Exploring the intersection of technology and history: gifted students’ journey in mathematics

The study was purely quantitative and employed descriptive analysis. The study used stratified and simple random sampling techniques to sample 205 students from 431 first-year students pursuing “BSc mathematics education”. The study exclusively utilized a structured questionnaire as its research tool, adopting a quantitative approach. To evaluate the proposed pathways, structural equation modeling was conducted using Amos 23. The study results revealed that the history of mathematics (HoM) had a direct and statistically significant positive effect on both math interest and student motivation (SMOT). Additionally, SMOT significantly and positively influenced math interest. Consequently, SMOT partially mediated the relationship between the HoM and students’ math interests (SMI), which was statistically significant. The study concluded that both the HoM and SMOT directly and positively influence math interest, and the HoM positively affects SMOT. Finally, SMOT partially mediates the relationship between the HoM and math interest. Most studies have examined the influence of the HoM on students’ interest, and the effect of students’ motivation on their math interest, but there are inadequate empirical studies that examine the effect of students’ motivation on their math interest and the mediating effect of students’ motivation on the nexus between the HoM and SMI. This study adds to knowledge by examining the mediating role of students’ motivation on the nexus between the HoM and SMI.

This qualitative study aimed to explore the perspectives of gifted students on incorporating the history of mathematics into their lessons. The research involved 51 fifth-grade students, identified as gifted, attending a Science and Art Center in Ankara, Turkey. The study spanned 12 weeks, equivalent to one semester, during which the lesson plans were enhanced and diversified with various instructional activities. Data were gathered through the History of Mathematics Student Questionnaire (HMSQ), worksheets, and students’ reflections on the instructional activities. The HMSQ data were subjected to descriptive analysis techniques such as percentages, frequencies, and arithmetic means. Additionally, responses to short-answer questions were independently reviewed by another mathematics teacher, leading to the formation of distinct categories. Reflections from the students were analyzed through the lenses of “history as a tool” and “history as a goal.” Employing history as a tool increased students’ motivation and curiosity while viewing history as a goal enriched their understanding of mathematics’ evolution and the lives of mathematicians. Moreover, survey findings revealed a significant shift in their perceptions regarding the integration of the History of Mathematics into mathematics lessons.

History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions.The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective.The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.

More than a century ago, Hieronymus Georg Zeuthen wrote a book about the history of mathematics (Zeuthen, 1902). Of course, this was not the first book on the topic, but what made Zeuthen’s book different was that it was intended for teachers. Zeuthen proposed that the history of mathematics should be part of teachers’ general education. His humanistic orientation fitted well with the work of Cajori, 1894 who, more or less by the same time, saw in the history of mathematics an inspiring source of information for teachers. Since then, mathematics educators have increasingly made use of the history of mathematics in their lesson plans, and the spectrum of its uses has widened. For instance, the history of mathematics has been used as a powerful tool to counter teachers’ and students’ widespread perception that mathematical truths and methods have never been disputed. The biographies of several mathematicians have been a source of motivation for students. By stressing how certain mathematical theories flourished in various countries, the diverse contributions of various cultures to contemporary mathematics becomes evident. Specialized study groups have emerged in the past years as a result of the increasing interest in the history of mathematics in educational circles. Two of these are the Commission INTER-IREM Epistemologie et Histoire des Mathematiques in France and the International Study Group on the Relations between History and Pedagogy of Mathematics, which is related to International Commission on Mathematical Instruction (ICMI). In addition, regular conferences are organized, such as the European Summer Universities on the History and the Epistemology in Mathematics Education (see Lalande, Jaboeuf, & Nouaze, 1995, and Lagarto, Vieira, & Veloso, 1996, for proceedings). Concomitantly, an important numberof books are now available to help teachers use the history of mathematics (Calinger, 1996; Chabert, Barbin, Guillemot, Michel-Pajus, Borowczyk, Djebbar, & Martzloff, 1994; Dhombres, Dahan-Dalmedico, Bkouche, Houzel, & Guillemot, 1987; Fauvel & van Maanen, 2000; Katz, 2000; Reimer & Reimer, 1995; Swetz, Fauvel, Bekken, Johansson, & Katz, 1995). Instead of offering an overview of the different domains in which the pedagogical use of the history of mathematics is now ramified, we want, in this chapter, to focus on something that Cajori started and in which mathematics educators interested in the history of mathematics are still involved. That is, in considering history not only as a window from where to draw a better knowledge of the nature of mathematics but as a means to transform the teaching itself. The specificity of this pedagogical use of history is that it interweaves our knowledge of past conceptual developments with the design of classroom activities, the goal of which is to enhance the students’ development of mathematical thinking.

