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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 - 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 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: The purpose of this paper is to describe the design and development of a final year undergraduate mathematics module designed to address professional skills development at a UK university, including via input to curriculum and assessment from employers, and to investigate student acquisition of skills from this module. Design/methodology/approach: Literature on skills development in mathematics informs module design and development. Students optionally completed Likert-style competency questionnaires before and after the taught module content, and reflected on skills development via an end of module questionnaire. Data collection took place over three academic years. Findings: Several key competencies exhibit median increases over the course of the module in each academic year, indicating a perceived skills development. Problem solving and presentation skills are particularly highlighted. Research limitations/implications: Numbers of students were small, though the study is repeated with three different cohorts. Some students study mathematics jointly with another discipline and hence may have experience in skills development from the other subject. Practical implications: This study indicates that innovations in teaching style and assessment in mathematics modules can enhance student confidence and competence with key professional skills. Originality/value: Undergraduate modules in mathematics which have a focus on professional skills development are still fairly rare in UK universities. Often such modules do not embed the professional skills development activities with subject-specific technical tasks and projects as this module does. There are few formal studies of the effectiveness of this style of module, especially longitudinal studies covering several academic years. [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]

Purpose – The purpose of this paper is to enhance students’ mastery of course material in a second semester calculus course and assess the effectiveness of a traditional “lecture-based” instructional model compared to a modified “flipped classroom” model using a mixed method research design. Design/methodology/approach – Evaluation of effectiveness was measured by having students in all four courses take the same pre-post exams and participate in a survey to assess their opinion of each instructional model. Undergraduate students covered the same content using two different modes of instruction. Findings – Within a comparable group of students, participants in the flipped course had similar content knowledge gains as the lecture-based course. Based on responses obtained in blinded student surveys, the authors found that the use of an online homework system (WebAssign) and in-class quizzes were critical motivating factors that likely contributed to the increase in student performance. The flipped classroom instruction was more effective at increasing interest in the subject and promoting student discourse around problem solving. Taken together, the findings support the flipped classroom model as an equally effective means in which to disseminate key calculus concepts to undergraduate students. Research limitations/implications – Findings from this study are limited to content knowledge gains in calculus over a 14-week time period, and student attitudes toward the mode of instruction they received. More research is needed to study the depth of learning that occurs in small group problem solving and interactions between faculty-and-student and student-to-student. Originality/value – While many course redesigns focus on incorporating more project-based or laboratory-based learning opportunities, the redesign used in this study was focussed on different ways to deliver the same content. Results from this study suggest that a blended type of learning would be optimal for learning calculus concepts with a strategic use of video content concepts. [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 investigate the gender stereotype of science by analysing the semantic attributes of gender in relation to three science subjects -- chemistry, mathematics, and physics -- among students and their science teachers. Design/methodology/approach -- This cross-sectional study applied a survey of 3,045 students and 123 teachers in secondary schools. The gendered image of science was assessed using a semantic differential consisting of 25 pairs of adjectives with semantically opposite meanings. Findings -- In summary, the results of the study demonstrate that from the female students' perspective mathematics and physics are negatively related to female gender, whereas chemistry is neither significantly related to the male nor to the female profile. From the male students' point of view mathematics is negatively related to the female gender, whereas chemistry and physics are positively related to the male gender. In the science teachers' perception chemistry and physics combine feminine and masculine attributes, whereas the teachers' perception of mathematics matches only with the male, but not with the female gender. Originality/value -- In contrast to previous research, the study is the first to analyse the gender stereotype of chemistry as well as to assess the gender image of three science subjects from students' and teachers' perspectives. [ABSTRACT FROM AUTHOR]

