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Automatic test paper design is critical in education to reduce workloads for educators and facilitate an efficient teaching process. However, current designs fail to satisfy the realistic teaching requirements of educators, including the consideration of both test quality and efficiency. This is the main reason why teachers still manually construct tests in most teaching environments. In this paper, the quality of tests is quantitatively defined while considering multiple objectives, including a flexible coverage of knowledge points, cognitive levels, and question difficulty. Then, a model based on the technique of linear programming is delicately designed to explore the optimal results for this newly defined problem. However, this technique is not efficient enough, which cannot obtain results in polynomial time. With the consideration of both test quality and generation efficiency, this paper proposes a genetic algorithm (GA) based method, named dynamic programming guided genetic algorithm with adaptive selection (DPGA-AS). In this method, a dynamic programming method is proposed in the population initialization part to improve the efficiency of the genetic algorithm. An adaptive selection method for the GA is designed to avoid prematurely falling into the local optimal for better test quality. The question bank used in our experiments is assembled based on college-level calculus questions from well-known textbooks. The experimental results show that the proposed techniques can construct test papers with both high effectiveness and efficiency. The computation time of the test assembly problem is reduced from 3 hours to 2 seconds for a 5000-size question bank as compared to a linear programming model with similar test quality. The test quality of the proposed method is better than the other baselines.

In this paper, through the collection and analysis of data, the art of Guangling paper-cutting is theoretically researched, and the general features and shapes of Guangling paper-cutting are summarized. In order to overcome the limitations of traditional algorithms in the extraction of features of Guangling paper-cutting, the combination of spatial pyramid matching and context-dependent histogram methods are used to extract the shape features of paper-cutting images with stronger differentiation. The support vector machine is used to solve the problem of recognizing and classifying the image patterns in the digitized display. The design of the digital promotion of the Shanxi Guangling paper-cutting brand is carried out. Research variables are designed to analyze the effect of digital transformation and promotion of paper-cutting brands. The results show that the discrepancy of Guangling paper-cutting features extracted by the algorithm in this paper is very low, the e1 difference is maintained within 0.1, and the total recognition rate of SVM on Guangling paper-cutting features can reach 88.06%, and the overall effect is more satisfactory, and the regression equation of the influence of paper-cutting = −0.807+0.111*history+0.122* style+0.234*paper-cutting+0.216*display+0.136 * linkage, and propose strategies to enhance the influence of paper-cutting brand. The technical methods used in this study guarantee the quality of the digital transformation of Guangdong paper-cutting from the source.

To deeply analyze the performance of paper-cutting elements in interior space design, this paper explores the artistic expression of paper-cutting elements. The BIM model is constructed based on the TVL algorithm, and a noise-reducing style migration method with an additional total variable loss function is used to fuse the texture features of a specific paper-cutting style so that the paper-cutting texture is generated in the target object area more intensively. The algorithm is supplemented with a U-shaped network structure to obtain the mask map of the target object, modify and expand the ScanNet training data set, and input a content map and a style map to generate the stylized paper cutout image automatically. The results show that compared with other elements, the stability of paper-cut elements reaches 96.31%, the image smoothness reaches 89.34%, and the retention of significant regions reaches 93.26%. In modern design, the peak signal-noise of paper-cut elements improved by 13.418d on average, the structural similarity also improved by 0.34807, and the recognition rate of paper-cut elements in the furnishing category reached 95%. Applying paper-cut art in interior space design can give interior furnishing design better visual effects, provide inspiration and ideas for interior space design innovation, and contribute to improving aesthetics.

In this paper we extend the SuperHyperAlgebra, SuperHyperGraph, SuperHyperTopology, SuperHyperSoft Set, endowed with SuperHyperOperations, SuperHyperAxioms, and SuperHyperFunctions, to the most general form of structure, from our real world, called SuperHyperStructure in any field of knowledge. A practical application of the SuperHyperStructure is presented at the end. The prefix “Hyper” [Marty, 1934] stand for the codomain of the functions and operations to be P(H), or the powerset of the set H. While the prefix “Super” [Smarandache, 2016] stands for using the Pn (H), n ≥ 2, or the n-th PowerSet of the Set H {because the set (or system) 𝐻 (that may be a set of items, a company, institution, country, region, etc.) is organized in sub-systems, which in their turn are organized in sub-sub-systems, and so on} in the domain and/or codomain of the functions and operations.

