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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]

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]

Curriculum-based measurement (CBM) tools are increasingly administered through technology-based modalities such as computers and tablets. Two studies were conducted to examine whether students perform similarly on paper-based and tablet-based math fact probes. Ten students completed 1-min addition or multiplication math probes using a single-case multielement design. Students completed the probes using traditional paper and pencil, a tablet using a stylus to write the answer, or a tablet application using a keyboard to type the answer. Visual analysis of time series graphs showed that the majority of students performed better on the paper-based probes than on either the keyboard or stylus probes. Nonoverlap of all pairs (NAP) effect size measures indicated medium to large differences between paper and stylus probes and paper and keyboard probes but weak effects between stylus and keyboard probes. Discussion focuses on the implications for educators and the use of different CBM modalities for interindividual and intraindividual comparisons. [ABSTRACT FROM AUTHOR]

We attempt to identify the 25 most-cited statistical papers, providing some brief commentary on each paper on our list. This list consists, to a great extent, of papers that are on non-parametric methods, have applications in the life sciences, or deal with the multiple comparisons problem. We also list the most-cited papers published in 1993 or later. In contrast to the overall most-cited papers, these are predominately papers on Bayesian methods and wavelets. We briefly discuss some of the issues involved in the use of citation counts. [ABSTRACT FROM AUTHOR]

Summarizes the construction of paper folding. Method for approximating rational subdivisions or arbitrary angles and line segments; Angle-folding algorithm; Approximating angles, regular polygons and star polygons; Dissection of angles into equal parts.

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]

Research in psychology and education indicates that corrective feedback can be a powerful learning tool. We provide a developmental perspective to focus specifically on how corrective feedback influences learning in childhood (∼ages 3–11). Based on a systematic search, we review 44 empirical papers published between 1990 and 2022 examining the effects of corrective feedback on children's performance in the domains of literacy (n = 18), mathematics (n = 14), and problem solving (n = 12). Across these domains, we synthesize research on how children respond to lessons and practice with, versus without, corrective feedback to provide theoretical and practical insights into (1) the effectiveness of corrective feedback in early childhood, (2) the features of effective feedback messages at different ages, and (3) the role of individual learner differences. We make several novel recommendations with some focused on future research questions and others focused on ways teachers can provide effective feedback to children. [ABSTRACT FROM AUTHOR]

There have been many studies of the comparability of computer-administered and paper-administered tests. Not surprisingly (given the variety of measurement and statistical sampling issues that can affect any one study) the results of such studies have not always been consistent. Moreover, the quality of computer-based test administration systems has changed considerably over recent years, as has the computer-experience of students. This study synthesizes the results of 81 studies performed between 1997 and 2007. The estimated effect size across all studies was very small (-.01 weighted, .00 unweighted). Meta-analytic methods were used to ascertain whether grade (elementary, middle, or high school) or subject (English Language Arts, Mathematics, Reading, Science, or Social Studies) had an impact on comparability. Grade appeared to have no affect on comparability. Subject did appear to affect comparability, with computer administration appearing to provide a small advantage for English Language Arts and Social Studies test (effect sizes of .11 and .15, respectively), and paper administration appearing to provide a small advantage for Mathematics tests (effect size of -.06). [ABSTRACT FROM AUTHOR]

The article offers information on dynamical systems and irrational angle construction by paper-folding. Construction of rational angle to any desired accuracy by folding a strip of paper requires approximating method. The construction uses a periodic sequence composed of two types of folding moves, guided by number-theoretic properties of the angle's fractional representation. The number-theoretic scheme must be replaced by something new, the Folds and Switchfold prescription, in the construction of irrational angles.

The present study aimed at validating a computerized mental rotation task developed for use in functional Magnetic Resonance Imaging (fMRI) studies. Eighty-three females and 74 males completed the computerized task, two pencil-and-paper tests of mental rotation, and reported their high school grades in mathematics, English, and history. The computerized task involved the presentation of pairs of three-dimensional stimuli that differed in orientation by 0, 40, 80, 120, or 160 degrees. Results showed significant gender differences in favor of males in the three main tasks, although gender interacted with angle of rotation in the computerized task. Evidence for concurrent validity was obtained in the form of significant correlations between performance on tasks relevant to mental rotation (paper and pencil tests and mathematics grades), whereas discriminant validity was demonstrated by a lack of correlation with tasks deemed irrelevant to mental rotation (English and history grades). These findings support the use of our computerized mental rotation task as a valid measure of mental rotation abilities in fMRI studies. [ABSTRACT FROM AUTHOR]

