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The main purpose of this study is to investigate mathematics teachers' mathematical thinking process while they are constructing the length of [cube root of 2] by paper folding. To carry out this aim, two teachers--who are PhD. students--were interviewed one by one. During the construction, it was possible to observe the consolidation process of Pythagorean and Thales Theorem. All interviews were videotaped and analyzed through descriptive methods, according to abstraction in context, characteristics of consolidation and mathematical habits of mind. It was found that both two teachers constructed the knowledge of Pythagorean and Thales Theorems before the study and also these knowledges were consolidated. In addition, it was determined that these two approaches (abstraction in context and mathematical habits of mind) were close and corroborated each other. Moreover, consolidation process corroborated mathematical habits of mind.

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.

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.

Paper-cut elements in the design of boat space can effectively improve the homogenisation tendency of existing boat space design, effectively enhance the characteristics of traditional Chinese culture and enrich the development ideas of boat space design. Therefore, based on the Chinese folk art of paper cutting, this paper combines theoretical analysis and empirical research to deeply analyse the artistic expression of paper-cut elements in the spatial design of boats. This paper mainly studies the artistic integration of paper-cut elements in the decorative design of boats and the artistic integration of paper-cut elements in the practical design of boats. Through the calculation and analysis of the sparse autoencoder algorithm model, it can be seen that the decorative integration of paper-cut elements in wallpaper is 82%, which is higher than that of traditional materials (24%). The integration of paper-cut elements in the space design of cabins and guest rooms is as high as 97% and 94%, respectively, which is far better than the integration of traditional materials in the space design of cabins and guest rooms. This shows that the application of folk paper-cut elements to the space design of boats not only highlights the theme of boats but also enhances the cultural value of boats.

English is a universal language and is widely used. In order to deepen the cognition of language, this paper proposes to analyse the variation of metadiscourse verb patterns in English academic papers from within and between disciplines. By comparing the metadiscourse chunks used in various disciplines, it is concluded that there are obvious differences in the verb types of the subject papers. Analysing various identification algorithms of verb types, it is obtained that the combination of the word movement distance (WMD) model and the R&L density peak clustering algorithm is the best. Using the R&L density peak clustering, identification parameters are easy to determine, and when combined with the WMD model to calculate the similarity of words, it improve the accuracy of verb pattern clustering. By comparison, it is proved that the accuracy of the algorithm combining the WMD model and R&L density peak clustering reaches 30.06%, and the effect of identifying verb pattern variation is the best.

In 1921 Mellin published a Comptes Rendu paper computing the principal solution of a polynomial using generalized hypergeometric functions of its coefficients. He used an integral transform nowadays bearing his name. Slightly over three pages, the paper is written in French in a terse style befitting the language. This article makes Mellin’s landmark result accessible to people who are not experts in hypergeometric functions and complex analysis by deriving detailed proofs that were omitted in Mellin’s paper.

This paper focuses on the Southern African Association for Research in Mathematics, Science and Technology Education's (SAARMSTE's) role as a platform supporting research dissemination and connecting researchers in early grades mathematics (EGM) in the Southern African region. A review of the Long Papers in SAARMSTE over the last 20 years supports the finding of the other review papers in this Special Issue: that there has been substantial growth of attention to EGM since 2013. However, two distinctions are marked when looking at conference papers rather than journal papers. Firstly, there is a particularly large expansion of work in the last 5 years, with a broadening base of participation in this work. Second, looking across all the formats of conference presentations indicates SAARMSTE's role in supporting and building EGM as a key focus of research attention, and bringing together regional and international groups with interests in this area. Given that conference proceedings usually offer a broader picture of emerging interests than journal papers, we reflect on the range of foci of attention within EGM in the SAARMSTE Proceedings, and trends within this. These trends also help us to point to areas that are likely to be of key interest in the next decade. [ABSTRACT FROM AUTHOR]

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.

Multicultural or integrative art education helps students understand themselves and the diverse changing visual world around them. This article highlights the the tradition of Chinese joss paper and shows how it can be added to the repertoire of a multicultural art curriculum or an integrative art curriculum that enables the teacher to infuse social studies, math, and science by offering probable connections embedded in this artistic practice. Exploring the context and content of Chinese joss paper through both artistic and spiritual lenses, the authors first examine this tradition and its origins and discuss its visual characteristics and the associated meanings of both traditional and modern joss paper. Next, they suggest several classroom activities for high school students to give them a better understanding and appreciation of this cultural practice.

In this paper, we consider a robust combinatorial optimization problem with uncertain weights and propose an uncertainty set that generalizes interval uncertainty by imposing lower and upper bounds on deviations of subsets of items. We prove that if the number of such subsets is fixed and the family of these subsets is laminar, then the robust combinatorial optimization problem can be solved by solving a fixed number of nominal problems. This result generalizes a previous similar result for the case where the family of these subsets is a partition of the set of items.

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.

As the number of computerized curriculum-based measurement (CBM) tools increases, it is necessary to examine whether or not student performance can generalize across a variety of test administration modes (i.e., paper or computer). The purpose of this study is to compare math fact fluency on paper versus computer for 197 upper elementary students. Students completed identical sets of probes on paper and on the computer, which were then scored for digits correct, problems correct, and accuracy. Results showed a significant difference in performance between the two sets of probes, with higher fluency rates on the paper probes. Because decisions about levels of student support and interventions often rely on measures such as these, more research in this area is needed to examine the potential differences in student performance between paper-based and computer-based CBMs.