In the realm of Chinese traditional arts, paper-cutting symbols embody deep-seated aesthetic and cultural values. Within the framework of artificial intelligence, the fusion of these conventional symbols with contemporary pattern design through intelligent reconstruction processes promotes innovation in modern design. This paper introduces a novel pattern feature extraction algorithm specifically designed for identifying and extracting the essence of traditional paper-cutting art. Utilizing Deep Convolutional Generative Adversarial Networks (DCGAN), an automated method for generating woven patterns is developed, integrating conventional motifs with modern design elements. Additionally, a segmentation model based on DeepLabV3+ semantics is constructed to facilitate this integration. The study focuses on the fusion of traditional paper-cutting symbols with fabric patterns, providing a new direction for textile design research. The empirical evaluation involved seven experimenters who predominantly favored patterns that blended abstract and traditional styles, with the average style rating exceeding 3.2. Moreover, the color performance analysis of the reconstructed fabric patterns across five regions showed color difference values greater than 4, indicating superior color fidelity. These findings underscore the potential of combining AI-driven techniques with traditional art forms to enhance and revolutionize modern design practices.

The study of metadiscourse word resources is an important way to reveal academic knowledge constructs and genre features in English papers. This paper selects intra- and interdisciplinary English academic papers as data samples, and the text representation is based on the vector space model. The text similarity is calculated using the word movement distance model to complete the clustering based on the density peak, and then the semantic annotation of metadiscourse verb patterns is performed using the conditional random field. Then, the intra- and interdisciplinary metadiscourse annotations are compared to analyze the variation of verb patterns. The intra-disciplinary variation of metadiscourse verb patterns was mainly found using attitude markers, where the log-likelihood ratios of 48.56, 30.25, and 35.64 were obtained for affirmative, critical, and critical declarative attitudes, respectively. In interdisciplinary studies, basic disciplines preferred to use verb patterns as transitions, while applied disciplines preferred to express the author’s point of view. The study of metadiscourse verb patterns effectively enriches the linguistic resources in academic English teaching and deepens the understanding of the characteristics of disciplinary essay genres.

In an era overwhelmed by academic big data, students grapple with identifying academic papers that resonate with their learning objectives and research interests, due to the sheer volume and complexity of available information. This study addresses the challenge by proposing a novel academic paper recommendation system designed to enhance personalized learning through the nuanced understanding of academic social networks. Utilizing the theory of social homogeneity, the research first constructs a sophisticated academic social network, capturing high-order social relationships, such as co-authorship and advisor–advisee connections, through hypergraph modeling and advanced network representation learning techniques. The methodology encompasses the development and integration of a hypergraph convolutional neural network and a contrastive learning framework to accurately model and recommend academic papers, focusing on aligning with students’ unique preferences and reducing reliance on sparse interaction data. The findings, validated across multiple real-world datasets, demonstrate a significant improvement in recommendation accuracy, particularly in addressing the cold-start problem and effectively mapping advisor–advisee relationships. The study concludes that leveraging complex academic social networks can substantially enhance the personalization and precision of academic paper recommendations, offering a promising avenue for addressing the challenges of academic information overload and fostering more effective personalized learning environments.

This investigation delves into the evolving patterns and regional variances in industry-academia collaboration (IAC) within Functional Nucleic Acids (FNAs) research. Analyzing publications and patents from 1990 to 2021, we dissected IAC at individual and collective levels, documenting the count and share of IAC endeavors, key partners, and regional differences. Results indicate a rising trend in IAC publications and collaborating institutions, while patent trends display a mix of increases, decreases, and steady states. The United States leads in IAC activities, correlating with its prowess in scientific research and technological innovation. Notably, regional discrepancies in IAC are mainly due to intra-regional variations, with Asia and Europe experiencing the most pronounced disparities.

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.)

