in functional networks involved in number processing. The weaker connectivity between the R posterior superior parietal lobule and the L inferior frontal gyrus suggests that impaired verbal processing and visuospatial working memory may play a role in number processing deficits, while weaker connectivity between the R intraparietal sulcus and the R precentral gyrus points to poorer finger‐based numerical representation, which has been linked to arithmetic computational skills. [ABSTRACT FROM AUTHOR]

This article argues that the first important comprehensive efforts by US mathematicians to survey, translate, and disseminate the work of Chinese mathematicians resulted from Cold War geopolitical and scientific competition and economic pressures that emerged in the 1950s and 1960s. The success of the American Mathematical Society's (AMS) translation program and its journal Chinese Mathematics depended less on official diplomatic channels and more on an informal network of Chinese American mathematicians and librarians in the United States, which provided the infrastructure and hidden labor necessary for transnational mathematical exchange and translation. The history of the Chinese translation project demonstrates the importance of moving beyond the biographies and work of established mathematicians to capture the broader transpacific social history of Chinese American mathematical research and technical labor in the early Cold War. Moreover, the article demonstrates the importance of bringing Asian American history and the history of Cold War science together, as the mathematical and linguistic expertise and labor required came from recently immigrated Chinese American mathematicians caught at the nexus of Cold War anticommunist politics and the incomplete repeal of Chinese exclusion. Historians of mathematics have mostly narrated the late 1940s and early 1950s as a time of anti-communist purges that impacted the lives of Chinese scientists and derailed US–China scientific exchange. Meanwhile, the 1960s have remained unexamined. Instead, we see the ways in which the AMS's translation program generated important mathematical exchanges that widely impacted mathematics and adjacent fields. [ABSTRACT FROM AUTHOR]

A d$d$‐dimensional invertible topological field theory (TFT) is a functor from the symmetric monoidal (∞,n)$(\infty,n)$‐category of d$d$‐bordisms (embedded into R∞$\mathbb {R}^\infty$ and equipped with a tangential (X,ξ)$(X,\xi)$‐structure) that lands in the Picard subcategory of the target symmetric monoidal (∞,n)$(\infty,n)$‐category. We classify these field theories in terms of the cohomology of the (n−d)$(n-d)$‐connective cover of the Madsen–Tillmann spectrum. This is accomplished by identifying the classifying space of the (∞,n)$(\infty,n)$‐category of bordisms with Ω∞−nMTξ$\Omega ^{\infty -n}MT\xi$ as an E∞$E_\infty$‐space. This generalizes the celebrated result of Galatius–Madsen–Tillmann–Weiss (Acta Math. 202 (2009), no. 2, 195–239) in the case n=1$n=1$, and of Bökstedt–Madsen (An alpine expedition through algebraic topology, vol. 617, Contemp. Math., Amer. Math. Soc., Providence, RI, 2014, pp. 39–80) in the n$n$‐uple case. We also obtain results for the (∞,n)$(\infty,n)$‐category of d$d$‐bordisms embedding into a fixed ambient manifold M$M$, generalizing results of Randal–Williams (Int. Math. Res. Not. IMRN 2011 (2011), no. 3, 572–608) in the case n=1$n=1$. We give two applications: (1) we completely compute all extended and partially extended invertible TFTs with target a certain category of n$n$‐vector spaces (for n⩽4$n \leqslant 4$), and (2) we use this to give a negative answer to a question raised by Gilmer and Masbaum (Forum Math. 25 (2013), no. 5, 1067–1106. arXiv:0912.4706). [ABSTRACT FROM AUTHOR]

Researchers increasingly identify virtual reality (VR) simulations as a potentially effective professional development tool. However, simulations used in education and behavior analysis typically require active oversight from technicians and instructors. "Smart" VR integrated with artificial intelligence could independently administer simulation components, alleviate logistical challenges associated with high-quality professional development such as behavioral skills training (BST), and provide trainees with opportunities to extensively practice skills across a range of disciplines. The limited research in this area has yet to demonstrate a functional smart VR application with the ability to provide instruction related to a primarily vocal skill. The current study used a randomized, combined multiple probe across behaviors and participants design to examine a smart VR application's ability to deliver components of BST and assess participants (n = 2) acquisition of a mathematical questioning strategy designed to examine covert student problem solving in general education settings. Results suggest that automated assessment of participants corresponded with results of direct observation. Although insufficient to demonstrate a functional relation between training and participant performance, the iterative experiment provides qualified support for the use of automated BST as a tool for skill acquisition. Findings indicate smart VR represents a promising means of improving professional development and a fruitful area of interdisciplinary collaboration. [ABSTRACT FROM AUTHOR]

