Integrated Virtual Laboratory in Engineering Mathematics Education: Fourier Theory

The widespread adoption of virtual and remote laboratories has transformed practical education by offering scalable, safe, and flexible environments for developing technical skills. Despite these benefits, challenges remain in providing timely, meaningful feedback that supports self-regulated learning and improves student outcomes. In this study, we analyze anonymized interaction logs from a virtual laboratory system focused on Industrial Electrical Control Training Lab, used by 839 students enrolled in Electrical, Electromechanical, Mechanical, or Industrial Automation vocational programs offered by the National Service of Industrial Apprenticeship of Santa Catarina (SENAI/SC, Brazil). We introduce a novel methodology that combines sequential pattern mining (SPM) with automatic performance-based segmentation to analyze student behavior in virtual laboratory environments. Using interaction logs from students containing time-stamped cable connections and interface interactions, we segment learners into performance (High, Intermediate, and Low) based on the z-scores of accuracy and speed, using two strategies: (i) a K-means clustering approach, and (ii) a rule-based decision function. Building on this segmentation, we propose an algorithm to identify frequent action sequences and recurrent error patterns specific to each group. We further apply chi-square analysis to determine statistically significant associations between specific errors and performance profiles. Our findings indicate that students in the high-performance group are likely to refer to schematics beforehand, whereas those in the lower performance group frequently begin with montage connections. Inference analysis demonstrated that these segmented groups, for both the rule-based and K-means segmentation approaches, commit statistically distinct types of errors. These results can be integrated into LA dashboards to support real-time feedback for students and instructors, ultimately enhancing teaching strategies and learning in practical disciplines.

In learning the geometry of the parallels, there is a misconception between the position of the two lines and the position of the two angles. One way by which students can learn this material better is by virtual reality-based virtual lab media that is able to display objects like in the real world. The purpose of this research is to design the learning media, Virtual Laboratory Geometry Based on Virtual Reality so that students of the mathematics education study program at the Universitas PGRI Semarang are able to understand the alignment material accurately. This study uses ADDIE model development research with five steps that are carried out systematically. Virtual reality-based geometry lab application products have been validated by learning materials experts and learning media experts with scores of 91 and 92, which are categorized as very suitable for use in learning geometry in the classroom.
 Keywords: Design; Virtual Geometry Lab; Supplements; Learning Media

Cloud computing enables the provision of virtual personal computers (PCs), known as virtual machines (VMs), using virtualization. VMs with specific applications can thus provide a generic usage concept for virtual PCs. As stated in [1] the concept of digital twins is based on the idea that a digital informational construct about a physical system could be created as an entity of its own. The combination of both concepts leads to the definition of virtual labs using digital twins for engineering education, which was defined in [2] as follows: “The merger of a digital twin (the test rig model) with a virtual PLC (the control system) as part of a virtualized PC accessible through a VPN network connection are the components that merge into the virtual lab environment.” Based on earlier works, this paper presents some advances in developing the IT concept for massively scaling up virtual lab environments using public cloud service providers and describes some major virtualization concepts.

This paper investigates the instructional effectiveness of learning modalities towards enhancing learners’ conceptual understanding of crystal field theory (CFT) using a multimedia rich platform such as Virtual Laboratory. The virtual laboratory in the present work has integrated modalities such as graphics, images, animations, videos and simulations for simultaneous demonstration of concepts related to CFT. This study aims to evaluate the impact of these modalities on the learning outcomes of visual, auditory and kinesthetic learners irrespective of their preferred learning modality. A case study of 524 undergraduate chemistry students from four higher educational institutes was carried out as part of the evaluation. Assessment of knowledge, conceptual understanding, application and analysis with and without the virtual lab platform was done using assessment quizzes. Results showed that students that underwent a combination of visual, auditory and kinesthetic learning modalities within virtual lab environment had significantly improved their understanding resulting in better performance. The study also characterizes the effectiveness of integrated modalities on the enhancement of learning amongst the three types of learners.

Development of Teacher Guidance Materials Based On 7E Learning Method In Virtual Laboratory Environment

This study explores the complex interplay between teacher attributes, learner instructional approaches, and the integration of Information and Communication Technologies (ICTs) in mathematics education, highlighting their collective impact on educational outcomes. Through a comprehensive survey of 196 teachers and 315 learners, the research delves into the relationships between teacher experience, educational qualifications, and the frequency and manner of technology use in the classroom. The analysis reveals that younger educators and those possessing advanced academic credentials are more inclined to actively incorporate ICTs into their teaching practices, demonstrating a higher level of comfort and enthusiasm for leveraging these tools to enhance student learning. Conversely, the study finds that more experienced teachers, particularly those with lower qualifications, tend to utilize technology less frequently, possibly due to a preference for traditional teaching methods or a lack of confidence in their ability to effectively integrate new technologies. Additionally, the study investigates the strategies employed by learners, with a particular focus on web-based self-learning approaches, such as the use of online educational videos and interactive platforms. The data indicates a significant positive correlation between these strategies and improved academic performance in mathematics, suggesting that learner-centered approaches that emphasize self-directed, technology-mediated learning can lead to better educational outcomes. These findings underscore the critical importance of considering both teacher characteristics and learner-centered instructional methods when developing strategies for the effective integration of technology in mathematics education. By tailoring these strategies to meet the diverse needs and preferences of educators, while simultaneously promoting effective self-learning techniques among students, educational institutions can better harness the potential of ICTs to improve learning outcomes in mathematics and beyond.

