Mathematical Development Research Articles

A resource supporting the development of mathematics: The IMU/ICMI Archive

A resource supporting the development of mathematics: The IMU/ICMI Archive

Teaching mathematical concepts based on the principle of "Consistency in Explanation"

This paper explores the importance and methods of achieving "self-consistency" in the teaching of mathematical concepts. It first emphasizes the central role of mathematical concepts in learning mathematics and, through the example of teaching the eccentricity of an ellipse, points out the complexity of understanding mathematical concepts. Then, by exploring the history of "eccentricity," the paper demonstrates the human conventions and historical development behind mathematical concepts, highlighting the need for teachers to delve into the origins and meanings of concepts in their teaching. The paper proposes four strategies to achieve "self-consistency": sorting out the history of mathematical development, finding applications of mathematics in daily life, rebuilding connections between mathematical knowledge, and utilizing perspectives from other disciplines. Finally, the paper argues that "self-consistency" is not only a teaching method but also a teaching philosophy, aimed at helping students gain a deep understanding of mathematical concepts.

Considerations for Intensifying Word-Problem Interventions for Students With MD: A Qualitative Umbrella Review of Relevant Meta-Analyses.

Word problem-solving (WPS) poses a significant challenge for many students, particularly those with mathematics difficulties (MD), hindering their overall mathematical development. To improve WPS proficiency, providing individualized and intensive interventions is critical. This umbrella review examined 11 medium- to high-quality meta-analyses to identify intervention and participant characteristics, informed by the Taxonomy of Intervention Intensity (TII) framework, that consistently moderate WPS outcomes for students with MD. Our analysis identified four characteristics with consistent moderating effects: intervention model, number of treatment sessions, group size, and academic risk area. This result suggests that these variables are potential considerations when customizing and intensifying WPS interventions to maximize their effectiveness for students with MD. We discuss the implications of these findings for practice and research and acknowledge the limitations of our review.

Mathematical Thinking and Learning in Early Childhood: A Consolidated Qualitative Synthesis of Cutting-Edge Research Literature

This study aims to synthesize current research on early childhood mathematical thinking and learning, focusing on cognitive development, instructional strategies, and environmental influences. The study provides a comprehensive qualitative analysis, integrating diverse theoretical frameworks and recent empirical findings for a nuanced understanding of early math education. Methodologically, it employs a thematic synthesis of qualitative studies, systematically reviewing literature from various academic databases to identify key patterns and themes. The research design involves coding text, developing descriptive themes, and generating analytical themes from peer-reviewed studies published between 2014 and 2024. The primary outcomes highlight the significant impact of play-based learning, interdisciplinary approaches, and parental involvement on early mathematical development. Additionally, the study underscores the role of technology and supportive learning environments in enhancing children's math skills. Conclusions emphasize the importance of holistic and culturally responsive educational practices. The practical implications provide valuable insights for educators, policymakers, researchers, and parents aiming to improve early childhood math education.

Exploring The Perceptions and Use of Information and Communication Technology Tools Among High School Mathematics Teachers in The Northern Region of Ghana

This study explored the extent to which senior high school mathematics teachers in the Northern Region of Ghana use Information and Communication Technologies (ICTs) in teaching and learning mathematics. A descriptive survey design was employed for the investigation. Using a stratified sampling technique, 20 public high schools in the northern region of Ghana were selected for the study. A simple random sampling was used to select 100 teachers (i.e., 50 teachers from urban and 50 teachers from rural schools) from the 20 schools for the study. Questionnaires were used to collect data for the study. The findings revealed that the mathematics teachers’ perceived knowledge of the benefits of ICT usage for instructional delivery, assessment, and professional learning networks in mathematics were low compared to their actual usage of the ICTs for the same purposes. The findings suggest that the participants utilize ICTs more for social networking than for instructional delivery, assessment, and professional development in mathematics. Further, the findings showed a positive relationship between the teachers’ perceived knowledge of the benefits of ICTs usage for instructional delivery and their actual use of ICTs for instructional delivery. Mathematics teachers from urban schools use ICTs for all instructional purposes more than their peers from rural schools. Implications for ICT policies, teacher training, and professional development are provided.

