Proponents of the history and pedagogy of mathematics (HPM) argue that the integration of the history of mathematics can help inculcate positive attitudes towards the study of mathematics. However, to the best of our knowledge, little has been done on the opportunity for the integration of the narrative accounts of the history of circle theorems. In this paper, senior high school students were exposed to a lesson that integrates a brief narrative of the history of Euclidean geometry with particular focus on Book III of the Elements. It was shown that students held positive beliefs and higher confidence about learning circle theorems after being exposed to the story of the history of the Elements. The findings imply that teachers could incorporate the history of mathematics concepts into lessons to promote students’ attitudes towards learning. Further research is needed to investigate the effect that history-integrated instruction may have on students’ performance in circle theorems and extend the study to other geometric topics.

This study highlights the importance of developing critical thinking skills in modern mathematics, particularly when students face ill-structured problems. Using a scoping review method, the research followed five stages: formulating research questions, identifying relevant articles, removing duplicates, mapping data, and summarizing findings. Data were collected from Google Scholar, Publish or Perish, and Connected Papers, covering publications from 2015 to 2025. Based on the PRISMA selection process, 20 relevant articles were analyzed. The findings reveal that students’ critical thinking and mathematical problem-solving abilities in ill-structured contexts are still relatively low. Many students struggle with key aspects of critical thinking, such as verifying information, conducting in-depth analysis, and reflecting on their solutions. These limitations indicate that students are not yet fully equipped to handle complex, open-ended mathematical problems. Thematic analysis shows a shift in research focus over time. Between 2015 and 2020, studies primarily identified students’ difficulties and barriers. However, from 2021 to 2025, research has increasingly emphasized the development of higher-order thinking skills (HOTS), numeracy literacy, and preparedness for the Industrial Revolution 4.0. The study recommends future research to explore innovative learning interventions that integrate creativity, critical thinking, and ill-structured problem-solving.

This article attempts to intervene in the scholarly debate about Monique Wittig’s status as an “anti-identitarian” thinker by highlighting the ways that mathematics appears throughout her oeuvre as a privileged site of pre-linguistic creativity, wherein a form identification seems to remain possible. Whereas Wittig pointed to language as the semiotic system that allows discourse to smuggle heterosexual and masculinist determination into all the identificatory acts of the speaking and writing subject, the counting and numbering subject seems for her to escape a similar critique. I investigate how this distinction structures her novel The Lesbian Body: I apply concepts drawn from mathematics, focusing especially on the concept of homology, to ask under what conditions we can understand Wittig’s lesbian as having, or rather producing through her particular approach to enumeration, an identity. I claim that Wittig gives us an example of how mathematical thinking can bleed into literary thinking in the domain of sex, gender, and identity, without imagining that bleed as dangerous abstraction, a masculinist domination of the affective, or a cheap metaphor. As Wittig’s importance as an author and philosopher undergoes reevaluation, my wager is that it would be useful to attend to her interventions in the way that the Western philosophical canon and the history of mathematics have been entwined.

The integration of digital technology, particularly artificial intelligence, is crucial in addressing the challenges of mathematics learning in higher education, which often triggers cognitive anxiety and low student interest due to overly theoretical conceptualization. This study aims to analyze the implementation of intelligent systems as a tool to bridge psychological barriers and increase learning motivation through a personalized approach. The research method employed a descriptive literature review of sixteen reputable scientific articles from 2020 to 2025. The systematic steps included data identification, raw information reduction, narrative presentation, and drawing conclusions through continuous verification. The research findings indicate that instant feedback features and algorithm-based dynamic visualizations can strengthen the depth of understanding of mathematical concepts independently. The adaptive learning system successfully creates a flexible learning experience that accommodates individual pace, thus further enhancing the transformation of students into active subjects. However, structural barriers such as limited technological infrastructure and low digital literacy among educators remain major obstacles to the distribution of quality intelligent education. The main conclusion confirms that although artificial intelligence has transformative potential in boosting academic achievement and critical thinking skills, its success is highly dependent on the readiness of human resources and the support of adequate institutional facilities to create an inclusive, modern, and progressive mathematics learning ecosystem in the future for the advancement of a more effective global educational civilization.

In the context of digitalization of education and the rapid development of artificial intelligence (AI) technologies, the problem of developing students’ logical and analytical thinking becomes particularly important. Modern mathematics education requires not only mastery of algorithmic skills but also the ability to reason, argue, and find solutions independently. The application of AI technologies in mathematics education makes it possible to reorganize the learning process - to make it adaptive, interactive, and oriented toward the cognitive characteristics of students. AI tools such as Intelligent Tutoring Systems (ITS), Computerized Dynamic Assessment (CDA), Automatic Speech Recognition (ASR), Natural Language Processing (NLP), and chatbots provide new forms of interactive engagement, analytical observation, and reflective learning. Therefore, the relevance of this study lies in the need for a scientific and methodological understanding of the role of AI technologies in developing logical thinking during mathematics education and in justifying the pedagogical conditions for their effective use in a digital learning environment.

