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This paper presents a semester-long bottle design project for an undergraduate Numerical Analysis course. Students implement numerical methods in MATLAB to design and 3D print a bottle. Employing mathematical methods to compute features of their designs enhances students' understanding of numerical techniques in design applications. Student feedback highlights the project's efficacy in demonstrating the intersection of mathematics and design, fostering creativity, and instilling a deeper appreciation for mathematical principles in real-world contexts. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we will consider parallel summable operators on Hilbert space. Operators A and B are said to be parallel summable if and . We will prove that the parallel sum can be represented as A: B = A(A + B)† B without additional assumption of the closedness of the range of the operator A + B. Furthermore, we will derive the equalities C (A : B) = C A : C B and (A : B) : C = A : (B : C ) under weaker conditions than the ones represented in [X. Tian, S. Wang, C. Deng, On parallel sum of operators, Linear Algebra Appl. 603 (2020) 57–83] and [W. Luo, C. Song, Q. Xu, The parallel sum for adjointable operators on Hilbert C* -modules, Acta Math. Sin. 62 (2019) 541–552]. Finally, we will extend some recent result for Hermitian positive semi-definite matrices to bounded linear operators. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a two-species reaction–diffusion competition model with Gompertz growth, where the intrinsic growth rates and carrying capacities of environments are heterogeneous. At firstly, assuming two competing species only admit different diffusive rates, we show that 'slower diffuser prevails', which is consistent with the well-known result in Dockery J, Hutson V, Mischaikow K, Pernarowski M. [The evolution of slow dispersal rates: a reaction–diffusion model. J Math Biol. 1998;37(1):61–83; Hastings A. Can spatial variation alone lead to selection for dispersal? Theor Popul Biol. 1983;24:244–251]. Then, for the "weak competition" case, we establish a prior estimate, which combined with the theory of monotone dynamical system and spectral analysis implies that the model admits a unique coexistence steady state, which is globally asymptotically stable. Finally, for the "strong–weak competition" case, we give the expression of critical competition intensity and the weak competitor will be wiped out. [ABSTRACT FROM AUTHOR]

Even prior to COVID-19, there had been an increase in the use of technology in undergraduate mathematics education to support the development of mathematical understanding and skill, and to enhance the student learning environment. Technology-enhanced resources can be used to provide formative assessment which can help students identify gaps in their knowledge and point towards appropriate action. In this paper, we report on the evaluations of a number of technology-enhanced resources that used formative assessment techniques and were provided for students attending non-specialist first-year undergraduate mathematics modules in Ireland. Analysis of the evaluations and consultation with literature identified 12 decisive factors that encourage students' successful engagement with the resources, covering aspects such as the educational context, affordances and types of technology, technological communication and formative assessment. These factors constitute important knowledge for practitioners as they can use them in the planning, design, and development of technology-enhanced resources for use in their modules. The measures observed during the evaluations indicated both positive and negative engagement providing a link between observations and resultant student engagement, which was found lacking in previous studies on student engagement. [ABSTRACT FROM AUTHOR]

Given the wealth of research available on what components to include in a syllabus and how that affects instructor perception, there is a lack of research on how to present the syllabus to engage students in learning about the course. Our study examined the implementation of two multimedia syllabi developed for large lecture math courses: a graphic syllabus and a video version. After reviewing their respective syllabi, students were given a syllabus content quiz and course perception survey. Findings indicate no significant difference between students' syllabus quiz performance and overall survey responses between groups. Students responded favorably to the survey regardless of syllabus type. Last, there was no observed relationship between the length of each syllabus segment video and the frequency at which students watched each segment. Implications of this study will address engagement with the syllabus and provide additional considerations for syllabus development. [ABSTRACT FROM AUTHOR]

The proliferation of videos with educational purposes on social media offers unprecedented opportunities for informal learning in virtual space. Yet, research on learner engagement with educational videos in informal learning on social media has been scarce, despite its central role in learning. This study addresses this research gap. Specifically, we investigate how signalling mechanisms (signals and anchors) affect cognitive engagement. We sample YouTube educational videos and analyse the effects of signals and anchors on cognitive engagement on Reddit. Our analyses show that different signals and anchors affect cognitive engagement differently. Textual signals positively associate with cognitive engagement, while visual signals do not. Mathematical models are negatively related to cognitive engagement, and physical models are not correlated with cognitive engagement significantly. Our findings provide valuable empirical knowledge on cognitive engagement with educational videos on social media. This study enriches the understanding of signalling mechanisms and extends the literature on educational videos and multimedia learning. It is also beneficial for video designers and developers to optimise cognitive engagement with the appropriate use of signals and anchors and make online experiences more engaging. [ABSTRACT FROM AUTHOR]

A fundamental question in early childhood mathematics concerns the relationship between young children's own informal signs and the formal abstract symbolic language of mathematics. This study presents research investigating the genesis of mathematical semiosis from a Vygotskian cultural-historical (social-semiotic) perspective. In this study we look at the premature stages of dealing with quantity and their relationships. Our aim is to reveal the interweaving of young children's sign-use and to consider the role of intertextuality in mathematisation. Longitudinal, ethnographic data were gathered from case studies of seven children aged 3–4 years in an inner-city nursery school in England, documenting observations of their spontaneous pretend play. The data are interrogated through interpretive analysis and show that some graphical signs moved between individuals' texts, also borrowed from others including the teacher, and woven together. Children's progressive understandings of mathematical sign-use appear to be attained in part through intertextual exchanges in social and culturally meaningful contexts, such as pretend play. [ABSTRACT FROM AUTHOR]