This study examines the expression of students’ motivation and engagement in primary mathematics education through the use of interactive digital tools. The relevance of the topic is highlighted by the increasing integration of digital technologies into the educational process, aiming to enhance students’ active participation, deepen understanding of mathematical concepts, and develop essential competencies that form the foundation for further learning. Mathematics in primary education plays a crucial role in developing conceptual understanding, procedural fluency, strategic problem-solving skills, logical and spatial reasoning, the ability to communicate mathematical ideas, and collaboration with peers. Additionally, fostering a positive attitude toward mathematics is particularly important, allowing students to perceive the subject's relevance and applicability in everyday life. Digital tools such as GeoGebra, Matific, ClassWise, augmented reality (AR), virtual reality (VR), and the EDUKA platform support these objectives by promoting student motivation, engagement, and academic achievement (Bertrand et al., 2024; Radović et al., 2018; Gulbinas & Arkušauskaitė, 2015). The research problem is based on the observation that although interactive digital tools are increasingly used in mathematics lessons, empirical data on their impact on student motivation and engagement are limited. Student behavior, activity levels, and collaboration depend on lesson structure, pedagogical methods, classroom microclimate, and the nature of the tools used, necessitating analysis in authentic educational contexts (Mula et al., 2025; Radišić & Baucal, 2024). The study aimed to analyze students’ motivation and engagement during mathematics lessons employing interactive digital tools. Research tasks included reviewing scientific literature, outlining the advantages and challenges of integrating digital tools, and analyzing observational data to identify forms of behavioral and emotional motivation. The study employed a qualitative research methodology, using structured observation to systematically record students’ engagement and motivation in lessons incorporating GeoGebra, Matific, ClassWise, AR/VR, and EDUKA. Data were analyzed using qualitative content analysis to identify key themes and interpret findings (Kardelis, 2016). The observation protocol focused on three domains: student behavior, emotional expression, and teacher activity. Approximately 40 students and four teachers from two Lithuanian primary schools participated in eight mathematics lessons, allowing for a diverse dataset reflecting different educational contexts. Results revealed that student engagement and motivation are closely linked to the type of interactive tool, the incorporation of gamified elements, and the structure of lesson activities. Lessons using Matific, GeoGebra, or ClassWise promoted higher attention, active participation, collaboration, and emotional involvement. Gamification features, such as point collection and visual performance indicators, enhanced extrinsic motivation, while Matific’s star ratings supported intrinsic motivation, encouraging students to achieve understanding beyond task completion (Noverianto & Munahefi, 2023). Less interactive tools, such as EDUKA modules without gamified features, elicited lower engagement and mechanical task completion. AR and VR applications stimulated curiosity, spatial reasoning, and visual understanding, although technical difficulties occasionally reduced motivation temporarily. Nevertheless, students’ overall responses to AR/VR experiences were positive, demonstrating interest and willingness to repeat activities (Bulut & Borromeo Ferri, 2023; Cao, 2023). The findings also indicated that long-term motivation depends on pedagogical context—consistent teacher support, structured lessons, clear objectives, and high interactivity levels reinforce not only short-term engagement but also sustained interest in mathematics. The study highlighted that technical challenges, including equipment availability, system failures, and platform licensing, can temporarily hinder motivation. Pedagogical preparedness is critical, as even advanced technologies do not yield results without structured lesson planning, gamification, and teacher guidance. Digital tools are most effective when combined with a positive classroom climate, social context, and diverse pedagogical strategies. In conclusion, interactive digital tools significantly enhance students’ motivation, engagement, collaboration, and ability to visualize complex mathematical phenomena. Their effectiveness, however, depends on teacher preparation, technological competence, classroom microclimate, and proper structuring of activities. Integrating interactive, gamified digital resources with social and pedagogical support provides conditions for meaningful, effective, and sustained learning in primary mathematics. The study emphasizes that successful digital tool implementation can maintain intrinsic motivation, foster ongoing learning enthusiasm, and improve academic outcomes, while also providing teachers with flexibility to differentiate tasks according to individual student abilities.