A Cultural History of Mathematics in the Early Modern Age

UDC 512.5 We focus on recent promising trends in the application of the key concepts and approaches from the classical infinite-group theory to various branches of algebra, such as modules over group rings, infinite-dimensional linear groups, Leibniz algebras, other generalizations of the Lie algebras, and braces. The efficacy of these trends has been well-documented in a series of recent books from reputable publishers. In our article, we present a concise overview of these emerging trends. The analysis of the mutual influence of algebraic systems promotes deeper understanding of their individual and collective significance and illustrates the unity and diversity typical of contemporary mathematics. We believe that the subsequent development of investigations in this field would promote the appearance of new discoveries and innovations clarifying the fundamental role played by the groups, rings, algebras and other algebraic structures in modern mathematics.

In this modern era, mathematics and technology go hand-in-hand paving way for better lifestyle. To comprehend many situations, it requires special tool and applications by which those situations can become manageable. One such mathematical tool is the concept of graphs whose applications spread far and wide. Graphs are not complex structures that are hard to fathom. Neither they are just dots and lines nor intricate edifices. but they represent multifarious situations into simple structures of dots and lines. Of all topics in graph theory, the one that stood out and provided the much needed impetus is the concept of vertex antimagic edge labeling. The concept of vertex antimagic edge slither labeling is a special case of vertex antimagic edge labeling.

The paper explores the history of set theory and its philosophies, with special focus on the early work of Georg Cantor. The revolutionary change of thought in the 19th century introduced set theory as a rigorous method to study infinite sets, continuity, and the structure of mathematical objects. Cantor’s introduction of transfinite numbers, cardinality, and the diagonal argument established the distinction between countable and uncountable infinity, fundamentally altering the concept of mathematical infinity. The study examines mathematics as an applied system, a philosophical investigation, and a reflection of human cognition. It traces the history of mathematical abstraction in the form of conditional notions, as opposed to formal systems based on axioms, including Zermelo–Fraenkel set theory (ZF) and Zermelo–Fraenkel with the Axiom of Choice (ZFC), through an analysis of Cantor’s work in relation to number theory, Fourier series, and the modeling of infinite sets. It also addresses historical paradoxes, such as the Galileo paradox and the Russell paradox, which set theory resolved, establishing a consistent foundation for modern mathematics. Furthermore, the paper investigates the impact of Cantor’s work on modern mathematical disciplines including topology, analysis, algebra, and logic, and emphasizes the ongoing applicability of his contributions in both theoretical and applied mathematics. The study highlights the philosophical implications of the absence of limits and the aesthetic virtue of mathematics and set theory, central to the development of meta-thinking in human cognition. Overall, this study contributes to the historical and conceptual framework of Cantor’s works and explains how set theory was born, ultimately revitalizing the principles of modern mathematics.

Studies show that using original historical sources as a context for teaching problem-solving enhance students problem-solving skills and mathematical understanding. Despite, the extent to which it can improve students’ strategy flexibility in problem-solving is not well reported. This paper present quasi-experimental study that sought to examine whether history-integrated lessons on cubic equations improves senior high school students’ strategy flexibility. Participants were 128 Form 2 science students from two senior high schools in the Ashanti Region of Ghana, assigned to an experimental group or a control group. The experimental group was taught original historical approaches to solving cubic equations. Lessons emphasised the algebraic methods developed by early mathematicians such as del Ferro, Tartaglia, and Cardano. The control group, on the other hand, were taught the standard algebraic methods such as rational root test and factorisation. Afterwards (i) post-test data was collected using strategy flexibility test and was analysed to identify if there was statistically significant difference between the flexibility scores of the control and experimental groups; and (ii) qualitative data was collected from selected students using an interview to explain the reasons behind the difference observed within the post-test data. Findings showed that the experimental group had improved flexible and innovative first-step strategy use than the control group. Thematic analysis of the qualitative data revealed three themes that support the observed difference in strategy flexibility (i) expansion of strategy repertoire, where students reported that they now have knowledge of alternative methods for solving cubic equations, (ii) situational strategy selection where students reported of having improved ability to select strategies appropriate to a given equation structure, and (iii) motivational dispositions where students reported of becoming interested, enjoyed, engaged and confident. The results suggest that teaching students’ non-linear equation-solving by history-integration can meaningfully enhance strategy flexibility. These findings align with the theory of adaptive expertise and findings of existing empirical studies in the history and pedagogy of mathematics. The study recommends that teachers should teach problem-solving in algebra using the historical context of concepts. The study is limited in the sense that participants were assigned to groups non-randomly, lessons were short in duration, and sample was not larger enough. Future research should employ more rigorous designs, larger samples, extended lesson periods, and follow-up assessments to evaluate long-term retention and transfer of strategy flexibility.