The intention of the study was to examine the effects of a fraction intervention in a whole-class environment. The intervention aimed to enhance students' conceptual fraction knowledge, with a major focus on fraction magnitude understanding. This study included 120 fifth-grade students in standard classroom settings. Utilizing a cluster randomized controlled trial design, students were divided into either an intervention group (n = 64) or a control group (n = 56). Students in the intervention condition received a series of seven 35-minute lessons. Students in the control condition received "treatment as usual". Both post-test and delayed post-test results revealed that students in the intervention group performed significantly better than those in the control group on fraction concepts, with a stronger effect in measurement aspects compared to part–whole aspects. The intervention group also outperformed the control group on fraction arithmetic on both post-tests, while no significant difference was observed on fraction word problems. [ABSTRACT FROM AUTHOR]

Prior research highlights a positive effect of incorrect worked examples on mathematics learning. Yet the mechanisms underlying these benefits are unclear. To investigate potential mechanisms of the benefits of various worked example types, we examined process data from a previously published classroom-based experiment. More specifically, we analyzed students' explanations made while explaining worked examples in three varying example conditions as well as students' problem-solving errors made when solving problems. These data operationalize two potential mechanisms: a reduction of misconceptions (i.e., fewer targeted conceptual errors), and an increase in principled algebra knowledge (i.e., explanations focusing on principles underlying procedures). Mediation analyses revealed both as important mechanisms of varying effects. A reduction of misconceptions explained greater benefits of all three worked example conditions, compared to a problem-solving control, on an algebra concepts posttest. More principled explanations of procedures explained the benefits of incorrect worked examples on problem-solving at posttest compared to the two other example conditions. These findings help explain differential findings in prior work by example type and may elucidate potential avenues for errorful instruction. [ABSTRACT FROM AUTHOR]

We present simple procedures for estimating non linear panel data models in the presence of unobserved heterogeneity and possible endogeneity with respect to time-varying unobservables. We combine a correlated random effects approach with a control function approach while accounting for missing time periods for some units. We examine the performance of the approach in comparisons with standard estimators using Monte Carlo simulation. We apply the methods to estimate the effects of school spending on student pass rates on a standardized math exam. We find that a 10% increase in spending leads to an approximately 2 percentage point increase in math pass rates. [ABSTRACT FROM AUTHOR]

Let a be an ideal of a given commutative Noetherian ring R which satisfies the condition of the first problem of R. Hartshorne in [Affine duality and cofiniteness, Invent. Math. 9 (1970), 145–164]. In this paper, we prove that a also satisfies the condition of his second problem in the same article. We also provide an example to show that the converse statement does not hold in general. [ABSTRACT FROM AUTHOR]

AbstractMathematics is often thought to have a unique association with certainty. The present study investigated a possible consequence of this association, namely that general conditionals are interpreted more deterministically in math than in other domains. To test this hypothesis, in two studies (Ns = 146 and 117), adults were presented general conditionals involving fictional categories in math and science and were asked to judge whether the conditionals were compatible with various frequencies of exceptions to them. Participants indicated that even rare exceptions (e.g., 1 exception per 99 confirming cases) would falsify a conditional (Studies 1 and 2), that a conditional could not be true and rare exceptions to it at the same time exist (Study 1), and that the truth of a conditional precluded the existence of even rare exceptions (Study 2), more when the conditionals involved math than science. The findings are consistent with the hypothesis that mathematical context is particularly likely to elicit deterministic interpretations of general conditionals. Implications of the findings for theories of conditional reasoning, and for individual differences in conditional reasoning, are discussed. [ABSTRACT FROM AUTHOR]

School mathematics is not universal. It produces and is produced by social norms. What is considered as normatively appropriate school mathematics may vary when immigrant students (re)produce school mathematics in transitions between school mathematical practices at home and at school. In this study, one group of primary school students and two groups of secondary school students were interviewed to investigate their experiences with school mathematics in transitions. In contrast to some previous studies, the present study reveals instances where students positioned their parents as mathematically knowledgeable. To some students, it was important to know mathematical concepts in the mother tongue to be positioned as knowledgeable in mathematical conversations at home. This suggests that pedagogical practices should not only facilitate the transition of students’ everyday experiences into mathematics classrooms but also explore how school mathematics can be transitioned out of school, particularly considering transnationalities where ways of knowing transcend national boundaries. [ABSTRACT FROM AUTHOR]

