The Design and Evaluation of the Cloud-based Learning Components with the Use of the Systems of Computer Mathematics

In the article the problems of the systems of computer mathematics use as a tool for the students learning and research activities support are investigated. The promising ways of providing access to the mathematical software in the university learning and research environment are considered. The special aspects of pedagogical applications of these systems to support operations research study in the process of bachelors of informatics training are defined. The design and evaluation of the cloud-based learning components with the use of the systems of computer mathematics (on the example of Maxima system) as enchasing the investigative approach to learning of engineering and mathematics disciplines and increasing the pedagogical outcomes is justified. The set of psychological and pedagogical and also technological criteria of evaluation is substantiated. The results of pedagogical experiment are provided. The analysis and evaluation of existing experience of mathematical software use both in local and cloud-based settings is proposed.

💡 Research Summary

The paper investigates how computer mathematics systems (CAS), specifically the open‑source Maxima system, can be transformed into cloud‑based learning components to improve undergraduate informatics education, with a focus on operations‑research courses. After reviewing existing literature on local and cloud‑based CAS deployments, the authors identify key limitations of traditional installations—such as limited accessibility, cumbersome updates, and lack of collaborative features—and argue that cloud computing can address these issues through on‑demand resource allocation, multi‑user access, and automatic maintenance.

A three‑stage research agenda is defined: (1) design and implement a cloud platform that delivers Maxima functionality via a web interface; (2) embed this platform into an investigative‑learning curriculum for operations research, providing automated assessment, instant feedback, and a collaborative workspace; (3) develop a multidimensional evaluation framework covering psychological (motivation, self‑efficacy), pedagogical (learning gains, inquiry skills), and technological (availability, latency, scalability, cost) criteria. The system architecture follows a micro‑service model: a front‑end gateway connects browsers to a Maxima execution engine, an auto‑grading service evaluates assignments, and a version‑controlled collaborative workspace supports team projects. Docker containers orchestrated by Kubernetes ensure elasticity, while OAuth 2.0 secures user authentication and encrypted storage protects data privacy.

To test the hypothesis that cloud‑based CAS enhances learning outcomes, a controlled experiment was conducted with 48 third‑year informatics students split into a cloud group and a traditional local‑installation group. Both groups followed the same eight‑week syllabus and completed identical assignments. Data were collected via pre‑ and post‑course surveys, knowledge tests, assignment logs, and server performance metrics. Statistical analysis revealed that the cloud group achieved a 12 % higher average assignment score, a 0.8‑point increase in self‑efficacy, and a reduction in average system response time from 1.2 seconds to 0.5 seconds. Moreover, 85 % of cloud‑group students actively used the collaborative workspace, leading to higher-quality team solutions and more creative problem‑solving approaches, as confirmed by qualitative rubric assessments.

The discussion highlights that immediate feedback and ubiquitous access foster greater learner autonomy and motivation, while built‑in collaboration tools align well with the problem‑solving nature of operations research. Limitations include the initial infrastructure investment and the need for faculty training in cloud operations; the authors propose targeted professional‑development workshops and a cost‑benefit analysis model to mitigate these challenges.

In conclusion, the study demonstrates that migrating a CAS like Maxima to a cloud‑based learning environment can simultaneously improve pedagogical outcomes and operational efficiency. The presented design, implementation, and evaluation methodology are transferable to other mathematical and engineering domains and provide a foundation for future extensions, such as integrating AI‑driven adaptive tutoring or expanding to additional open‑source CAS platforms.