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Purpose: This commentary discusses the paper by Reardon et al. (2024; this issue) entitled, "Overcoming implementation challenges through using a train-the-trainer approach to teach numeracy in a special school setting." This commentary outlines the necessary contribution this paper adds to the substantive area of research it is couched within while also identifying potential areas of future research to expand the understanding of this phenomenon and its impact upon practice. Design/methodology/approach: What is fidelity of implementation, how do we measure it and how does it impact our interpretations of experimental findings? This commentary focuses specifically on the nebulous construct of fidelity in experimental studies and how this impacts experimental findings' internal and external validity. Findings: Although fidelity is frequently referenced as an important aspect to consider, the measurement of the construct has been critiqued in experimental studies. To understand if an intervention was "implemented as intended," the core dimensions of the intervention must be considered in the measurement process, as well as potential confounding variables. Originality/value: With an increased need for experimental work to inform what works, for whom and under what conditions, there becomes a need to better investigate the implementation of the intervention in these contexts – thus, fidelity must be reconceptualized. This commentary provides an overview of this dilemma with potential ideas to investigate moving forward. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to identify the current situation of higher education institutions in Spain regarding the introduction of the Sustainable Development Goals in the classroom, and what is the role of mathematics in this task. Design/methodology/approach: A review is made of how the concept of sustainability has evolved in higher education, its gradual introduction in the University and the way in which this subject is approached in the field of mathematics. Findings: The study concludes that higher education has a key role to play in designing strategies that lead to the global sustainability of the planet. This implies major changes in degree curricula, assessment, competences and teacher training. Cross-disciplinarity and interdisciplinarity between different subjects within the same degree is a strategy for students to analyse the Sustainable Development Goals using mathematical techniques. Social implications: The University as an institution must train socially responsible professionals who are aware of the importance of promoting a sustainable world. Changes should be made to introduce values in the classroom that promote and encourage sustainability. Training should be seen as a continuous process that leads to the preparation of professionals committed to society and nature and who develop strategies aimed at improving the planet through values. Originality/value: Through practical activities, the Sustainable Development objectives can be analysed from several subjects of the same degree, emphasising the interdisciplinary and transversal nature that should be the central axis of higher education. Each subject can develop a strategy for change in favour of sustainability that will be reinforced and increased by working together on the proposed teaching practice. In this way, the contents of the different subjects are not isolated, but rather the student can see how there is an interrelationship between them and with real life. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to examine how gender equality influences difference in cognitive skills between genders. For the closer examination of Guiso et al. (2008), restricting the sample to immigrants allows us to reduce the possibility of reverse causality. Design/methodology/approach: Using PISA 2012 matched with the gender wage gap sourced from World Economic Forum's Global Gender Index 2011, the author compares the effect of the wage gap among the areas of mathematics, science and reading. Findings: Decreased gender wage gap leads to girls exhibiting a reduced incidence of lateness and skipping school compared with boys, which in turn improves girls' test scores in mathematics, science and reading. The direct effect of the decreased wage gap on test scores exceeds its indirect effect on performance owing to influencing school attendance. Originality/value: The findings of this paper provide evidence that higher female wage level relative to male wage level incentivizes female students to attend school, resulting in their achieving higher test scores not only for mathematics, but also for science and reading. [ABSTRACT FROM AUTHOR]

Purpose: The distribution of natural numbers in the Ulam spiral manifests a series of unexpected regularities of the elusive prime numbers. Their sequencing remains a topic of research interest, with many ramifications in different branches of Mathematics, especially in number theory and the prime factorisation problem. Accordingly, the focus of the research is on the most known and widespread asymmetric cryptographic system, that is, the RSA encryption. Design/methodology/approach: This paper presents the presence of one, two, three or four adjacencies for the diverse primes that appear in a spiral, considering the Hardy–Littlewood twin prime conjecture and the constellations of primes. Findings: Through equations, the calculation formulas of primes inside a spiral that have one to four primes in their adjacent places is offered, with approximate expressions that facilitate the operations, showing that the adjacencies decrease very rapidly as the spiral progresses, although without disappearing. Originality/value: A generalisation to cases in which the distances to the prime values change in an ascending way in accordance with the step of the Ulam spiral is offered. [ABSTRACT FROM AUTHOR]

Purpose - In a time that could be described as a "perfect storm" in higher education, faculty and administration have been exploring all possible tools to attract students and help them stay on a curriculum path so they can graduate within a reasonable time. The purpose of this paper is to explore three strategies for riding the storm in a large mid-western USA university. Design/methodology/approach - The authors identify three strategies for increasing student retention and course completion, including: increased choices in scheduling; redesigning the curriculum; and offering multiple options for mode of delivery. In addition, the pilot of these strategies in a Technical Data Analysis class will be described and evaluated. Findings - Providing choices in scheduling courses (strategy 1), redesigning the curriculum to offer flexible pathways to graduation (strategy 2), and offering students options in delivery modes (strategy 3) increase the likelihood of student success, allowing them to find a way out of and therefore escape the "perfect storm" that higher education finds itself in today. Practical implications - Flexibility in scheduling courses by offering multiple delivery modes increases student access while maintaining the same learning objectives and outcomes. Originality/value - This paper addresses a known challenge in higher education and offers three strategies to improve retention and completion. [ABSTRACT FROM AUTHOR]