Recently, W. Berndt and S. Sra (Hlawka-Popoviciu inequalities on positive definite tensors. Linear Algebra Appl. 2015;486:317–327) proved a Popoviciu type inequality for any arbitrary finite number of positive definite matrices. In this paper, we proved a quantitative Popoviciu type inequality for four positive semi-definite matrices, which is stronger than Berndt-Sra's corresponding result and also a generalization of Hong-Qi's (Refinements of two determinantal inequalities for positive semidefinite matrices. Math Inequal Appl. 2022;25(3):673–678) result. As applications, we partially recovered our early result in F. Wang (A quantitative Popoviciu type inequality, submitted.] and obtained a quantitative Hartfiel inequality. [ABSTRACT FROM AUTHOR]

In this paper, the existence and the uniqueness of an evolutionary anisotropic $ p_i(x) $ p i (x) -Laplacian equation with a damping term are studied. If the damping term is with a subcritical index, by the Di Giorgi iteration technique, the $ L^{\infty } $ L ∞ -estimate of the weak solutions can be obtained. The existence of weak solution is proved by the renormalized solution method, and how the anisotropic characteristic of the considered equation affect the $ L^{\infty } $ L ∞ -estimate of the weak solutions is revealed. The uniqueness is true strongly depending on subcritical index of the damping term, and this result goes beyond previous efforts in the literature (Bertsch M, Dal Passo R, Ughi M: Discontinuous viscosity solutions of a degenerate parabolic equation. Trans Amer Math Soc. 1990;320:779–798; Li Z, Yan B, Gao W. Existence of solutions to a parabolic $ p(x)- $ p (x) − Laplace equation with convection term via $ L^{\infty }- $ L ∞ − Estimates. Electron J Differ Equ. 2015;46:1–21; Zhang Q, Shi P. Global solutions and self-similar solutions of semilinear parabolic equations with nonlinear gradient terms. Nonlinear Anal. 2010;72:2744–2752; Zhou W, Cai S. The continuity of the viscosity of the Cauchy problem of a degenerate parabolic equation not in divergence form. J Jilin University (Natural Sci.). 2004;42:341–345), etc. [ABSTRACT FROM AUTHOR]

In the literature, besides the assumption of strict complementarity, superlinear convergence of implementable polynomial-time interior point algorithms using known search directions, namely, the HKM direction, its dual or the NT direction, to solve semi-definite programs (SDPs) is shown by (i) assuming that the given SDP is nondegenerate and making modifications to these algorithms [Kojima et al. Local convergence of predictor–corrector infeasible-interior-point algorithms for SDPs and SDLCPs, Math. Program. Ser. A 80 (1998), pp. 129–160], or (ii) considering special classes of SDPs, such as the class of linear semi-definite feasibility problems (LSDFPs) and requiring the initial iterate to the algorithm to satisfy certain conditions [Sim, Superlinear convergence of an infeasible predictor–corrector path-following interior point algorithm for a semidefinite linear complementarity problem using the Helmberg–Kojima–Monteiro direction, SIAM J. Optim. 21 (2011), pp. 102–126], [Sim, Interior point method on semi-definite linear complementarity problems using the Nesterov-Todd (NT) search direction: Polynomial complexity and local convergence, Comput. Optim. Appl. 74 (2019), pp. 583–621]. Otherwise, these algorithms are not easy to implement even though they are shown to have polynomial iteration complexities and superlinear convergence [Luo et al. Superlinear convergence of a symmetric primal–dual path following algorithm for semidefinite programming, SIAM J. Optim. 8 (1998), pp. 59–81]. The conditions in [Sim, Superlinear convergence of an infeasible predictor–corrector path-following interior point algorithm for a semidefinite linear complementarity problem using the Helmberg–Kojima–Monteiro direction, SIAM J. Optim. 21 (2011), pp. 102–126], [Sim, Interior point method on semi-definite linear complementarity problems using the Nesterov-Todd (NT) search direction: Polynomial complexity and local convergence, Comput. Optim. Appl. 74 (2019), pp. 583–621] that the initial iterate to the algorithm is required to satisfy to have superlinear convergence when solving LSDFPs however are not practical. In this paper, we propose a practical initial iterate to an implementable infeasible interior point algorithm that guarantees superlinear convergence when the algorithm is used to solve the homogeneous feasibility model of an LSDFP. [ABSTRACT FROM AUTHOR]

Significant attention has been paid to the use of ICT by teachers, especially during the COVID-19 health crisis. This usage has mostly been captured through self-reported survey measurements. Learning analytics can complement such findings, by using log data to document precisely how long teachers use ICT, and what ICT behaviors they perform online. Using log data of 800 teachers, the present study documents their use of ICT in mathematics on a digital learning platform used across Luxembourg during COVID-19 remote education. Our findings confirm the large differences between teachers' use of ICT found in previous research, measured here through the time spent active on the platform. The types of ICT behaviors teachers engage with online, measured via the SAMR model, explain most of this variation. Specifically, more time on the platform is associated with activities that create a meaningful learning experience, and redefined tasks that could engage students as active learners. Experience with the technology, and participation in incentive events and teacher training, explain another significant part of this variation. [ABSTRACT FROM AUTHOR]

Prior research in Western contexts has tested the hypothesis that stereotype threat induces a prevention focus and that in contexts where both prevention focus and stereotype threat are simultaneously activated, members of stereotyped groups experience a performance boost due to the fit between one's goal orientation and the task demands (i.e. regulatory fit or stereotype fit). The present Study tested this hypothesis with high school students in Uganda, East Africa. Study findings revealed that in this cultural context where high-stakes testing fosters a predominantly promotion-focused testing culture, individual differences in regulatory focus interacted with the broader cultural, regulatory focus test culture to impact student performance. [ABSTRACT FROM AUTHOR]