This study aims to shed light on the association between private tutoring and academic achievement in mathematics among primary school students in Qatar. Utilizing data from the Trends in International Mathematics and Science Study (TIMSS) 2019, we employ a propensity score technique to elucidate the disparities in mathematics achievement levels between two distinct groups: students who receive private tutoring and those who do not. Our findings indicate that students who engage in private tutoring have lower odds of attaining higher achievement scores in mathematics. [ABSTRACT FROM AUTHOR]

Gender stereotypes about science, technology, engineering, and math (STEM) are salient for children and adolescents and contribute to achievement-related disparities and inequalities in STEM participation. However, few studies have used a longitudinal design to examine changes in gender stereotypes across a range of STEM fields. In a large, preregistered study, we examined the developmental trajectories of two gender stereotypes (involving interest and ability) in four STEM fields across three time points within a calendar year, starting in Grades 2–8. The diverse sample included 803 students ages 7–15 years old at the start of the study (50% girls; 8.5% Asian, 6.0% Black, 25.5% Hispanic/Latinx, 43.7% White, and 16.3% other). Multilevel growth modeling was used to examine developmental trajectories in students' stereotypes for four STEM fields (math, science, computer science, and engineering) while considering both gender and grade level. We found that different STEM disciplines displayed different developmental patterns: Math ability and science interest stereotypes more strongly favored girls over the year among elementary school participants, whereas computer science stereotypes less strongly favored boys over time, and engineering stereotypes (which largely favored boys) were stable across time. The results highlight that the development of stereotypes is not the same for all STEM fields as well as the need to understand the complexity and specificity of developmental change across fields and types of stereotypes. Public Significance Statement: This study tracked changes in children and early adolescents' STEM-gender stereotypes over the course of a calendar year, specifically focusing on gender stereotypes about who is interested and capable in STEM. We found greater stability in stereotypes about engineering than math, science, and computer science, and among middle school students compared to elementary school students. Based on patterns within the present study, we suggest that efforts to reduce gender stereotyping in STEM fields should begin early, before stereotypes take root. [ABSTRACT FROM AUTHOR]

In this paper, for d ≥ 1 and s ∈ (0 , d 2) , we study the Bianchi–Egnell quotient Q (f) = inf f ∈ H ˙ s (R d) \ B ‖ (- Δ) s / 2 f ‖ L 2 (R d) 2 - S d , s ‖ f ‖ L 2 d d - 2 s (R d) 2 dist H ˙ s (R d) (f , B) 2 , f ∈ H ˙ s (R d) \ B , where S d , s is the best Sobolev constant and B is the manifold of Sobolev optimizers. By a fine asymptotic analysis, we prove that when d = 1 , there is a neighborhood of B on which the quotient Q (f) is larger than the lowest value attainable by sequences converging to B . This behavior is surprising because it is contrary to the situation in dimension d ≥ 2 described recently in König (Bull Lond Math Soc 55(4):2070–2075, 2023). This leads us to conjecture that for d = 1 , Q (f) has no minimizer on H ˙ s (R d) \ B , which again would be contrary to the situation in d ≥ 2 . As a complement of the above, we study a family of test functions which interpolates between one and two Talenti bubbles, for every d ≥ 1 . For d ≥ 2 , this family yields an alternative proof of the main result of König (Bull Lond Math Soc 55(4):2070–2075, 2023). For d = 1 we make some numerical observations which support the conjecture stated above. [ABSTRACT FROM AUTHOR]

In this paper, we prove sharp isoperimetric inequalities for lower order eigenvalues of Neumann Laplacian on bounded domains in both compact and noncompact rank-1 symmetric spaces. Our results generalize the work of Wang and Xia for bounded domains in the hyperbolic space (Xia and Wang in Math Ann 385(1–2):863–879, 2023), and Szegö–Weinberger inequalities in rank-1 symmetric spaces obtained by Aithal and Santhanam (Trans Am Math Soc 348(10):3955–3965, 1996). [ABSTRACT FROM AUTHOR]