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.

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

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.)

This paper focuses on pattern generalisation as a way to introduce young students to early algebra. We build on research on patterning activities that feature, in their work with algebraic thinking, both looking for sameness recursively in a pattern (especially figural patterns, but also numerical ones) and conjecturing about function-based relationships that relate variables. We propose a new approach to pattern generalisation that seeks to help children (grades 2 and 3) work both recursively and functionally, and to see how these two modes are connected through the notion of variable. We argue that a crucial change must occur in order for young learners to develop a flexible algebraic discourse. We draw on Sfard's (2008) communication approach and on Châtelet's (2000) notion of the "virtual" in order to pursue this argument. We also root our analyses within a new materialist perspective that seeks to describe phenomena in terms of "material entanglement," which include, in our classroom research context, not just the children and the teacher, but also words, gestures, physical objects and arrangements, as well as numbers, operations and variables.

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.

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.

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]

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

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.

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.

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.

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]

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

Perception is an individual's ability to respond, interpret, and distinguish a view of any information to a stimulus. So the aims of this study was to find out: (1) students' perceptions of the use of an equation editor in writing mathematical notation as assignments for calculus class I papers, (2) students' perceptions of writing calculus I paper assignments using the manual method (handwriting). The research subjects consisted of 16 students majoring in Extension Informatics Engineering (afternoon class) Semester I. The type of research was descriptive qualitative. Data collection techniques are interviews. The analysis stage is to analyze the results of the interviews. The results of the study concluded that: (1) 11 (eleven) students agreed to use the equation editor in writing calculus I paper assignments,the rest were still confused about the use of the equation editor; and (2) all students do not agree if the paper is written using the manual method (handwriting) because the results are not neat and take a long time.

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.

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

Paper waste in the mockups design with regular, irregular, and amorphous patterns is a critical problem in digital printing presses. Paper waste reduction directly impacts production costs, generating business and environmental benefits. This problem can be mapped to the two-dimensional irregular bin-packing problem. In this paper, an iterated local search algorithm using a novel neighborhood structure to detect overlaps between amorphous shapes is introduced. This algorithm is used to solve the paper waste problem, modeled as one 2D irregular bin-packing problem. The experimental results show that this approach works efficiently and effectively to detect and correct the overlaps between regular, irregular, and amorphous figures.

This Special Issue comprises the first collection of papers submitted by the Editorial Board Members (EBMs) of the journal Mathematical and Computational Applications (MCA), as well as outstanding scholars working in the core research fields of MCA [...]

This issue of featured papers from 2020 is related to the study of symmetry phenomena in various different fields, but mainly in theoretical physics [...]

This editorial is a short review of papers accepted in the Mathematics and Symmetry/Asymmetry section in 2020–2021 about the symmetry methods [...]

Abstract In a recently published theorem on the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings, Tang et al. (J. Inequal. Appl. 2015:305, 2015) studied a uniformly convex and 2-uniformly smooth real Banach space with the Opial property and best smoothness constant κ satisfying the condition 0 < κ < 1 2 $0

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.

This Special issue contains top-tier physics-related and mathematical research, among other topics, written by scholars who are well-known in their field [...]

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.

Mathematics anxiety can be defined as negative feelings towards mathematics and mathematical operations in general. Math anxiety is seen in many students, and even in parents. In fact, parents' own anxiety regarding mathematics may lead to their children experiencing angst over the subject as well. This can be a problem considering parents are considered one of the basic components of education and have important responsibilities to guide the education process of their children. Mathematical literacy is one of the research topics that have come into prominence in recent years due to PISA. Consequently, the purpose of this study is to determine the relationship between the parents' mathematical literacy self-efficacy and mathematics anxieties. Additionally, through examining the participation of parents in mathematic teaching during the COVID-19 pandemic, it is hoped to better understand their views and methodologies. All participants in this study are parents themselves. The study is designed with an explanatory sequential design among mixed method research designs. The grade in which the students are educated does not make any difference in the self-efficacy and anxiety perceptions of the parents regarding their mathematics literacy. Also, the parents' mathematical literacy self-efficacy and anxiety levels were high. [Paper presented at International Congress of Educational Research (13th, Hatay, Turkey, Sep 3-6, 2020).]

The administration of A/B exams usually involves the use of items. Issues arise when the pre-establishment of a question bank is necessary and the inconsistency in the knowledge points to be tested (in the two exams) reduces the exams ‘fairness’. These are critical for a large multi-teacher course wherein the teachers are changed such that the course and examination content are altered every few years. However, a fair test with randomly participating students should still be a guaranteed subject with no item pool. Through data-driven decision-making, this study collected data related to a term test for a compulsory general course for empirical assessments, pre-processed the data and used item response theory to statistically estimate the difficulty, discrimination and lower asymptotic for each item in the two exam papers. Binary goal programing was finally used to analyze and balance the fairness of A/B exams without an item pool. As a result, pairs of associated questions in the two exam papers were optimized in terms of their overall balance in three dimensions (as the goals) through the paired exchanges of items. These exam papers guarantee their consistency (in the tested knowledge points) and also ensure the fairness of the term test (a key psychological factor that motivates continued studies). Such an application is novel as the teacher(s) did not have a pre-set question bank and could formulate the fairest strategy for the A/B exam papers. The model can be employed to address similar teaching practice issues.