The aim of this pilot study is to evaluate the relevance of the use of history in mathematics education. This paper presents an experiment carried out in France with sixth-grade students (n=108) in which an ancient number system is used, an approach that is commonly suggested in French sixth-grade textbooks but has previously been unassessed. Based on the data of a pretest and a post-test surrounding an activity on an ancient Chinese numeration system, a statistical analysis using Rasch modeling shows a specific added value of the history of mathematics for students with low abilities in mathematics. For these students, a significant increase in observed abilities of +0.67 logit in mean is measured with a large effect size (Cliff delta +0.52). This effect is then weighted by considering the regression to the mean (RTM) effect, leading to a value around +0.14 logit in mean and a negligible effect size (Cliff delta +0.10). So, this pilot study shows the important effect of RTM, which suggests a very strong rebalancing of students' results. In the last part of the paper, we discuss how RTM can nonetheless be positively interpreted in this specific context where students' disorientation is one of the purposes of history in mathematics education.

This project explored what constitutes "ethical practice of mathematics". Thematic analysis of ethical practice standards from mathematics-adjacent disciplines (statistics and computing), were combined with two organizational codes of conduct and community input resulting in over 100 items. These analyses identified 29 of the 52 items in the 2018 American Statistical Association Ethical Guidelines for Statistical Practice, and 15 of the 24 additional (unique) items from the 2018 Association of Computing Machinery Code of Ethics for inclusion. Three of the 29 items synthesized from the 2019 American Mathematical Society Code of Ethics, and zero of the Mathematical Association of America Code of Ethics, were identified as reflective of "ethical mathematical practice" beyond items already identified from the other two codes. The community contributed six unique items. Item stems were standardized to, "The ethical mathematics practitioner…". Invitations to complete the 30-min online survey were shared nationally (US) via Mathematics organization listservs and other widespread emails and announcements. We received 142 individual responses to the national survey, 75% of whom endorsed 41/52 items, with 90-100% endorsing 20/52 items on the survey. Items from different sources were endorsed at both high and low rates. A final thematic analysis yielded 44 items, grouped into "General" (12 items), "Profession" (10 items) and "Scholarship" (11 items). Moreover, for the practitioner in a leader/mentor/supervisor/instructor role, there are an additional 11 items (4 General/7 Professional). These results suggest that the community perceives a much wider range of behaviors by mathematicians to be subject to ethical practice standards than had been previously included in professional organization codes. The results provide evidence against the argument that mathematics practitioners engaged in "pure" or "theoretical" work have minimal, small, or no ethical obligations., (© 2024. The Author(s).)

The International Sirius Mathematics Center, located on the Black Sea coast, was founded in 2019 by the Talent and Success Foundation for organizing mathematical conferences and other events promoting the development of mathematics in Russia. In 2024, the Center has acquired its own Russian-language journal for publication of original research papers by participants of conferences held at the Center. The authors are invited to submit papers to the journal at https://ef.msp.org/submit/sirius [ABSTRACT FROM AUTHOR]

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.)

Mathematics is often treated as different from other disciplines, since arguments in the field rely on deductive proof rather than empirical evidence as in the natural sciences. A mathematical paper can therefore, at least in principle, be replicated simply by reading it. While this distinction is sometimes taken as the basis to claim that the results in mathematics are therefore certain, mathematicians themselves know that the published literature contains many mistakes. Reading a proof is not easy, and checking whether an argument constitutes a proof is surprisingly difficult. This article uses peer review of submissions to mathematics journals as a site where referees are explicitly concerned with checking whether a paper is correct and therefore could be published. Drawing on 95 qualitative interviews with mathematics journal editors, as well as a collection of more than 100 referee reports and other correspondence from peer review processes, this article establishes that while mathematicians acknowledge that peer review does not guarantee correctness, they still value it. For mathematicians, peer review 'adds a bit of certainty', especially in contrast to papers only submitted to preprint servers such as arXiv. Furthermore, during peer review there can be disagreements not just regarding the importance of a result, but also whether a particular argument constitutes a proof or not (in particular, whether there are substantial gaps in the proof). Finally, the mathematical community is seen as important when it comes to accepting arguments as proofs and assigning certainty to results. Publishing an argument in a peer-reviewed journal is often only the first step in having a result accepted. Results get accepted if they stand the test of time and are used by other mathematicians. [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.)