Thermal engineering and chemical kinetics of wood pellets torrefication

Relevance. The widespread distribution and availability of biomass in the regions of Russian Federation make it possible to consider it as a renewable energy source with a lower negative impact on the environment compared to fossil fuels, since biomass is recognized as a carbon-neutral fuel. The use of biomass as a fuel in the form of pellets is increasing, which provides increased density and heat value. At the same time, pellets as a fuel or as a technological raw material have a significant disadvantage – low hydrophobicity. This problem is solved by torrefaction – low-temperature pyrolysis at a temperature of 200–300°C to produce bio-carbon. The study of the wood pellets torrefaction in order to improve it is an urgent task. Aim. To identify the impact of the parameters of the torrefaction of wood pellets on the thermal characteristics of the product (the highest heat value of bio-coal) and the regime parameters of the process (mass and energy yields), as well as to determine the parameters of the chemical kinetics of low-temperature pyrolysis as the basis for mathematical modeling and development of efficient torrefaction reactors. Object. Torrefied coniferous wood pellets of domestic production (Moscow region). Methods. Experimental study of the low-temperature pyrolysis thermal characteristics; synchronous thermal analysis in an inert atmosphere. Results. It was found that during the torrefaction of wood pellets in an inert atmosphere, a change in the holding time in the range of 30–60 minutes does not significantly affect the higher heat value, mass and energy yield of bio-coal, while an increase in temperature from 250 to 300°C reduces mass and energy yield, and the higher heat value increases by 26%. The dynamics of mass loss and thermal effects when heated to 600°C at a rate of 10 K/min are determined by means of the synchronous thermal analysis. It is established that the chemical kinetics of the process is described by a generalized reaction of the order n=1.507, in the Arrhenius equation the activation energy E=71.25 kJ/mol, the pre-exponential factor A=4772 s–1.

Preschool class pupils’ enhanced subitizing abilities by learning study interventions

PurposeThis study explores variation theory-based interventions’ contribution to enhancing preschoolers’ subitizing abilities during iterative lessons. Results are presented according to low, middle and high achievers, focused on those with prominent challenges.Design/methodology/approachIn total 68 Swedish preschoolers participated. They were randomly assigned to one of the intervention/control groups: 23 mixed design, 24 variation theory design and 21 controls. Data from 59 pupils were analyzed. A learning study with three lesson designs for each intervention group was used in autumn 2022 and spring 2023, respectively. The mixed design met ordinary textbook material and variation theory (VT) group instructions designed by VT during autumn, whereas all met instructions designed by VT in spring. Each group was divided into two subgroups. The controls followed business-as-usual math teaching. Two tests assessed pupils’ results before and after the interventions.FindingsAll groups showed significant improvements between pre- and post-tests. Pupils in the mixed and VT groups developed more knowledge than the controls. The low-achieving group developed the most. The VT group exhibited a more complex pattern of variation and a greater increase than the mixed group. The intervention groups showed a greater improvement in both tests’ results than the controls.Originality/valueThere is agreement on the importance of subitizing abilities as a predictor of future mathematical development; however, lesson design and research on pupils’ development regarding lessons offered are limited.

Curriculum approaches to strengthening student employability and improving graduate outcomes in the STM disciplines

ABSTRACT In Australia and elsewhere, curriculum improvements are needed to improve the development of Science, Technology and Mathematics (STM) graduates for future work and careers. Several studies document significant STM student attrition, poor graduate preparedness for work, relatively weak employment rates post-graduation, and mismatched expectations of graduate capabilities by employers. The inclusion of work-integrated learning (WIL) activities within curricula can better prepare students for relevant employment by bridging discipline-specific teaching with work practices. Traditionally, access to WIL has been limited for STM Bachelor students and a better understanding of WIL’s benefits and impact is needed to refine and extend STM WIL curricula for different disciplines and cohorts. Through the lens of personal capital resources, this article reports on the perspectives of 34,000 recent Bachelor graduates of Australian STM degrees on their participation in WIL and its impact on their perceived employability and transition to work. Findings indicated differences in engagement in WIL across STM disciplines and underrepresented student groups, yet consistent benefits of WIL on preparedness for work and graduate employment. The study provides valuable insights on gaps in WIL provision and potential ways to improve WIL offerings that support the development of future-capable STM graduates with positive labour market experiences.

Decentralising mathematics: Mutual development of spontaneous and mathematical concepts via informal reasoning

AbstractThis paper aims to shed light on an overlooked but essential aspect of informal reasoning and its radical implication to mathematics education research: Decentralising mathematics. We start to problematise that previous studies on informal reasoning implicitly overfocus on what students infer. Based on Walton’s distinction between reasoning and argument, and Ernest’s concept of intrapersonal dialogue, we propose two theoretical perspectives for understanding the roles of informal reasoning in argumentation: the semi-formal, and the negotiation perspectives. From the latter perspective, we can say that informal reasoning involves creating alternatives, eschewing the relatively unpromising ones, and choosing the most promising one. To illustrate the advantage of the negotiation perspective over the semi-formal perspective, we present two examples of students’ statistical written reports from a previous study. These examples illustrate that spontaneous concepts influenced the students’ creation of multiple alternatives, and choice of the most promising one, in informal reasoning. Therefore, to better understand the development of mathematical concepts, we need to recognise the role of spontaneous concepts through decentralising mathematics. Finally, we introduce inferentialism as an additional theoretical perspective for investigating both the mathematical development of spontaneous concepts, and the spontaneous development of mathematical concepts. The inferentialist idea of the game of giving and asking for reasons indicates how to empirically investigate the mutual development of spontaneous and mathematical concepts.