Theoretical, methodological, and empirical contributions regarding networks within the context of graph theory constitute a valuable interface between geography and mathematics. Seeking to assess mathematical network geography's past, present, and future, this article addresses such research and literature by discussing new knowledge produced from networked geographic phenomena—especially Erdös collaboration graphs depicting mentorships or authorships among scholars; outlining a brief history of networks in geographical analysis; and couching spatial autocorrelation within its geographic network links. General commentary transitions into examples of Erdös graphs and their implications for collaborations. The narrative also speaks to networked space challenges of established geographic thought (e.g., Tobler's first law of geography), with special reference to contributions by Boots and his coauthors. This article concludes with a treatment of graph theory, networks, and spatial autocorrelation. [ABSTRACT FROM AUTHOR]

This article details the development of a physical activity curriculum used in an after-school program for youths. The program, Get Fit! With Math & Lit, employed culturally relevant pedagogies as its guiding framework and the Teaching Personal and Social Responsibility Model to structure its content. This multifaceted framework of the curriculum elevates holistic health considerations of youths to include social, emotional, mental, and physical needs, especially in relation to academic achievement. Particularly, positively engaging youths in physical activity and academics necessitates an integrated approach to instruction. The program utilized multimodal literacies to engage participants in collaborative games, physical exercises, mathematical problems, literacy practices, and reflective discussions. These multimodal literacies can be incorporated into various settings such as middle school classrooms, after-school programs, and physical education contexts. The purpose of this article is to share the curriculum's objectives, content, learning activities, materials, processes, evaluation, and implications. [ABSTRACT FROM AUTHOR]

In his book Prejudice, Endre Begby argues that people who hold paradigmatically prejudiced beliefs – for example, the belief that women are less adept at math than men – might be fully rational in holding those beliefs. In this article, I argue that Begby fails to provide compelling examples of beliefs that are both rational and prejudiced. On Begby's account, whether a belief is prejudiced is determined by its content: it follows that any two token beliefs with the same content will either both be prejudiced, or both unprejudiced, regardless of how they differ in other respects. I sketch an alternative account, on which whether a person's belief counts as prejudiced might be sensitive to a greater range of factors. I then turn to Bebgy's discussion of 'evidential preemption,' a phenomenon by which certain speech acts seem to inoculate themselves from having their contents disconfirmed or falsified by later counterevidence. I argue for skepticism about evidential preemption. To the extent that there is a genuine normative phenomenon in the neighborhood, it is the familiar one of testimonial defeat, in which testimony from one source is neutralized by conflicting testimony from another source that one has reason to think is more reliable. [ABSTRACT FROM AUTHOR]

Summary: This article is about the planar configurations of the toy called Rubik's Snake (or Rubik's Twist), where all Snake pieces have a triangular face lying in the same plane. Any such configuration with n corners can be obtained from the straight Snake with exactly n twists of the physical toy (in such a way that the Snake does not self-intersect during the construction). We also discuss a number of other interesting properties; in particular, we classify all convex subsets of the plane that can be precisely covered by such a planar configuration. The proofs only require high school mathematics. [ABSTRACT FROM AUTHOR]

Summary: Are you having trouble getting married? These days, there are lots of products on the market for dating, from apps to websites and matchmakers, but we know a simpler way! That's right—your path to coupled life isn't through Tinder; it's through Sudoku! Read our fabulous paper, where we explore the Stable Marriage Problem to help you find happiness and stability in marriage through math. As a bonus, you get two Sudoku puzzles with a new flavor. [ABSTRACT FROM AUTHOR]

We investigated university students' engagement with digital textbooks by analysing their real-time viewing and use in a linear algebra course taught at four different universities in the United States. Viewing data over a semester was complemented with responses to bi-weekly open-ended surveys and other course artefacts, such as course syllabi. With our approach to ask students about their viewing data in surveys, we were able to relate student majors to textbook engagement and to document more and different uses of textbook elements than what has been reported so far. We used descriptive statistics and frequency graphs to analyse the viewing data and a grounded analytical approach to survey data. By using the didactical tetrahedron, we found that textbook engagement dropped when the algebraic language and content of the textbook was not institutionally legitimized and when the textbook did not directly satisfy interests associated with earning a degree. Textbook engagement was higher than what could have been anticipated by syllabi for students majoring in disciplines other than mathematics. We propose areas for further research. [ABSTRACT FROM AUTHOR]