We consider the mixed local and nonlocal functionals with nonstandard growth u↦∫Ω[|Du|p−f(x)u]dx+∫RN∫RN|u(x)−u(y)|q|x−y|N+sqdxdy$$\begin{eqnarray*} \hspace*{80pt}&& u\mapsto \int _{\Omega }[|Du|^p-f(x)u]\,dx\\ &&\quad +\,\int _{\mathbb {R}^N}\int _{\mathbb {R}^N}\frac{|u(x)-u(y)|^q}{|x-y|^{N+sq}}\,dxdy \end{eqnarray*}$$with 1

Mathematics incorporates a broad range of skills, which includes basic early numeracy skills, such as subitizing and basic counting to more advanced secondary skills including mathematics calculation and reasoning. The aim of this review was to undertake a detailed investigation of the severity and pattern of early numeracy and secondary mathematics skills in people with epilepsy. Searches were guided by the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement. Twenty adult studies and 67 child studies were included in this review. Overall, meta-analyses revealed significant moderate impairments across all mathematics outcomes in both adults (g= -0.676), and children (g= -0.593) with epilepsy. Deficits were also observed for specific mathematics outcomes. For adults, impairments were found for mathematics reasoning (g= -0.736). However, two studies found that mathematics calculation was not significantly impaired, and an insufficient number of studies examined early numeracy skills in adults. In children with epilepsy, significant impairments were observed for each mathematics outcome: early numeracy (g= -0.383), calculation (g= -0.762), and reasoning (g= -0.572). The gravity of impairments also differed according to the site of seizure focus for children and adults, suggesting that mathematics outcomes were differentially vulnerable to the location of seizure focus. [ABSTRACT FROM AUTHOR]

Noticing is an essential skill for all teachers of mathematics. Mathematics teacher educators have utilized a variety of tools to practice and develop preservice teachers' (PSTs') ability to notice, which we extend to include photographs and learning trajectories. This article explores PSTs' noticing skills by analyzing work samples from a methods course assignment that examined teacher noticing and planning for future instruction. The work samples were analyzed using structural coding. Results indicate that PSTs can: (a) notice students' mathematical thinking in photographs they captured; (b) attend to and interpret the mathematics in photographs, but need additional support to consider how to respond to the mathematical thinking; and (c) use learning trajectories or progressions to help them notice, but there is less evidence of them using learning trajectories or progressions as a tool to respond to students' mathematical thinking. Implications for mathematics teacher education and future research are considered. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has highlighted the need to use infection testing databases to rapidly estimate effectiveness of prior infection in preventing reinfection (⁠|$P{E}_S$|⁠) by novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants. Mathematical modeling was used to demonstrate a theoretical foundation for applicability of the test-negative, case–control study design to derive |$P{E}_S$|⁠. Apart from the very early phase of an epidemic, the difference between the test-negative estimate for |$P{E}_S$| and true value of |$P{E}_S$| was minimal and became negligible as the epidemic progressed. The test-negative design provided robust estimation of |$P{E}_S$| and its waning. Assuming that only 25% of prior infections are documented, misclassification of prior infection status underestimated |$P{E}_S$|⁠ , but the underestimate was considerable only when > 50% of the population was ever infected. Misclassification of latent infection, misclassification of current active infection, and scale-up of vaccination all resulted in negligible bias in estimated |$P{E}_S$|⁠. The test-negative design was applied to national-level testing data in Qatar to estimate |$P{E}_S$| for SARS-CoV-2. |$P{E}_S$| against SARS-CoV-2 Alpha and Beta variants was estimated at 97.0% (95% CI, 93.6-98.6) and 85.5% (95% CI, 82.4-88.1), respectively. These estimates were validated using a cohort study design. The test-negative design offers a feasible, robust method to estimate protection from prior infection in preventing reinfection. [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]

