History Of Mathematics Research Articles

“Everyone Can Master the Correct Use of Mathematical Methods”: The Relevance of L.D. Kudryavtsev’s Ideas for Modern Mathematics Education

The article discusses the ideas, devoted to mathematics education, of Lev D. Kudryavtsev, corresponding member of the USSR Academy of Sciences, professor-mathematician. These ideas are based on more than half a century of practical experience of L. D. Kudryavtsev at the Moscow Institute of Physics and Technology – he presented his vision of the problems of educating students, the unity of mathematics, as well as methods of teaching it in the collection of articles. The thoughts and ideas of L. D. Kudryavtsev are still relevant today, in the age of digital transformation of the education system and of the entire life of society.

Bridging cognitive neuroscience and education: Insights from EEG recording during mathematical proof evaluation

BackgroundMuch of modern mathematics education prioritizes symbolic formalism even at the expense of non-symbolic intuition, we contextualize our study in the ongoing debates on the balance between symbolic and non-symbolic reasoning. We explore the dissociation of oscillatory dynamics between algebraic (symbolic) and geometric (non-symbolic) processing in advanced mathematical reasoning during a naturalistic design. MethodEmploying mobile EEG technology, we investigated students' beta and gamma wave patterns over frontal and parietal regions while they engaged with mathematical demonstrations in symbolic and non-symbolic formats within a tutor-student framework. We used extended, naturalistic stimuli to approximate an authentic educational setting. ConclusionOur findings reveal nuanced distinctions in neural processing, particularly in terms of gamma waves and activity in parietal regions. Furthermore, no clear overall format preference emerged from the neuroscientific perspective despite students rating symbolic demonstrations higher for understanding and familiarity.

Analysing Hermann Graßmann’s works – retrospecting and re-assessing

ABSTRACT The life and work of Hermann Günther Graßmann (1809–1877) attract not only ever again the attention of mathematicians, mathematical historians and those interested in the history of mathematics, they constitute also a challenge for the methodology of historiographical research. This challenge persists since Friedrich Engel’s biography of 1911; there, two sources were presented and interpreted in a not legitimate manner which even mislead since then various scholars. This paper faces the intricate task to unravel not only the methodological shortcomings of Engel’s biography, but also to re-assess the misinterpretations – particularly of alleged influences on Graßmann’s approaches – induced by Engel’s misleading claims. Based upon broader historically contextualised analyses of Graßmann’s innovative elements in his theory of extension and upon new primary sources for his student times at the Gymnasium and Berlin University, the paper presents a novel assessment of Graßmann’s approaches.

Logic Matters – Gender and Diversity, Too

Abstract This interview features Andrea Reichenberger. Currently she holds a substitute professorship for history of technology at TUM Technical University of Munich. She is junior research group leader at the Department of Mathematics, University of Siegen, Germany, and leads the research project “Rethinking the History of Mathematics and Physics: Women in Focus.” Reichenberger has held several postdoctoral positions, e.g., at the Center for the History of Women Philosophers and Scientists (HWPS) at Paderborn University (Germany) and in the DFG research project “Thought Experiment, Metaphor, Model” at the Institute for Philosophy I at the Ruhr University Bochum. Between 2019 and 2021, she was a fellow at the University of Paderborn and principal investigator of the research project “Foundational research in mathematical logic – relativity – quantum physics. Case studies on the integration of women philosophers.” Reichenberger has written a book on Émilie du Châtelet (Springer, 2016) and has published many articles in journals, collected editions, and encyclopedias.

Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics

Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics

A Short Note on the Early History of the Spectrum Problem and Finite Model Theory

Finite model theory is currently not one of the hot topics in the philosophy and history of mathematics, not even in the philosophy and history of mathematical logic. The philosophy of mathematics and mathematical logic has concentrated on infinite structures, closely related to foundational issues. In that context, finite models deserved only marginal attention because it was taken for granted that the study of finite structures is trivial compared to the study of infinite structures. In retrospect, research on finite structures turned out to be neither trivial nor irrelevant but had an important impact on theoretical computer science. A closer look at the early history of the spectrum problem shows that the birth of finite model theory has roots in formal logic, at a time when computer science did not yet exist.