Dividing times: the views of early adopters of a new assessment framework on mathematics in England

ABSTRACT This paper explores the views of early years teachers who were ‘early adopters’ of a revised assessment framework for children aged 4–5 years in England (2020–21). Based on interviews with four teachers and a survey involving 58 early adopters (part of a larger sample), the paper examines how these teachers have adapted their practice in mathematics in response to the reforms. It is argued that existing frames of understanding of good practice, drawn from external maths schemes and previous guidance, guide the enactment of the revised framework, suggesting a layering-over of new and past policies. This policy sedimentation, as we describe it, reduces the significance of the reforms, assuaging to some extent the concerns raised by maths specialists relating to the impact on children’s mathematical and spatial development. These findings provide further insights into the enactment of policy among early childhood educators.

The case classification and their development for would-be mathematics teachers’ training

Abstract The article looks into the issue of the case classification for the training of Mathematics teachers. The analysis, which was carried out, and the survey of 47 University teachers of methodical disciplines allowed to highlight the classification features of cases in the process of teaching methodical disciplines: the amount of time to complete, the way of presentation, the level of complexity and the breadth of the covered problem. Classifying cases by the amount of time for their implementation contributed to the separation of mini-cases, medium-term cases, and long-term cases. Classification by the method of presentation of cases in the process of studying methodical disciplines ensured their use in printed (handwritten) form, multimedia presentation of cases, and video cases. According to the level of complexity, the cases were divided into reproductive-training, partial-research, and creative-innovative cases. Thematic and integrated cases ensured the breadth of coverage of the problem during the teaching of methodical disciplines. The article presents general requirements for the selection and development of cases in the process of studying methodical disciplines. These requirements are based on the principles of accessibility, scientificity, contextuality, systematicity, methodological expediency, and practical orientation. The classification and specific requirements became the basis for the development of cases that can be used in the process of teaching methodological disciplines of would-be Mathematics teachers.

Predictive modelling of the effectiveness of vaccines against COVID-19 in Bogotá: Methodological innovation involving different variants and computational optimisation efficiency

The uncertainty associated with the future of viruses such as SARS-CoV-2 poses a challenge to public health officials because of its implications for welfare, economics and population health. In this document, we develop an age-stratified epidemiological-mathematical model to predict various health outcomes, considering the effectiveness of COVID-19 vaccines. The analytical model proposed and developed for this research is based on the approach constructed by the COVID-19 International Modelling Consortium. Following this approach, this paper innovates at the frontier of knowledge by including the various variants of SARS-CoV-2 in the Consortium model. Furthermore, for the first time in international literature, a complete compilation of the formal mathematical development of this entire quantitative model is presented. Our model accurately fits the observed historical data of new infections, cumulative mortality, symptomatic infections, hospitalisations, and Intensive Care Units admissions, capturing the waves of contagion that have occurred in Bogotá, Colombia. In turn, the prognosis obtained indicates a considerable decrease in the incidence and lethality caused by SARS-CoV-2 under current conditions, thus evidencing the effectiveness of vaccines against infection, hospitalisation, and death. This model enables the evaluation of different scenarios in response to changes in the dynamics of this infectious disease, providing information to policymakers for real-world evidence-based decision-making.

Mathematics Performance and Polya’s Method in Problem Solvin

The perpetual challenge of uncertain problem-solving skills among local education administrators is underscored by data from a public science and technology high school despite being a performing public science high school, students have been still struggling to enhance their critical thinking skills, posing an unceasing issue. The purpose of this study is to determine the impact of Polya's four-step method on the Grade 9 students' performance in mathematics. Utilizing a one-group pretest-posttest design, the researcher aimed to determine which aspects of Polya's method improved students' mathematics performance. The data analysis indicated a significant improvement in students' problem-solving performance using Polya’s four-step method from pre-test to post-test. This study reaffirms that Polya’s method helps students develop a structured way of thinking and solving problems, which is fundamental for their mathematical development.