The increase in online education has implications for mathematics teacher educators who are tasked with teaching mathematics content and pedagogy to pre-service teachers (PSTs) who do not attend on-campus. Concerns about PSTs' content knowledge continues to be an ongoing issue, and ways to address this, especially in an online environment, require further investigation. While online courses offer accessibility and flexibility, it can be challenging to translate synchronous on campus teaching and experiences into the online environment. The importance of productive mathematical discourse has been identified as an appropriate pedagogy, yet the opportunity to engage in such discourse can be limited in the online environment. This paper provides the results from a case study of an online forum, which highlights how pre-service teachers can be engaged in productive online mathematical discussions, particularly when facilitated by the instructor's and other learners' interactions and presence. The findings indicated that social, cognitive, and teaching presence influenced the nature and frequency of online mathematical discourse. The study contributes to existing research through conceptualizing how productive mathematical conversations can occur outside of the classroom setting, with implications for mathematics teacher educators who are tasked with teaching content, pedagogy and practices to PSTs. [ABSTRACT FROM AUTHOR]

This article describes an instructional sequence used with inservice secondary mathematics teachers as part of a graduate course. The instructional sequence focused on designing tasks using Interactive Geometry Software (IGS). This study answers a call for replication studies to investigate the use of an established instructional sequence. Results confirm previous findings when implementing the instructional sequence with preservice teachers and demonstrate that the instructional sequence supported inservice teachers in creating high-level tasks that use IGS as a reorganizer to support student thinking. Comparison of previous and current results point to several implications for potential revisions to improve the instructional sequence, as well as revisions to the IGS Framework. [ABSTRACT FROM AUTHOR]

For students taking higher level mathematics courses, the transition from computational to proof-based courses such as analysis and algebra not only introduces a new format of writing and communication, but also a new level of abstraction. This study examines the affordances of one particular tool to aid students in this transition: a proof template. We highlight four cases based on interviews conducted at two universities, both from transition-to-proof classes in which templates were explicitly used and not. Results indicate that when introduced to this tool, students viewed these templates favourably. Two detailed cases provide evidence that templates can contribute to deep understanding and student ownership of learning by deconstructing the template structures for themselves. In settings where explicit templates were not introduced, two cases address possible concerns with templates as well as demonstrate that students may be intuiting this structure. Our work provides evidence for the benefits of templates as a learning aid to struggling and strong students alike that does not reduce creativity in proving, along with students' appreciation of templates for structure and as guidelines to make sense of the increased abstraction required for proof-writing. [ABSTRACT FROM AUTHOR]

In this paper we studied the personal mathematical work of 14 students in initial teacher training, in their first year of studies at a public university in Chile, based on two tasks on complex numbers. These tasks were set in a Computer Aided Assessment System (CAA) based on Moodle and Wiris and it was proposed to solve them using different Computer Algebra Systems (CAS), such as GeoGebra, Symbolab, Photomath and Wolfram Alpha among others. Difficulties and potentialities were observed in the mathematical work of the students. In the difficulties, it was observed that the students had problems interpreting the information from the CAS and the CAA feedback because their previous mathematical knowledge was not solid enough to do so. In the potentialities, it was observed that different characteristics of the task, together with the articulation of two or more artifacts allowed students to give meaning to the mathematical objects involved. [ABSTRACT FROM AUTHOR]

Creativity and problem solving are considered to be twenty-first-century competencies, therefore promoting mathematical creativity should be an important part of school mathematics. The study presented in this paper is inspired by the notion of mathematical creativity and the utilization of multiple solution tasks (MSTs) to investigate students' creativity. Multiple solution tasks are mathematical tasks with an explicit requirement to be solved with different methods. For the purpose of the study, we used a textbook question which allows multiple solution pathways as our research instrument. This MST was administered to first-year mathematics students (18–20 years) along with additional questions related to their experience in school mathematics. The results of the study showed that students had difficulties complying with the demands of the task, but generally have a positive disposition toward MSTs. Moreover, the results underline the necessity of incorporating MSTs in mathematics classroom teaching to create a more coherent corpus of mathematical knowledge. The study also provides an example of how a regular textbook task can be used as an MST. [ABSTRACT FROM AUTHOR]

While research on the opportunity to learn about mathematics concepts provided by textbooks at the secondary level is well documented, there is still a paucity of similar research at the undergraduate level. Contributing towards addressing this knowledge gap, the present study examined opportunities to engage in quantitative and covariational reasoning, in the context of the derivative concept, provided by two textbooks commonly used in the teaching of calculus in the United States-a regular calculus textbook and an applied calculus textbook. Analysis of expository sections, examples, and exercises related to the derivative provided in these textbooks revealed three main results. First, the applied calculus textbook provides plenty of opportunities to engage in quantitative reasoning. Similar opportunities are limited in the regular calculus textbook. Second, opportunities to engage in covariational reasoning are not only minimal in both textbooks, but also limited to low levels of covariational reasoning, namely coordination, direction, and quantitative coordination. Third, the applied calculus textbook consistently defines ordinary and partial derivatives as rates of change while the regular calculus textbook consistently defines these concepts as limits of a difference quotient. Findings of this research have implications for several stakeholders, including calculus textbook authors and calculus instructors. [ABSTRACT FROM AUTHOR]

Four variations of the Koch curve are presented. In each case, the similarity dimension, area bounded by the fractal and its initiator, and volume of revolution about the initiator are calculated. A range of classroom exercises are proved to allow students to investigate the fractals further. [ABSTRACT FROM AUTHOR]

