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The ability to compare symbolic numerical magnitudes correlates with children's concurrent and future mathematics achievement. We developed and evaluated a quick timed paper-and-pencil measure that can easily be used, for example in large-scale research, in which children have to cross out the numerically larger of two Arabic one- and two-digit numbers (SYMP Test). We investigated performance on this test in 1,588 primary school children (Grades 1-6) and examined in each grade its associations with mathematics achievement. The SYMP Test had satisfactory test-retest reliability. The SYMP Test showed significant and stable correlations with mathematics achievement for both one-digit and two-digit comparison, across all grades. This replicates the previously observed association between symbolic numerical magnitude processing and mathematics achievement, but extends it by showing that the association is observed in all grades in primary education and occurs for single- as well as multi-digit processing. Children with mathematical learning difficulties performed significantly lower on one-digit comparison and two-digit comparison in all grades. This all suggests satisfactory construct and criterion-related validity of the SYMP Test, which can be used in research, when performing large-scale (intervention) studies, and by practitioners, as screening measure to identify children at risk for mathematical difficulties or dyscalculia.

Predicting stock prices is contained in the basic approach is fundamental and technical analysis which is needed by entrepreneurs who invest their capital, this analysis is to determine the company's financial performance and must continue to be carried out, to carry out this analysis we use the help of several financial ratios where several types of ratios Return on Assets, Debt to Equity Ratio, Return on Equity, and Book Value per Share are some examples. The authors applied a quantitative descriptive approach to companies listed on the Indonesia Stock Exchange in the Pulp & Paper sector for this study. According to the Correlation and Regression tables, all of the variables ROA, ROE, DER, and BVS have an effect on stock prices, but the stock session obtained on the variables ROA, ROE, and DER has a very significant effect on stock prices but has no significant effect on stock prices on the BVS variable. So in the long term the company must implement one of two policies, namely low solvency means using less debt than own capital and a low solvency policy will not cause high interest expenses to be borne by the company so that it will affect growth.

This study aims at understanding the role of the tools chosen throughout the processes of solving a non-routine mathematical problem and communicating its solution. In assuming that problem-solving is a synchronous activity of mathematization and expression of mathematical thinking we take our proposed Mathematical Problem Solving with Technology (MPST) model to analyze the processes of solving-and-expressing-problems. Resorting to qualitative methods for data collection and analysis, we report on the case of an 8th grader working on a covariation problem to examine the role that paper-and-pencil and digital tools play in the development of a conceptual model of the situation. We found that the resources used throughout the solving-and-expressing activity influenced the depth of the conceptual model developed, within a process of progressive mathematization. Whereas paper-and-pencil led to the emergence of a conceptual model based on exploring particular cases, the digital transformation of the solution was triggered by the process of communicating its mathematical justification and expanded the previous model. Moreover, the complexity of this activity is evidenced by its multiple sequences of processes. Finally, the integration process seems crucial as the concomitant use of technological and mathematical resources precedes major advancements in the expansion of the conceptual model.

We construct a two discrete parameter family of compact minimal surfaces embedded in the Berger sphere which may be considered as the analogue of the helicoidal Karcher-Scherk surfaces.

Frank and Wolfe’s celebrated conditional gradient method is a well-known tool for solving smooth optimization problems for which minimizing a linear function over the feasible set is computationally cheap. However, when the objective function is nonsmooth, the method may fail to compute a stationary point. In this work, we show that the Frank–Wolfe algorithm can be employed to compute Clarke-stationary points for nonconvex and nonsmooth optimization problems consisting of minimizing upper-$C^{1,\alpha }$ functions over convex and compact sets. Furthermore, under more restrictive assumptions, we propose a new algorithm variant with stronger stationarity guarantees, namely directional stationarity and even local optimality.

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.

Standards are a set of guidelines or criteria used to ensure consistency, quality, safety, and compatibility in products, services, and processes [...]

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.)

This contribution focuses on paper models of architectural surfaces, in particular on some roofing systems describable by developable ones. Drawing on an interdisciplinary approach, between Architecture and Mathematics, potentialities and criticalities of these models in explicitly conveying Geometry are investigated, in relation to educational and communicative tasks, both when they are used in a direct, tangible way, and when the use is mediated by images generated by them (thus indirect); we discuss on the possibility for models and images to communicate their explicit and implicit Geometries. The main issue discussed is that a material or analytical description unequivocally allows to grasp all the peculiarities of geometrical shapes, while other representations are subject to critical selection of data and are therefore affected by subjective interpretations; similarly, the translation of the physical model into images is the result of choices which emphasize certain object peculiarities over others and is thus less objective. Hence the importance of the physical model (as well as its digital counterparts) which, even if not used directly, can be complementary to a content that, alone, would be partial and/or misleading.