This paper reports on the results of a study of English children's performance on a computer mathematics assessment compared with a pencil-and-paper assessment. Two matched samples of children were each assessed on one of two mathematics pencil-and-paper tests and assessed a month later on a cloned computer test. The performance scores were better on the computer tests than on the pencil-and-paper tests, although this was not statistically significant in every case. The paper goes on to discuss some of the differences between performance and approach to the question between the two media, and explores possible reasons for these differences. In conclusion, the computer tests were found to have an overall positive effect on children's performance, although not for every child and, in some instances, the computer assessment limited the way in which a question could be answered. [ABSTRACT FROM AUTHOR]

In this article we describe a method for determining the elastic constants for paper from a measured displacement field. Our model is based on the finite element method using quadrilateral elements. A method for finding the first and second order derivatives with respect to the unknown parameters plays a crucial role in the optimization process used to solve the inverse problems in this article. To reduce the influence of the noise of the input data, an efficient continuation method is used for the regularization term in the cost function. Some numerical results for synthetic data and measurement will verify the efficiency of our approach. [ABSTRACT FROM AUTHOR]

De Broglie's contribution in the Philosophical Magazine from 1924 is fascinating from many standpoints: for its moderate use of mathematics, the close connection to Einstein's special theory of relativity, and of course for the proposal of matter waves. We revisit this mostly speculative publication, which contributed crucially to the birth of quantum mechanics. [ABSTRACT FROM AUTHOR]

Integrating socioscientific issues (SSI) into education is gaining widespread adoption in classrooms due to its positive impact on student's critical thinking, environmental awareness, holistic knowledge and/or the idea of combining science and mathematics. This paper explores the idea of using comics as appropriate media for elementary school students to engage with SSI content. Because of the difficulties in integrating SSI into classrooms, SSI-based learning is more commonly applied in high school and higher education settings, with limited implementation in earlier education. To answer this gap, we developed comics that have SSI content for elementary schools. Comics are chosen as reliable tools for visualising and simplifying complex concepts and making SSI content more accessible and engaging. This paper describes our comics on earthquake-related issues in Indonesia and the principles that guided its design. SSI inherently involves multiple perspectives, so the integration brings together science, and mathematics within the one comic. In integrating different disciplines of comic content, we utilised the rule-of-five framework, widely employed to merge five representational models (experiential, verbal, numerical, visual, and symbolic) commonly used in developing content combining two or more different academic disciplines. [ABSTRACT FROM AUTHOR]

This article introduces some efficient generalized class of factor-type exponential imputation techniques and their corresponding estimators using auxiliary information. Generalized ratio, product, and dual to ratio type exponential estimators are the special cases of our suggested imputation techniques. Biases and mean squared error expressions are derived up to the first order of large sample approximations. The proposed imputation techniques can be viewed as efficient extensions of the work of Singh and Horn [Compromised imputation in survey sampling. Metrika. 2000;51(3):267–276. doi: 10.1007/s001840000054], Singh and Deo [Imputation by power transformation. Statist Papers. 2003;44(4):555–579. doi: 10.1007/BF02926010], Toutenburg and Srivastava [Amputation versus imputation of missing values through ratio method in sample surveys. Statist Papers. 2008;49(2):237–247. doi: 10.1007/s00362-006-0009-4], Kadilar and Cingi [Estimators for the population mean in the case of missing data. Commun Stat Theory Methods. 2008;37(14):2226–2236. doi: 10.1080/03610920701855020], Singh [A new method of imputation in survey sampling. Statistics. 2009;43(5):499–511. doi: 10.1080/02331880802605114], Gira [Estimation of population mean with a new imputation methods. Appl Math Sci. 2015;9(34):1663–1672] and Singh et al. [An improved alternative method of imputation for missing data in survey sampling. J Stat Appl Probab. 2022;11(2):535–543. doi: 10.18576/jsap]. Our proposed estimators are compared with these estimators, including the mean, ratio, and regression imputation techniques. Thereafter, a numerical illustration and simulation study are conducted for a comparative study using real and simulated data sets, and the demonstration shows that our suggested estimators are the most efficient estimators. [ABSTRACT FROM AUTHOR]

Discusses which shapes are possible and impossible to construct using origami. Algebraic characterization of origami; Construction process; Possibility to construct a line parallel to a given line through any given point; Construction of a cube with twice the volume of a given cube.

