Numerous studies have been conducted from the perspective of high school students, examining the factors that contribute to their refusal to pursue higher education institutions (HEIs). Presently, there is limited study investigating teachers’ viewpoints regarding their roles as change agents in encouraging students towards HEIs. Therefore, this study seeks to provide new insights from educators that can strengthen teacher training and development, as well as inform the creation of customised intervention strategies designed to promote a culture of academic aspiration and achievement among students. Grounded in the philosophical premise of social constructivism, the study employed a qualitative methodology, analysing a sample of ten teachers selected by purposive sampling. In-depth interviews were conducted, and the data were analysed using thematic analysis. Our findings provide a comprehensive understanding of the strategies teachers used and the challenges they faced when motivating students to pursue HEIs. We proposed a conceptual study framework built from these findings, illustrating the interaction between teachers’ duties, educational problems, and students’ aspirations for further education. Our research is significant as it advances theory development in educational psychology and motivation theory by revealing new themes and relationships that can enhance existing theoretical frameworks.
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The journal welcomes original work on advancing research integrity in the form of empirical research, conceptual assessment, and critical analysis in all fields of science, including biology, chemistry, physics, medicine, law, economics, statistics, management studies, public policy, politics, sociology, history, psychology, philosophy, ethics, and information science. The journal seeks to publish research that makes a significant contribution to the literature and advances knowledge of accountability and integrity in research. With some exceptions, the journal is not interested in publishing studies that merely duplicate previous work or are limited in generalizability (e.g., due to problems with statistical design or research focus) or that in other ways fail to contribute meaningfully to the scholarly literature
The science, technology, engineering, and mathematics (STEM) education has emerged as a global education priority, many countries have printed their development strategies to national blueprints and recognized STEM education as a key role in the effective implementation of skills training in the
21st-century. Project-based learning (PjBL) and problem-based learning (PrBL) or PBL is significant in cultivating students’ knowledge and skills, integrating PBL into STEM (PBL-STEM) education is a new attempt in recent years to integrate student-centered learning methods into the STEM learning process. This study aims to explore the development trends of PBL-STEM and provide recommendations to support talent cultivation in the digital era. Based on a systematic review of 1999 articles in SCOPUS database, this study uses content analysis to identify key themes in PBL-STEM. The findings indicate that the construction of student-centered PBL curriculum, the development of innovative teaching models, and interdisciplinary integration are central to the evaluation of PBL-STEM. Moreover, the integration of emerging technologies and multi-disciplinary approaches enhances STEM competency to cultivate 21st-century skills. PBL-STEM emphasize students’ higher-order abilities, positioning it as a strategic reform for future society. This study reveals the importance of curriculum innovation, instructional reform, evaluation mechanisms, and the professionalization of STEM educators are fundamental with the rapid technological advancement.
Fundamental Theorem of Arithmetic
Every integer greater than 1 can be written uniquely (up to ordering) as a product of prime numbers. The existence half follows from the well-ordering principle; uniqueness is proved by induction together with Euclid’s lemma that a prime dividing a product must divide one of the factors.
In the language of unique factorization domains the statement simply asserts that \(\mathbb{Z}\) is a UFD.
Fermat’s Little Theorem
If \(p\) is prime and \(a\) is an integer not divisible by \(p\), then \(a^{p-1}\equiv 1\pmod{p}\). Equivalently \(a^p\equiv a\pmod{p}\) for every integer \(a\). The result is a special case of Euler’s theorem once one observes that \(\varphi(p)=p-1\).
Quadratic Reciprocity
Let \(p\) and \(q\) be distinct odd primes. Then
\[
\Bigl(\frac{p}{q}\Bigr)\Bigl(\frac{q}{p}\Bigr)=(-1)^{\frac{p-1}{2}\cdot\frac{q-1}{2}},
\]
where \(\bigl(\frac{\cdot}{\cdot}\bigr)\) denotes the Legendre symbol. The law completely determines the solvability of the congruence \(x^2\equiv p\pmod{q}\) in terms of the solvability of \(x^2\equiv q\pmod{p}\).
Dirichlet’s Theorem on Arithmetic Progressions
If \(a\) and \(d\) are coprime positive integers, then the arithmetic progression \(a,a+d,a+2d,\dots\) contains infinitely many primes. The original proof proceeds by showing that the Dirichlet \(L\)-function \(L(s,\chi)\) attached to the non-principal character modulo \(d\) does not vanish at \(s=1\).
Prime Number Theorem
The number \(\pi(x)\) of primes not exceeding \(x\) satisfies \(\pi(x)\sim\frac{x}{\log x}\) as \(x\to\infty\). Equivalently the \(n\)th prime \(p_n\) is asymptotic to \(n\log n\). The classical proofs rely on the non-vanishing of the Riemann zeta function on the line \(\operatorname{Re}s=1\).
Quantum dots are semiconductor nanocrystals composed of elements of the II-VI, III-V or IV-VI groups, such as CdS, ZnSe and InP, with sizes ranging from 2 nm to 10 nm and a core–shell structure. They exhibit properties not found in bulk semiconductor materials and demonstrate excellent photostability and non-bleaching properties even after exposure to light for a prolonged time. Some of their applications are summarized in [1]. Quantum dots are also used for optical data storage applications to induce chemical or physical changes in the nanoparticles through laser irradiation and as electron donors to enhance the sensitivity of photoswitchable molecules [2,3,4]. According to their band alignments, InP/ZnS QDs are type-I core–shell QDs and contain shell materials with a wider band gap than that of the core, which can improve the quantum yield (QY) remarkably [5]. These tiny particles find applications in various fields, such as biomedicine research and patient care, as a non-toxic alternative to Cd-based quantum dots, focusing on non-invasive imaging, preventive oncology [6], and optics, because of their peculiar optical properties. Research on II-VI and IV-VI semiconductor quantum dots (QDs) is quite widespread, while the exploration of the vast compositional space of MCQDs is still in its infancy. Significant progress has been achieved in ternary and multinary I–III–VI quantum dots, enabling precise control over band structure and optical properties. Systems such as AgInS2 with ZnS shells exhibit tunable absorption and emission, along with enhanced quantum yields due to band alignment effects [7,8]. Environmentally friendly multinary structures, e.g., Ag–In–Zn–S, have also been developed, offering near-infrared emission and suitable band offsets. More complex core–multishell architectures further improve band engineering and significantly enhance photoluminescence through optimized band alignment and surface passivation [9,10].
While policy encourages data-sharing, practice has yet to catch up. Existing literature indicates various reasons for not sharing research data. These include unavailability, privacy concerns, ethical concerns, lack of publisher compulsion, and others. It is important to address the issue of authors not responding to requests despite a promise. Policymakers also need to examine this issue to identify ways to improve data-sharing and promote open science.
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