Interest in socioeconomic differences in academic motivation has been longstanding. However, previous research has often treated both low- and high-SES students as homogenous groups. This study aims to address this gap by investigating the developmental trajectory profiles of mathematics motivation during early adolescence, with a focus on variations within and across SES groups. Multigroup latent class growth analysis was used on a sample of 3718 early adolescents in China (initial M age was 9.40 ± 0.52 years; 48.0% girls) across 2 years from grades 4 through 6. The analysis identified three distinct self-determined mathematics motivation trajectory profiles within each SES group: a good-quality profile (i.e., initially high autonomous but low controlled), a high-quantity profile (i.e., initially high both autonomous and controlled), and a low-quantity profile (i.e., initially low both autonomous and controlled). A greater proportion of low-SES students were observed within the low-quantity profile than within the good-quality profile. The study found that the failure-is-enhancing view was a protective factor against two relatively maladaptive motivational trajectory profiles (i.e., high-quantity profile and low-quantity profile), irrespective of socioeconomic background. These findings emphasize the importance of implementing motivational interventions for early adolescents that consider both structural factors (e.g., socioeconomic backgrounds) and psychological factors (e.g., failure beliefs), to foster students' academic development., (© 2024. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)

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.)

Purpose: This paper defines and assesses student learning patterns under the influence of problem-based learning (PBL) and their classification into a reasonable minimum number of classes. Study utilizes PBL implemented in an undergraduate Statistics and Operations Research course for techno-management students at a private university in India. Design/methodology/approach: Study employs an in situ experiment using a conceptual model based on learning theory. The participant's end-of-semester GPA is Performance Indicator. Integrating PBL with classroom teaching is unique instructional approach to this study. An unsupervised and supervised data mining approach to analyse PBL impact establishes research conclusions. Findings: The administration of PBL results in improved learning patterns (above-average) for students with medium attendance. PBL, Gender, Math background, Board and discipline are contributing factors to students' performance in the decision tree. PBL benefits a student of any gender with lower attendance. Research limitations/implications: This study is limited to course students from one institute and does not consider external factors. Practical implications: Researchers can apply learning patterns obtained in this paper highlighting PBL impact to study effect of every innovative pedagogical study. Classification of students based on learning behaviours can help facilitators plan remedial actions. Originality/value: 1. Clustering is used to extract student learning patterns considering dynamics of student performances over time. Then decision tree is utilized to elicit a simple process of classifying students. 2. Data mining approach overcomes limitations of statistical techniques to provide knowledge impact in presence of demographic characteristics and student attendance.

Understanding the concepts related to real function is essential in learning mathematics. To determine how students understand these concepts, it is necessary to have an appropriate measurement tool. In this paper, we have created a web application using 32 items from conceptual understanding of real functions (CURF) item bank. We conducted a psychometric analysis using Rasch model on 207 first-year students. The analysis showed that CURF is a dependable and valid instrument for measuring students' CURF. The test is uni-dimensional; all items are consistent with the construct and have excellent item fit statistics. The results indicate that the items are independent of each other and unbiased towards the gender and high school background of the students.

STEM education is on demand more than ever as the workforce relies on 21st century skills and STEM disciplines. This paper presents a framework (IMS-TEAM) for integration of mathematics and science with the use of technology and modeling in an authentic context. The activity based on this framework is designed for and implemented with forty-four 8th grade students in Turkey. The study was conducted to investigate the impact of the activity as well as the IMS-TEAM framework. A qualitative methodology was utilized. Data analysis revealed that different components of our conceptual framework fostered the integration of mathematics and science affecting the nature of students' engagement with the activity. Different frameworks are required to be adapted to different environments with the consideration of learners and teachers. Future research investigating the effectiveness of IMS-TEAM framework adapted to different content and disciplines would provide more evidence on the effectiveness of the framework.

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.)