Abstract Very recently Jain et al. (J. Inequal. Appl. 2022:73, 2022) introduced the concept of multivalued F-contraction with altering distance function and investigated the existence of best proximity points for this class of mappings. In this article we prove that the existence of best proximity points for multivalued F-contraction non-self mappings can be obtained from the corresponding fixed point result for multivalued F-contraction self mappings, and so the main conclusion due to Jain et al. is not a real generalization of fixed point theory.

A scheme for the integration of $ \, {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)} $-type fractional differential equations (FDEs) is presented in this paper. The approach is based on the expansion of solutions to FDEs via fractional power series. It is proven that $ \, {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)} $-type FDEs can be transformed into equivalent $ \left(\, {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)}\right)^n $-type FDEs via operator calculus techniques. The efficacy of the scheme is demonstrated by integrating the fractional Riccati differential equation.

From time to time, we hear in the news about a breach or attack on some well-known companies as just news, but it is a serious problem because it is the privacy of citizens, their money in trade and managing their businesses and projects. In this paper, we offer a review of the honey encryption planner. Honey Encryption is the encryption system that ensures flexibility versus the brute-force attack through the provision of plain reasonable text, but false for each key is invalid utilized by a trespasser to decrypt a message, two key areas are open it is difficult to create a compelling message trap that's perfect enough to deceive the striker even when he believes that he has the message in its original form. The next problem, the typo issue, where a valid phony plain text seem to a lawful user when he accidentally enters the wrong key. Our goal is to have more satisfaction disguised tricks that are perfect enough to prevent a trespasser from getting the original message, We also need new security methods because the attackers are looking for new ways to attack the systems, so we proposed a new way to protect messages and passwords well and difficult to break and take all the possibilities of attack, including the brute-force, and then the data is hidden in an image with a public secret key.

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).)

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.)

Recently, the systems of e-learning are improved technologically and the led to the emergence of e-learning systems that reached the level of adaptation to students. Through which, it changed the entire education system during the Internet era. Nonetheless, the use of rule-based, assumption-based, and network-based method have some vital methodologies used to implement learner models across adaptive learning systems. The so common way to structure the learner models approaches rely on the personalization and user modelling. However, personalization and user modeling found out to be the best approaches-not only in developing students' talents but also in allowing students to take their own learning direction and making sure that they are using their potential to the fullest. The mismatching in viewpoints and perceptions between teachers and technicians along with a lack of appropriate technical knowledge have been identified as some of the major challenges affecting the learner model development. the main objective of this article is to show the use of different approaches through the recent scholars’ in implementing learner models within adaptive e-learning systems. Moreover, approaches and challenges in implementing learner models are also described

In school, at least in the US, we were taught to multiply by hand according to a standard algorithm. Most people find that algorithm difficult to use, and many children fail to learn it. We propose a new way to make sense of this difficulty: to treat explicit computation as perceptually supported physical and mental action. Based on recent work in neuroscience, we trace the flow of arithmetic information to emphasize demands on visual working memory and attention. We predict that algorithms that make moderate demands on memory and attention will work better than others that make stronger demands. We suggest that the judicious use of spatial schemas can reduce such cognitive demands. Experimental evidence from children in an inner-city school supports this claim. Our work suggests new ways to think about instruction. The goal should be to minimize demands that present obstacles and maximize instead what human eyes, bodies, and brains do well. (Contains 7 figures and 2 tables.)

We investigated the influence of mental imagery expertise in 15 pen and paper role-players as an expert group compared to the gender-matched control group of computer role-players in the difficult Vandenberg and Kuse mental rotation task. In this task, the participants have to decide which two of four rotated figures match the target figure. The dependent measures were performance speed and accuracy. In our exploratory investigation, we further examined midline frontal theta band activation, parietal alpha band activation, and parietal alpha band asymmetry in EEG as indicator for the chosen rotation strategy. Additionally, we explored the gender influence on performance and EEG activation, although a very small female sample section was given. The expected gender difference concerning performance accuracy was negated by expertise in pen and paper role-playing women, while the gender-specific difference in performance speed was preserved. Moreover, gender differences concerning electro-cortical measures revealed differences in rotation strategy, with women using top-down strategies compared to men, who were using top-down strategies and active inhibition of associative cortical areas. These strategy uses were further moderated by expertise, with higher expertise leading to more pronounced activation patters, especially during successful performance. However, due to the very limited sample size, the findings of this explorative study have to be interpreted cautiously.