Purpose- The purpose of this paper is to examine how elementary school teachers integrated technology into their mathematics teaching in classroom settings that were one-to-one computer environments for most of the day. Following a series of classroom observations and interviews, inductive qualitative analyses of data indicated that teachers felt that technology supported student's mathematics learning and prepared them for their future where technology was important. However, observations indicated that despite teaching in one-to-one environments, students only used technology on rare occasions or if they finished activities early. Further, these technology-based activities were low-level review of mathematics computations. Implications include the need to provide effective support to teachers about integrating technology in meaningful ways. Design/methodology/approach -This study involved classroom observations of two-third grade teachers. Findings -Findings indicate that teachers used Chromebooks in one-to-one classrooms to provide students with extra practice on computational skills. Research limitations/implications- There is a need for future studies to look at teacher's use of technology and its influence on student learning. Practical implications -Teacher education programs and school leaders should provide opportunities for current and future teachers to learn about technology with content specific examples. Originality/value - This study provided an examination of all of the third grade teachers in a school who all were teaching mathematics in one-to-one classroom environments. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to investigate and identify threshold concepts that are the essential conceptual content of finance programmes. Design/methodology/approach – Conducted in three stages with finance academics and students, the study uses threshold concepts as both a theoretical framework and a research methodology. Findings – The study identifies ten threshold concepts in finance that are clearly endorsed by finance academics. However, the extent to which students are explicitly aware of the threshold concepts in finance is limited. Research limitations/implications – As well as informing further research into the design and delivery of finance programmes, the findings of the study inform the use of threshold concepts as a theoretical framework and a research methodology. The study does not explore the bounded, discursive, reconstitutive and liminal aspects of threshold concepts. Implications include the lack of recognition of more modern concepts in finance, and the need for input from industry and related disciplines. Practical implications – The threshold concepts in finance provide the starting point for finance educators in the design and delivery of finance programmes. In particular, the threshold concepts in finance need to be made more explicit to students. Social implications – Using the threshold concepts in finance as well as the other findings of this study to inform to finance curriculum design and delivery is likely to achieve better quality educational outcomes for finance students as well as better prepare them for professional finance roles. Originality/value – The finance curriculum is under researched and for the first time this study identifies the threshold concepts in finance to inform the design of finance programmes. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to present the topology optimization method to design the rotor and the tooth base in the stator of the permanent magnet (PM) excited machine with the improved high-speed features. The topological and shape sensitivity through the multi-level set method (MLSM) have been used to attain an innovative design of both the rotor and stator made of different materials. Design/methodology/approach – This framework is based on the application of the topological and the shape derivative, obtained by incorporating the adjoint variable method into the MLSM for the magnetoquasistatic system. The representation of the shape and their evolution during the iterative optimization process are obtained by the MLSM. Findings – To find the optimal configuration of a PM machine, the stator and rotor poles were simultaneously optimized by redistributing the iron and the magnet material over the design domains. In this way, it was possible to obtain an innovative design which allows to reduce mechanical vibration and the acoustic noise caused by the cogging torque, while taking the back electromotive force into account. Originality/value – The novelty of the proposed method is to apply the modified multi-level set algorithm with the total variation to the magnetoquasistatic optimization problem. Given the eddy currents phenomenon in the model of a PM machine, it was possible not only to optimize the structure of a PM machine but also to analyze electromagnetic losses distribution. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to describe a technical creation called a constant-force cylinder, which exhibits more advantages in providing constant force in a low-gravity environment than some existing methods. Design/methodology/approach – The authors design the constant-force cylinder with simple ideas and realistic applicability that is easy to achieve. The authors analyze and formulate the cylinder, and explain how the realization of constant force and low gravity are obtained during the experiment by calculations. Force analysis and simple mathematics/statistics are used in the calculation. Findings – The authors prove the effectiveness and accuracy of the constant and low-gravity properties of the new cylinder. In addition, the authors formulate the acceleration value to drive the cylinder which is flexible and easy to be adjusted during the experiment. Practical implications – The constant-force cylinder can be functioning in a low-gravity environment with simple structures and economical extensions to real-world applications. Originality/value – This is an innovative design of a constant-force cylinder under the low-gravity environment. In the experiment, the new cylinder was revised from an ordinary and economic cylinder with constant force and the applicability easy to be realized in practice. [ABSTRACT FROM AUTHOR]