Proving mathematical theorems at the olympiad level represents a notable milestone in human-level automated reasoning 1-4 , owing to their reputed difficulty among the world's best talents in pre-university mathematics. Current machine-learning approaches, however, are not applicable to most mathematical domains owing to the high cost of translating human proofs into machine-verifiable format. The problem is even worse for geometry because of its unique translation challenges 1,5 , resulting in severe scarcity of training data. We propose AlphaGeometry, a theorem prover for Euclidean plane geometry that sidesteps the need for human demonstrations by synthesizing millions of theorems and proofs across different levels of complexity. AlphaGeometry is a neuro-symbolic system that uses a neural language model, trained from scratch on our large-scale synthetic data, to guide a symbolic deduction engine through infinite branching points in challenging problems. On a test set of 30 latest olympiad-level problems, AlphaGeometry solves 25, outperforming the previous best method that only solves ten problems and approaching the performance of an average International Mathematical Olympiad (IMO) gold medallist. Notably, AlphaGeometry produces human-readable proofs, solves all geometry problems in the IMO 2000 and 2015 under human expert evaluation and discovers a generalized version of a translated IMO theorem in 2004., (© 2024. The Author(s).)

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This paper aims to investigate whether online private supplementary education, also known as shadow education, can alleviate educational inequality and what types of mechanisms can help alleviate it. We investigate this using an online learning platform dataset (3,603 anonymous students from China) with additional data from multiple sources and employ geospatial analyses to measure students' socioeconomic, regional and rural/urban inequalities. We find that taking part in online education narrows the performance gap in mathematics between privileged and unprivileged students in terms of school status and regional disparity in China. Theoretically, two micro-level mechanisms explain the alleviating differences: (1) equal access mechanism: students from lower city tiers and low-status schools show greater score improvement when having equal access to online education; (2) equal quality mechanism: students from rural regions improve their in-class rankings more substantially if they receive equal quality online education with the same tutoring and learning environment alongside urban students. This study comprehensively looks at the different effects of two mechanisms of online education--equal access and equal quality--for alleviating various types of inequality. Thus we speak to both educational inequality and digital inequality theory, finding that equal access to online education is not enough for rural students, as they also need access to classes of equal educational quality with their urban counterparts.

This systematic review aims to provide a complementary to existing synopses of the state-of-the-art of mathematics education research on proof and proving in both school and university mathematics. As an organizing framework, we used Cohen et al.'s triadic conceptualization of instruction, which draws attention not only to the main actors of the didactical process (i.e., the Teacher and Students) and the Content around which the actors' work is organized (herein, content related to proof and proving), but also to the relationships among the actors and the content. Out of the 103 papers we reviewed, almost half fell in the Student-Content category, which is consistent with the existence of a substantial number of frameworks, methods, and research findings related to students' engagement with proof and proving. About a quarter of the papers fell in the Student–Teacher-Content category, which reflects an emphasis on viewing instructional practice in proof and proving in a holistic, systemic way. Only few papers fell in the categories that did not include Content in them, namely, the categories of Student, Teacher, and Student–Teacher; this suggests mathematics education research on proof and proving has a strong disciplinary identity, which potentially differentiates it from other mathematics education research strands. About a fifth of the papers were oriented towards 'breaking ground' through making an explicit theoretical and/or methodological contribution (Student–Teacher-Content and Content were the main categories where such contributions appeared), whilst the majority of the papers were focused on 'building ground' through elaborating or employing existing methodological and/or theoretical approaches. [ABSTRACT FROM AUTHOR]

Working with approximations is a common practice in physics. This paper presents an exploratory study of student understanding of some of the elementary aspects of approximations encountered in college physics. For this purpose, a questionnaire (a set of 14 multiple-choice questions) was developed to probe how students dealt with these aspects in a variety of contexts. The questionnaire was finalized after a trial of its pilot version on 7 students on the basis of their written scripts and interviews. After content validation by three external experts, the test was administered to a sample of 141 senior undergraduate physics students from a diverse set of colleges and national institutes. Data analysis reveals several significant student pitfalls in the topic related principally to (i) the identification of a dimensionless ratio to characterize an approximation, (ii) the notion of the order of approximation and consistent handling of a problem up to the required order, and (iii) the notion of the order of infinitesimal in calculus-based derivations. The findings are of direct pedagogic relevance.