This paper extends some results of Mattila (J. Fractal Geom. 66 (2021) 389–401 and Ann. Acad. Sci. Fenn. A Math. 42 (2017) 611–620), in particular, removing assumptions of positive lower density. We give conditions on a general family Pλ:Rn→Rm,λ∈Λ$P_{\lambda }:\mathbb {R}^n\rightarrow \mathbb {R}^m, \lambda \in \Lambda$, of orthogonal projections which guarantee that the Hausdorff dimension formula dimA∩Pλ−1{u}=s−m$\dim A\cap P_{\lambda }^{-1}\lbrace u\rbrace =s-m$ holds generically for measurable sets A⊂Rn$A\subset \mathbb {R}^{n}$ with positive and finite s$s$‐dimensional Hausdorff measure, s>m$s>m$. As an application we prove for Borel sets A,B⊂Rn$A,B\subset \mathbb {R}^{n}$ with positive s$s$‐ and t-dimensional$t{\text{-dimensional}}$ measures that if s+(n−1)t/n>n$s + (n-1)t/n > n$, then dimA∩(g(B)+z)⩾s+t−n$\dim A\cap (g(B)+z) \geqslant s+t - n$ for almost all rotations g$g$ and for positively many z∈Rn$z\in \mathbb {R}^{n}$. We shall also give an application to the estimates of the dimension of the set of exceptional rotations. [ABSTRACT FROM AUTHOR]

We establish higher dimensional versions of a recent theorem by Chen and Haynes [Int. J. Number Theory 19 (2023), 1405–1413] on the expected value of the smallest denominator of rational points in a randomly shifted interval of small length, and of the closely related 1977 Kruyswijk–Meijer conjecture recently proved by Balazard and Martin [Bull. Sci. Math. 187 (2023), Paper No. 103305]. We express the distribution of smallest denominators in terms of the void statistics of multidimensional Farey fractions and prove convergence of the distribution function and certain finite moments. The latter was previously unknown even in the one‐dimensional setting. We furthermore obtain a higher dimensional extension of Kargaev and Zhigljavsky's work on moments of the distance function for the Farey sequence [J. Number Theory 65 (1997), 130–149] as well as new results on pigeonhole statistics. [ABSTRACT FROM AUTHOR]

This study investigated the effects of group rational emotive behaviour therapy on the mathematics anxiety of students in Nigerian secondary schools. In total, 118 senior secondary school students constituted the sample for the study: 63 learners were allocated to the experimental group and 55 learners to the control group. The instruments used for data collection were the Mathematics Anxiety Scale (primary outcome measure) and the Irrational Beliefs in Mathematics Scale (secondary outcome measure). The Mathematics Anxiety Scale was used to elicit information from the participants that enabled the researchers to randomly allocate them to the programmes of the treatment groups. The experimental group was exposed to the rational emotive behaviour therapy treatment, while the control group received conventional counselling. The treatment programme lasted 6 weeks. The results reveal that students in group rational emotive behaviour therapy, post-test, had experienced significantly more positive effects relating to mathematics anxiety and irrational beliefs about mathematics (effects that remained consistent at follow-up) than students in the control group. [ABSTRACT FROM AUTHOR]

Oscillatory shear tests are frequently used to determine viscoelastic properties of complex fluids. Both the amplitude and frequency of the input signal can be independently varied, allowing rheologists to probe a wide range of material responses. Historically, most oscillatory tests have focused on the measurement and application of the total strain. However, the total strain is a composite parameter consisting of recoverable and unrecoverable components. Use of only the total strain therefore provides an incomplete description of the rheology. In this work, we provide a mathematical derivation for the determination of the recoverable and unrecoverable components in steady-state linear viscoelastic oscillatory flows via a simple experimental procedure. The relationship between the total strain and its components is fully explored and challenged in the context of how rheologists define moduli and common rheological models. These relations are demonstrated via experimental measurements on model viscoelastic and viscoplastic materials: wormlike micelles and Carbopol 980. Additionally, we show how the derived mathematics fully details the conditions where the Cox-Merz rules are valid in terms of recovery rheology. Finally, we demonstrate how a thorough understanding of the strain components can be used to create a simple nonlinear model that reproduces all common amplitude sweep behaviors. [ABSTRACT FROM AUTHOR]