Emerging digital technologies offer a transformative potential to redefine learning tasks and many examples of this potential are now available. The scaling of the innovative pedagogies emerging from the research into widespread and sustainable practice, however, remains problematic. This paper addresses the issue of scaling by using Design Based Research (DBR), also known as Educational Design Research, within teacher professional development to reposition teachers' thinking about the place of digital tools in their teaching. Using a project seeking to support the use of new digital technologies to develop children's spatial reasoning as a 'worked example', this paper highlights how the bringing together of the knowledge of educational research and knowledge of teaching practice in DBR can provide a catalyst for epistemic change. The paper will argue that DBR positions the knowledge and practice objects of both research and teaching as 'epistemic' or 'not yet known' objects and, therefore, the legitimate focus of experimentation and reflection. [ABSTRACT FROM AUTHOR]

The majority of children in mainstream (no fee, poorly resourced, African language dominant) public schools in South Africa fall significantly behind curricular norms in mathematics by Grade 3; the early learning gap grows across time. The provision of quality instructional materials is a well-recognised component of effective strategies to improve early grade mathematics in low- and middle-income contexts. However, there has been little explication of what constitutes quality instructional materials, nor long-term design work to contribute theory to this instructional design challenge. Across 15 years, the author has been working in an education design hub with teacher educators and teachers in the rural Eastern Cape, with the goal of improving early grade mathematics. The gains in mathematics performance have been among the most significant reported in research literature. This paper presents the design principles emerging from the work. Engaging the theoretical layers discussed by diSessa and Cobb, the paper contributes to design theory by emphasising the relationship between explicit instructional assumptions and design principles, integrating four ontological categories (motive, pedagogy, language use and mathematical meaning-making). Since 2011, the Department of Basic Education has provided learner workbooks to support teaching and learning in foundation phase mathematics at system scale. It is hoped that this paper will contribute to the ongoing development of this vital national resource. The paper makes explicit instructional assumptions and design principles (available for critique, adaptation, and refinement), and provides a more nuanced framework through which to assess and improve materials across time. [ABSTRACT FROM AUTHOR]

There is a lack of research examining the use of curriculum-based measurements (CBMs) with special populations, particularly English Language Learners (ELLs). The current study used an alternating treatments single-case design with five Latinx ELL students to examine scores across three math fluency CBM modalities. One-minute probes using either traditional paper-pencil, iPad with a stylus, and iPad with a keyboard were alternated, with students taking two assessments per day. Visual analysis of time-series graphs suggested that most students answered more questions correctly on paper-pencil probes compared to either iPad modalities; scores on iPad with stylus were higher than iPad with keyboard for all students. Non-overlap of all pairs effect sizes indicated small to large differences between probe modalities. All students preferred the traditional paper-pencil probes to either iPad modality. Discussion focuses on the implications for educators using CBMs of different modalities for ELL students. [ABSTRACT FROM AUTHOR]

The Mathematical Sciences Department at Shenandoah University focused on increasing the participation of women in the mathematics program by fostering a welcoming learning community and promoting double majors. Data from the past decade is presented. During this time, the program saw an increase in women undergraduate mathematics majors from 11% to as high as 71%. This paper describes the initiatives taken to make these changes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper discusses several linear algebra activities designed to help enhance students' skills in collaborating, exploring mathematics, and linking together abstract and visual ways of approaching mathematics. Most of these activities are short, accessible, engaging, and easy to incorporate into any classroom. In addition, we discuss some questions instructors can ask themselves to design novel and engaging activities when constrained to teaching from a particular curriculum. [ABSTRACT FROM AUTHOR]

In order to learn the concept of statistical techniques one needs to run real experiments that generate reliable data. In practice, the data from some well-defined process or system is very costly and time consuming. It is difficult to run real experiments during the teaching period in the university. To overcome these difficulties, statisticians developed simple and very economical experiments, which can be performed in the class by the students. Stone studied the variation, bias, stability and statistical quality control through the Blind Paper Cutting (BPC) experiment. In this article, the Blind Paper Cutting experiment is demonstrated on the basis of basic principles of experiment design. A BPC experiment is performed considering different factors, and important factors to optimise the response are identified through complete factorial design. The appropriate response model using important factors has been constructed. [ABSTRACT FROM AUTHOR]

