Mathematical modelling with digital tools—a quantitative study on mathematising with dynamic geometry software

Розглянуто особливості використання цифрових інструментів відповідно до потреб забезпечення сталого розвитку в суспільстві. Вивчено специфіку застосування цифрових інструментів у різних сферах життєдіяльності суспільства. Проаналізовано еволюцію розвитку цифрових інструментів у світі протягом останніх двадцяти років. Представлено напрями активізації застосування цифрових інструментів забезпечення сталого розвитку на сучасному етапі трансформаційних змін в Україні.

This paper reports on an aspect of a larger research study conceptualised within a teacher development project in Mthatha, Eastern Cape Province. The project was initiated with the objective to develop appropriate skills to use dynamic geometry software (DGS) effectively and strategically as a teaching and learning tool for mathematics. The study reported in this paper aims specifically to ascertain how selected mathematics teachers integrated co-developed technologically aided visualisation tools in the observed lessons. The case study involved two teachers from different schools. The data sources were the classroom observations followed by stimulated reflective interviews with the teachers. The data were analysed to study the use of DGS visualisation tools in relation to Kilpatrick’s framework of teaching proficiency. The lessons evidenced a displayed alignment with the elements of teaching proficiency in the context of teaching geometry. The dynamic visualisation opportunities offered by DGS proved to supplement the teaching repertoire for the participating teachers. Pedagogical practices influence the use of DGS, as evident from the lessons when the participating teachers incorporated collaboratively developed GeoGebra applets into their classrooms. We argue that the collaborative engagement between teachers appears to be a positive way forward in closing the gap between having access to technology and adapting it for effective use in mathematics classrooms.

In the present study, the effects of using dynamic geometry software in active learning framework on students’ problem posing skills and their views about problem posing were examined. The participants consisted of 16 eighth-grade students. Data were collected by problem posing tests, open-ended questions, student diaries, and dynamic geometry software supported tasks. The study, designed with the embedded mixed method, lasted 13 weeks. The dependent t-test was used in the analysis of quantitative data, and descriptive analysis was performed in qualitative data. Problem posing skills of students examined according to use of mathematical language, grammar and expression, suitability to acquisitions, quantity and quality of data, solvability, originality, solution of the problem criteria. In the present study, it was determined that the use of dynamic geometry software in active learning framework developed students’ problem posing skills. The problems that students posed in the dynamic geometry software during the implementation process indicated improvement in terms of problem posing skills as the weeks passed. It was found that students had positive views about the problem posing process, while they experienced some difficulties in this process.

Digital tools have a potential to change significantly the form of mathematical learning taking place in classrooms, with research pointing to various affordances in comparison with physical tools such as paper-and-pencil environments. Nevertheless, there is a scarcity of research that has examined in-depth the interrelated roles these two types of tools fulfil in mathematics learning. This issue of inter-related roles is important because, when digital tools are incorporated into classrooms, students usually also have notebooks and worksheets within which they carry out actions complementary to their use of digital tools. In this article, we focus on the use of dynamic geometry environments (DGEs) in conjecturing and proving, and, in particular, we examine the interplay between students’ paper-and-pencil activity and their use of a DGE during the producing and proving of a generalisation of a statement. We analyse a series of lessons involving secondary school students (aged 14–15, Grade 9) and show that, while DGE use supported the students in generalising a statement, they were initially unable to prove the generalisation while using the DGE, but subsequently succeeded through their paper-and-pencil activity. Our research illustrates the affordance of paper-and-pencil environments to support students in working on different representations, and thus highlights how the interplay between paper-and-pencil activity and DGE use can be important for the progress of conjecturing and proving. We also show the roles taken by the teacher in supporting the students’ work, and point to the need for further research into the back-and-forth use of digital and physical tools.