Recently, the prospects of virtual laboratory environments developed using commercial multi-player computer game engines and their associated software development kits for providing undergraduate engineering and science students with engaging and interactive laboratory experiences have started to be explored. There is a strong potential for such virtual laboratory environments to be readily accepted by today’s students who are accustomed to using advanced communication and entertainment technologies. While online laboratories based on either remotely operated hardware or pure software simulations are often criticized for lacking student interactivity and for being limited to the data collection and result analysis aspects of traditional hands-on laboratories, these shortcomings can be overcome with virtual laboratory environments implemented based on multi-player computer game engines. For instance, game engines allow one to include into the experimental procedure the assembly process of the experimental setups before carrying out any data collection. Furthermore, such virtual laboratory environments can facilitate and even force certain interactions by the students of a laboratory group. This paper discusses recent developments at Stevens Institute of Technology (SIT) that enable students to assemble laboratory equipment inside a virtual laboratory environment implemented using the “Source” game engine (1) and “Source” software development kit (2). In this environment, the students can interactively select and assemble components of laboratory hardware into complete experimental setups, which are subsequently used in experimental procedures. This assembly process can be performed in a cooperative fashion with multiple students collaboratively interacting with each other as well as with the experimental equipment. Such game-based educational tools are expected to find applications for teaching and training in a wide array of fields.

The aim of the current research was to develop students' skills in designing computer circuits among computers and information students through the development of an integrated virtual educational environment represented in (Moodle platform -virtual lab -educational software -YouTube channel). The researcher used the descriptive method and the experimental research method by applying the model of "Abdul Latif Al-Jazzar" ( The research sample consisted of two groups, a control group and an experimental group, numbering (60) students, 30 students for one group on first-year computer students. After applying the research procedures on the experimental and control sample, and using statistical treatments, the results showed that there were statistically significant differences at the significance level (0.01) between the mean scores of the students in the post-application of the achievement test. And the observation card in favor of the post application between the two groups in favor of the experimental group One of the most important recommendations of the research is to create virtual environments in the scientific fields in general and in the field of computers and engineering.

The use of digital technology in mathematics education has gained significant interest over the past few years with the rapid development of technology and the changing practices in education all around the world. Technology-enhanced learning of mathematics has been increasingly used to enhance conceptual understanding, engagement and problem-solving skills of the students. This study was an attempt to identify and synthesize the pedagogical opportunities of technology enhanced mathematics learning and examine the practical constraints associated with the integration of technology in mathematics education. This research is a systematic review of the studies published between 2020 and 2025 concerning the pedagogical opportunities and practical limitations regarding the use of technology in mathematics education. Following the PRISMA framework, a systematic identification, screening, and analysis of peer-reviewed journal articles were performed. After a rigorous selection process eighteen studies were identified to have met the predefined inclusion criteria, and included in the final review. The selected studies were analyzed with the method of thematic analysis used to identify recurring patterns in the literature and key themes. The results indicated that technology-enhanced mathematics learning provides important pedagogical opportunities such as better conceptual understanding, better student motivation, and development of higher-order thinking skills as well as individualized learning experiences and inclusive education support. However, persistent practical problems were also identified, including insufficient preparedness of teachers, insufficient technological infrastructure, digital inequity, misalignment of curriculum and ethical issues concerning artificial intelligence. The findings in this study conclude that while technology has great potential to transform mathematics education, the effectiveness of technology depends on pedagogical alignment, teacher competence and institutional support. Addressing these constraints is crucial to ensuring sustainable and meaningful integration of technology in mathematics classrooms.

This study aims to analyze the theses conducted using the eye-tracking technology in mathematics education based on Council of Higher Education (CoHE) Theses Center. In this study, a total of 12 scientific theses, 7 of which were master's theses and 5 of which were doctoral theses, were evaluated. Data were analyzed with content analysis technique. The theses were analyzed under three headings: descriptive, methodology and topic information. The use of eye-tracking technology in mathematics education theses in Türkiye started with a master's theses in 2010. The universities that produced the most publications are Middle East Technical University and Hacettepe University. The departments that produced the most theses were Computer Education and Instructional Technology and Information Systems. While most of the master's theses were designed in accordance with the mixed research method, most of the doctoral theses were designed in accordance with the quantitative research method. In the theses conducted, mostly undergraduate and graduate students were studied. Applications were generally carried out with between 51-70 participants. While interviews were used in most of the master's theses, interview method was not used in all of the doctoral theses. The most preferred eye tracker was Tobii X2-60. Problem solving strategies and usability studies are the main topics studied using eye-tracking technology in mathematics education.