Foundations of Information Security Mathematics is a core foundational course for information security–related majors, covering topics such as number theory, abstract algebra, and elliptic curves, and other essential mathematical topics. Due to its high level of abstraction, intensive use of formal proofs, and substantial mathematical rigor, students often experience significant learning difficulties and lack sustained motivation. In the context of curriculum ideology and politics in higher education, this paper explores an instructional approach that integrates the history of mathematics and mathematicians’ narratives into classroom teaching. Taking Fermat’s Little Theorem and Euler’s Theorem as representative examples, we analyze how historical narratives can enhance student engagement, deepen conceptual understanding, and foster scientific spirit and academic values. Teaching practice indicates that employing the history of mathematics as an entry point for curriculum ideology facilitates the organic integration of professional knowledge transmission and value education, offering a viable reference for instructional reform in mathematics courses for information security programs.

This paper presents a unified study of integer partition theory, a foundational area of number theory and combinatorics. The subject is situated within its historical development, from Euler’s generating function framework to Ramanujan’s profound congruences, and then advances beyond classical exposition by synthesizing these ideas with modern combinatorial perspectives. The work systematically develops essential tools—including Ferrers and Young diagrams, Durfee squares, and generating functions—within a single coherent framework. Classical theorems are rigorously proved using both Algebraic and Combinatorial Techniques, Highlighting the Complementary Nature of these approaches. A novel aspect of this paper lies in its integrative treatment of partitions across different number systems and its qualitative exploration of applications extending beyond pure mathematics, demonstrating how partition theory interfaces with broader mathematical structures. By combining historical insight, illustrative constructions, and formal proofs, this study not only consolidates foundational knowledge but also clarifies pathways toward contemporary research questions in partition theory. The results underscore the continuing relevance of integer partitions as a unifying language in modern mathematics and provide a pedagogically strong and research-oriented framework for future investigations in combinatorics and number theory.

This study examines emerging branches of mathematics, focusing on how theoretical constructs are transformed into practical applications across contemporary fields. It is a review‑based analysis that synthesises mathematical theories and their applications across artificial intelligence, epidemiology, and sustainability. The research aims to: (1) trace major directions in modern mathematical development and their practical implementations, and (2) analyse how theoretical advancements evolve into applied methodologies. A mixed‑methods approach is employed, combining a qualitative review of scholarly literature (2010–2025) with quantitative demonstrations using mathematical modelling and numerical simulations. Applications in artificial intelligence, epidemiology, and sustainability are explored to illustrate the growing reliance on algebraic structures, optimisation techniques, and differential equations. Recent studies also highlight the integration of artificial intelligence with epidemiological modelling and public‑health analytics. The findings underscore mathematics as a central interdisciplinary tool for addressing global challenges such as pandemics, climate change, and technological innovation. The mathematical equations and simulations presented are illustrative, serving to demonstrate key concepts rather than introduce new theoretical developments. Overall, the study emphasises the reciprocal relationship between theoretical progress and the development of implementable solutions to complex real‑world problems.

Poniższy tekst zawiera informacje o XXXVI Konferencjiz Historii Matematyki, która odbyła się w Będlewie w dniach 18–22maja 2025 roku.

Teaching algebra at the senior high school level often privileges procedural fluency at the expense of deeper conceptual understanding, which has left students unable to reason about the underlying structures of algebraic objects. This study investigates the potential of integrating the history of mathematics (HoM) as a pedagogy to foster students' structural reasoning in cubic equations. Grounded in the structural reasoning framework of Harel and Soto, the study employed a quasi-experimental non-equivalent control group design involving 128 senior high school students from two schools in Ghana. The experimental group received history-integrated lessons on cubic equations, drawing on historical developments such as the classification of cubic forms, transformations to depressed cubics, and early solution methods, while the control group received standard curriculum-based lessons. Quantitative data were collected using structural reasoning test and analysed using Quade's non-parametric ANCOVA to control for pre-existing differences. Results revealed statistically significant and practically meaningful difference in structural reasoning between groups. Qualitative data collected using semi-structured interviews further illuminated how historical contexts enhanced students' recognition of algebraic structure, deepened conceptual understanding, and shifted problem-solving approaches from procedures execution to structural analysis. The findings provide empirical evidence that the HoM can function as more than an enrichment tool; it can serve as a powerful instructional resource for promoting advanced algebraic thinking. This study contributes to research in history-and-pedagogy-of-mathematics by demonstrating how historically informed lessons can support structural reasoning in higher-order polynomial contexts and offers a theoretically grounded model for integrating HoM into secondary algebra teaching.