Purpose. The purpose of this article is to consider the role of the main digital tools, their advantages, and challenges of use in the marketing management system of enterprises. Design/methodology/approach. The research used the following general scientific methods of scientific knowledge: comparative analysis and synthesis, systematization, and theoretical and logical generalization. Scientific works and articles on the Internet of domestic and foreign scientists who study issues related to the field of digital marketing became the informational, theoretical, and methodological basis of the research. A systematic review of literary sources and scientific publications made it possible to get acquainted with existing theories, concepts, and research in the field of digital marketing. This method is used for conducting comparative analysis and synthesis to generalize information. The method of theoretical and logical generalization of the advantages and challenges of using digital tools made it possible to draw reasonable conclusions about their use in the marketing management of enterprises. Findings. The article examines the key roles of digital tools in the modern marketing management of domestic enterprises: attracting and retaining an audience, increasing brand awareness, personalizing communication, increasing the effectiveness of advertising, measuring results, interacting with the audience, and global access. Popular digital marketing management tools are highlighted, which include a wide range of technologies, online platforms, and web services that help businesses interact with audiences, promote their products or services, and measure the effectiveness of their marketing efforts, including websites, contentmarketing, search engine optimization website, search advertising, social media, e-mail, web analytics, virtual and augmented reality technologies, chatbots, QR coding. Advantages are considered and attention is paid to the challenges associated with the use of digital tools in the marketing management system of enterprises. Practical implications. The results of the study demonstrate the importance of adaptation of domestic enterprises to the digital environment in modern business. Digital tools have become a necessary part of marketing strategy, and understanding and using them play a critical role in achieving success. Businesses that have a proper understanding of digital marketing can help improve the effectiveness of their marketing campaigns, creating a competitive advantage in the market. It also helps to increase sales, increase profitability, and improve interaction with customers. However, using digital tools also brings challenges, including the need to keep up with rapid changes in technology and the competitive environment. Businesses must be ready to adapt and learn to remain competitive. In practical terms, the study provides enterprises with useful information and recommendations on the effective use of digital tools in marketing management. This will help enterprises to grow, develop, and successfully compete in the conditions of digitalization. Originality/value. The article reflects a modern approach to considering digital tools in the marketing management of enterprises and takes into account the latest technological trends and changes in the Internet environment. Consideration of digital tools of marketing management of enterprises is carried out from a comprehensive approach, taking into account their role, advantages, and challenges of use in one context. This makes the article a valuable source of information for entrepreneurs and marketers looking to improve their digital marketing strategies and practices.

The research question addressed by this study is whether or not students made effective use of dynamic geometry software to explore the validity of a geometrical statement. Particular attention was paid to the use of definitions and the types of justifications students employed. Interviews conducted with six secondary mathematics preservice teachers were video and audio taped and video output of the interviewee's Geometer's Sketchpad (GSP) work was recorded on video tape. The interviews were transcribed along with a synchronized record of the GSP work. The transcripts and videotapes were analysed and coded. Results indicated that reasoning based on prototypically constructed categories and difficulty correctly parsing mathematical statements, especially the ‘for all’ quantifier, interfered with the effective use of dynamic geometry software in justifying mathematical assertions. It may be that explicit instruction in how to make use of software programs to explore the validity of an assertion is needed.

As COVID-19 strained health systems around the world, many countries developed or adapted digital health tools to detect and respond to the novel coronavirus. We identified transferable lessons from an assessment of implementation factors that led to the rapid launch and scale-up of eight digital tools in low- and middle-income countries during the COVID-19 pandemic. These lessons should inform the development of digital health tools to support public health objectives such as the Sustainable Development Goals. Using the mHealth Assessment and Planning for Scale Toolkit, we assessed the implementation of eight digital tools through desk research and stakeholder interviews. Three core lessons emerged from our findings: (1) user-centered design is key to the widespread adoption of digital tools; (2) strong, country-led partnerships are essential for scaling up and sustaining digital tools; and (3) using adaptable digital tools enables implementers to focus on the content of the solution rather than the technology. Lessons learned from implementing and adapting digital tools quickly during the COVID-19 pandemic can inform the use of digital tools for additional health applications, such as bolstering primary health care, reaching vulnerable and marginalized populations, and empowering health workers with the real-time information necessary to optimize their work and improve the health of their target populations. Future efforts should focus on robust monitoring and evaluation of digital tools and sustainable financing models.