"The Bedrock of Logical Thought" was a television show produced in 1957 by NBC and ETRC with the goal of promoting interest in mathematics among young people. The show featured mathematicians Clifton Fadiman and John Wilder discussing the axiomatic method and its applications. Recently, the script for the show was discovered in the Archives of American Mathematics, providing insight into the history of mathematics on television in the 1950s. The show was well-received by viewers, including teachers, students, and families, who appreciated the opportunity to learn about mathematics in an engaging and accessible way. This article emphasizes the significance of educational television in reaching a broad audience and fostering interest in mathematics. [Extracted from the article]

Objective: The aim of this study was to evaluate executive function (EF), such as inhibition and working memory, in children with isolated growth hormone deficiency (IGHD) using performance-based tests and parent-report scales. Methods: A total of seventy children between the ages of 7 and 12 years were included in the study. Half (n=35) had children with IGHD and half were healthy controls. To evaluate the EF performances of the participants, the Visual Aural Digit Span Test-B Form (VADS-B) and Stroop task were applied. EF was also evaluated using the Behavior Rating Inventory of Executive Function (BRIEF). Results: Children with IGHD scored lower on the VADS-B form for short-term memory (p<0.05) compared to healthy controls. In addition, the completion time for the Stroop-color/word test was significantly longer in children with IGHD (p<0.05). For children with IGHD, their parents reported higher scores on all sub-scales of the BRIEF scale, with statistically significant differences for all sub-scales with the exception of “organization of materials” (p<0.05). Conclusion: In this study, children with IGHD had poorer EF skills compared to unaffected peers. EF skills may influence academic success by affecting children’s language skills, mathematical comprehension, cognitive flexibility, and hypothetical thinking. We believe that psychiatric evaluation of children with IGHD before and during treatment may positively contribute to both their academic performance and social relationships. [ABSTRACT FROM AUTHOR]

National policy initiatives in Ireland, such as Project Maths and the Science, Technology, Engineering, and Mathematics (STEM) Education Policy Statement have sought to increase the engagement and performance of students in mathematics and science. The current study investigated the performance of students in Ireland in these areas and in reading in international large-scale assessments (Programme for International Student Assessment [PISA], Trends in International Mathematics and Science Study [TIMSS], and Progress in International Reading Literacy Study [PIRLS]), with a view to better understand the performance of high-achieving students, relative to their counterparts in other countries in general, and in countries with similar average performance. Lower than expected proportions of high achievers were noted and a pattern of relative underachievement was observed among high achievers – those performing at the highest levels of proficiency, and those performing at key benchmarks, including the 75th and 90th percentiles – in mathematics and science to a greater extent than in reading. These issues were found to be consistent over time, and more prevalent at post-primary level, compared with primary level. The findings of this study are discussed with reference to individual and societal costs, and specific issues that need to be investigated further are identified. [ABSTRACT FROM AUTHOR]

There are several classical characterisations of the valuative dimension of a commutative ring. Constructive versions of this dimension have been given and proven to be equivalent to the classical notion within classical mathematics, and they can be used for the usual examples of commutative rings. To the contrary of the classical versions, the constructive versions have a clear computational content. This paper investigates the computational relationship between three possible constructive definitions of the valuative dimension of a commutative ring. In doing so, it proves these constructive versions to be equivalent within constructive mathematics. [ABSTRACT FROM AUTHOR]

Based on a degenerate proximal point analysis, we show that the Douglas-Rachford splitting can be reduced to a well-defined resolvent, but generally fails to be a proximal mapping. This extends the recent result of [Bauschke, Schaad and Wang. Math. Program. 2018;168:55–61] to more general setting. The related concepts and consequences are also discussed. In particular, the results regarding the maximal and cyclic monotonicity are instrumental for analysing many operator splitting algorithms. [ABSTRACT FROM AUTHOR]

Montessori is a highly individualized pedagogy that prioritizes following each child's individual interests over standardized test scores. This quasi-experimental study compares groups of Montessori students (treatment groups, N = 535–710) with control groups of non-Montessori students, matched through the simple matching method, which controls for the effect of background variables on schooling outcomes. The tested hypothesis is that the treatment groups achieve mean scores that are not significantly lower and have a significantly higher standard deviation on standardized tests of mathematics and language. The study encompassed students in Grade 2, 5, 8, and 10 across two separate cohorts. Results indicate that Montessori students attain either comparable or significantly higher scores than non-Montessori students, depending on grade and cohort, with greater score variability observed, particularly at Grade 8 and in mathematics. This finding implies the necessity for future investigations into the effect of Montessori teachers' instructional practices. [ABSTRACT FROM AUTHOR]