This editorial provides an introduction to the special issue, Infusing active learning into precalculus and calculus courses: Insights and lessons learned from mathematics departments in the process of change. We begin with providing the background for the special issue, including an overview of the current status of active learning in precalculus through calculus, what many of the papers in this issue mean by the term "active learning" (inquiry based mathematics education), and a brief overview of the literature on institutional change. We then offer an overview of each of the three issues, explaining how various papers relate to each other within each issue. We conclude the editorial with some reflections on the institutional changes efforts in light of the COVID-19 pandemic. [ABSTRACT FROM AUTHOR]

This paper set out to contribute to mathematics education research by elaborating on a methodology developed during a study, trying to understand, view and follow shifts in prospective teachers' discursive patterns. The methodology aims to illustrate and describe how prospective teachers adapt to the context of teaching through a flexible process. This flexible process is then described in the result as a narrative. It is argued that the methodology can be used in relation to different theoretical directions, such as research about beliefs, knowledge, or identity. Another contribution is that the methodology presented gives insights into bridging the gap between different analytical levels, micro and macro. With a theoretical foundation in 'Cultural Worlds' [Holland, D., Skinner, D., Lachicotte, W., & Cain, C. (1998). Identity and agency in cultural worlds. Harvard University Press.] the Social Semiotic approach of Systemic Functional Linguistics, SFL [Halliday, M., & Hasan, R. (1989). Language, context, and text: Aspects of language in a social-semiotic perspective (2nd ed.). Oxford University Press] is used as a methodological tool. SFL offers a toolkit that allows the analysis of meaning at the clause level to uncover how and why a speaker produces a particular wording rather than any other in a specific social practice. The paper aims to illustrate and describe how to go beyond findings in the micro-analysis and then present the result as a narrative case. [ABSTRACT FROM AUTHOR]

In the article, by virtue of Maclaurin's expansions of the arcsine function and its square and cubic, the authors (1) give a short proof of a sum formula of a Maclaurin's series with coefficients containing reciprocals of the Catalan numbers; (2) establish four sum formulas for finite sums containing the ratio or product of two central binomial coefficients or the Catalan numbers. The instant proof simplifies discussions in the journal papers: College Math. J. 43 (2012), no. 2, 141-146; Amer. Math. Monthly 121 (2014), no. 3, 267-267; Amer. Math. Monthly 123 (2016), no. 4, 405-406; Elem. Math. 71 (2016), no. 3, 109-121; and Mathematics 5 (2017), no. 3, Article 40, 31 pages. [ABSTRACT FROM AUTHOR]

This paper revisits Wittgenstein’s heavily criticized claims about the admissibility of inconsistencies in mathematics. It argues from the perspective of mathematics as a tool and combines material from the history and practice of engineering that makes Wittgenstein’s claims about contradiction and inconsistency look much more plausible. Against this background, the paper interprets passages from Wittgenstein, including his exchange with Alan Turing where he highlights that basic laws of thought are at issue and that reflecting on them would be “the most important thing” he has talked about. [ABSTRACT FROM AUTHOR]

This paper employs two scalar parameters to extend auxiliary function-based integral inequality into a new formulations, say a parametrised auxiliary function-based integral inequality. Using these formulations, the constituent signals are utilised more efficiently by exploiting the interaction between them to reduce conservatism. Numerical example for stability analysis of linear systems with time-varying delay shows the improved performance of the proposed new formulations in terms of maximum delay bounds and decision variables. [ABSTRACT FROM AUTHOR]

For a simple graph G on n vertices the Seidel Estrada index of G, denoted by $ SEE(G) $ SEE (G) , is defined as $ SEE(G)=\sum _{i=1}^ne^{\theta _i} $ SEE (G) = ∑ i = 1 n e θ i , where $ \theta _1,\ldots,\theta _n $ θ 1 , ... , θ n are the Seidel eigenvalues (the eigenvalues of the Seidel matrix) of G. In this paper, we find the maximum and minimum values of the Seidel Estrada index among all graphs with the fixed number of vertices. Our results confirm some conjectures on Seidel Estrada index of graphs that have been posed in [M. Hakimi-Nezhaad, M. Ghorbani, On the Estrada Index of Seidel Matrix, Mathematics Interdisciplinary Research5 (2020) 43–54]. [ABSTRACT FROM AUTHOR]