Integration of Mathematics History into Junior Middle School Education: A Pedagogical Approach to Enhance Mathematical Literacy

The integration of the history of mathematics into junior middle school mathematics education represents a significant focus of international research in mathematics and education. The mathematics curriculum standards for compulsory education have emphasized the importance of incorporating the history of mathematics, aiming to gradually integrate it into the mathematics classroom. However, in the practical implementation of junior middle school mathematics education, the effective combination of the history of mathematics with teaching methodologies remains largely unexplored. This article explores the integration of junior middle school mathematics education and the history of mathematics, aiming to provide classroom teaching recommendations for teachers and promote the formation of students’ mathematical literacy.

Project Design and Educational Reform Achievements of Mathematics under the Guidance of “Integration of Doing, Learning and Teaching”

Aiming at higher vocational students’ confusion about mathematics learning, we draw on the “integration of doing, learning and teaching” to change the closed state of mathematics teaching, serving the lifelong development of students. The theoretical basis is Dewey’s educational theory, Tao Xingzhi’s educational thought, Bandura’s activity theory, Marx’s theory on the comprehensive development of human, and system science. Dewey’s theory emphasizes active work, Tao Xingzhi’s educational thought emphasizes a high degree of integration of students’ practice, teachers’ guidance and their joint learning, Bandura’s theory emphasizes the relative effectiveness of teaching and learning, Marx’s theory of “whole person” emphasizes treating human as a whole, and his theory of systematic science emphasizes the synergistic collaboration between education reform and other aspects. Through the research, we have developed an open classroom, an effective teaching structure, an effective teaching methodology, an effective curriculum carrier for constructing mathematical literacy-mathematical culture and practice activities, enabling the integration of mathematical history with teaching and learning, and the emotional input for mathematical diary.

The Game Theory Application in the Transport Flows Control Algorithm Development in the Intelligent Transport System

Traffic management in modern intelligent transport systems includes monitoring the actual traffic situation in real time (volumes, speeds, incidents, etc.) and management or controlling transport traffic using this information. At the same time, cars as intelligent transport systems components must be equipped with communication capabilities for exchanging information with other vehicles (V2V) and with road infrastructure (V2I). All this is connected with the presence of special equipment connected to the on-board network for local data collection, which can be exchanged between cars and with a central communication station using wireless Internet. At the same time, the issue of developing the traffic organization algorithms themselves is still open. This problem can be solved with the help of game theory, a fairly new but rapidly developing part of modern mathematics. Unlike optimization theory, which studies the possibilities of constructing an optimal solution for the entire system as a whole, game theory studies ways to optimize individual benefits in competition with other persons (events) that rationally seek to satisfy their own benefits. The problem of “smart” regulation of intersections is quite difficult to solve, it combines the efforts of scientists from different fields of knowledge. However, the rapid development of ICT technologies and their rapid application to transport tasks makes it possible to develop some approaches to optimize the current situation at the intersection.

Algorithm for Control of Traffic Flow in an Intelligent Transport System

Traffic management in modern Intelligent Transport Systems (ITS) includes monitoring the actual traffic situation in real time and management transport traffic using this information. At the same time, cars as ITS components must be equipped with communication capabilities for exchanging information with other vehicles (V2V) and road infrastructure (V2I). Such approach is connected with usage of special equipment connected to on-board network for local data collection, which can be exchanged between cars and with a central communication station using wireless Internet. At the same time, the issue of developing the traffic organization algorithms themselves is still open. This problem can be solved with the help of game theory, a fairly new but rapidly developing part of modern mathematics. Unlike optimization theory, which studies the possibilities of constructing an optimal solution for the entire system as a whole, game theory studies ways to optimize individual benefits in competition with other persons (events) that rationally seek to satisfy their own benefits. The problem of "smart" regulation of intersections is quite difficult to solve a problem, nevertheless it is possible due to rapid development of ICT technologies. Keywords: ITS, transport crossroads, game theory

Generative AI and accuracy in the history of mathematics

Generative AI systems designed to produce text do so by drawing on inferences made from training data, which may mean they reproduce factual errors or biases contained in that data. This process is illustrated by querying ChatGPT with questions from a history of mathematics quiz designed to highlight the common occurrence of mathematical results being misattributed. ChatGPT's performance on a set of decades-old common misconceptions is mixed, illustrating the potential for these systems to reproduce and reinforce historical inaccuracies and misconceptions.