This article explores the challenges and importance of GCSE English and maths resits for students in England. It highlights the low pass rates and the lack of research literature on this topic. The Education Endowment Foundation conducted a practice review, which identified key themes for improving resits, including curriculum, resources, learner needs, teacher development, and leadership. The article emphasizes the need for further research and effective strategies to support students in their resit exams, particularly those from disadvantaged backgrounds. It suggests incorporating strategies from Key Stage 4 and the university sector, but cautions that easily adoptable approaches are limited. The authors stress the importance of investing in the post-16 workforce and institutions and encourage practitioners, leaders, and researchers to contribute to their work. [Extracted from the article]

Teaching music often focuses on developing musical concepts, through comparisons and discriminations. This paper contributes to the discussion on concept development in music through recognition of common elements in a situation and a shift from a local to a general level, considering theoretical approaches to mathematical generalisation. It sets to explore preschool children's understanding of tempo and its use in new musical situations. The research involved a musical intervention in six preschool classrooms. Critical incidences from focus group discussions and non-participant observation recorded children's understanding of tempo from their musical actions, drawings, responses and reflection to teacher questions. The findings highlight that children could go beyond the specific content of the activities and focus on the basic characteristics of tempo, integrating them into their song creations. A teaching approach oriented to generalisation through concept development can assist teachers to elaborate musical content and realise students' level of understanding. [ABSTRACT FROM AUTHOR]

Study on fragmentation and defragmentation of reflective thinking structures has never been conducted. Therefore, the purpose of this study was threefold: (1) to identify the types and forms of fragmentation of students' reflective thinking structures in solving mathematical problems, (2) to describe attempts to defragment students' reflective thinking structures in each type and form of fragmentation, and (3) to find out if such defragmentation attempts can work for reflective thinkers who experience fragmentation. This research was qualitative, exploratory, and descriptive. The subjects included in this study were students who thought reflectively and experienced fragmentation at each level of reflective thinking when solving mathematical problems. Data collection was conducted using tests, interviews, think-aloud protocols, and observation. Data analysis was conducted using constant comparative method. Data validity was established using method and source triangulation. The results showed: (1) Scanning Defragmentation work for Less-Strict Fragmentation, (2) Schema Emergence Defragmentation work for Pseudo-True Fragmentation, (3) Schema Activation work for Pseudo-False Fragmentation, (4) Connection Emergence Defragmentation work for Nonexistent-Connection Fragmentation, (5) Compare-Reflect Defragmentation work for Confidence-False Fragmentation. The results of this study can be reference for mathematics researchers and educators to develop learning models that can prevent the occurrence of fragmentation of reflective thinking structures. [ABSTRACT FROM AUTHOR]

This note corrects an error in our paper Anosov flows, growth rates on covers and group extensions of subshifts, Invent. Math. 223:445–483, 2021. This leaves our main results, Theorem 1.1, Corollary 1.2, Theorem 1.3 and Theorem 5.1, unchanged. We also fill a gap in the arguments presented in Sect. 9; this requires a small modification to the results in this section. [ABSTRACT FROM AUTHOR]

In this paper, we study a discrete momentum consensus-based optimization (Momentum-CBO) algorithm which corresponds to a second-order generalization of the discrete first-order CBO [S.-Y. Ha, S. Jin and D. Kim, Convergence of a first-order consensus-based global optimization algorithm, Math. Models Methods Appl. Sci. 30 (2020) 2417–2444]. The proposed algorithm can be understood as the modification of ADAM-CBO, replacing the normalization term by unity. For the proposed Momentum-CBO, we provide a sufficient framework which guarantees the convergence of algorithm toward a global minimum of the objective function. Moreover, we present several experimental results showing that Momentum-CBO has an improved success rate of finding the global minimum compared to vanilla-CBO and show the stability of Momentum-CBO under different initialization schemes. We also show that Momentum-CBO can be used as the alternative of ADAM-CBO which does not have a proper convergence analysis. Finally, we give an application of Momentum-CBO for Lyapunov function approximation using symbolic regression techniques. [ABSTRACT FROM AUTHOR]