To assess the integration of information and communication technologies (ICTs) in teaching and learning, a new construct for ICT competence was developed by the Programme for International Student Assessment (PISA) in 2022. The framework for ICT assessment involves four major dimensions; access to ICT, use of ICT, students' ICT competencies, and subject-related ICT use. In this paper, we analysed this ICT assessment in terms of validity construction of test scores with data from PISA 2018 and investigated ICT competence in relation to the variables of mathematics, science, and reading literacy. The analyses were based on public data from PISA 2018 for Turkey (N = 6890). After removal of univariate and multivariate outliers from the Turkish sample, factor analysis, correlation analysis, and structural equation modelling were performed on 5438 data items. In the study, we confirmed the four-dimensional structure of ICT competence for the Turkish sample. In this study, the construct validity of the PISA 2018 application ICT test was verified using the Turkish sample. The ESCS variable was included as a control variable in the analyses due to its significant impact on the relevant variables. The analysis showed that the mathematical literacy scores of the PISA 2018 Turkish students were positively low affected by the availability of ICT, negatively low affected by the entertainment of ICT, and positively low affected by the interest and perceived competence in ICT, use of ICT for educational purposes at school and outside school, and the use of ICT related to the subject. Considering the ICT variables that affected the PISA 2018 students' science literacy scores; the entertainment of ICT and the interest and perceived competence in ICT significantly low affected the students' use of ICT on the subject. On the other hand, the availability of ICT negative significantly low affect their science literacy scores. While the entertainment of ICT negatively low affected the science literacy scores, interest and perceived competence in ICT and use of ICT for educational purposes at school and outside school positively low affected the students' use of ICT on the subject. Finally, when we look at the ICT variables that low affected the students' reading literacy scores; and use of ICT for educational purposes at school and outside school and the interest and perceived competence in ICT significantly positive low affected the use of ICT on the subject. On the other hand, the availability of ICT negative significantly low affect reading literacy scores. While the entertainment of ICT negatively low affected reading literacy scores; interest and perceived competence in ICT positively low affected the use of ICT on the subject.

QR decomposition is widely used for solving the least squares problem. However, existing materials about it may be too abstract for non-mathematicians, especially STEM students, and/or require serious background in linear algebra. The paper describes theoretical background and examples of GNU Octave compatible MATLAB scripts that give relatively simple but complete explanations about how to use QR decomposition for the least squares problem solution. Only basic knowledge of linear algebra and calculus are required. Both Givens rotations and Householder reflections usage for the linear least squares problem were considered. It was shown that the algorithm based on Givens rotations is even easier to program than explicit formation of the normal equations with subsequent usage of Gaussian elimination.

The University of Minnesota Talented Youth Mathematics Program (UMTYMP) is a selective, five-year accelerated mathematics program for students in grades 6-12. During the program, students take college mathematics courses on University of Minnesota campuses, starting with algebra and continuing through logic and proofs, linear algebra, and multivariable calculus. The majority of UMTYMP students come from two demographic groups: White and Asian/Asian American. In 2020, we surveyed UMTYMP students to understand the impact of model minority stereotypes (MMS) on Asian/Asian American students, particularly girls, who are labeled as "gifted" and/or "talented." In this paper, we reveal the preliminary results of this study, discuss their implications, and provide recommendations for addressing the MMS in mathematics programs.

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

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

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

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

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

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

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

Leveraging artificial intelligence (AI), this study revolutionizes examination management and education in universities by developing an intelligent system encompassing comprehensive management, pre-examination activities, scheduling, and preparation. The system also features a quality management component for educational outcomes. An enhanced genetic algorithm introduces an adaptation function to optimize intelligent grouping, facilitating effective exam paper distribution. Applied at Y University, our innovative approach significantly refines exam paper difficulty (ranging between 0.5016 and 0.5581) and differentiation (0.3845 to 0.4596), showcasing the intelligent algorithm’s effectiveness in exam management and contributing valuable insights to educational research.