Effects of Perceived Mathematics Connection on Mathematics Motivation: Mediating Role of History of Mathematics Concepts

The present study assessed the mediating effects of history of mathematics concepts on the relationship between mathematics connection and mathematics motivation. The study was a descriptive survey carried out on 390 students randomly selected from Asuoso Senior High School in the Offinso-North District of Ghana’s Ashanti region. Data was collected using Likert type structured questionnaires. Reliability analysis was computed in SPSS (V. 23) and confirmatory factor analysis was computed in AMOS (V. 23). In addition, average variance extracted (AVE), convergent validity, and discriminant validity were computed in Microsoft Excel from factor loadings. Also, composite reliability was calculated at https://www.thestatisticalmind.com/composite-reliability/. Structural Equation Modelling (SEM) was computed in Amos (V. 23) to determine direct, and mediating effects among the main constructs. The study found that mathematics connection positively and significantly influenced mathematics motivation of senior high school students. The indirect effects of mathematics connection on mathematics motivation through history of mathematics concepts was positive and significant. The study recommended that mathematics teachers should desist from merely topic explanations and rote memorization of solution procedures. They should rather make mathematics connections and history of mathematics concepts imminent in their lesson planning and delivery. To implement this, mathematics topics should be linked to real-life scenarios, other subjects, and students’ lives, and the history behind such concepts are explained in plain language. Not only teachers, NaCCA should ensure that the mathematics syllabus and textbooks for senior high schools have incorporated real-life scenarios as well as the historical background of concepts to ensure learners develop the interest and motives for studying mathematics.

English Speaking Teaching Strategies Based on Natural Language Processing

The study of cognitive processes in English teaching methods from the perspective of HPM (History and Pedagogy of Mathematics) provides valuable insights into how students learn and understand the English language. Cognitive research in language learning focuses on the mental processes involved in acquiring, processing, and using language skills. By incorporating the principles of HPM, which examines the historical development and pedagogical approaches in mathematics education, researchers can draw parallels and apply similar methodologies to English language instruction. This paper constructed Bloom’s taxonomy Fuzzy Decision Support System (BTF-DSS). Bloom’s taxonomy provides information about the teacher’s understanding towards the teaching. Through BTF-DSS model offers teachers provides the knowledge and expertise for effective teaching with the fuzzy model. The BTF-DSS model uses the fuzzy logic decision support system for the appropriate significant teaching and learning experience. The simulation analysis of the BTF-DSS model expressed that the fuzzy model exhibits significant performance for the English teaching method in China through the HPM process.

A historical analysis of the independent development of calculus by Newton and Leibniz

This paper undertakes a historical investigation of the separate and independent development of calculus by Isaac Newton and Gottfried Leibniz in the late 17th century. Through analysis of primary sources and historiographical perspectives, it explores the differences in notation, methods, and applications used by each mathematician to formulate foundational concepts of calculus. The research demonstrates that Newton relied more on geometric intuition, developing calculus concepts like fluxions and fluents rooted in kinematic problems. His 1687 Philosophiae Naturalis Principia Mathematica synthesized many calculus innovations. Meanwhile, Leibniz approached calculus from an algebraic mindset, utilizing infinitesimal differentials and comprehensively explaining integral and differential calculus in publications like Nova Methodus pro Maximis et Minimis. Evaluation of letters and documents from the 1670s and 1680s shows no direct collaboration or communication about calculus between Newton and Leibniz. This lack of transmission, coupled with the disparities in their notation and calculus techniques, provides evidence for independent creation. However, Newton and Leibniz shared key insights regarding rates of change, derivatives and integrals, hinting at a broader zeitgeist in early modern mathematics and science. Thus, this dual achievement illustrates how the Scientific Revolution facilitated conceptual convergence despite geographic separation between great thinkers. Investigating this case study offers perspective on the interplay between individual genius and wider social contexts in driving scientific progress. This paper concludes by assessing the legacy of the Newton-Leibniz debate over priority and analyzing work that paved the way for modern unified calculus notation and applications.