Mathematical problem posing, or authoring mathematical tasks, can allow students to integrate their interests and experiences into the classroom. Little research has explored different designs for scaffolding or facets of posed problem quality, particularly when problem posing is based on students' interests. We created an environment that enabled 39 community college students to author algebra problems related to their career interests, and explore four problem-posing scaffolds – video, vignette, example problem, and template. We use a design-based research approach to examine affordances of career problem-posing. Engaging in problem-posing was associated with increased interest in learning mathematics. Use and time spent with scaffolds and time-on-task were related to quality of posed problems, and problem quality features were related to students' ability to solve problems they posed. Text analyses revealed scaffold use was associated with the language students used in the problems they posed. Implications for problem posing in mathematics classrooms are discussed. [ABSTRACT FROM AUTHOR]

The paper investigates uniformly closed subspaces, sublattices, and ideals of finite codimension in Archimedean vector lattices. It is shown that every uniformly closed subspace (or sublattice) of finite codimension may be written as an intersection of uniformly closed subspaces (respectively, sublattices) of codimension one. Every uniformly closed sublattice of codimension n contains a uniformly closed ideal of codimension at most $ 2n $ 2 n. If the vector lattice is uniformly complete then every ideal of finite codimension is uniformly closed. Results of the paper extend (and are motivated by) results of Abramovich Y.A., Lipecki Z. [On ideals and sublattices in linear lattices and F-lattices. Math Proc Cambridge Philos Soc. 1990;108(1):79–87.; On lattices and algebras of simple functions. Comment Math Univ Carolin. 1990;31(4):627–635.], as well as Kakutani's characterization of closed sublattices of $ C(K) $ C (K) spaces. [ABSTRACT FROM AUTHOR]

In this article, we consider how to make data more meaningful to students through the choice of data and the activities we use them in drawing upon students lived experiences more in the teaching of statistics and data science courses. In translating scholarship around culturally relevant pedagogy from the fields of education and mathematics education we develop the idea of culturally relevant data. We see this development as a key ingredient to implementing culturally relevant pedagogy in teaching data-intensive courses leveraging the centrality of context through data in both statistics and data science to engage students particularly from historically marginalized groups in STEM. We provide suggestions as to ways of finding or creating culturally relevant data and using them in implementing culturally relevant pedagogy to support the learning and flourishing of students in statistics and data science courses. We also present findings from pilot work we have done in implementing these data in statistics courses. Finally, we discuss lingering questions and possible next steps for research in this area. for this article are available online. [ABSTRACT FROM AUTHOR]

The Science, Technology, Engineering, Arts and Mathematics (STEAM) approach has a variety of benefits for all children as it triggers multiple senses through hands-on activities, experiential learning, exploration opportunities on different scientific topics, and various tools and materials. Five STEAM activities were designed and implemented with fifteen 60–72-month-old children over a five-week period. Each activity required children to make their own designs to create their product, and was prepared to emphasize a particular feature of STEAM education. Instrumental case study was utilized in this study. It was observed that children engage more and spend more time, demand additional materials and use their imagination to design more creative and various products in STEAM activities. [ABSTRACT FROM AUTHOR]

Following the increasing impacts on the value of Western play-based pedagogy, early childhood (EC) teachers in China face developmental challenges related to understanding and implementing play-based mathematical education. The purpose of this paper is to explore Chinese EC teachers' perspectives on play-based mathematics teaching. In this qualitative study, semi-structured interviews and lesson plans are collected from six EC teachers in a Chinese kindergarten. Hedegaard's model is applied to frame analysis for capturing EC teachers' views and practices from a holistic perspective. The findings show that all six EC teachers valued play as a pedagogical tool for teaching mathematics, while their pedagogical decisions in applying play to children's mathematics are determined by the various demands from society, parents and children. The multiple demands from different perspectives result in challenges for teachers in designing collective play. This study revealed that only when play activity caters to the possibility of satisfying those demands can teachers pedagogically implement play for children's mathematical learning. The insights emerging from this study might address the pragmatic challenges that teachers face by enhancing teachers' professional development to support the advance of culturally sensitive play-based mathematics teaching in China. [ABSTRACT FROM AUTHOR]

The study evaluated the effects of board games on children in a range of cognitive areas, considering both inclusion (i.e. pre- and post-comparisons, playing style [board games], participants belonging to PreKinder and Kindergarten, and experimental approach) and exclusion criteria (i.e. video games). Nineteen articles were selected using both PsycInfo and PubMed as databases. All of them, except one study, focused on exploring the relationship between board games and mathematical knowledge and numerical skills. These studies show that in 52% of the analysed tasks, significant gains were found considering pre- and post-comparisons in math skills. When comparing intervention and control groups, significant differences appeared for 32% of the cases. Board games enhance mathematical abilities for children from 45.6 to 100.6 months since they help achieve statistically significant gains. Future studies should be designed to explore the effects that these games could have on other cognitive and developmental skills. [ABSTRACT FROM AUTHOR]