The paper discusses the possibilities of using contents of history of mathematics as a supporting strategy in the teaching of mathematics. There is plenty of research that promotes using historical content in mathematics lessons, but only a few of them are of empirical nature. We will give the brief overview of some studies and consider different possibilities of integrating contents of history of mathematics into the teaching and learning process. Moreover, we will point out some benefits of using the history of mathematics such as: increasing students' motivation, decreasing anxiety related to the subject, building positive attitude towards mathematics, better understanding and development of mathematical concepts, changing the students' perception about mathematics, development of multicultural approach to the subject, more chances for individual work and learning by discovery, helping students to understand the role and importance of mathematics in society etc. Furthermore, we are analyzing the current state of mathematical education in Serbia and some other countries from the aspect of integrating the contents of the history of mathematics into teaching. The main goal of this paper is to investigate the teachers' beliefs and attitudes about possibilities of using history of mathematics in their practice. Based on the results of the inquiry we will suggest possible ways of how to include and use the history of mathematics in mathematics classrooms.

Student textbooks and the tasks that they feature play a crucial role in mathematical lessons (Hiebert et al. 2003). While there have been several international studies on the history of mathematics in textbooks (Lakoma 2000; Shen et al. 2013; Smestad 2000a; Smestad 2000b; Smestad 2002; Xenofontos and Papadopoulos 2015), a comparable German study has yet to be published. This study analyzes and classifies one hundred and fifty-one tasks associated with the history of mathematics in mathematics textbooks and groups each task into one of four dimensions: “connection between the present and the past,” “evolution of mathematics over time,” “people throughout mathematics history” and “the aims and purposes of mathematics.” The results show five types of tasks: informative present, acting present, informative past, acting past and personalization type.

This research aimed at describing the improvement of the students’ attitude towards mathematics lesson after following the lesson using mathematics history. This was a best practice research implemented in two phases: preparation and implementation. The subjects of this research were the students of class XII MIA 2 of SMA N 1 Kubu in the first semester of academic year 2019/2020. There were 25 students consisting of 10 male students and 15 female students. The data of students’ attitude were collected through attitude questionnaires. The collected data were then analyzed descriptively. This research showed that the students’ attitude of class XII MIA 2 of SMA N 1 Kubu in the first semester of academic year 2019/2020 towards mathematics lesson after following the lesson using mathematics history improved. The students’ attitude improved from pre-learning to post-learning using mathematics history. The average of students’ attitude was 48.21 before learning and in the fair category, meanwhile after learning, the average of students’ attitude towards mathematics lesson improved to 74.00 with good category. The improving students’ attitude had positive effect towards the improvement of mathematics learning achievement. The average of students’ daily test improved from 75.48 with learning mastery 92% at the first daily test to 78.72 with learning mastery 100% at the second daily test.

Several studies have explored the importance and benefits of teaching the history of mathematics as part of regular math classes. Some of these studies addressed the question of using the history of mathematics as a motivational factor. For instance, some found that teaching or using the history of mathematics boosted students‟ interest in the topics, lowered mathematical anxiety, and increased motivation, as well as supporting student learning and increasing the understanding of mathematical concepts. In the present paper, we analyze the positive effects that integrating elements of the history of mathematics into regular math classes could have on student motivation. We argue that students could greatly benefit from the inclusion of topics from the history of mathematics in regular classes.

Many authors have discussed the question why we should use the history of mathematics to mathematics education. For example, Fauvel (For Learn Math, 11(2): 3–6, 1991) mentions at least fifteen arguments for applying the history of mathematics in teaching and learning mathematics. Knowing how to introduce history into mathematics lessons is a more difficult step. We found, however, that only a limited number of articles contain instructions on how to use the material, as opposed to numerous general articles suggesting the use of the history of mathematics as a didactical tool. The present article focuses on converting the history of logarithms into material appropriate for teaching students of 11th grade, without any knowledge of calculus. History uncovers that logarithms were invented prior of the exponential function and shows that the logarithms are not an arbitrary product, as is the case when we leap straight in the definition given in all modern textbooks, but they are a response to a problem. We describe step by step the historical evolution of the concept, in a way appropriate for use in class, until the definition of the logarithm as area under the hyperbola. Next, we present the formal development of the theory and define the exponential function. The teaching sequence has been successfully undertaken in two high school classrooms.