Virtual laboratories are increasing for all areas of scientific domains. However, the concept of such laboratories can be extended to include educational activities. But the point is, how to do it? We have been involved in the development of a virtual laboratory on mathematics education for the past 15 months. Our institution is involved in the training of primary school teachers. On their final year, our students go to primary schools and teach there in some supervised classes. Our idea is to create an instrument that can be used with primary school children by our students, during the earlier-mentioned practice in schools. Therefore it has to be an instrument with features that include being appealing to children, easy to use, and helpful to novice primary school teachers.

Solving many environmental challenges requires connecting a variety of datasets with advanced statistical or AI models, and to access distributed computing resources to create workflows or digital twins. Digital twins are particularly challenging because they require the integration of many datasets and models, resulting in complex interactions. Furthermore, researchers rely on interdisciplinary collaboration to build workflows and digital twins. To that end, they need to discover, reuse, and sometimes modify existing assets. While this can be supported by Virtual Research Environments (VREs), most existing solutions are tailored to a specific domain or use case, making it difficult to integrate external resources or to support the complex model composition required by digital twins.To address these limitations, we have developed Notebook-as-a-VRE (NaaVRE), a VRE solution built on top of JupyterLab. NaaVRE enables researchers to create computational blocks by containerizing the cells of notebooks, to organize them into workflows, and to manage the full experimental cycle, including data and workflow sharing. The tool includes features such as metadata-driven resource discovery, workflow automation, and compatibility with external repositories. Designed for cloud infrastructures, NaaVRE provides cost-efficient and scalable solutions to support digital twin development.Using NaaVRE, we build customized virtual labs to address specific scientific problems. These gather models, data access tools, workflows, and documentation into a shared space, where a community of users can develop, share and reuse them. We present a framework to guide the development and operations of virtual labs throughout their entire lifecycle.We showcase NaaVRE and by building customized virtual labs for scientific data processing workflows and prototype digital twins. Those virtual labs are managed by LifeWatch ERIC and the University of Amsterdam following the aforementioned development framework. They include characterizing ecosystem structures with LiDAR data, tracking bird migration using radar, mapping invasive species, deriving essential variables in the context of the ENVRI-Hub NEXT project, and developing digital twins of ecosystems in the context of the Dutch NWO LTER-LIFE project.

With the development of mobile technologies, mobile applications are increasingly designed and developed. In the field of science, technology, engineering, and mathematics (STEM) education, the idea of using mobile devices for teaching and learning has gradually gained popularity and gained in-depth research. Owing to the advantages of convenience, portability and excellent interactive abilities, mobile devices are a good choice for accessing remote laboratories. In propose of promoting the massive online experimentation of control education, a mobile application with framework based on React-Native is implemented in this paper. The overall remote laboratory architecture adopts front-end and back-end separation scheme, which benefits the mobile application focusing on the construction of front-end interface and user experience. Various functional modules and technologies are applied in the mobile application, allowing users to access various experiment test rigs in the remote laboratory with intuitive experimental immersion. Moreover, a complete laboratory management system to manage the massive users from different universities has also been integrated into the mobile application. At the end, a remote networked control experiment has been conducted to prove the practicability of the mobile application.

This chapter discusses the specific synergies created when combining Artificial Intelligence and 5G education technologies, provides a structured implementation synergistic role, and recognizes current challenges, opportunities, and solutions. It explores basic ideas of AI and 5G and their complementary roles in facilitating real-time feedback, immersive learning, and remotely-acquired education. We analyze current applications including personalized learning systems, smart classrooms, virtual labs and proctoring, and AI-based teacher assistance in the article. The synergistic role specifies short-term targets (infrastructure investment, training) and mid-term goals (full-scale deployment, ethics frameworks), leading the way for a longer-term aspiration for fully autonomous learning systems. Including some key challenges such as technological challenges, data privacy, the digital divide, and resistance to change, as well as some opportunities for the future including increased student engagement, cost-effective education, continuous education for the rest of our lives, and global cooperation. This chapter introduces several recommendations from policy frameworks to public-private partnerships to teacher training and development of platforms and indicates best practices around monitoring and evaluation. Trends that wish for the future like Metaverse integration and Artificial Intelligence help for emotional learning are drawn as well. The work emphasizes the future-shaping influence of AI and 5G on education and urges action from stakeholders.

This chapter examines the evolution and future perspectives of in the integration of digital technologies in mathematics education through the work of two research groups: Entornos Tecnológicos en Educación Matemática (ETEM) from SEIEMand Educación Matemática y Tecnologías Digitales (EMTD) from SOMIDEM.The objectives and research lines of each group are presented, detailing the theoretical and methodological frameworks employed, as well as the most relevant results obtained to date. Furthermore, challenges and emerging areas in the use of technology in mathematics education are identified, such as the impact of artificial intelligence, computational thinking, and technology-mediated assessment. Finally, potential synergies between ETEM and EMTD are proposed to foster future collaborations that contribute to the advancement of the research in mathematics education and technology.