This study examined teacher behaviours, students' academic engagement, and classroom ecology in mainstream classrooms including children with intellectual disabilities, and examined the differences in academic engagement for students with and without intellectual disabilities. A mixed-method research methodology was employed. The study demonstrated that children with intellectual disabilities exhibited high level of engagement in the following situations: the classroom layout used grouping, the classroom organisation combined groups and independent learning, the learning tasks included reading aloud, copying, watching videos, and doing homework, and teachers paid attention to all students or to children with intellectual disabilities individually and walked around the classroom during lesson time. English was the discipline with most active engagement among children with intellectual disabilities, followed by music, art, science, Chinese, sports, social studies, and mathematics. Finally, academic engagement of children with and without intellectual disabilities was mostly passive. We discuss the factors related to academic engagement of children with intellectual disabilities and provide suggestions for improving their self-management skills and classroom organisation. [ABSTRACT FROM AUTHOR]

The International Journal of Mathematical Education in Science and Technology has published a special issue on the INDRUM2022 conference, which focused on research in university mathematics education. The conference featured numerous papers and posters on topics such as the transition to university mathematics, teaching and learning of mathematical concepts, teacher education, and student practices and assessment. The special issue includes 16 papers that provide in-depth analyses of these topics, using theoretical frameworks such as the Anthropological Theory of the Didactic and the Action, Production and Communication approach. The papers offer insights into the challenges and opportunities in university mathematics education and propose instructional strategies to enhance learning outcomes. The editorial encourages readers to explore the papers and join the INDRUM network. Additionally, the text titled "Commognition" is a chapter in the Encyclopedia of Mathematics Education, providing an overview of the concept of commognition, which refers to the cognitive processes involved in mathematical communication and collaboration. The chapter explores various aspects of commognition, including its theoretical foundations, its role in problem-solving and learning, and its implications for mathematics education. The text is part of a larger collection of proceedings from the fourth conference of the International Network for Didactic Research in University Mathematics. [Extracted from the article]

In this note, we discuss two specific cognitive biases towards closure property as a learning obstacle in school mathematics in the context of number sets. These biases are related to rational and irrational numbers, two important and challenging issues from an educational point of view. The first bias concerns incorrect application of rules and properties of closure property in rational numbers to irrational numbers, and the second deals with the improper generalisation of the closure property in finite states to infinite states. These biases indicate the importance of teaching and learning the closure property. [ABSTRACT FROM AUTHOR]

AbstractThe relation between mathematical achievement in early childhood and future academic success is well established. However, our knowledge about the effect of instruction on mathematical performance is often reliant upon self-report or videotaped instruction measures and standardized achievement assessments.The current study uses teacher audio recordings to examine the role of classroom mathematics instruction in the growth of adaptive early mathematical skills.Kindergarten children (N = 98, M(age) = 5.55 years, 53% male) were followed across the school year.Findings suggested children with the lowest levels of adaptive mathematics skills grew the most across the school year, suggesting that basic skills continue to be the focus in early elementary years. Further, no aspects of mathematics instruction predicted growth in children’s addition or counting skills.These results highlight the need for more robust and ecologically valid measurement in assessing classroom mathematics instruction in future research. [ABSTRACT FROM AUTHOR]

STEM is an exclusionary space for queer and trans* students of color (QTSOCs). A critical site of justice-oriented transformation to enhance support for QTSOCs is mathematics education, which has significant impacts on access to STEM majors and positive identities in the sciences. This article proposes a set of rights for QTSOCs as STEM learners to guide pedagogy that affirms intersectionality of their experiences in and beyond mathematics classrooms. QTSOCs in STEM have the rights to: (i) feel confused and receive support; (ii) take risks in participation and identity expression; and (iii) have affirming representation of identity in knowledge production. To illustrate how these rights are denied and embraced through STEM pedagogy, I present 2 narrative cases from my research study about QTSOCs’ intersectionality of STEM experiences where mathematics played a central role. I conclude with implications for practice to cultivate rehumanizing STEM educational opportunities that QTSOCs deserve. [ABSTRACT FROM AUTHOR]

AbstractThis study investigates the relationship between intrinsic motivation, mathematics performance, and digital game-based learning (DGBL) in kindergarten students. The research sample comprised 292 children aged 5 to 6 years from diverse socioeconomic backgrounds. Instruments included an adapted Children’s Basic Psychological Need Satisfaction Scale for measuring motivation and the Woodcock-Muñoz IV battery for mathematical assessment. DGBL was implemented using software designed for training early numeracy skills. Descriptive and correlational analyses revealed significant positive correlations between intrinsic motivation and general mathematical knowledge. However, no significant correlations were found between motivation and early numeracy skills in the DGBL environment. The findings highlight the importance of intrinsic motivation in early mathematical learning and suggest the potential effectiveness of DGBL in promoting mathematical skills, contributing to reducing the gap of knowledge at this educational level. This study provides valuable insights for educators seeking to enhance mathematical learning through intrinsic motivation and DGBL strategies in kindergarten education [ABSTRACT FROM AUTHOR]

"Numbers and the World: Essays on Math and Beyond" by David Mumford is a collection of essays that covers a wide range of topics, from mathematics to neuroscience, artificial intelligence, history, and social issues. Mumford, a highly acclaimed mathematician, offers his unique and creative perspectives on these subjects. The book is not a technical exposition of his mathematical work, but rather a collection of his thoughts and musings, originally posted on his blog. Mumford's writing style is clear and accessible, making this book an interesting read for both mathematicians and non-mathematicians alike. [Extracted from the article]