The paper responds to the need for understanding trends and gaps in extant research related to adult education in mathematics and numeracy, given changing skill demands and skill gaps regarding adults, and related policy, theorizing, and practice trends. This paper presents the results of a scoping review of recent empirical research related to adult education in mathematics and numeracy, published in 22 selected journals from 2019 to 2022, including 15 journals in adult education and seven in mathematics education. The results show that only 39 relevant empirical studies were found among over 2300 research papers reviewed, and that few of those focus on practice-related of adult education in mathematics and numeracy. The results provide quantitative evidence suggesting that the field of adult numeracy education is under-researched, and help to identify gaps in empirical research involving adult numeracy, including on emerging topics such as on modeling and critical interpretation. The results also point to research opportunities that can strengthen theorizing and practice in both mathematics education and adult numeracy education. [ABSTRACT FROM AUTHOR]

In this true story, one mathematics major supports another in an unexpected way. [ABSTRACT FROM AUTHOR]

This article describes the outcomes of a faculty partnership between a math professor and a composition professor to improve the final paper in a research-focused senior capstone math course. Much attention has been paid in recent years to the importance of undergraduate research experiences and how to best create and support such endeavors. However, little space has been dedicated to helping math faculty design and scaffold writing assignments to support their students' development as scholars. We describe how our partnership took place, the changes we made to existing assignments and the creation of new ones, and an assessment of our efforts completed by an interdisciplinary group of faculty and students, which showed marked improvement in the areas of information literacy, critical thinking, and quality of writing. [ABSTRACT FROM AUTHOR]

The interrogation of often unintended practices of marginalisation has gained focus in research on mathematics teaching and mathematics teacher education throughout the last decades. In this introductory survey paper, work against marginalisation in these contexts of mathematics education is viewed in terms of work towards equity, diversity and inclusion. Based on this interpretation, we present a framework on awareness and practice of equity, diversity and inclusion in mathematics teaching and mathematics teacher education research. We then use this framework and a survey method of mapping review to identify and comment on a selection of studies. As a result, we illustrate three research moves towards equity, diversity and inclusion, in the form of interconnected themes: (1) Widening the understanding of the mathematics and the mathematics education curricula (2) Improving the practice and discussion of mathematics teaching (3) Unpacking ideologies in mathematics teaching and mathematics teacher education. We finally examine the themes and the special issue papers together to foreground commonalities regarding awareness of discriminatory discourses and practices of creating and distributing opportunities for all groups, including those historically and currently marginalised. Despite the important increase of equity-driven principles of awareness, we conclude that mathematics education research on teaching and on teacher education needs more examples of practices whose development has been proved to challenge marginalisation. [ABSTRACT FROM AUTHOR]

ISO 15189 requires laboratories to estimate the uncertainty of their quantitative measurements and to maintain them within relevant performance specifications. Furthermore, it refers to ISO TS 20914 for instructions on how to estimate the uncertainty and what to take into consideration when communicating uncertainty of measurement with requesting clinicians. These instructions include the responsibility of laboratories to verify that bias is not larger than medically significant. If estimated to be larger than acceptable, such bias first needs to be eliminated or (temporarily) corrected for. In the latter case, the uncertainty of such correction becomes part of the estimation of the total measurement uncertainty. If small enough to be acceptable, bias becomes part of the long term within laboratory random variation. Sources of possible bias are (not limited to) changes in reagent or calibrator lot variation or calibration itself. In this paper we clarify how the rationale and mathematics from an EFLM WG ISO/A position paper on allowable between reagent lot variation can be applied to calculate whether bias can be accepted to become part of long-term imprecision. The central point of this rationale is to prevent the risk that requesting clinicians confuse changes in bias with changes in the steady state of their patients. [ABSTRACT FROM AUTHOR]