Selected Regular Lectures from the 12th International Congress on Mathematical Education

This study examined the opinions of classroom teachers on the reflections of mind games used in mathematics lessons on the teaching and learning process. The phenomenology method, one of the qualitative research types, was used in the study. The views of 15 classroom teachers who used mind games in primary school mathematics lessons and received training on mind games were examined. The criterion sampling method determined whether the teachers would participate in the study. The data were collected using a semi-structured interview form prepared by the researcher and a mathematics lesson observation form. The collected data were analyzed using the content analysis method. As a result of the content analysis, the participant views were presented in 14 categories under five themes. As a result of the research, it was determined that the mind games used by classroom teachers in mathematics lessons contribute to meaningful and permanent learning in the cognitive sense, support students' higher-order thinking skills, improve their problem-solving skills, and positively affect the attitude towards mathematics lessons in the social and emotional sense and increase motivation for mathematics lessons. For this reason, a mind games activity guide can be prepared by classroom teachers in elementary school mathematics lessons.

In mathematics, it is aimed to teach the learning outcomes in the curriculum in order to increase student learning to the desired level. It is possible to understand whether this aim has been achieved or not by the process of assessment and evaluation. Assessment and evaluation in mathematics education is as important as the teaching of the subject. During the process of assessment and evaluation, it is aimed that students can express what they have learned comfortably. The concept maps are stated as a method arousing students’ interest and providing them to express themselves comfortably not only during the process of teaching but also during the process of assessment and evaluation. In this context, the aim of the study is the evaluation of secondary school fifth grades students’ learning the concepts related to the subject of angles by means of the concept maps. In the study, the case study design was used since it was aimed to determine the learning status of 40 middle school 5th grade students about the angles concept. The research was carried out with 20 working groups by forming two groups in the students' classes. After the data were collected, the concept maps were examined by the researchers and the codes were determined by the content analysis. According to the results obtained; it was observed that students have mistakes in the types of angles and their definitions; and the concept of full and right angles. It has been reached that the students have generally made the definition and drawing of the angle types they determined correctly. In addition, it has been concluded that the concept map can be used easily in mathematics as an assessment and evaluation tool and it is a more efficient tool for students than the traditional methods. It is also concluded that students have expressed the relations between concepts correctly in their concept maps they created themselves. It is recommended that teachers should give more space to the concept maps in mathematics lessons.

The drill method is serious repetitive activities do the same thing to strengthen or hone skills and make it permanent. The aim of this research is 1) To find out how to apply the drill method in mathematics lessons in class 4 at SDN 039 Air Terbit, 2) To find out whether the drill method is able to overcome students’ difficulties in understanding mathematics lessons, 3) To increase students’ learning motivation by applying the drill method in mathematics lessons in class 4 at SDN 039 Air Terbit. The method in this research uses classroom action research.. PTK is an approach to improving education through change by encouraging teachers to think about ttheir own practice so that they are critical of these actors an teachers want to change them. The results of this research are that students’ learning motivation is increasing. This can be seen from the results of the initial test. Learning engagement increased from 30% to 45% at the end of cycle 1 test and increased again at the end of cycle 2 test to 80%. So from the test result above it can be concluded that learning using the drill method can increase students’ learning motivation in mathematics lessons, the material on operations for calculating fractions can be seen from the increased learning result, so student motivation also increases.

The purpose of this research is to recognize the difference of students' learning motivation in taking mathematics lesson before and after the application of Emotive Rational Counseling. This research includes quantitative research. Sample of the research was 30 students. It was selected by purposive sampling technique. Data was collected by questionnaire. It was then analyzed using descriptive statistical analysis and t-test. The result of this research obtained an experimental subject before taking Emotive Rational counseling of which average value was equal to 61,03. It indicates that the level of student's motivation to participate in math lesson is in low category. After the treatment of Emotive Rational counseling, it obtained an average result of 82.86. It denotes that the students' motivation level is in high category. From the t-test it obtained the value of tcount of 14.620, while the ttable value at the level of significance is 5 percent with dk = 29 of 2.045. It states that the research hypothesis was rational emotive counseling therapy can increase student learning motivation.