Robust principal component analysis (RPCA) is devoted to tackling grossly corrupted datasets with noise. However, the performance of RPCA is usually circumscribed by the lack of efficiency of singular value decomposition (SVD), which rules out its potential applications to many large-scale real-world problems. In this paper, we develop a nonconvex optimization algorithm customized to SVD-free RPCA models. The proposed algorithm, which is built upon proximal alternating linearized minimization Bolte et al. [Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math Program. 2014;146(1–2):459–494], can reduce computational efforts by partially linearizing data fidelity and increase efficiency by leveraging inertial techniques. Under the Kurdyka-Łojasiewicz assumption on the objective function and some mild premises on stepsizes, the sequence produced by the proposed algorithm converges globally to a critical point of SVD-free RPCA models. Numerical simulations on synthetic and real datasets demonstrate the compelling performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic prompted a shift in K-12 educational delivery from primarily in-person classroom instruction to remote learning. Developing broadcast instruction is one way to provide learners who experience barriers to contemporary forms of remote learning, which are typically provided over the internet, a way to access quality mathematics instruction. Producing classroom-style video lessons for children is not as simple as recording a lecture, and ways to engage and interact with learners are limited. There is a little interplay between design principles used in mathematics-focused broadcast television programmes and mathematics classroom pedagogy. More research is needed to understand how teachers may adapt mathematics education design principles to develop broadcast lessons. We utilized an exploratory case study design to investigate how teachers conceptualize, enact, and reflect upon mathematics pedagogy in a broadcast environment. Data from created lessons, videotaped feedback sessions and semi-structured interviews were collected and analyzed. Results yielded three themes related to the instructional design, barriers and challenges, and equity: (a) Goal-focused planning and delivery, (b) Centrality of discourse, and (c) Time. We discuss the results in relation to prior work at the intersection of mathematics and broadcast pedagogy and share implications for future research. [ABSTRACT FROM AUTHOR]

My first aim in this paper is to use time diagrams in the style of Brentano to analyze constructions in Brouwer's separable mathematics more precisely. I argue that constructions must involve not only pairing and projecting as basic operations guaranteed by the intuition of twoity, as sometimes assumed in the literature, but also a recalling operation. My second aim is to argue that Brouwer's views on the intuition of twoity and arithmetic lead to an ontological explosion. Redeveloping the constructions of natural numbers and systems sketched in an appendix to Brouwer's Cambridge lectures, I observe that the only plausible way he can make some elementary arithmetic in his separable mathematics is by allowing for the same canonical number to be determined by multiple separable entities, resulting in an overabundant mathematical ontology. [ABSTRACT FROM AUTHOR]

This study investigates the impact of systematic desensitization (SD) on mathematics anxiety and achievement among Nigerian secondary school students. Employing a quasi-experimental design with a pretest and post-test nonequivalent control group design, we selected 120 students (58 boys, 62 girls) from a pool of 3390 senior class one students using a multi-stage sampling procedure. Assessment tools included the Mathematics Achievement Test and Mathematics Anxiety Scale. The six-week intervention demonstrated significant results with moderate effect sizes, revealing that SD significantly reduced mathematics anxiety (F[1,115] = 86.66, p <.001) and enhanced academic achievement (F[1,115] = 92.458, p <.001). Gender showed no substantial influence on mathematics anxiety (F[1,115] =.365, p =.547) or achievement under SD treatment (F[1,115] =.006, p =.937). This study underscores the effectiveness of SD in reducing mathematics anxiety and improving mathematics performance among Nigerian students. [ABSTRACT FROM AUTHOR]

Making connections within and between different aspects of mathematics is recognised as fundamental to learning mathematics with understanding. However, exactly what these connections are and how they serve the goal of learning mathematics is rarely made explicit in curriculum documents with the result that mathematics tends to be presented as a set of discrete, disconnected topics. Interest in establishing a more coherent approach to the teaching and learning of school mathematics has led to a focus on big ideas. That is, networks of related concepts, skills and ways of thinking that facilitate learning mathematics with understanding. Research on learning progressions has helped identify what these big ideas are and how they serve to build connections within and between different aspects of mathematics. This paper draws on research that provides an evidenced-based learning progression for multiplicative reasoning to illustrate the connective role of multiplicative thinking in the development of algebraic, geometrical, and statistical reasoning. [ABSTRACT FROM AUTHOR]

The importance of mathematical connections in teaching mathematics is broadly acknowledged in the literature. Nevertheless, more research is needed to clarify how different types of mathematical connections manifest in classroom interactions and how they can support student learning. This article uses the commognitive framework to analyse 15 pre-service secondary teachers' (PSTs') discussions on mathematical connections that hypothetically could be made in a pattern generalisation task. The study seeks to explore the types of connections produced by the PSTs and to examine the potential opportunities for object-level and meta-level learning in algebra discourse. The findings are discussed in light of ongoing efforts to refine teachers' pedagogical knowledge and practice regarding mathematical connections and to develop better pedagogical tools to communicate about mathematical connections. [ABSTRACT FROM AUTHOR]