The study aims to determine the views of final-year pre-service mathematics teachers towards their experience of the use of dynamic geometry software in teaching, following the implementation processes that they carried out when using this software in a real classroom environment. The study was designed as a case study, which is one of the qualitative research methods. The study was conducted with four pre-service teachers studying in the mathematics teaching department at the education faculty of a university in Turkey during the 2016 to 2017 academic year. As one of the results of the study, it was observed that the pre-service teachers, following the theoretical lessons that they had in the education faculty prior to implementation, gave more limited opinions, whereas during the school experience application of dynamic geometry software, following its application in a classroom environment, they mentioned more features of this software for use in teaching. The pre-service teachers, in relation to their real classroom experiences, expressed their views on the features “concretisation and visualisation”, “possibility of presenting many examples”, “making students feel that mathematics is valuable”, “permanence and facilitation of learning”, and “preventing erroneous mental representations” with regard to the role of dynamic geometry software (DGS) use in teaching and learning. Yet, prior to using DGS in the classroom, these pre-service teachers had given importance only to the “concretisation and visualisation” and “permanence and facilitation of learning” characteristics. Key words: Dynamic geometry, pre-service mathematics teacher, geometric shapes, views.

English vocabulary mastery has undergone significant changes with the emergence of digital technology. This study aims to examine the use of digital tools in English vocabulary learning by students in the English Language Education Study Program at the University of Mataram, focusing on the utilization of various digital tools. This study used a descriptive qualitative design. Data were collected through online questionnaires completed by 52 participants and in-depth interviews with 10 purposively selected participants. Data were analyzed using thematic analysis based on the Braun and Clarke (2006) model. The results show that students use various digital tools in an integrated manner, combining social media, learning applications, digital dictionaries, and artificial intelligence (AI) in the vocabulary learning process. This process occurs continuously through the stages of discovering new words, understanding their meanings, and using them in sentences or conversations. Furthermore, the effectiveness of digital materials is evident in the multimodal support provided, such as visual and auditory aids to support understanding of meaning and pronunciation. The study also identified barriers to the use of digital tools, including distractions from non-educational content and technical issues related to internet connection. These findings indicate that the functional effectiveness of digital learning tools is directly related to students' strategies and their independent learning abilities. Theoretical and practical implications for the development of technology-based vocabulary learning are also discussed.

The integration of digital learning tools in school science classes has garnered significant attention, prompting an investigation into their effects on student engagement and achievement. This study examines the impact of students' access to technology, teachers' digital competency, and the frequent use of digital tools on the engagement and academic performance of middle school students in science subjects. Utilizing a cross-sectional survey design, data were collected from 309 middle school science teachers across 45 public schools in Punjab, Pakistan, through validated, self-administered questionnaires. Six hypotheses were formulated and tested using SPSS and SmartPLS. The findings indicate that access to technology, teachers' digital competency, and the frequent use of digital tools positively influence student engagement and achievement in science. Digital tools significantly enhance engagement by providing interactive and personalized learning experiences, leading to increased motivation and interest among students. Furthermore, improved academic outcomes are evident in higher test scores and performance in science assessments. Teachers also noted a positive shift in classroom dynamics, characterized by increased collaboration and inquiry among students. These results highlight the critical need for ongoing investment in educational technology and professional development for educators to fully leverage the benefits of digital learning tools.

The paper explores the possible strategies to increase the use of digital tools in modern banking. The conceptual study proposes four strategies banks should focus on to be competitive and satisfy diverse customer needs. The primary focus is enhancing the customer experience through digital tools, such as online payments, credit requests, and bill payments while acknowledging the security and technical limitations with which users may have issues—the strategies banks can utilize have a customer-centric approach that includes user-friendly design and personalization. The technology focus would encompass technological advancements with security features like encryption and biometric verification and integration with broader services. Financial product innovation and effective marketing strategies are also essential for increasing the use of digital banking tools. Blockchain and AI, integrated marketing, and customer relationship management should be significant points of emphasis for the banks to serve the business and consumer markets effectively.

This research firstly aims to reveal the pedagogical potentials and limitations of dynamic geometry software (DGS). For this purpose, research on Cabri (2D/3D/Plus), the Geometer’s Sketchpad, GoogleSketchUp, GeoGebra and Logo software was reviewed and compiled. As a result of the research, it appears that DGS offers an effective pedagogical environment because of its ability to interact with digital materials and allow for geometric objects to be seen from all sides. However, we found that teachers have some problems in combining DGS with class pedagogy. In this study, the effects of gender, age, education level, skill in using technology and the influence of professional experience were also examined in relation to primary school mathematics teachers’ preferences in using DGS. As a result of this research, it was found that GeoGebra and Cabri were the most-used DGS packages by primary school mathematics teachers, while other geometry software was less preferred by teachers.