This editorial paper reviews the articles published in a special issue devoted to the application of active particle methods applied to the study of the collective dynamics of large systems of interacting entities in science and society. The applications presented in this special issue focus on the study of financial markets, cell dynamics in the context of cancer modeling, vehicle and crowd vehicle and crowd dynamics, and classical problems in the kinetic theory of active particles and swarm theory. A critical analysis is proposed to look forward to research. Perspectives with emphasis on the interaction of multiple social dynamics. [ABSTRACT FROM AUTHOR]

It is well-known that the famous Selberg integral is equivalent to the Morris constant term identity. In 1998, Baker and Forrester conjectured a generalization of the q-Morris constant term identity[J. Combin. Theory Ser. A 81 (1998), pp. 69–87]. This conjecture was proved and extended by Károlyi, Nagy, Petrov, and Volkov (KNPV) in 2015 [Adv. Math. 277 (2015), pp. 252–282]. In this paper, we obtain two symmetric function generalizations of the q-Baker–Forrester ex-conjecture. These include: (i) a q-Baker–Forrester type constant term identity for a product of a complete symmetric function and a Macdonald polynomial; (ii) a complete symmetric function generalization of KNPV's result. [ABSTRACT FROM AUTHOR]

We show the invalidity of finitary counterparts for three classification theorems: The preservation of being a Bernoulli shift through factors, Sinai's factor theorem, and the weak Pinsker property. We construct a finitary factor of an i.i.d. process which is not finitarily isomorphic to an i.i.d. process, showing that being finitarily Bernoulli is not preserved through finitary factors. This refutes a conjecture of M. Smorodinsky [ Finitary isomorphism of m-dependent processes , Amer. Math. Soc., Birkhauser, Providence, RI, 1992, pp. 373–376], which was first suggested by D. Rudolph [ A characterization of those processes finitarily isomorphic to a Bernoulli shift , Birkhäuser, Boston, Mass., 1981, pp. 1–64]. We further show that any ergodic system is isomorphic to a process none of whose finitary factors are i.i.d. processes, and in particular, there is no general finitary Sinai's factor theorem for ergodic processes. Another consequence of this result is the invalidity of a finitary weak Pinsker property, answering a question of G. Pete and T. Austin [Math. Inst. Hautes Études Sci. 128 (2018), 1–119]. [ABSTRACT FROM AUTHOR]

Deligne proved in [Extensions centrales non résiduellement finies de groupes arithmetiques, C. R. Acad. Sci. Paris 287 (1978) 203–208] (see also 7.1 in [R. Hill, Fractional weights and non-congruence subgroups, in Automorphic Forms and Representations of Algebraic Groups Over Local Fields, eds. H. Saito and T. Takahashi, Surikenkoukyuroku Series, Vol. 1338 (2003), pp. 71–80]) that the weights of Siegel modular forms on any congruence subgroup of the Siegel modular group of genus g > 1 must be integral or half integral. Actually he proved that for a system v (M) of complex numbers of absolute value 1 v (M) det (C Z + D) r (r ∈ ℝ) (0. 1) can be an automorphy factor only if 2 r is integral. We give a different proof for this. It uses Mennicke's result [Zur Theorie der Siegelschen Modulgruppe, Math. Ann. 159 (1965) 115–129] that subgroups of finite index of the Siegel modular group are congruence subgroups and some techniques from [Solution of the congruence subgroup problem for SL n (n ≥ 3) and Sp 2 n (n ≥ 2) , Publ. Math. Inst. Hautes Études Sci. 33 (1967) 59–137] of Bass–Milnor–Serre. [ABSTRACT FROM AUTHOR]