This article will present a summary of Abel’s proof, in the style in which he presented it, in which it will be seen both as the culmination of a long story in the history of mathematics and the beginning of a new one.

This study aimed to design a prototype mathematics museum for use in mathematics education, drawing on pre-service teachers’ views following a museum education course and a visit to the Tales Mathematics Museum. Employing a basic qualitative research design, this study involved 20 pre-service mathematics teachers selected through criterion sampling. Data were collected via an interview form developed by researchers and analyzed using content analysis. Findings were presented in tables and supported by direct quotations from participants. The results demonstrated that both the course and the museum visit positively influenced pre-service teachers’ perceptions of museums as out-of-school learning environments. According to participants, museums provide opportunities to establish interdisciplinary connections, enrich knowledge of mathematical history, model and concretize abstract concepts, engage students, and support diverse activities. Pre-service teachers recommended that a mathematics museum should incorporate technology-supported simulations, representations of mathematical history, concrete models of theorems, and connections to daily life and art, while being designed to sustain student engagement. In conclusion, a prototype mathematics museum was developed based on these suggestions, underscoring the potential of museum-based approaches to foster meaningful, interdisciplinary, and engaging mathematics learning experiences.

The article examines the problem of developing students’ critical thinking through the study of the history of mathematical discoveries. It emphasizes that, within the modern educational paradigm focused on the competence-based approach, the formation of critical thinking is one of the key objectives of learning. The views of foreign and Ukrainian scholars (J. Dewey, M. Lipman, D. Halpern, P. Saukh, S. Terno, O. Pometun, and others) on the essence of critical thinking as a conscious, reflective, and independent process of reasoning based on evidence and logic are analyzed. It is substantiated that the history of mathematical discoveries has great potential for developing critical thinking, as it demonstrates the evolution of scientific ideas, the path from mistakes and doubts to proven truths. A set of effective methodological techniques is proposed, including the creation of problem-based situations with historical content, the use of interactive methods, the organization of research projects, the preparation of digital products (presentations, videos), and the solving of historical mathematical problems. It is emphasized that engaging students in exploring the history of science contributes to the development of analytical abilities, fosters skills of comparison, argumentation, evaluation of various viewpoints, and the ability to make reasoned decisions. The article concludes that the history of mathematics serves as a powerful didactic tool for fostering critical thinking, combining cognitive, research, and educational potential, and promoting the development of creative, thoughtful, and independent learners.

Modern mathematics education must shift from merely "knowing" mathematics to "doing" mathematics. This "doing" process inherently demands strong problem-solving skills, which can only flourish in students who have internalized Habits of Mind as part of their intellectual character. In this study, we report on the effect of a flipped classroom learning model, assisted by the eXe-Learning application, on the mathematical problem-solving abilities of students with high, moderate, and low categories of Habits of Mind. This study employed a quantitative method with a quasi-experimental design. The sampling technique used was cluster random sampling, with classes serving as the clusters. Research data were collected using two types of instruments: test and questionnaires. The data were analyzed using a two-way ANOVA with unequal cell sizes, preceded by prerequisite tests for normality and homogeneity. Based on the analysis, it can be concluded that the flipped classroom model assisted by the eXe-Learning application has a significant effect on both students' mathematical problem-solving abilities and their Habits of Mind. However, the interaction between the flipped classroom model and students' Habits of Mind did not have a significant effect on their mathematical problem-solving abilities. Keywords: Flipped classroom; problem-solving skills; exe-learning; habits of mind

School mathematics instruction remains shaped by pedagogical traditions rooted in nineteenth-century industrial models that privilege static, indoor, and calculation-focused learning. Alternative possibilities for mathematical understanding emerge through embodied, arts-based, and outdoor pedagogies that engage movement, sensory experience, and the living world. Drawing on more than a decade of pedagogical design experiments with educators, preservice teachers, and students, mathematics learning is examined in campus gardens, forests, beaches, and other outdoor environments. Mathematical ideas are developed through bodily movement, artistic practice, and multisensory engagement with land, materials, and seasonal cycles, alongside more familiar forms of mathematical representation. These pedagogical experiments suggest that learning mathematics in and with the more-than-human world can deepen conceptual understanding, foster collaboration, and reconnect mathematics with its historical and ecological roots. Rather than displacing indoor classrooms or paper-and-pencil work, a more balanced mathematics curriculum is advanced—one that integrates embodied and outdoor approaches as complementary ways of knowing across STEM/STEAM education. Keywords: mathematics education, embodied learning, arts-based approaches, greater-than-human world, outdoor classrooms, dance, movement, and mathematics, mathematics and fibre arts, history of mathematics and astronomy, geometry, mathematical understanding