To the 115th Anniversary of the Birth of Mykola Bogolyubov

On August 21, we mark the 115th anniversary of the birth of the outstanding scientist Mykola Mykolayovych Bogolyubov. During the current times of severe trials for our country caused by the war, we obtain moral support by recalling the selfless activity of this remarkable person. His life was devoted to science, and he made an invaluable contribution to the development of physics and mathematics in Ukraine.

Study on Concepts of Domination in Fuzzy Graphs

Fuzzy theory is one of the developing discipline of math, preceeding with its application in many different fields. Fuzzy graph theory is one of the branch of fuzzy theoretical area, which is advanced with many real life applications in new mathematical developments. In this research article we have studied and examined few new theoretical concepts of domination in fuzzy graphs. Some useful application for both fuzzy graphs have been given in this research article.

Mathematical developments on the naked singularities

Mathematical developments on the naked singularities

Matemáticas en el mundo árabe: Un recorrido por la edad de oro del saber

The history of Arabic mathematics is crucial to the development of mathematics. During the Islamic Golden Age (8th-14th centuries), Arab mathematicians made important contributions in algebra, geometry, trigonometry, and arithmetic, applying their knowledge in astronomy, navigation, and engineering. A significant advance was the introduction of the Hindu-Arabic numeral system, which facilitated arithmetic operations. Prominent mathematicians such as Al-Khwarizmi, who developed methods for solving equations and wrote about algebra, and Omar Khayyam, known for his work in algebraic calculus, made fundamental contributions. Thabit ibn Qurra also contributed to geometry and number theory. In addition, Arabic mathematics preserved and translated works of ancient civilizations, which allowed the transmission of this knowledge to Europe and its influence on the Renaissance.

Design of Mathematics Learning Media Using Genially Combined Quizwhizzer Platfrom for Class X Senior High School Students

This study aims to develop and evaluate the effectiveness, practicality, and validity of learning media in improving student academic achievement. The method applied is R&D (Research and Development) by adopting the ADDIE model (Analysis, Design, Development, Implementation, and Evaluation). The research findings indicate that the Genially platform- based math learning media combined with Quizwhizzer is declared Valid, based on the assessment of material experts and media experts. Practicality test shows good results, seen from student observation sheets and teacher observation sheets. Meanwhile, the effectiveness of the media in improving math learning outcomes is said to increase. In conclusion, the development of mathematics learning media using a combination of the Genially platform and Quizwhizzer proved to be very effective in improving students' understanding of quadratic equation material.

Khan Academy Platform for Mathematics Teaching and Learning

Objective: To assess the impact of Khan Academy on the Mathematics educational process for UNDAC students and determine the relevance and efficacy of its content and strategies within the Mathematics-Physics program. Methodology: This research is framed within the positivist paradigm and takes on a quantitative approach. An experimental pre-experimental design was used with pretest and posttest in a single group. The study is applied in nature and is grounded in the contributions of expert researchers and methodologists on the subject. Analytical tools were developed with a reliability coefficient of 0.90, and the investigated population consisted of students from the Mathematics-Physics program at UNDAC. Results: Students who incorporated Khan Academy exhibited significant improvements in their mathematical performance. Persistence in using the platform led to significant enhancements in academic achievement. 70 % of the students reached high levels of mathematical skill development. The majority expressed high satisfaction with the platform. Conclusions: Khan Academy has a meaningful and positive impact on mathematics learning among university students at UNDAC. The platform not only promotes content mastery but also fosters learning autonomy. These findings advocate for the adoption of innovative educational technologies in teaching, especially within STEM disciplines.

볼록 육각형의 나폴레옹의 정리 확장에 대한 연구

This study was based on the research results conducted as a R&E project for the gifted students with a financial support from the Korea Foundation for the Advancement of Science and Creativity. In this study, the Napoleon hexagon ofhexagons was explored by expanding the Fermat-Torricelli point defined in a triangle and the Napoleon triangle into a convex hexagon. The results of this study are as follows. First, the equivalence condition for convex hexagons in which the Napoleon hexagon exists was discovered. Second, the area formula for Napoleon’s hexagon was shown. Third, we found various regular hexagons related to the Napoleon-containing hexagon and found that the centers of each regular hexagon were identical. Through this study, the concepts of the Fermat-Torricelli point and Napoleon triangle of triangles were expanded to convex hexagons, and it is expected that the expansion of mathematical concepts willcontribute to the development of mathematics. In addition, it is expected that additional research will be conducted in the future by exploring attractive regular hexagons whose centers coincide with the searched hexagons including Napoleon.