This chapter discusses how the use of Dynamic Geometry Software (DGS) can be used to support students’ engagement with the Standards for Mathematical Practice as outlined in Common Core State Standards for Mathematics (CCSS-M). In particular, the aim of this chapter is to (1) describe what students’ strategic use of appropriate tools might entail in a DGS environment, and (2) argue that for students to engage in these practices in a DGS environment, they must construct meaning for and with these tools in the process of instrumental genesis. Illustrative examples are provided from three secondary mathematics classrooms, and the chapter concludes with recommendations for future research and teacher education in this area.

Background:Investing in women leaders in global health catalyzes growth and positive outcomes for individuals and their communities, yet large gender disparities persist in leadership within the field due to several barriers. The use of digital tools facilitates cross-institutional and international collaborations to allow individuals or groups to create or share information, ideas, career interests, and other forms of expression via virtual communities. Digital tools can dramatically expand access to and the quantity and quality of opportunities for networking, mentoring, and collaboration to support women in their professional development.Objectives:The objective of this paper is to document tangible examples of positive experiences, connections, or collaborations resulting from connecting with other participants in a Slack network. We aimed to evaluate this network to understand how to better build, model, and scale advantageous digital networks of women leaders in global health moving forward.Methods:Semi-structured interviews were conducted virtually with seven members of the Slack network from Africa and North America who volunteered to share their experiences. Transcripts of six of these interviews were analyzed for key points using thematic analysis to derive short vignettes from each interview.Findings:The findings of this study indicate that Slack is a highly beneficial tool for women in global health to use for facilitating job searches, mentoring opportunities, promoting project collaborations, and proposing programming and outreach ideas in a remote environment. We found distinct recommendations for utilizing this digital networking tool in a way that best supports and engages women in global health. It is important to spread awareness and ensure visibility of the network to recruit and maintain members, design the network in a way that inspires internal motivation, encourage consistent and meaningful engagement, send weekly emails, and maintain accessibility for a global membership base.Conclusions:The Slack network provides an engaging digital tool that facilitates communication, opportunities, and growth among women in global health. Digital tools such as Slack can help to increase opportunities for participants from low- and-middle-income countries to engage in the same networking and leadership opportunities as individuals from high-income countries. It remains critical to continue to build, advance, and scale advantageous networks like Slack to promote equity and accessibility among women leaders in the global north and south into the post-pandemic world.

BackgroundPatients living with diabetes and chronic conditions may face a significant burden managing their health. Many of these patients use digital medicine tools such as continuous glucose monitoring systems. Although measures exist to assess treatment burden from tasks such as managing medications and attending healthcare visits, there is no patient-reported measure that captures the burden of digital care. Therefore, the purpose of this study is to validate the Treatment Burden Questionnaire Plus Digital (TBQ + D), a patient-reported measure of treatment burden that includes using digital tools for adults with diabetes.MethodsAdult patients with type 1 or type 2 diabetes mellitus completed the 25-item TBQ + D (scored 0 [none] to 10 [maximum] per item, total score range 0–250). We evaluated ease of administration, internal consistency, and tested hypotheses about the relationship between TBQ + D scores and treatment complexity, digital tool use intensity, social risk factors, and digital comfort to assess TBQ + D’s validity.ResultsOf 324 patients approached, 300 (93%) consented and completed the TBQ + D (mean age 57 [SD 17], 50% female, 50% with type 2). The mean TBQ + D score was 53.7 (SD 41.6). Internal consistency was excellent (Cronbach’s α = 0.94). As hypothesized, higher TBQ + D scores were reported by patients with type 1 vs. type 2 diabetes mellitus (61.7 vs. 45.7, p = .0008), maximal/moderate vs. minimal to no digital tool use (56.5/60.7 vs. 41.3, p = .001), those on intensive insulin therapy vs. other treatments (61.4 vs. 38.0, p < .0001), and those with greater social vulnerability (p < .0106). TBQ + D scores were not significantly higher in patients with HbA1c ≥ 8% (p = .055) or less comfortable with digital technology (p = .08).ConclusionsTBQ + D is a novel and valid measure of treatment burden in patients living with diabetes, inclusive of digital burden, which can play a role in fostering minimally disruptive care for patients with diabetes.Supplementary InformationThe online version contains supplementary material available at 10.1186/s12916-025-04579-w.