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 the design, implementation, and evaluation of cloud‑based learning components that integrate systems of computer mathematics (SCM), focusing on the open‑source Maxima system, to enhance investigative learning in engineering and mathematics courses for informatics bachelor students. Beginning with a discussion of modern ICT‑driven educational environments, the authors argue that SCMs such as Maxima provide powerful symbolic computation, modeling, and visualization capabilities that can foster a research‑oriented approach to learning.

A cloud service model was developed at the Institute of Information Technologies and Learning Tools of NAES of Ukraine between 2012 and 2014. The model employs a “virtual desktop” architecture: Maxima’s computational engine and a web‑based interface reside in a data centre, while students access the system through standard web browsers without any local installation. This architecture eliminates the need for per‑machine software updates, reduces licensing costs, and simplifies maintenance for educators.

To assess the pedagogical impact, the authors constructed a multi‑dimensional evaluation framework comprising psychological, educational, and technological criteria. Psychological measures captured learner motivation and cognitive load; educational metrics included pre‑ and post‑test scores, task completion times, and quality of operations‑research models; technological indicators monitored system availability, response latency, and concurrent user capacity.

A controlled experiment was conducted at Drohobych Ivan Franko State Pedagogical University. Two groups of 45 students each—one using the cloud‑based Maxima environment (experimental group) and the other using a traditional locally installed SCM (control group)—took the same operations‑research course over a semester. The experimental group achieved an average exam score increase of 9 points (from 78 to 87) and reduced average assignment completion time by 31 % (from 45 minutes to 31 minutes). Survey results indicated that 85 % of students perceived improved accessibility and 90 % of instructors reported reduced administrative burden, allowing greater focus on instructional design. System logs showed an average response time of 1.2 seconds and 99.5 % uptime, comparable to commercial cloud services.

The study concludes that cloud‑based SCMs can significantly enhance learning outcomes, increase student engagement in research activities, and streamline instructional logistics. However, limitations are acknowledged: reliance on stable network infrastructure, the relative functional gap of Maxima compared with commercial packages like MATLAB or Mathematica for large‑scale numerical tasks, and the potential cumulative cost of cloud service provisioning.

Future work is proposed to explore hybrid cloud architectures that balance privacy, cost, and scalability, to integrate multiple SCMs for broader functionality, and to conduct longitudinal studies tracking the persistence of learning gains beyond the classroom. The authors advocate for policy‑level support to standardize and fund cloud‑based mathematical software in higher education, thereby extending the benefits observed in this study to a wider academic community.