Background: Game‐based learning can frame problem‐solving as a sense‐making experience with domain‐specific tasks for school students. However, multiple challenges arise when trying to support learners in such a complex, problem‐oriented learning environment. Objectives and Methods: With an architecture‐themed mathematics learning game, we conducted two mixed‐method studies to explore the impact and design of game‐based mathematical experience on the math problem‐solving performance of middle school students. Results and Conclusions: The study findings suggested a positive impact of game‐based math experience on math problem‐solving for middle school students. Problematization‐oriented game‐based math tasks with structuring features enhanced students' reasoning with problems and channelled it to doing mathematics. Takeaways: The current research findings support the initiative to frame learning as a sense‐making experience with domain‐specific tasks and inform the design of game‐based mathematical experience and learning support. Lay Description: What is already known about this topic: Realistic mathematical practices frame learning as a sense‐making experience.Challenges arise when involving learners in realistic mathematical experiences driven by domain‐specific tasks. What this paper adds: Game‐based simulation of math tasks framed learning as sense‐making experience.Game‐based math experiencing promoted math contextual problem‐solving performance.Structuring features enhanced problematized experiencing with math tasks. Implications for practice and/or policy: Teachers can integrate and facilitate game‐based math experiencing in class.Efforts should be made to make game‐based math tasks meaningful for students. [ABSTRACT FROM AUTHOR]

Background: Even though monitoring and control enactment are key aspects of self‐regulated learning (SRL), Adaptive learning technologies (ALTs) may reduce the need for learners to monitor and control their learning. Personalized dashboards are effective in supporting learners' monitoring and can potentially support control behaviour. Allowing learners to enact control over their learning process, seems to hold potential for increasing their motivation. Objectives: Therefore, this study's aim was to investigate the relation between control enactment and motivation. We examined how learners enacted control while learning with an ALT with personalized dashboards and examined the relation between learners' enactment of control and their motivation. Methods: Seventy‐eight primary school learners (Grade 5) participated. During the lesson, learners worked on mathematics in the ALT and concurrently were shown personalized visualizations that supported monitoring and enacting control over their learning process. Learners could enact control to change problems' difficulty to easy, medium, or hard. Motivation was measured before and after learning. Results: The SEM analyses showed that how learners enacted control was related to their motivation. Choosing difficult problems was related to more enjoyment and competence while choosing easy problems related to more pressure and tension. Learners who complied with the suggested difficulty level experienced less choice, but also less pressure/tension and more enjoyment and competence. Conclusions: These results provide avenues to account for broader learner characteristics like SRL and motivation to optimize learning. This way, hybrid systems in which control enactment is a shared responsibility of the system and learner, can be improved to support SRL development. Lay Description: What is currently known: Monitor and control enactment are key aspects of self‐regulated learning (SRL).Adaptive learning technologies may reduce the need for learners to monitor and control their learning.Personalized dashboards support learners' monitoring behaviour and can potentially also support control enactment.Enactment of control could positively affect learners' motivation. What does this paper add: There is a large variation in how learners enact control and whether they comply with the scaffold.Learners who chose more difficult problems experienced more enjoyment, while learners choosing easy problems, experienced more pressure.Learners complied with the scaffold, experienced less choice, but also less pressure and more enjoyment.This study provides avenues to account for broader learner characteristics like SRL and motivation to optimize learning. Practical implications: Support control enactment by actively involve learners in choice during the learning process.Offer monitor and enactment in conjunction, as learners can only make well‐founded choices if they can monitor their learning process.Intrinsically and extrinsically motivated learners showed different choice patterns and learning experience.It is important to have an understanding and monitoring of learners' motivation. [ABSTRACT FROM AUTHOR]

The present study empirically investigates how school-based bullying victimization affects students' learning outcomes, taking into consideration international and gender perspectives. The main objective of the present research is to provide a better understanding of the consequences of bullying victimization in the learning process of adolescents. We estimate a statistical function that empirically establishes the relationship between the students' outcomes in mathematics, reading, and science (output) and a wide set of explanatory variables (educational factors), one of which is that of being bullied. The present study uses a large sample of 612,004 students between 15 and 16 years old, attending 21,903 schools in 79 countries. The data come from the 2018 round of the Programme for International Student Assessment. The results indicate that bullying victimization is associated with decreases in academic achievement in mathematics, reading, and science. In addition, no relevant differences by gender are observed in reading and science but, other factors being equal, bullied males score less than bullied females in mathematics. [ABSTRACT FROM AUTHOR]