Purpose: The study explored the impact of the King and Queen of Mathematics Initiative (KQMI) in promoting students' interest in learning mathematics and improving their achievement. The specific objectives of the study focused on the impact of the initiative in promoting interest in mathematics, assessing the contribution of the initiative to students' achievements and investigating challenges encountered by the initiative. Design/methodology/approach: The study used a case study design with a mixed-method approach. One ward secondary school was involved. The sample size was N = 79, where 77 were grade three students in a science class and two teachers. Data collection involved documentary review, observation and interviews. Data analysis employed both content analysis and a dependent t-test to determine the effect size of the initiative. Findings: The findings revealed that KQMI had a significant impact on improving performance in mathematics among students (t (71) = −7.917, p < 0.05). The study also showed that male students improved their performance more than their counterparts throughout the KQMI. The mathematics teacher revealed that students still need assistance to solve mathematical questions with different techniques to develop the expected competencies. Research limitations/implications: The initiative was conducted only in one school, limiting the findings' generalization. Also, the innovation faced different challenges, such as accessing adequate resources and students with little knowledge of mathematics, which the initiative aimed to address. Practical implications: Pedagogical innovations enhance the promotion of students' interest in learning mathematics and hence improve their performance. Also, through pedagogical innovations, teachers improve their teaching skills and practices from students' feedback. Originality/value: The KQMI is a new pedagogical innovation modified from the existing innovations such as game-based method, task design, mobile learning and mathematics island. [ABSTRACT FROM AUTHOR]

Purpose: Internet technology in the classroom has become the primary demand of every student in this era. Moreover, information and communication technology aids students' learning involvement and progress by providing learning assistance by improved instructor, pupil and interactions with fellows. Using an asynchronous Web-based learning environment (WBLE) is one way to manage such assistance. This study aims to identify to what extent the asynchronous WBLE affects students' interest and motivation in learning mathematics at Shah Abdul Latif University (SALU), Khairpur. Design/methodology/approach: This research uses a survey research design under a quantitative approach. Therefore, data are collected through a questionnaire about students' motivation and interest in learning mathematics via asynchronous WBLE. Data are collected from the students of four departments (BEd, BSCS, BBA, BS Mathematics) of SALU, Khairpur. However, as the nature of this study is quantitative, both descriptive and inferential statistics were used in the results and discussion, and a one-way ANOVA test was used. The Cronbach alpha test was also used to assess the item's reliability, and the items were found to be acceptable. Findings: The findings of this study discovered that asynchronous WBLE has a significant impact on students' intrinsic, extrinsic and interest levels. The results indicated that there is a positive impact based on the level of mean range of asynchronous WBLE on mathematics students. Research limitations/implications: The outcome of this study can be used as a guideline to understand and further plan or develop educational interventions based on the level of motivation and interest of mathematics students towards asynchronous WBLE in other contexts. Originality/value: This is first study of its nature in the context of Khairpur district of Sindh that emphasizes on the motivation and interest of mathematics students toward asynchronous WBLE. [ABSTRACT FROM AUTHOR]

Purpose: The aim of this study was to measure the readiness of science and mathematics supervisors to utilize technology and online learning platforms for teachers' plans and professional development, during and after the period of the COVID-19 pandemic. Design/methodology/approach: To achieve this aim, the researchers developed a questionnaire comprising of 55 items based on the instruments used in pertinent studies. A mixed-methods research design was employed, whereby a quantitative online survey was supplemented by focus group discussions with selected supervisors. Survey data were subjected to one-way analysis of variance and t-test, while information obtained via focus groups was coded to identify common themes related to the obstacles and challenges supervisors face. Findings: When completing the survey, the supervisors approached proficiency using technology; however, focus group discussions revealed misconceptions related to e-leaning and limitations in their abilities to use technology in schools, as well as obstacles imposed by the structure and management of the educational system. T Practical implications: These findings indicate that supervisors need support in acquiring the competencies required for integrating technology in education, and that their support to teacher community needs to be grounded in clear and systematic approaches and best educational practices. Originality/value: These findings indicate that supervisors need support in acquiring the competencies required for integrating technology in education, and that their support to teacher community needs to be grounded in clear and systematic approaches and best educational practices. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to focus on electronic applications that have an effective role in raising the awareness of the dangers of viruses' transmission from person-to-person and their positive and important impact on people's lives. Design/methodology/approach: The authors illustrated the effects of socializing with infected people on a human body by a model in geometry and how the prospected antibiotic annihilates the structure of the virus. The authors discussed vital operations inside the human body to expound the geometry of objects that are closed under their operations, such as viruses, especially Coronaviridae. Findings: Also, the authors discussed some of the e-health applications in Jordan. As e-health activities, programs and applications have been given attention, the authors focused on potentials for constructing strategies that lead to create a featuring health technology. Originality/value: Moreover, in this study, the authors explored the structure and geometry of Coronaviridae family, especially coronavirus that causes lots of diseases, and explained its movement mechanism using the mathematical structures. [ABSTRACT FROM AUTHOR]