This paper deals with a new stochastic method to solve Lotka's Law with higher degree of Newton-Cotes Quadrature Rule as an alternate method to existing solution of the value determination of the constant part of the power law; so far, M.L. Pao gave a solution with an equation to determine the area under the curve with numerical integration rule with degree=1 which is also known as Trapezoidal Rule. Here, next higher degree 2, popularly known as Simpson's 1/3 rule at closed interval [x 1,] has been used to establish a deterministic equation form to solve authors' productivity realized through Lotka's Law. Re-estimating the value of C with higher degree quadrature rule is very crucial as the probability of inclusion of more area and exclusion of unnecessary area under the curve is more precise. Another area of investigation is the determination of p value (Pao determined p=20), i.e. whether p=20 can be altered? Or equation derived through Simpson's 1/3 rule, whether it can give a minimal residual error beyond p=20. This paper is dedicated to build up a mathematical equation to solve the constant value(C) of the Lotka's law equation as well as enlighten all these investigating points. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with the identity 1R, and let R* be the multiplicative group of units in R. An element a ∈ R* is called an exceptional unit if there exists a b ∈ R* such that a + b = 1R. We set R** to be the set of all exceptional units in R. In this paper, we consider the residue-class ring Zn. For any positive integers n, s, and c ∈ Zn, let Ns(n, c) :=#{(x1, ..., xs) ∈ (Z** n ) s : x1 + ... + xs(n, c). Later on, Yang and Zhao (Monatsh. Math. 182 (2017)) extended Sander’s theorem to finite terms by using exponential sum theory. In this paper, using matrix theory, we present an explicit formula for N2(n, c). Later on, Yang and Zhao (Monatsh. Math. 182 (2017)) extended Sander’s theorem to finite terms by using exponential sum theory. In this paper, using matrix theory, we present an explicit formula for Ns(n, c). This extends and improves earlier results. [ABSTRACT FROM AUTHOR]

The goal of this paper is to establish new Maximum Principles for parabolic equations in the framework of mixed local/nonlocal operators. In particular, these results apply to the case of mixed local/nonlocal Neumann boundary conditions, as introduced by Dipierro, Proietti Lippi, and Valdinoci [Ann. Inst. H. Poincaré C Anal. Non Linéaire 40 (2023), pp. 1093–1166]. Moreover, they play an important role in the analysis of population dynamics involving the so-called Allee effect, which is performed by Dipierro, Proietti Lippi, and Valdinoci [J. Math. Biol. 89 (2024), Paper No. 19]. This is particularly relevant when studying biological populations, since the Allee effect detects a critical density below which the population is severely endangered and at risk of extinction. [ABSTRACT FROM AUTHOR]

This paper describes a Lesson Study in which in-service mathematics secondary-school teachers, collaborating with researchers, involve grade 10 students in tessellation problems. The data are collected by an experiment carried out in the context of the "Liceo Matematico" project, with three volunteer teachers. The experiment goal was to craft a collaborative design of the research lesson between teachers and researchers. The research aim of the paper is to examine the use of Lesson Study in the institutional and cultural context of Italian secondary school with the use of Cultural Transposition as a theoretical framework. The research is qualitative with idiographic aims, based on video research. The educational aim of the research is to provide a solid basis for a revamped in-service teacher education first in the context of the project, then in curricular context. Semiotic mediation is used to provide, within Lesson Study, the conceptual framework for teachers and researchers collaborative design of the research lesson. The results show that Lesson Study, as a foreign practice, is an opportunity for teachers to confront their teaching practices, to enrich their professional development, resulting in more awareness on their didactical action in and outside the classroom. [ABSTRACT FROM AUTHOR]

This paper illustrates how years 1 and 2 students were guided to engage in data modelling and statistical reasoning through interdisciplinary mathematics and science investigations drawn from an Australian 3-year longitudinal study: Interdisciplinary Mathematics and Science Learning (https://imslearning.org/). The project developed learning sequences for 12 inquiry-based investigations involving 35 teachers and cohorts of between 25 and 70 students across years 1 through 6. The research used a design-based methodology to develop, implement, and refine a 4-stage pedagogical cycle based on students' problem posing, data generation, organisation, interpretation, and reasoning about data. Across the stages of the IMS cycle, students generated increasingly sophisticated representations of data and made decisions about whether these supported their explanations, claims about, and solutions to scientific problems. The teacher's role in supporting students' statistical reasoning was analysed across two learning sequences: Ecology in year 1 and Paper Helicopters in year 2 involving the same cohort of students. An explicit focus on data modelling and meta-representational practices enabled the year 1 students to form statistical ideas, such as distribution, sampling, and aggregation, and to construct a range of data representations. In year 2, students engaged in tasks that focused on ordering and aggregating data, measures of central tendency, inferential reasoning, and, in some cases, informal ideas of variability. The study explores how a representation-focused interdisciplinary pedagogy can support the development of data modelling and statistical thinking from an early age. [ABSTRACT FROM AUTHOR]