In this paper, we consider a singular Adams' inequality with logarithmic weights in the unit ball of $ \mathbb {R}^4 $ R 4 . Our results extend the results of Zhu and Wang [Adams' inequality with logarithmic weights in $ \mathbb {R}^4 $ R 4 . Proc Amer Math Soc. 2021;149(8):3463–3472] on Adams' inequality with logarithmic weights to singular case. Then, we study the existence of solutions for some weighted mean field equations, relying on variational methods and the singular Adams' inequality with logarithmic weights we previously established. [ABSTRACT FROM AUTHOR]

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

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

This paper proposes an account of why proof is the only way to acquire knowledge of some mathematical proposition's truth. Admittedly, non-deductive arguments for mathematical propositions can be strong and play important roles in mathematics. But this paper proposes a necessary condition for knowledge that can be satisfied by putative proofs (and proof sketches), as well as by non-deductive arguments in science, but not by non-deductive arguments from mathematical evidence. The necessary condition concerns whether we can justly expect that if the mathematical proposition is actually false, despite the evidence for its truth, then this fact has an explanation. [ABSTRACT FROM AUTHOR]

Provides a mathematical explanation on paperfolding. Some observations from paperfolding experiments; Theorems that explain the observations.

This paper outlines the difficulties with the current system of tiering in GCSE Mathematics exams, indicating both the problem of equality across tiers of the same grade and a particular problem in Mathematics, which with three tiers has a foundation tier on which it is not possible to gain a C grade.The authors outline a different system in which all candidates take basic papers on which all grades from G to C can be awarded and then an extension paper is available for the higher grades. This system has been tried out with a sample of pupils from a number of schools and a non-operational award was made. The authors describe the results of this and discuss potential difficulties with this system. Comparisons between the systems are made, showing that the established system of tiering is inherently unstable, while the proposed system, though not perfect, has much to commend it. [ABSTRACT FROM AUTHOR]

This paper deals with a less well-known connection between Thomas Reid's conception of common sense and pragmatism. The paper starts with an exposition of the different principles of common sense one can find in Reid's writings and a discussion of their epistemic status. The main focus of the paper is on what one may call 'Reid's dilemma of common sense'. I argue that Reid's writings not only present us with a dilemma of common sense but that they also offer a way out of the dilemma, one that is pragmatist in a certain sense. I also discuss the question whether the proposed way out can work. [ABSTRACT FROM AUTHOR]

Mathematics is not just the queen of the sciences; it permeates through art, commerce, and in fact, every aspect of modern life. However, while we as mathematicians see beauty in the mathematical way of thinking and problem-solving, our students tend to think of mathematics as a set of rules and abstract computations. Our pleasure of doing mathematics usually does not transfer over to our students. In this paper, we describe two liberal arts general education courses which seek to develop a broad appreciation of mathematics for students who may not require any technical mathematics course for their academic major or chosen career path. We present mathematics as it relates to everyday life, with the goal of improving student appreciation of mathematics. [ABSTRACT FROM AUTHOR]

In Australia, there have been a growing number of nature-based early childhood education initiatives [Alme, H., and M. A. Reime. 2021. "Nature Kindergartens: A Space for Children's Participation." Journal of Outdoor and Environmental Education 24: 113–131]. Research into early years' nature education internationally remains under-theorised particularly in STEM teaching and learning. The nature or bush kindergarten programme (often referred to as 'bush kinders' in the Australian context), is one such programme where nature play and education occur. This paper considers how children's mathematical thinking develops through their time spent in bush kinder settings. Using an ethnographic lens, this longitudinal study is the first of its type in Australia with a focus on STEM in bush kinders. In this paper, eight 'powerful mathematical ideas' are used to analyse how educators can approach teaching mathematics with only what nature provides. The paper reports one main finding, that bush kinders provide opportunities for children through educator support to build mathematical understandings through nature play. Drawing on fieldwork data and the analysis of research literature, this paper contributes to the conceptualisation of mathematics in early childhood nature play and bush kinder programmes. [ABSTRACT FROM AUTHOR]