Purpose: The national mathematics curriculum of Pakistan has emphasized on improving content knowledge, reasoning abilities and problem-solving skills of students about thinking, communicating and solving mathematics (national mathematics curriculum of Pakistan, 2006). Whereas, there is a need to understand the point of view of teachers about the challenges they face in achieving the goals of national mathematics curriculum. This will help leading teacher training institutions to revisit their math teacher continuous professional development (CPD) programs and facilitate school leadership in improving the quality of math education in rural schools of the province. However, the purpose of this research study is to figure out the challenges that teachers are facing while achieving the goals of the national curriculum by teaching mathematics at the primary level in educational institutes of Pakistan. Design/methodology/approach: In this research study qualitative research approaches have been utilized, in which focus group discussions (FGDs) were used as data collection techniques. Furthermore, thematic analysis of the data led toward the development of four overarching themes such as teachers' knowledge about mathematics curriculum, challenges relating to mathematics content and pedagogy, difficulties in developing conceptual understanding and designing lesson plans to address students' diversity. Findings: The overall findings of this research study suggested that the majority of teachers are facing difficulties in mathematics content teaching such as decimal fraction, unitary method, measurement principles, practical geometry and data handling. Moreover, teachers are also facing challenges and difficulties in developing hands-on and minds-on activities in the teaching of mathematical concepts to the students of primary level in educational institutes of Pakistan. Practical implications: This research study will facilitate the teachers and stakeholders to address the problematic issues in the domain of content delivery of mathematics. Whereas, this study recommends educating teachers about national mathematics curriculum and to develop a CPD framework for mathematics teachers for the enhancement of their pedagogical content knowledge. The study also recommends orientating school heads about the different aspects of math curriculum so that they can mentor math teachers in achieving math curriculum goals. Originality/value: This is the first research study of its nature, which targets and highlights the teacher's perceptions toward the achieving the goals of national mathematics curriculum of Pakistan and addressing the pedagogical challenges faced in mathematics teachers. There is a dearth of studies in mathematics education in Sindh province. The issue is of immense importance, the findings will help teachers to improve mathematics instructions at primary level. [ABSTRACT FROM AUTHOR]

Purpose Self-efficacy and outcome expectations influence the development of career interests, which, in turn, affect career choices. This study aims to understand self-efficacy beliefs and expectancy outcomes for African-American graduate students and faculty with a focus in science, technology, engineering and mathematics (STEM) degree programs, namely, the computing sciences.Design/methodology/approach This qualitative study examined the lived experiences of 23 African-American graduate students and faculty members in the STEM field of computing sciences.Findings This study reveals that in different stages of the STEM trajectory, self-efficacy of STEM and computing needs to be reestablished. This research captures a novel space in the self-efficacy literature, presenting self-efficacy as a mobile construct to be re-achieved as students’ progress toward advanced STEM degrees. In addition, this study asserts that the contribution and input of teachers, parents, mentors, counselors and peers has a deep impact on the level of self-efficacy and persistence in computing sciences.Originality/value Findings suggest a greater need for interventions designed to reestablish self-efficacy at each level (e.g. undergraduate, masters and doctoral degrees) of the STEM educational trajectory in an effort to broaden STEM participation at the highest levels of degree attainment. [ABSTRACT FROM AUTHOR]