Matematik Öğretiminde Matematik Tarihi Kullanımına Örnekler: Ascalon Çarpma Yöntemi, Gelosia Çarpma Yöntemi ve Napier’in Çubukları Yöntemi

The aim of this study is to present the Ascalon multiplication method, Gelosia multiplication method and Napier's rods method, which take place in the history of mathematics, to sixth grade students through activities and to determine the effect of these methods on student achievement, and to get student opinions about this activity. The study group of the research consisted of 60 sixth grade students. A worksheet was used as a data collection tool and an interview form was used at the end of the activity to obtain students' opinions about the activity. According to the quantitative analysis results obtained from the research data, it was determined that the methods taught were effective in increasing student achievement. According to the results of the qualitative analysis, it was concluded that students generally did not encounter such activities much, that they learned the lesson by having fun with such activities, and that their interest in mathematics increased.

Assessing the added value of a history-based activity for students with low mathematics skills

The aim of this pilot study is to evaluate the relevance of the use of history in mathematics education. This paper presents an experiment carried out in France with sixth-grade students (n=108) in which an ancient number system is used, an approach that is commonly suggested in French sixth-grade textbooks but has previously been unassessed. Based on the data of a pre-test and a post-test surrounding an activity on an ancient Chinese numeration system, a statistical analysis using Rasch modeling shows a specific added value of the history of mathematics for students with low abilities in mathematics. For these students, a significant increase in observed abilities of +0.67 logit in mean is measured with a large effect size (Cliff delta +0.52). This effect is then weighted by considering the regression to the mean (RTM) effect, leading to a value around +0.14 logit in mean and a negligible effect size (Cliff delta +0.10). So, this pilot study shows the important effect of RTM, which suggests a very strong rebalancing of students’ results. In the last part of the paper, we discuss how RTM can nonetheless be positively interpreted in this specific context where students’ disorientation is one of the purposes of history in mathematics education.

РОЛЬ МАТЕМАТИКИ В РАЗВИТИИ STEM ОБРАЗОВАНИЯ

In the last decade, increased attention has been paid to the integration of science, technology, engineering and mathematics (STEM) education. It is important for a modern mathematics teacher in elementary and high school to understand the role of mathematics as an academic discipline in the development of STEM education. Practical, meaningful and varied learning strategies can help develop high-level thinking and 21st century skills in teaching and learning mathematics. Research towards integrating STEM is in its infancy. So far, there is no clear understanding of the role of individual subjects in integrated STEM. While it is widely accepted that mathematics is at the core of all other STEM disciplines, there is evidence that it plays an underestimated role in integrated STEM education. The article, based on contemporary publications, examines the role of mathematics in interdisciplinary STEM education, including a synthesis and analysis of research conducted over the past ten years; discusses the integration of STEM subjects with an emphasis on mathematics (integrated STEM); About the productive models of integrated STEM that are emerging as STEM education in general and mathematics education in particular can better prepare people for the challenges of the twenty-first century.

Thermal performance of fractal meta-surface and its mathematical model

How can we explain the thermal phenomenon by a fractal meta-surface? This has been puzzling scientists and engineers for at least ten years, and so far no answer has been found. Now, modern mathematics offers a completely new window to physically understand the magical phenomenon that lies far beyond the Fourier law for heat conduction. A fractal-fractional modification of the Fourier law is elucidated, and its extremely high thermal conductivity is mathematically revealed. This article shows that thermal science is the key to nanotechnology.

Golden Ratio: Construction, Geometry, Beauty, and Diversity

Nature is attractive due to the proper ratios of various components in them and in between others. In nature, leaves, flowers, fruits, Himalayas, hills, valleys, springs, rivers, etc. show a rhythmic balance and seem harmonic and aesthetically pleasing. The golden ratio or the golden (divine) proportion is considered the most pleasing to human visual sensation and is not limited only to aesthetic beauty but also found prominently in the natural world. It is an irrational number denoted by φ and is approximately 1.618034. It is a fascinating topic for mathematicians, artists, natural scientists, philosophers, biologists, artists, architects, musicians, psychologists, designers, etc.
 This research work presents a panoramic view of the golden ratio; their construction algorithms, and structures; mathematical presentations, geometry, patterns, and properties from mathematical perspectives and opens the broad horizon for further research. Besides these, the paper also presents their existences, diversities, their relationships with nature, the universe, arts, design, architecture, and engineering in ancient and modern mathematics and sciences.

The Impact of Using Model-Based Activities Based on the History of Mathematics in Geometry Instruction on Students' Geometry Anxiety

The Impact of Using Model-Based Activities Based on the History of Mathematics in Geometry Instruction on Students' Geometry Anxiety