This paper presents a research framework for investigating the role of language use in mathematics learning. The paper draws on the wider M2EID study, which explores whether differences in languages (English and Irish) and their use by bilingual mathematical students have a differential impact on their mathematics meta-level developments. A primary consideration of the M2EID study was to design a rigorous research framework to support such complex, real-world educational research. In particular, the study explored how to integrate the varied theoretical constructs underpinning this type of research and how to design the most appropriate data capture and analysis procedures. It is focused on adapting a discursive approach to examining bilingual students' mathematical thinking. The resultant LCM2 research framework outlines four phases for designing research within the combined fields of linguistics and mathematics. Exemplars from the M2EID study are provided. [ABSTRACT FROM AUTHOR]

Developing mathematical connections for pupils continues to be at the forefront of educational policies worldwide. One strategy suggested to support the connections pupils make is the idea of developing “coherence”. Research regarding coherence has increased within mathematics education, however, the term is used widely. It therefore becomes necessary for coherence to be further conceptualised. In this systematic scoping review, five databases were searched for literature on the topic of coherence in school-based mathematics education. A total of 11,587 pieces of literature were extracted. Following further screening, 35 papers were reviewed. The findings suggest that there is limited consensus regarding the conceptualisation of coherence, leading to fragmented perceptions across the literature. This paper presents a framework for coherence based on the TIMSS curriculum model to support international comparisons of coherence and provide clarity for mathematics education researchers and school colleagues when considering which aspect of coherence they are addressing. [ABSTRACT FROM AUTHOR]

In the paper 'Composition operators on weighted Bergman spaces of Dirichlet series. J Math Anal Appl. 2015;426:340–363', Bailleul completely characterized the boundedness of composition operators on weighted Bergman spaces of Dirichlet series for the case of symbols with $ c_0\ge 1 $ c 0 ≥ 1. But the sufficient conditions for the other case $ c_0=0 $ c 0 = 0 were unsolved. In this paper, we follow this line and study the boundedness of composition operators on weighted Bergman spaces of Dirichlet series for the case $ c_0=0 $ c 0 = 0. Moreover, we also obtain the compact characterizations of composition operators with $ c_0\geq 1 $ c 0 ≥ 1. [ABSTRACT FROM AUTHOR]

This paper describes the implementation of a STEM scholarship program which utilized a holistic approach to providing a multi-dimensional student support system. The program has been successful in encouraging and supporting women in Applied Mathematics and Computer Science by offering a diverse suite of extracurricular opportunities, actively engaging them in organized events, research projects, and participation in STEM communities, and helping them achieve higher GPAs and shorter times to graduation. The supported women also benefitted from close mentoring relationships with the faculty mentors. The program emphasized the development of empowering settings for women's engagement and achievement, which act to sustain and expand interest in mathematics and computing, and thereby help them to see themselves as future professionals in the field. [ABSTRACT FROM AUTHOR]

We exploit the existence and non-existence of positive solutions to the eigenvalue problem driven by the nonhomogeneous fractional $ p\& q $ p &q Laplacian operator with indefinite weights \[ \left(-\Delta_p\right)^{\alpha}u + \left(-\Delta_q\right)^{\beta}u = \lambda\left[a \left|u\right|^{p-2}u + b \left|u\right|^{q-2}u \right]\quad{\rm in}\ \Omega, \] (− Δ p) α u + (− Δ q) β u = λ [ a | u | p − 2 u + b | u | q − 2 u ] in Ω , where $ \Omega \subseteq \mathbb {R}^N $ Ω ⊆ R N is a smooth bounded domain that has been extended by zero. We further show the existence of a continuous family of eigenvalues in the case $ \Omega =\mathbb {R}^N $ Ω = R N and $ b\equiv 0 $ b ≡ 0 a.e. Our approach relies strongly on variational Analysis, in which the Mountain pass theorem plays the key role. Due to the lack of spatial compactness and the embedding $ \mathcal {W}^{\alpha, p}\left (\mathbb {R}^N\right) \hookrightarrow \mathcal {W}^{\beta, q}\left (\mathbb {R}^N\right) $ W α , p (R N) ↪ W β , q (R N) in $ \mathbb {R}^N $ R N , we employ the concentration-compactness principle of P.L. Lions [The concentration-compactness principle in the calculus of variations. The limit case. II, Rev Mat Iberoamericana. 1985;1(2):45–121]. to overcome the difficulty. Our paper can be considered as a counterpart to the important works [Alves et al. Existence, multiplicity and concentration for a class of fractional $ p\& q $ p &q Laplacian problems in $ \Bbb R^N $ R N , Commun Pure Appl Anal, 2019;18(4):2009–2045], [Benci et al. An eigenvalue problem for a quasilinear elliptic field equation. J Differ Equ, 2002;184(2):299–320], [Bobkov et al. On positive solutions for $ (p,q) $ (p , q) -Laplace equations with two parameters, Calc Var Partial Differ Equ, 2015;54(3):3277–3301], [Colasuonno and Squassina. Eigenvalues for double phase variational integrals, Ann Mat Pura Appl (4), 2016;195(6):1917–1956], [Papageorgiou et al. Positive solutions for nonlinear Neumann problems with singular terms and convection, J Math Pures Appl (9), 2020;136:1–21], [Papageorgiou et al. Ground state and nodal solutions for a class of double phase problems, Z Angew Math Phys, 2020;71:1–15], and may have further applications to deal with other problems. [ABSTRACT FROM AUTHOR]