Toilet paper (TP) composition and physical characteristics were used to model scientific investigations that combined several "National Science Education Standards." Experiments with TP permitted the integration of TP history, societal change resulting from invention, mathematics (including geometry and statistics), germ theory, and personal hygiene practices, along with microbiology techniques.

Let $ R $ be a ring with identity. The commuting graph of $ R $ is the graph associated to $ R $ whose vertices are non-central elements in $ R $, and distinct vertices $ A $ and $ B $ are adjacent if and only if $ AB = BA $. In this paper, we completely determine the automorphism group of the commuting graph of $ 2\times 2 $ matrix ring over $ \mathbb{Z}_{p^{s}} $, where $ \mathbb{Z}_{p^{s}} $ is the ring of integers modulo $ p^{s} $, $ p $ is a prime and $ s $ is a positive integer.

Investigating the research trends within a scientific domain by analyzing semantic information extracted from scientific journals has been a topic of interest in the natural language processing (NLP) field. A research trend evaluation is generally based on the time evolution of the term occurrence or the term topic, but it neglects an important aspect—research publication latency. The average time lag between the research and its publication may vary from one month to more than one year, and it is a characteristic that may have significant impact when assessing research trends, mainly for rapidly evolving scientific areas. To cope with this problem, the present paper is the first work that explicitly considers research publication latency as a parameter in the trend evaluation process. Consequently, we provide a new trend detection methodology that mixes auto-ARIMA prediction with Mann–Kendall trend evaluations. The experimental results in an electronic design automation case study prove the viability of our approach.

Simonas Vainbergas, a teacher of Jewish primary schools in prewar Lithuania (1894?), was one of few his colleagues that actively collaborated with Lithuanian pedagogical journals. He published in them 11 papers in didactics of mathematics about teaching mathematics at primary schools. The said papers helped young teachers of primary schools to improve their qualification. There is a great probability that S. Vainbergas was a victim of holocaust.

Recently, there has been a growing emphasis on basic number processing competencies (such as the ability to judge which of two numbers is larger) and their role in predicting individual differences in school-relevant math achievement. Children's ability to compare both symbolic (e.g. Arabic numerals) and nonsymbolic (e.g. dot arrays) magnitudes has been found to correlate with their math achievement. The available evidence, however, has focused on computerized paradigms, which may not always be suitable for universal, quick application in the classroom. Furthermore, it is currently unclear whether both symbolic and nonsymbolic magnitude comparison are related to children's performance on tests of arithmetic competence and whether either of these factors relate to arithmetic achievement over and above other factors such as working memory and reading ability. In order to address these outstanding issues, we designed a quick (2 minute) paper-and-pencil tool to assess children's ability to compare symbolic and nonsymbolic numerical magnitudes and assessed the degree to which performance on this measure explains individual differences in achievement. Children were required to cross out the larger of two, single-digit numerical magnitudes under time constraints. Results from a group of 160 children from grades 1-3 revealed that both symbolic and nonsymbolic number comparison accuracy were related to individual differences in arithmetic achievement. However, only symbolic number comparison performance accounted for unique variance in arithmetic achievement. The theoretical and practical implications of these findings are discussed which include the use of this measure as a possible tool for identifying students at risk for future difficulties in mathematics.

Very recently, P. Saha et al. [A global optimality result in probabilistic spaces using control function. Optimization. 2021;70:2387–2400] studied the existence of best proximity points for Banach type ϕ-proximal contractions in the framework of Menger probabilistic metric spaces. In this paper, we present a simple proof of their main existence result which is based on a fixed point theorem for ϕ-contractive self-mappings in complete Menger PM-spaces due to B.S. Choudhury and K. Das [A new contraction principle in Menger spaces. Acta Math Sin. 2008;24:13791386]. [ABSTRACT FROM AUTHOR]

Computer-based interventions are being used more in the classroom. Student responses to these interventions often contribute to decisions making regarding important outcomes. It is important to understand the effect of these interventions within the context of the intervention as well as across related context. The current study examined the generalization of math fact fluency gains resulting from a computer-based intervention to paper-and-pencil performance. A total of 31 second grade students completed fluency drills on the computer or with paper and pencil. Pretest-posttest performance on both computer and paper and pencil for all students was evaluated using a doubly multivariate repeated measure ANOVA. Results indicated that gains achieved on the computer did not generalize to paper-and-pencil performance., (Copyright © 2012 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.)

The human capability to react or adapt to upcoming changes strongly relies on the ability to forecast them [...]