In this paper, we explore the roles of gender social norms in explaining the gender gap in maths test scores across the entire distribution. Applying generalized quantile regression models, we show that gender-equal cultural norms eliminate the gender gap in maths scores at the top of the distribution. Moreover, this effect is concentrated among students in the higher grade level. An investigation of the underlying mechanisms shows that girls from more gender-equal regions are less likely to hold maths-specific stereotypes and are likely to receive more attention from maths teachers. Additionally, girls from more gender-equal regions tend to perceive that parents have higher educational aspirations for them and are more confident about their future. Our paper provides compelling evidence that policy initiatives aiming at fostering egalitarian gender norms could serve as powerful tools to alleviate the gender gap in maths at the top of the distribution. [ABSTRACT FROM AUTHOR]

D'Arcy Thompson (1860–1948) is most remembered for his influential book On Growth and Form (1917), which looked to maths to explain why biological creatures take the shapes that they take. In January 1917, a few months before this book was released, Thompson had a letter to the editor published in Nature titled 'Stability in Flight'. Using this paper, and the response to it, as a basis, this article will investigate Thompson's relationship with mathematics, uncovering his ideas on an ideological hierarchy of subjects, where mathematics informs biology, but the reverse case is not true. It will also explore the ideas of flight Thompson discusses in the article, from the aeronautical physics paper which inspired Thompson, to the ideas on modern ornithology which agree with his work. [ABSTRACT FROM AUTHOR]

The paper addresses the potential relationships between shared authority in mathematics classrooms and students' mathematical reasoning. Even though tensions and challenges related to shared authority are explicated in the literature, there are few examples of how these issues play out in mathematics teaching. We investigate the case of a mathematics teacher attempting to share authority as well as applying several moves recognized as supporting meaningful student learning. Data has been collected in a fourth-grade Norwegian classroom and is analyzed by means of open coding, inspired by literature. We identify the moves used by the teacher, and we rank these moves along two dimensions: (1) their potential to support mathematical reasoning and (2) their potential for sharing authority. From this, we uncover how a teacher's work of orchestrating mathematical discussions involves moves in all four quadrants, and we discuss how the interplay of moves affects the authority structures and the collaborative reasoning in the classroom. [ABSTRACT FROM AUTHOR]

Among the problems identified at Technical and Vocational Education and Training (TVET) colleges, low achievement in mathematical subjects is the most prominent one. This paper documents a qualitative case study undertaken at TVET College in Gauteng with the purpose of exploring the National Certificate Vocational (NC(V)) Level 4 students' errors and associated misconceptions when answering optimisation questions in differential calculus. The participants were 60 students who were registered for a course in mathematics. Data were generated from the written student responses to two non-routine test items followed by interviews. Using the Newman error hierarchical model to analyse the data, it was discovered that students errors were conceptual and procedural as well as systematic and non-systematic. The literature also alluded to instructional approaches as some of the causes of students' misconceptions and the errors and that interventions should target students as well as the instructors. [ABSTRACT FROM AUTHOR]